Danilo Fernandes

Douglas L L Moura
email: douglas.moura@dcc.ufmg.br

Gean Santos
email: gean.santos@laccan.ufal.br

Geymerson S Ramos
email: geymerson.ramos@inria.fr

Fabiane Queiroz
email: fabiane.queiroz@laccan.ufal.br

Andre L L Aquino

Towards Edge-Based Data Lake Architecture for Intelligent Transportation System

Keywords: Distributed Systems → Edge Computing, Data Lake, • Intelligent Transportation Systems → Vehicular Sensor Network, Handover, Driver Identification Logical Data Lake, Edge Computing, Intelligent Transportation Systems

published or not. The documents may come

INTRODUCTION

Urbanization is a global phenomenon characterized by the growth and development of large cities resulting from migrating people from rural to urban areas. It involves concentrating economic activities and infrastructure in urban centers [START_REF] Seto | The new geography of contemporary urbanization and the environment[END_REF]. Rapid urbanization has modernized many people's lives and brought numerous challenges to transportation systems. These challenges include air pollution, noise, traffic congestion, and accidents [START_REF] Zheng | Urban Computing: Concepts, Methodologies, and Applications[END_REF]. In this context, Intelligent Transportation System (ITS) emerges as a potential solution to address the impacts of urbanization and improve the efficiency and safety of transportation systems [START_REF] Dimitrakopoulos | Intelligent Transportation Systems[END_REF]. ITS integrates advanced communication and information technologies with transportation infrastructure to support various applications and services, such as real-time traffic management, road safety, smart parking, and autonomous vehicles [START_REF] Zhu | Big Data Analytics in Intelligent Transportation Systems: A Survey[END_REF].

These applications transmit data through various communication technologies and obtain them from heterogeneous data sources, such as vehicles, road infrastructure, and citizens. The rapid growth of ITS systems made analyzing and processing the data challenging for traditional data processing systems presenting a new Big Data scenario [START_REF] Geymerson | Toward Data Lake Technologies for Intelligent Societies and Cities[END_REF]. However, solutions are emerging to provide a flexible and scalable data store to handle the new ITS Big Data [START_REF] Sawadogo | On Data Lake Architectures and Metadata Management[END_REF]. To provide this support, the Logical Data Lake (DL) concept [START_REF] Geymerson | Toward Data Lake Technologies for Intelligent Societies and Cities[END_REF] enables efficient management of ITS Big Data, allowing advanced analytics, inference, and making data-driven decisions. Despite their proven benefits, existing DL architectures suffer from certain limitations when applied in the context of ITS: (i) Vehicles typically move at high speeds, resulting in frequent disconnections, especially when combined with reduced communication range; (ii) ITS data is dispersed and heterogeneous, which poses a significant challenge for data integration; (iii) Cloud architectures can suffer from high communication and computing overheads due to the concentration of data and processing in a single central server.

To address these challenges, we propose a novel edge-based data lake architecture that provides an abstraction layer and enables efficient data integration, cleansing, and inference for decision-making applications in ITS. Multi-access Edge Computing (MEC) infrastructure provides processing and storage resources at the network edge, such as at the cellular base station [START_REF] Taleb | On Multi-Access Edge Computing: A Survey of the Emerging 5G Network Edge Cloud Architecture and Orchestration[END_REF]. In our approach, we design a distributed architecture across servers located at the network edge and in the cloud, with each layer utilizing the data differently. The main contribution of this research is a novel edge-based data lake architecture that offers a scalable and efficient solution to handle the diverse data requirements of ITS, enabling enhanced decisionmaking, improved operational efficiency, and innovative services for a more intelligent and connected transportation ecosystem. In our approach, data ingestion is performed logically and allows the direct and transparent utilization of distributed data, resulting in more efficient use of resources. We analyze three use cases. The first use case is a Vehicular Sensor Network (VSN) application, which relies on vehicle data to determine a subset of vehicles to act as aggregation points and perform data offloading. The second use case is a mobile network application, which uses data from mobile devices to optimize the handover process. Finally, the third use case is the driver identification application, which integrates data from different automotive sensors to identify individual drivers. The results show our proposed architecture's effectiveness in providing seamless data integration, low-latency processing, and flexible support for advanced data analysis in transportation systems.

RELATED WORK

Big Data Analytics has the potential to revolutionize transportation systems, bringing significant improvements to traffic management, reducing congestion, and increasing road safety. However, many issues and challenges still need to be addressed to ensure the effective use of these technologies, such as effective management, storage, and processing of large and complex data sets. Existing architectures explore using advanced big data management technologies, such as cloud computing, data warehousing, and data lakes, to address these issues and handle this data efficiently and cost-effectively.

Guerreiro et al. [START_REF] Guerreiro | An architecture for big data processing on intelligent transportation systems. An application scenario on highway traffic flows[END_REF] propose an ETL (Extract, Transform, and Load) architecture for big data analytics in ITS applications, addressing an application scenario on dynamic toll charging for highways. The proposed architecture can efficiently process and model large volumes of raw traffic data using Apache Spark and SparkSQL for data processing and MongoDB for data storage. Similarly, Ramos et al. [START_REF] Geymerson | Toward Data Lake Technologies for Intelligent Societies and Cities[END_REF] present a zone-based data lake architecture for smart cities and governments. Their approach enables the ingestion and integration of heterogeneous data sources from IoT systems, social media, data streams, information systems databases, and Data Warehouses. Additionally, they integrate all data via a flexible metadata system, which enables manual data labeling, automatic metadata extraction, and data queries through the metadata.

Zhu et al. [START_REF] Zhu | Big Data Analytics in Intelligent Transportation Systems: A Survey[END_REF] provided a comprehensive survey of Big Data Analytics in ITS and introduced a three-layer architecture composed of a data collection layer, a data analytics layer, and an application layer. They also presented several use cases of Big Data Analytics in ITS, such as road traffic flow prediction, road traffic accident analysis, public transportation service planning, personal travel route planning, and others. Darwish and Bakar [START_REF] Tasneem | Fog Based Intelligent Transportation Big Data Analytics in The Internet of Vehicles Environment: Motivations, Architecture, Challenges, and Critical Issues[END_REF] proposed a fog-based architecture for ITS big data real-time processing called RITS-BDA. The fog nodes can form clusters vertically or horizontally, sharing computational and storage resources. Singh et al. [START_REF] Kumar Singh | BlockIoT-Intelligence: A Blockchain-enabled Intelligent IoT Architecture with Artificial Intelligence[END_REF] proposed BlockIoTIntelligence architecture of converging blockchain and AI for the Internet of Things (IoT). They present cloud, fog, edge, and device layers hierarchically and use Blockchain technology to mitigate the security and privacy issue and provide decentralized big data analysis.

Dang et al. [START_REF] Zhao | A zonebased data lake architecture for IoT, small and big data[END_REF] propose a zone-based data lake architecture for IoT, Small, and Big Data. The authors consider an analysis-oriented metadata model for data lakes that includes the descriptive information of datasets and their attributes and all metadata related to the machine learning analyses performed on these datasets. The authors implemented a web application of data lake metadata management that allows users to find and use existing data, processes, and analyses by searching relevant metadata stored in a NoSQL data store within the data lake. They also present two real-world use cases: dataset similarity detection and machine learning guidance. ✓ ✓ Zhu et al. [START_REF] Zhu | Big Data Analytics in Intelligent Transportation Systems: A Survey[END_REF] ✓ Darwish and Bakar [START_REF] Tasneem | Fog Based Intelligent Transportation Big Data Analytics in The Internet of Vehicles Environment: Motivations, Architecture, Challenges, and Critical Issues[END_REF] ✓ ✓ Singh et al. [START_REF] Kumar Singh | BlockIoT-Intelligence: A Blockchain-enabled Intelligent IoT Architecture with Artificial Intelligence[END_REF] ✓ ✓ Dang et al. [START_REF] Zhao | A zonebased data lake architecture for IoT, small and big data[END_REF] ✓ ✓ Our work

✓ ✓ ✓ ✓
Table 1 presents a comparison of the existing architectures for big data ITS. Although previous works have presented promising solutions for ITS big data, they often rely on centralized architectures based on cloud infrastructure. Furthermore, there is a lack of a deep discussion about the infrastructure level design and the exploration of potential use cases within the transportation ecosystem. Our study aims to introduce a novel data lake architecture for ITS that utilizes the capabilities of Edge Computing to address the limitations of previous works. The proposed architecture offers an abstraction layer and performs data lake operations at the network's edge in a virtualized and distributed manner, enabling scalability, efficiency, and transparency.

EDGE-BASED DATA LAKE ARCHITECTURE

The data lakes play a crucial role in the overall architecture corresponding to a data storage and intelligence layer. Dealing with heterogeneity in Big Data landscapes and scaling in distributed environments are the main features that make it well suited for ITS platforms [START_REF] Kirimtat | Future Trends and Current State of Smart City Concepts: A Survey[END_REF]. This layer collects, catalogs, cleans, and transforms data from IoT Devices. These tasks compose a process known as data wrangling, which enriches the data and makes it suitable for analysis. [START_REF] Koehler | Incorporating Data Context to Cost-Effectively Automate End-to-End Data Wrangling[END_REF]. Nevertheless, the ultimate feature is providing data analytics, the core of the application layer.

Data management is always a challenge when facing data heterogeneity. Data Lakes addresse this issue by storing all collected data in raw format and providing an evolving framework for data structuring and refinement [START_REF] Geymerson | Toward Data Lake Technologies for Intelligent Societies and Cities[END_REF]. Such a methodology is known as the Zone-Based Data Model [START_REF] Giebler | Leveraging the Data Lake: Current State and Challenges[END_REF]. Data collected from external sources are logically assigned to an ingested data zone [START_REF] Sawadogo | On Data Lake Architectures and Metadata Management[END_REF]. We transform the data enhancing the quality; thus, the outcome can move into the following zones [START_REF] Sawadogo | On Data Lake Architectures and Metadata Management[END_REF]. Such transformations run until the data reaches the maximum level of maturity at which it is ready to be analyzed by decision-makers [START_REF] Geymerson | Toward Data Lake Technologies for Intelligent Societies and Cities[END_REF].

A data governance layer traverses all the zones to assure data security, privacy, quality, and monitoring [START_REF] Giebler | Leveraging the Data Lake: Current State and Challenges[END_REF]. Data governance requirements are different for each zone. At the ingestion zone, data must satisfy conditions for security and consistency. The distillation zone should enforce data privacy by controlling access. The processing zone reinforces data quality, and the monitoring zone provides reports on the health of specific components and the general infrastructure of the data lake. Data governance should increase and stack as the data follows through the ingestion to the insights zone. However, this is only one of several variants of zone architecture. Such architectures generally differ in the number and characteristics of the zones [START_REF] Sawadogo | On Data Lake Architectures and Metadata Management[END_REF].

We usually deploy data lakes in the cloud due to the considerable computing resources available and the elasticity in their allocation. Their costs are often tied only to resource demand, skipping the infrastructure maintenance costs. However, in an environment with a considerable volume of sensors constantly providing data and demand for real-time analysis, the latency in uploading it to the cloud can be a bottleneck. Nevertheless, given its more constrained computing assets, this does not justify deploying the data lake at the edge. Thus, the cooperative adoption of both approaches can balance the trade-off between physical resources and latency minimize costs.

In this light, the proposed data lake architecture is internally composed of two distributed data lakes running in the edge and cloud. Although independent, these data lakes exchange data, operating together organically. Our architecture (Figure 1) considers four layers: IoT Device, Edge Data Lake, Cloud Data Lake, Application. The IoT Device layer represents the mechanisms used to handle the data used by devices embedded in vehicles and other traffic-related devices. The Edge Data Lake, and Cloud Data Lake layers, collect, store, and sprocesses the data in batches or in real-time using distributed technologies at the edge or cloud. The Application layer uses the processed data. Examples of applications for ITS applications are congestion detection, traffic management, accident prediction, and other urban mobility solutions. Finally, all these layers exchange their data horizontally through a Data Bus. The Data Bus implements a lightweight messaging protocol to enable communication between all architecture components. An example of such a protocol is the Message Queuing Telemetry Transport (MQTT) [START_REF] Pham | Multi-level just-enough elasticity for MQTT brokers of Internet of Things applications[END_REF], which is designed to work on top of the TCP/IP protocol. This event-driven protocol acts on a publish/subscribe model, facilitating real-time communication within an ITS ecosystem.

IoT Device Layer

The IoT Device layer, also known as the perception layer, is where the smart sensors are in the data lake architecture. These devices may include various types of sensors, such as intra-vehicular sensors (e.g., chemical detectors, video cameras, and vibration/acoustic sensors), traffic control sensors (e.g., traffic lights, radar, inductive loops), and infrastructure sensors (e.g., roadside units and roadside weather stations). This layer collects data from the environment In addition, the IoT Device layer has a Processing Engine to enable the performance of specific tasks and functions, such as data transformations, device actuator control, and communication. There is also a Storage System for local buffering of the data collected by the sensor and the processing outcome. This set of components can help reduce the amount of data that needs to be transmitted to the network and reduce bandwidth consumption. Finally, the DL interface handles all communication with the other layers.

Edge and Cloud Data Lake Layers

The Edge Data Lake layer is mainly responsible for: i) Collecting data from sensors; ii) Keep stored frequently used data (hot data); iii) Data cataloging and metadata model inference; iv) Real-time and reduced batch processing; v) Interfacing with MEC applications. Additionally, the goal of the Cloud Data Lake layer is to extrapolate the computer power of the edge. Then, we design it to: i) Storing huge volumes of sporadically used data (cold data); ii) Costly batch processing.

The data kept by the ITS infrastructure should be in any layer present in the architecture. The system sends the data from the lowest storage capacity tier to the highest as required for more costly processing or to free up storage space. It executes the reverse direction when a layer with less computing power requests data stored in the next layer. Consequently, hot data stays in the tiers closest to the application, while cold data accumulates in the cloud.

Edge and Cloud Data Lakes layers comprise Storage Systems, Processing Engines, and DL Interfaces. Nevertheless, the Edge Data Lake layer monitors and integrates the data, working as a virtual middleware in the data exchange of the other layers. For this purpose, the additional modules support the latter: Data Pipeline Orchestrator and Metadata System. The Data Orchestrator Pipeline is responsible for data ingestion from Applications and data exchange with Cloud Data Lake. For the first case, the DL Interfaces will intermediate the connection with the application, passing the received data (stream or batch) to the Orchestrator and indicating a location in the Edge Storage System. When exchanging data with the Cloud Data Lake, the DL Interface will inform the source and target data location in the cloud and edge Storage Systems, and the Orchestrator will transfer it in batches. Note that such Orchestrator is a distributed system; therefore, data transfer occurs in large volumes in parallel.

The Storage System stores the data on the edge. The Data Pipeline Orchestrator and the Processing Engine feed it. In the last one, the stored data results from some processing task. In addition, it returns data to all other components of the Edge Data Lake when requested via DL Interface. The Metadata System is in charge of logically integrating all data and making it accessible to the user through homogeneous modeling. It also stores and manages information about the usage and performance of the data lake, for example, data lineage, history of data access, and data transfers. When new data is ingested or created into the Edge Data Lake, it receives its location in the Storage System and the available elementary metadata.

In addition, it performs some processing and delegates the bulky ones to the Processing Engine to extract relationships, hidden patterns, and semantic descriptors. When the system transfers data from the edge to the cloud, we preserve the metadata, changing only its location to reflect its address in the cloud Storage System. In this way, this data remains ingested virtually at the Edge Data Lake and can be regressed when required. All metadata is essential to empower data governance, enabling discovery, integrated queries, and unsupervised meta-analysis. Note that big data implies big metadata, then Metadata System pushes toward implementation in a distributed environment. Then, the metadata structure is across the computing nodes, which share the content with others when requested.

The Processing Engine receives requests from Metadata System and DL Interface to extract meta-features and refine data when the data evolves, the output returns to the requester or saves into Storage System. The DL Interface communicates with the MEC Applications and translates the requests into coordinated tasks to the other modules within Edge Data Lake. Edge Data Lake runs distributed along the MEC servers, sharing computing resources with the applications. Figure 2 presents a possible implementation of edge services on a MEC server.

All Edge Data Lake module nodes run side-by-side with MEC Applications in virtual machines (VM). The Virtualization Layer manages the virtual machines, which allocates resources to each of them and intermediates the communication between them and external ones within other MEC servers or clouds. The MEC Platform consists of essential functionality required to run MEC applications. It can also enable MEC applications to provide and consume MEC

Application Layer

The Application layer is responsible for providing valuable services to end-users based on the data processed by the data lake. Applications typically run on the MEC host but can also run in the cloud, on the device, or a combination. The choice of execution location depends on factors like the application's requirements, resource availability, and network conditions. These applications include typical ITS use cases, such as autonomous vehicles, smart parking, environmental monitoring, and video streaming. Other ones can also be run on this layer, such as data lake operations (e.g., distributed processing) and complex tasks (e.g., video processing, machine learning, augmented reality, and gaming) offloaded by IoT devices.

The Application has a Storage System and Processing Engine to perform their operations autonomously and a DL Interface to communicate with the other layers of the architecture. In addition, they can interact with the Infrastructure that supports it by collecting and storing data in the storage system and changing its setup via the Processing Engine. This capability enables, for example, the adaptation of network settings to optimally meet the demand for services.

USE CASES OF ITS DATA LAKE

In this section, we illustrate the potential of the proposed architecture by discussing three examples of use cases that demonstrate its benefits in ITS applications. We consider Vehicular, Mobile Network, and Driver Identification applications, illustrated in Figure 3.

Vehicular Sensor Network Application

Vehicular Sensor Network (VSN) refers to a promising paradigm of Remote Sensing, in which vehicles equipped with various sensing devices, powerful processing units, and wireless communication can act as mobile sensors and perform monitoring of the urban environment. VSN will enable various new ITS applications through the remote processing of data periodically collected by vehicles, such as improving road safety, traffic management, intelligent navigation, pollution monitoring, urban surveillance, and forensic investigations. Many applications require a periodic upload of the sensory data transmitted to a monitoring center on the internet. However, transmitting massive data over the cellular network can compromise network resources. Data offloading is a potential solution to save bandwidth and prevent cell network overload, in which only a minimal number of vehicles, called aggregation points, will transmit data on the cellular network. An aggregation point is responsible for collecting sensory data generated by neighboring vehicles using Device-to-Device (D2D) communication, aggregating and uploading them. Our challenge is to determine which vehicles will act as aggregation points.

In this scenario, following the flow of Figure 3a, the vehicles represent the IoT Devices and generate sensing data with a high space-time correlation. We summarize these data through aggregation operators to combine data from several sources into a single value. First, vehicles share location information to the Edge Data Lake through the DL Interface. The MEC Host represents the Edge Data Lake. Next, the Processing Engine processes the raw data in parallel and transforms it into a suitable data format for storage in the Storage System. The Metadata System adds additional metadata information, such as creation date, data format, geographic location, and others. The MEC Host host the neighbor discovery service to provide a mechanism for devices to discover nearby devices. A MEC application will run the Centrality-based algorithm [START_REF] Douglas | Towards Data VSN Offloading in VANETs Integrated into the Cellular Network[END_REF] to solve the aggregation points selection problem. The algorithm uses the neighbor discovery service to model the graph and then selects the aggregation points. Finally, aggregation points collect sensory data from neighboring vehicles using D2D communication. The aggregation point stores the data locally in the Storage System, and the Processing Engine performs data aggregation. The aggregated data is transmitted to the Cloud Data Lake for later analysis through the DL Interface.

The proposed scheme has the following steps: i) Awareness -The neighbor discovery service establishes the proximity relationship between the vehicles using the processed location data stored in the Edge Data Lake; ii) Modeling -The MEC Application model the graph from the neighbor discovery service information;

iii) Selection -The Centrality-based algorithm uses closeness centrality in a greedy approach to select which vehicles will access the cellular uplink; iv) Upload -Finally, a vehicle selected to access the cellular uplink receives a message from the MEC Application requesting the upload. The vehicle can then transmit the collected data. The Data Pipeline Orchestrator intermediates the data exchange with Cloud Data Lake. The sensory data is ingested into the Cloud Data Lake via an API, processed, and stored in the distributed file system with added metadata for organization and additional information.

We evaluate the proposed solution in a realistic simulation scenario derived from data traffic (TAPASCologne [START_REF] Uppoor | Generation and analysis of a large-scale urban vehicular mobility dataset[END_REF]) containing more than 700,000 individual car trips for 24 hours. We compare our approach with a reservation-based algorithm [START_REF] Stanica | Offloading Floating Car Data[END_REF], and the results indicate an the aggregation rate improved by up to 10.45%

There is an increase in the cost of uploading during peak hours when there is a greater volume of vehicles on the roads. In the TAPASCologne data traffic, we observe that an upload cost reached 167.50 kB/s at peak time. The high cost of uploading, especially in periods of higher demand, requires offloading techniques to reduce the traffic generated on the network and save bandwidth. In this way, Figure 4 presents, in detail, the aggregation rate. It corresponds to the ratio between data volume after and before aggregation. The results suggest a significant reduction in sensing data transmitted over the cellular network in both approaches. When we use single-hop communication (1-hop), the Centralitybased algorithm has an aggregation rate close to the RB algorithm. In this scenario, the aggregation point will only collect data from its immediate neighbors. However, we can improve the aggregation rate by increasing the number of hops. Multi-hop communication (3hops) enables data collection from more distant vehicles, resulting in a better aggregation rate. The centrality-based algorithm has an aggregation rate equal to 83.14% in peak hours.

This use case presents a scenario in which the architecture enables the implementation of a solution to select aggregation points and offload sensing data.

Mobile Network Application

The ecosystem of mobile networks is highly dynamic, dense, and connected. As users move between communication technologies, they undergo handover processes, transitioning from one access point or base station (represented by the evolved Node B or eNB) to another [START_REF] Peltonen | A comprehensive formal analysis of 5G handover[END_REF]. It is essential to maintain users' connections without any perception of interruption or reduction in transfer rates while they are on the move. Mobile network solutions must ensure that user services are available even in scenarios of high mobility, such as airplanes traveling at speeds of up to 500 km/h [START_REF] Zhang | Network Slicing Based 5G and Future Mobile Networks: Mobility, Resource Management, and Challenges[END_REF]. Accurate strategies are essential for transferring and allocating users' resources. Handovers should happen seamlessly and quickly in areas that do not negatively affect mobility and connectivity. Optimizing the allocation of users in mobile network base stations can reduce the handover process. In typical 5G environments, the involvement of multiple stakeholders can hinder the open exchange of information regarding resource availability, operational status, performance capabilities, and service contracts [START_REF] Coronado | Zero Touch Management: A Survey of Network Automation Solutions for 5G and 6G Networks[END_REF]. The lack of data sharing is a big challenge that limits the capacity of systems to manage complex chains of end-to-end services. Considering the 5G architectures, these difficulties can be surpassed or minimized through a distributed ledger and an operational data lake [START_REF] Coronado | Zero Touch Management: A Survey of Network Automation Solutions for 5G and 6G Networks[END_REF]. The operational data lake is viewed as a logically centralized repository, as shown in Figure 3b.

In this scenario, the IoT Device can represent anything connected to the mobile network, such as a vehicle or smartphone. Through the DL Interface, it shares location updates, network service status, or consumes best route directions, optimized connection spots, and general information regarding anomalous events from the Data Lake. The Storage System stores this information. The Processing Engine processes this information and makes it available to mobile users, such as the vehicle. Additionally, the eNB represents the Edge Data lake. In this case, the Storage System keeps all data required to network management and optimization. The Metadata System enhances and provides additional information to the data in the Storage System. Data stored in data lakes receive little to no processing at the ingestion stage. The goal is to minimize and avoid information loss. Suppose a mobile data service provider realizes it needs to offer a new service or optimize existing ones. The data will be available to the Processing Engine, responsible for data filtering, transformation, aggregation, real-time analytics, event detection, and alerting. Furthermore, by harvesting the tools provided by the insights layer of the data lake, decision-makers can analyze and compare different models to select solutions while following data governance rules to attend to users' demands.

Once the application and data lake are on, we proceed to show the execution of it in a simulation way. The objective of our solution is to find the best eNB activation considering the vehicle trajectory. Figure 5 presents the mobility scenario of a user that starts at the bottom left and proceeds to the final destination at the top right. The eNB allocation considers the region of São Paulo City, Brazil. The real-world eNB locations are provided by Telebrasil's dataset [START_REF] Telebrasil | Mapa de ERBs Brasil (antenas[END_REF]. The simulation region covers an area of (1947.65 × 1878.95)m 2 and comprises 26 eNBs provided by a local phone carrier. Each base station is labeled from 0 to 25. We utilize the SUMO (Simulation of Urban MObility) simulator [START_REF] Krajzewicz | Recent Development and Applications of SUMO-Simulation of Urban MObility[END_REF] to generate the route (highlighted in blue in Figure 5) that yields 432 UE (User Equipment) location readings. These readings can serve as input for allocation models, such as the ones discussed by Ahmadi et al. [START_REF] Ahmadi | Softwaredefined networking to improve handover in mobile edge networks[END_REF] and Ramos et al. [START_REF] Geymerson | Optimizing 5G Networks Processes With Software Defined Networks[END_REF].

Figure 6 shows the allocation results for both models (inner results: Ahmadi et al.; outer results: Ramos et al.). We can see that the UE is allocated through the same eNBs and performs 7 handovers, following the allocation sequence 20 -> 8 -> 25 -> 5 -> 2 -> 3 -> 13 -> 19. The models present differences regarding the allocation period along the route. For instance, the model proposed by [START_REF] Geymerson | Optimizing 5G Networks Processes With Software Defined Networks[END_REF] kept the UE connected to eNB 5 for 32.9% of the entire route, while [START_REF] Ahmadi | Softwaredefined networking to improve handover in mobile edge networks[END_REF] kept it connected for 21.9%. A decision maker can interpret the results and choose models that can keep the UE connected for longer periods in each eNB. Since human mobility is highly predictable [START_REF] Song | Limits of predictability in human mobility[END_REF], we can use the data from this route stored in the Storage System of the data lake for the next time the UE starts this specific route. By planning ahead, the data lake can run prediction models through the Processing Engine to reduce the number of handovers by selecting the eNBs with minimal service loss for the user. For example, instead of the 7 handovers initially performed, eNB 25 and eNB 3 can be removed, resulting in the eNB handover sequence 20 -> 8 -> 5 -> 2 -> 13 -> 19.

Driver Identification Application

The problem of driver identification involves classifying drivers based on their behavior, in our case, using machine learning models. We consider a multivariate time series classification problem due to the nature of the data collected from various sensors over time.

In this study case, we focus on the feature generation process of machine learning models. This process is responsible for generating new features from existing ones to enhance the performance of machine learning models. It involves various techniques, such as mathematical transformations, aggregations, interactions, or domain-specific knowledge. We propose to use information theory quantifies [START_REF] Sabeti | Entropy and complexity measures for EEG signal classification of schizophrenic and control participants[END_REF] as new features in machine learning models. Information Theory allows quantifying the information in a dynamic system, such as driver identification. Integrating principles from Information Theory into feature generation can achieve a more comprehensive and meaningful representation of the data. These new features enhance machine learning models' capability to handle complexity and extract pertinent knowledge from the data.

We use as features the Complexity Statistical and Entropy measures, considering a time window of 30 seconds (i.e., a sequence of 30 samples). We assumed that each time window was a stationary series. For our study, we used a real-world dataset with driving data from four drivers [START_REF] Ho | This Car is Mine!: Driver Pattern Dataset extracted from CAN-bus[END_REF]. The drivers made several trips using the same vehicle along a fixed path. Each record contains 51 features associated with an automotive sensor. However, we used only nine features, which are commonly adopted in the literature [START_REF] Uvarov | Driver Identification with OBD-II Public Data[END_REF]. These features include accelerator pedal value, intake air pressure, absolute throttle position, long-term fuel, engine speed, torque of friction, engine coolant temperature, engine torque, and vehicle speed.

Figure 3c shows the driver identification framework. First, the IoT Device collects the data, represented by smartphones or OBD-II interface. After that, it transmits to the Edge Data Lake responsible for executing the driver identification models. With all features evaluated, we must generate these features and the model to allow this processing. To perform this generation, the Edge Data Lake sends the data to the Cloud Data Lake. Then, the data is processed, the features extracted, and the machine learning models trained. Finally, the trained model is transferred to the Edge Data Lake, enabling the user to perform low-latency inference tasks.

We compare our proposed features generation, based on Complexity Statistics and Entropy, with the commonly used approaches in the literature [START_REF] Ho | This Car is Mine!: Automobile Theft Countermeasure Leveraging Driver Identification with Generative Adversarial Networks[END_REF]. We trained seven classifiers using the One-vs-Rest method: K-Nearest Neighbors (KNN), Linear Support Vector Machine (SVM), Radial Basis Function (RBF) SVM, Decision Tree, Random Forest, Multi-Layer Perceptron (MLP), and Naive Bayes. We split the dataset into a training dataset (75%) and a testing dataset (25%), using a small dataset and a large dataset with 300 and 9,700 samples from each driver, respectively.

Figure 7 presents the accuracy of each classification model. The results indicate that the classifier's performance influences the features used and the size of the dataset. In the small dataset, we can see that Entropy-Complexity has a lower performance than the other approaches. Furthermore, we can significantly improve for most of the used classifiers when we combine them with the pre-processing scheme from the literature. However, in the large data set, the literature approach was equal or better in the used classifiers. It is noted that all approaches decreased the accuracy for the large dataset compared to the small dataset.

Information theory measures can provide additional features that help to distinguish patterns, behaviors, and classes in time series. Although the results for a large dataset show lower precision than the literature solution in some classifiers, for a small dataset we can obtain a significant improvement. The feature extraction step represents a significant computational overhead in training ML models. However, with the high computing power of Cloud Data Lake or a decentralized solution on Edge Data Lake, we can reduce the workload and improve the efficiency of real-time data processing.

CONCLUSION

In this work, we presented a distributed Edge-Based Data Lake Architecture for storing and processing ITS data. This architecture is a promising approach to handling different types of data, ranging from automotive to meteorological data, in which the data lake can provide a distributed platform for data integration. The convergence of edge computing and data lake technologies offers significant advantages, such as reducing latency, improving data security, and optimizing bandwidth usage.

We analyzed three use cases of the proposed architecture. Besides the data organization and easy access, through well-established interfaces, our qualitative analysis revealed significant improvement in the organization and structure of ITS applications, such as identifying explicitly where the data is collected, stored, and processed. In particular, for the driver identification one, we identify the possibility of increasing the performance using a distributed processing in the Edge Data Lake. Overall, the proposed architecture represents a valuable contribution to the field of ITS and can pave the way for new advancements in ITS. However, some challenges remain to be addressed, such as a data selection algorithm for offloading and a detailed metadata system architecture for complete data integration.

Figure 2 :

 2 Figure 2: MEC Implementation

Figure 3 :

 3 Figure 3: Evaluated use case scenarios.

Figure 4 :

 4 Figure 4: Aggregation rate obtained using the centralitybased algorithm compared to the RB algorithm.

Figure 5 :

 5 Figure 5: Simulated UE's route at a region in São Paulo city, Brazil, considering real-world eNB locations.

Figure 6 :

 6 Figure 6: The allocation results for Ramos et al. (outer) and Ahmadi et al. (inner) models.

  (a) Accuracy for small data (b) Accuracy for large data

Figure 7 :

 7 Figure 7: Classification accuracy results for driver identification.

Table 1 :

 1 Comparison with other approaches in the literature.

	Work	Edge	Data	Virtual data	ITS
		computing variety	integration	use cases
	Guerreiro et al. [6]				✓
	Ramos et al. [15]

ACKNOWLEDGMENTS

This study was partly financed by the Research Foundation of the State of Alagoas (FAPEAL) under grants E:60030.0000000352/2021 and the National Council for Scientific and Technological Development (CNPq) under grant 407515/2022-4.


Geymerson S Ramos
email: geymerson.ramos@inria.fr

Gean Santos
email: gean.santos@laccan.ufal.br

Douglas Moura
email: douglas.moura@laccan.ufal.br

Danilo Fernandes

Fabiane Queiroz
email: fabiane.queiroz@laccan.ufal.br

Osvaldo A Rosso
email: oarosso@laccan.ufal.br

Razvan Stanica
email: razvan.stanica@inria.fr

Andre L L Aquino

Left on read: Human behavior characterization based on messaging service applications

I. GENERAL PROBLEM AND MOTIVATION

The objective of this study is to analyze mobile data from messaging applications. We aim to understand messaging app usage and gather information that can enhance infrastructure and quality of life within a smart city context. We will conduct our analysis using the NetMob23 dataset [START_REF] Martínez-Durive | The netmob23 dataset: A high-resolution multi-region service-level mobile data traffic cartography[END_REF], which covers the period from March 16, 2019, to May 31, 2019, and provides uplink and downlink data for messaging applications such as WhatsApp, Telegram, Facebook Messenger, and Apple iMessage. Our observations pertain to the Lyon Metropolis in France. The traffic dataset provided is mapped through GeoJSON files using the WGS84 coordinate system. Each feature represents one square cell (tile) covering an area of (100 × 100) m 2 . The Lyon metropolitan area has a total of 54013 tiles, and we used the data provided by the Grand Lyon Portal [2] to label some of these tiles, grouping them in the following classes: C1) Education Centers (208 tiles); C2) Events (74 tiles); C3) Commerce (67 tiles); C4) Hotels (58 tiles); C5) Sports (57 tiles); C6) Restaurants (51 tiles); C7) Religious Centers (41 tiles); C8) Hospitals (31 tiles); C9) Train Station (5 tiles). Figs. 1((a) -(d)) show the tile distribution of 4 different classes across the Lyon metropolitan area. We considered these classes to explore the following hypothesis: "It is possible to characterize, based on information theory, the tiles where users are more likely to engage in online conversations". To verify this hypothesis, we conducted a detailed analysis of the tiles for each class, and looked for similar usage behavior categorized with the Complexity-Entropy Causality Plane (CECP) [START_REF] Freitas | Mapping network traffic dynamics in the complexity-entropy plane[END_REF]. Only WhatsApp network traffic was considered in the study because it is the application which generates more traffic.

II. RESULTS

Given that the NetMob dataset [START_REF] Martínez-Durive | The netmob23 dataset: A high-resolution multi-region service-level mobile data traffic cartography[END_REF] provides 77 time series S per tile (one observation for each day), we used What-sApp uplink data to compute the average traffic time series S c = {x 00:00 , x 00:15 , ..., x 23:30 , x 23:45 } as the typical traffic signature for each class. The average network traffic at a specific time is represented by x hh:mm . We also computed the average traffic per day for each time series, represented by µ S , and discarded the time series with average daily traffic below the median or above the 75th percentile (third quartile) values among all the averages. Therefore, each class has a representative and unique average time series generated from a set D = {S | median ≤ µ S ≤ Q 3 }. This helps to mitigate the impact of anomaly events, outliers, and low traffic days that might not be representative for our analysis. We also make a distinction between weekdays (Monday to Friday) and weekends. This results in an average class behavior, which can be seen in Fig. 2 for data of the Education Centers class.

In Fig. 2, we can observe that the traffic typically begins to increase earlier during week days, at around 5:00, as compared to weekends (6:00). It also starts to decrease around 22:30 for weekdays and around 23:30 for weekends. One reason for this difference may be attributed to the weekly responsibilities related to studies and teaching. The Education Centers class suggests that people tend to wake up earlier during weekdays to attend schools, universities, and similar institutions, which might also imply exchanging WhatsApp messages. On weekends, we see a higher traffic volume. People typically have a break from these obligations, and they may wake up and go to sleep later as well. For both cases, peak usage occurs between 12:00 and 21:30. The early activity on weekdays seems to occur for most of the analyzed classes, but this difference is reduced for the Train Stations class. This class has the highest average traffic volume, as shown in Figure 3 (C9). The peak time traffic for this class appears around 18:00. For train stations, this refers to the afternoon period when there is the highest demand for train services. This is typically when many people are commuting from work and school, a good moment to exchange messages with friends and family. Interestingly, there is no peak in WhatsApp traffic during the morning commute hours, when the train demand is even more significant.

We can take a deeper look at the underlying nature of C9 and the other classes by analyzing the Complexity-Entropy Causality Plane in Fig. 4. The Commerce class (C3) has the highest permutation entropy and statistical complexity, which means more randomness and hard to predict usage behavior if compared to the other classes. This behavior usually implies chaotic traffic, with the least existing patterns and minimal information. Uncorrelated stochastic processes have H ≈ 1 and C ≈ 0. If we look specifically at the Train Station and the Commerce classes, one possible explanation to why C3 is more chaotic than C9 is that train stations coordinate travels, and people arrive and leave stations at specific and

III. CONCLUSION AND FUTURE WORK

This work analyzed network traffic from messaging apps to identify user texting behavior. We defined classes based on

Fig. 1 .

 1 Fig. 1. Tile location and distribution for some of the mentioned classes in Lyon metropolitan area.

Fig. 2 .Fig. 3 .

 23 Fig. 2. The average uplink traffic during weekdays and weekends for the Education Centers tiles class.

Fig. 4 .

 4 Fig. 4. Complexity-Entropy Causality Plane for the tiles classes.


Nader Arafati
email: arafati@cnam.fr

Roger Ohayon
email: ohayon@cnam.fr

Jean Yves Lazennec

Gerard Saillant

FINITE ELEMENT MODELING AND MECHANICAL EVALUAT ION OF ANTEVERSION IN FEMUR AND FEMORAL PROSTHESIS

We studied the mechanical effects of anteversion of hip prosthesis, using a geometrical model of the femoral bone derived from computed tomography sections.

Linear elastic mechanical behavior was assumed for both cortical and trabecular bone. The results of finite element modeling were studied qualitatively. Stress distribution was evaluated during one-legged stance loading of models with various degrees of anteversion.

The undeniable impact of anteversion raises questions about the interpretation of bone remodeling. Anteversion modifies mechanical stresses, most notably those through the

femoral shaft; they are rotated around the vertical axis in the same direction as the anteversion.

Changes in Von Mises stresses were larger than changes in longitudinal stresses, suggesting that anteversion may have a more significant impact on shear stresses, which may cause failure at the prosthesis-cement interface, particularly toward the middle of the femoral shaft.

INTRO DUCTION

Anteversion of the femoral bone or of a femoral prosthesis is defined as the angle made by the femoral or prosthetis neck with the long axis of femur, in the horizontal plane [l]. This angle, which is open medially and anteriorly, ranges from 0° to 30° in normal individuals. In our study, we selected 15° as the standard angle of anteversion and studied anteversion angles of up to 40°.

The recent literature contains studies of proximal femur stresses and deformations under various loading conditions [START_REF] Oh | Proximal strain distribution in the loaded femur[END_REF][START_REF] Rohrle | The force flow in hip joint endoprostheses[END_REF][START_REF] Svensson | Stress analysis of human femur with implanted Charnley prosthesis[END_REF]. These studies explored particular loading conditions and did not focus on torsion, especially due to femoral neck anteversion.

Anteversion of the neck of the femur influences rotation of the femoral head within the acetabulum. However, the shift in the points of application of articular forces generated by these specific positions also affects the analysis of stresses [START_REF] Biegler | Effect of porous coating and loading conditions on total hip femoral stem stability[END_REF][START_REF] Taylor | Stress and strain distribution within the intact femur: compression or bending?[END_REF].

We used finite element modeling to investigate femoral stresses and deformations. Taking physiology, anatomy, and the mechanical behavior of bone components into account, we constructed models of the femur before and after femoral prosthesis implantation [START_REF] Arafati | Numerical simulation of femoral prosthesis implantation, preliminary results for implant loosening[END_REF].

We investigated the distribution of femoral stresses according to the degree of anteversion, to the maximum and minimum values of longitudinal stresses, and to the maximal Von Mises stresses. Our goal was to determine how increasing anteversion affected longitudinal and shear stresses, two factors likely to influence bone remodeling and to cause alterations at the cement-prosthesis interface [START_REF] Arafati | Deformation modeling of femur, before and after cemented hip prosthesis implantation: finite element analysis and proposition of mathematical model[END_REF].

MATERIAL AND METHO DS 1. MODEL OF THE FEMORAL BONE

Femoral geometry was modeled based on volume generation logic used in various finite element analysis computer programs (Abaqus®, Nastran®, and Algor®).

The gross structure of the femur is composed of two main components : cortical bone and trabecular bone. Cadaver femurs were modeled by delineating the contours of each component.

We used a digitizer (Wacom®) to analyze the magnified images of computer tomography cross sections of femur, for the intervals of 5 mm, to define inner and outer contours of each femoral component.

Using these contours, we carried out the mesh generation of femur, between neighboring sections. By combining the meshes obtained at each level, we constructed a geometric model of the femurs (Fig. 1). The model consisted of 1056 brick elements for the cortical bone and 532 for the trabecular bone.

Deformation was analyzed under standard one-legged stance conditions [START_REF] Pauwels | Biomechanics of the Normal and Diseased Hip[END_REF]. The Z axis was the long (longitudinal) axis of the femur, which was directed toward the proximal femur. The X axis was perpendicular to Z in the frontal plane and was directed toward the opposite leg. The Y axis was perpendicular to the surfaces of the Z and X axes (Y = Z x X).

The cortical bone and trabecular bone were assumed as linear elastic materials, with modulus of elesticity of 16 Gpa and 1 Gpa, consecutively. This simplification was used to conduct a strictly qualitative analysis of deformation.

MO DEL OF THE IMPLA NTE D FEMUR

We simulated implantation of a titanium femoral prosthesis (ALIZE®-F. H.) into the femoral model as described above.

Computed tomography images obtained after implantation were unsatisfactory as a result of X-ray refraction and diffraction by the metal implants. Medical imaging techniques capable of providing satisfactory images were not available.

We used the industrial plans of the femoral prosthesis to select the best prosthesis position and size. Implant selection relied on the principles listed below: 1. Implantation of the prosthesis should cause the least possible change in femoral structure. 2. The geometry of the proximal part of prosthesis should be adapted to the anatomy of the femur, most notably at the femoral neck, to avoid medialization or lateralization. 3. The position of the center of the prosthetis head should be similar to that of femoral head. 4. The size of the implant was selected as to provide the best fit with the smallest volume of cement (the thickness of the cement layer varies between different levels).

After defining the optimal position of the prosthesis, we delineated the outer contours of the prosthesis. These contours were drawn within each previously modeled cross section of femoral bone. The space between the prosthesis and the femoral bone was considered to be optimally filled by surgical cement.

Using the same method as for the femoral bone model, we constructed a model composed of 941 brick elements for cortical bone, 437 for trabecular bone, 760 for the surgical cement, and 756 for the femoral prosthesis (Fig. 2). The mechanical behavior of the cement and prosthesis was also assumed to be linear elastic, with modulus of elesticity of 2.8 Gpa and 200 Gpa, consecutively.

Strains on the implanted femur were evaluated using loads identical to those applied to the femoral bone.

We neglected the micromotion in our model.

RESULTS

FEMORAL BONE

Analysis of the posterior view of the proximal femur with 40° of anteversion demonstrated a reduction in the compression zone, as compared to standard anteversion (compare Fig. 3a-1 and 3a-2). The conversion of compressive stresses to traction forces at the femoral head was significant. Also, greater anteversion was associated with a decrease in the maximum stresses of femoral neck at the intertrochanteric line.

The neutral surface shifted medially when anteversion was increased. This shift is due to rotation around the vertical axis (Fig. 4 and5).

To clarify stress distribution, we evaluated the results of the finite element analysis on the femoral cross sections. The stress distribution curves were represented by the polar angle defined on the center of gravity of each section (Fig. 4). This method allows to evaluate the stress changes spatially.

The posterior and anterior views of the femoral shaft (Fig. 3-b and4) confirmed that the position of the neutral surface changed as a result of rotation around the vertical axis. Also, maximum compression and traction stresses were diminished.

Maximum traction and compression stresses of femur varied with the degree of anteversion. These variations were more marked at the femoral shaft than at the proximal femur (Fig. 4).

To gain insight into the effects of anteversion on applied stresses, we conducted a section-by-section comparison of stress distributions for a femur with standard versus 40° of anteversion (Fig. 5). Results were as follows :

Greater trochanter (Fig. 5a) Maximum traction stresses showed little change. Conversely, there was a significant increase in maximum compression stresses. The shift in the position of the neutral surface was small.

Lesser trochanter (Fig. 5b) None of the changes were significant. Changes were small for both stress magnitudes and stress distribution. However, the neutral surface showed a marked and visible medial shift.

Femoral shaft (Fig. 5c) Maximum traction and compression stresses were reduced. The neutral surface rotated around the vertical axis, coming closer to the medial region. (The levels are those shown in Figure 1c; ant.= anteversion) The magnitude of stresses applied to the proximal femur showed no significant changes. In contrast, stresses on the distal part of the femoral shaft were increased. Maximum compression and traction stresses were shifted distally.

Evaluation of the distributions of stresses on the femoral implant with 40° of anteversion showed results similar to those obtained prior to implantation.

a-Cortical bone

The maximum and minimum longitudinal stresses on the cortical bone of the implanted femur and on the femoral implant were compared across various degrees of anteversion (Fig. 6).

Greater anteversion was associated with an increase in the stresses on the distal part of the cortical bone. Changes in stresses on the implant were consistent from one site to the other. However, changes in longitudinal stresses on the cortical bone and femoral implant were small in absolute value.

We evaluated maximum Von Mises stresses for various degrees of anteversion (Fig. 7). The changes were larger, particularly at the distal part of the cortical bone, at the middle of the implant, and at the neck of the implant.

The fact that Von Mises stresses increased more than longitudinal stresses demonstrates the substantial impact of shear and torsion associated with exaggerated anteversion of the implant inserted in the femur.

DISCUSSION

The impact of femoral implant anteversion has not yet been the focus of extensive modeling studies. Soyer et al. [START_REF] Soyer | Comportement a long terme de !'implant femoral de Charnley : revue de 309 dossiers avec un recul minimum de 20 ans[END_REF] and Garcia-Cimbrelo et al. [START_REF] Garcia-Cimbrelo | Femoral osteolysis after low friction arthroplasty : a planimetric study and volumetric estimate[END_REF] have drawn attention to the deleterious effects of exaggerated anteversion.

Studies reported to date investigated the magnitude of anteversion-related shear and torsion in a qualitative and segmental manner [START_REF] Mccarthy | Rotational stability of noncemented total hip femoral components[END_REF]. Shear and torsion are believed to adversely affect cortical bone remodeling and to cause the development of failure at the cement-prosthesis interface.

One of the main limitations of available studies is inherent in the mesh generation technique, which is widely used. Our experience with 3-D mesh generation (Nastran®, and Algor®) suggests that this method fails to accurately replicate the geometry of a bone as complex as the femur. The meshes are sometimes found to show substantial differences as compared to bony anatomy, particularly when the reconstructions are analyzed in the horizontal plane.

Reported methods for mesh generation remain unsatisfactory either because they require a very large number of elements [START_REF] Keyak | Validation of an automated method of three-dimentional finite element modelling of bone[END_REF][START_REF] Keyak | Automated three-dimensional finite element modeling of bone: a new method[END_REF] or because they are not sufficiently flexible for use in individual patients [START_REF] Lengsfeld | Automatic generation of 3-d finite element codes of the human femur[END_REF][START_REF] Schmitt | Fully automated generation of hip prosthesis voxel models of the femur for finite element analysis : comparison of direct and subsequent prosthesis implantation[END_REF].

The complexity of the geometry of the proximal femur, particularly in the area between the greater and lesser trochanter, is the main stumbling block for mesh generation techniques. Between the two trochanters, the femur is tilted along two different directions; in addition, the femoral metaphysis is rotated from the lesser trochanter to the greater trochanter. These characteristics are major sources of distortion [START_REF] Van Der Sloten | The influence of geometrical distortion of three dimensional finite elements, used to model proximal femoral bone[END_REF] that limit contour segmentation for automatic mesh generation.

Nevertheless, finite element modeling remains an effective and appealing method for evaluating and designing femoral implants, as well as for performing preoperative evaluations [START_REF] Mcnamara | Relationship between bone prosthesis bonding and load transfer in total hip reconstruction[END_REF][START_REF] Verdonschot | Pre clinical testing of hip prosthesis designs: a comparison of finite element calculations and laboratory tests[END_REF].

A linear elastic mechanical behavior is frequently assumed for the areas supposed to represent the cortical bone and trabecular bone. This simplification is valid only for qualitative deformation analysis. If more realistic results are desired, preference should be given to nonlinear models [START_REF] Harrigan | A three dimensional non-linear finite element study of the effect of cement-prosthesis debonding in cemented femoral total hip components[END_REF][START_REF] Lotz | Fracture prediction for the proximal femur using finite element models: part I-linear analysis[END_REF][START_REF] Weinans | Trends of mechanical consequences and modeling of a fibrous membrane around femoral hip prostheses[END_REF] or to use of several modulus of elesticity for the bone, most notably its trabecular component [START_REF] Lotz | Fracture prediction for the proximal femur using finite element models: part I-linear analysis[END_REF][START_REF] Savvidis | Analyse der beanspruchung des proximalen femur bei verschiedenen arten der belastung mit hilfe der finite element methode[END_REF].

Another limitation of modeling studies is inherent in the representation of the space between the implant and the femoral bone. Our model assumed that this space was optimally filled by cement, i.e., disregarded any imperfections in filling [START_REF] Harrigan | A three dimensional non-linear finite element study of the effect of cement-prosthesis debonding in cemented femoral total hip components[END_REF][START_REF] Jansson | Mechanical failure of the femoral component in cemented total hip replacement -a finite element evaluation[END_REF].

We found that increasing the degree of anteversion caused a larger change in Von Mises stresses than in longitudinal stresses. This finding demonstrates that anteversion affects shear stresses, which may adversely affect cortical bone remodeling and cause the development of cracks at the cement implant interface.

We believe that this phenomenon, which is frequently disregarded, should be systematically investigated. At present, anteversion is evaluated only as a factor affecting prosthesis stability [START_REF] Herrlin | Femoral anteversion and restricted range of motion in total hip prostheses[END_REF] and dependent on the orientation of the acetabulum [START_REF] Seki | Analysis of optimal range of socket orientations in total hip arthroplasty with use of computer-aided design simulation[END_REF] and the design of the femoral implant. We suggest that it should be studied specifically because of its major impact on the implanted femur.

CONCLUSION

We constructed geometric femoral models before and after implantation of a cemented femoral prosthesis, based on computed tomography cross sections of femoral bone. A linear elastic mechanical behavior was assumed for both cortical and trabecular bone. Mesh generation was performed semiautomatically.

Using finite element modeling of the femur before and after prosthesis implantation, we performed a qualitative analysis of stress distribution. By comparing the effects of one-legged stance loading across various degrees of implant anteversion, we determined the impact of anteversion on mechanical stresses.

We found that implant anteversion affected mechanical stresses, suggesting that it may also affect femoral bone remodeling in the medium and long term. When anteversion was increased, the neutral surface rotated around the vertical axis in the same direction as the anteversion. In our model, changes in mechanical stresses were greater at the femoral shaft than at the proximal femur.

Our comparison of stress distribution curves for cortical bone obtained at various levels, defined relative to the center of gravity of each cross section, confirmed that greater anteversion resulted in rotation; the pattern of stress distribution suggested that segmental femoral remodeling may occur subsequently.

With our model and with the implant used in our study, stress distribution for the implanted femur was similar to that for the bony femur, most notably as regards the position of the neutral surface, which was very close to the linea aspera.

Increasing the degree of anteversion of the prosthesis increased the mechanical stresses on the distal part of the cortical bone and affected the distribution of stresses on the implant according to the same law.

Comparison of the changes in the maximum Von Mises stresses to the longitudinal stresses showed that anteversion affected shear more than longitudinal stresses. The effect of anteversion was most marked in the middle and distal parts of the femur, resulting in adaptation of the implanted bone.

ACK NOWLE DGME NTS

Thanks to the Biomedical Industrial Society of Fournitures Hospitalieres (FHi, France).

RE FERE NCES

1. Kapandji, I. A., 1980, "Physiologie articulaire Membre inferieur", Maloine SA, Paris, pp. 9-71.

  view of the femur

Fig. 1 -

 1 Fig. 1-Geometrical modelling of a left femur.

Fig. 2 -

 2 Fig. 2-Geometric modeling of the femur after implantation of a femoral prosthesis.

2 •

 2 Posterior view of the femoral shaft with 40° of anteversion.

Fig. 3 --' • 10 •I 10 l20Fig. 4 .

 310104 Fig. 3-Distribution of longitudinal stresses on the left femur with 15° and with 40° of anteversion.(* Neutral Surface)

Fig. 5 -

 5 Fig. 5 -Longitudinal stress distribution on femoral cross sections with 15° and with 40° of anteversion. (The levels are those shown in Figure 1 c; * Neutral Line)

Fig. 6 -Fig. 7 -

 67 Fig. 6-Comparison of maximum and minim � m lo �gitudi � al str 0 esses based . on all cross sections of the implanted femur, with 15 and with 40 of antevers1on. (The levels are those shown in Figure 2e; ant. = anteversion)

200


Jean-François Deü
email: jean-francois.deu@cnam.fr

Walid Larbi
email: walid.larbi@cnam.fr

Roger Ohayon
email: roger.ohayon]@cnam.fr

J.-F Deü

Structural-acoustic

Keywords: Structural-acoustic, Piezoelectric patches, Finite element, Noise and vibration attenuation, Shunt damping technique

INTRODUCTION

For noise and vibration reduction, various approaches can be employed depending on the frequency range to attenuate. Generally, active or passive piezoelectric techniques are effective in the low frequency range, while dissipative materials (such as viscoelastic treatments or porous insulations) are efficient for higher frequency domain. In this work, we propose a reduced order model to describe a fully coupled electro-mechanical-acoustic problem in the low frequency range. The system consists of an elastic structure with surface-mounted piezoelectric patches coupled with an inviscid, compressible and barotropic fluid, gravity effects being neglected. The piezoelectric elements, connected with a resonant shunt circuit, are used for the vibration damping of the coupled system.

First, a non-symmetric finite element formulation of the coupled system is derived from a variational principle involving structural displacement, electrical voltage of piezoelectric elements, and acoustic pressure inside the fluid cavity. This formulation, with only one couple of electric variables per patch, is well adapted to practical applications since realistic electrical boundary conditions, such that equipotentiality on the electrodes and prescribed global electric charges, naturally appear. The global charge/voltage variables are intrinsically adapted to include any external electrical circuit into the electromechanical problem and to simulate the effect of resistive or resonant shunt damping techniques.

The second part of this work is devoted to the introduction of a reduced-order model of the coupled problem. The proposed methodology, based on a normal mode expansion, requires the computation of the eigenmodes of the structure with short-circuited piezoelectric patches, and the rigid acoustic cavity. It is shown that the projection of the full-order coupled finite element model on the uncoupled bases, leads to a reduced order model in which the main parameters are the classical fluid-structure and electromechanical modal coupling factors. Despite its reduced size, this model is proved to be very efficient for simulations of steady-state and transient analyses of the coupled structural-acoustic system with shunt damping.

In the last part of the paper, a three-dimensional numerical example is investigated. The problem consists of an elastic plate equipped with piezoelectric elements and coupled with an acoustic cavity. This example is analyzed in order to show that the reduced order model is capable of capturing the main characteristics of the system dynamic behavior, notably in terms of attenuation.

FINITE ELEMENT FORMULATION OF THE STRUCTURAL ACOUSTIC PROBLEM WITH PIEZOELECTRIC PATCHES

We briefly recall in this section the variational formulation of a fluid/piezoelectricstructure interaction problem in terms of structural mechanical displacement u , electric potential in the structure  and fluid pressure p of the inviscid acoustic fluid (for more details, we refer the reader to [START_REF] Deü | Piezoelectric structural acoustic problems: Symmetric variational formulations and finite element results[END_REF][START_REF] Larbi | Structural-acoustic vibration reduction using switched shunt piezoelectric patches: A finite element analysis[END_REF]). Secondly, this coupled formulation is adapted to the general case of an elastic structure equipped with P piezoelectric patches (see Fig. 1) as done for structural vibrations in [START_REF] Thomas | Vibrations of an elastic structure with shunted piezoelectric patches: Efficient finite element formulation and electromechanical coupling coefficients[END_REF]. This modified formulation allows taking into account realistic electrical boundary conditions such as equipotentiality on patches electrodes and prescribed global charges. Finally, the resulting finite element formulation is applied to a structural acoustic problem with one piezoelectric patch connected to a RL series shunt circuit. It should be noted that standard indicial notations are adopted throughout the paper: subscripts i, j, k and l denote the three-dimensional vectors and tensor components and repeated subscripts imply summation. In addition, a comma indicates a partial derivative. on the remaining part D  . Thus, the total structure boundary, denoted

S  , is such that S u D              with u D              .
The linearized deformation tensor is

1 2 ij i j j i u u           
and the stress tensor is denoted by ij  . Concerning the electric field variables, i D is the electric displacement verifying the elec- tric charge equation for a dielectric medium 0 i i D   in S  and the electric boundary condi- tions

S d i i D n q   on D  ; i E denotes the electric field vector such that i i E     .
The linear piezoelectric constitutive equations write:

( ) ( ) ( ) ij ijkl kl kij k u c u e E        (1) ( ) ( ) ( ) i ikl kl ik k D u e u E       (2)
where ijkl c denotes the elastic moduli at constant electric field, kij e the piezoelectric constants and ik  the dielectric permittivity at constant strain. Moreover, we denote by S  the mass density of the structure. Let us introduce the admissible spaces u C and C  of regular functions i u and  defined in S  . We then consider the subspaces

  0on u i u i u C u C u       , on d d C C                  and 0on C C                  .
The variational formulation, corresponding to the response of the piezoelectric structure subjected to the prescribed boundary conditions and to the pressure field p on the interface  writes:

Find i u u C   and d C    such that: i u u C     : 2 2 d d d d d S S S d F i ijkl kl ij kij k ij S i i i i i u c v e E v u v F u s pn u s t                         (3)
where

1 2 ( ) ij i j j i u u        , kl
 and k E being functions of i u and  , and

C      : d d d S S D d ikl kl i ik k i e E v E E v q s              (4)
where

i i E      , kl
 and k E being functions of i u and  . This formulation must be completed by appropriate initial conditions.

We consider now the special case of an elastic structure (domain E  ) equipped with P piezo-electric patches and completely filled with an internal fluid (domain F  ). Each piezo- electric patch has the shape of a plate with its upper and lower surfaces covered with a very thin layer of conducting material to obtain electrodes. The p-th patch,  

1 p P     , occupies a domain ( ) p  such that (1) ( ) (
)

P E    
 is a partition of the all structure domain S  . A set of hypotheses, which can be applied to a wide spectrum of practical applications, are now formulated:

 The piezoelectric patches are thin, with a constant thickness ( ) p h for the p-th patch;  The thickness of the electrodes is much smaller than ( ) p h and is thus neglected;  The piezoelectric patches are polarized in their transverse direction (i.e. the direction normal to the electrodes).  The electric field vector, of components k E , is normal to the electrodes and uniform in the piezoelectric patch, so that for all  

1 p P     : ( ) ( ) ( ) in p p k k p V E n h    (5)
where ( )

( ) ( ) p p p V      
is the potential difference between the upper and the lower electrode surfaces of the p-th patch which is constant over ( ) p  and k n is the k-th component of the normal unit vector to the surface of the electrodes.

Under those assumptions and by considering successively each of the 2

P  subdomains (1) ( ) ( ) P F E      
, the variational formulation of the fluid/structure/piezoelectric-patches coupled system can be written in terms of the structural mechanical displacement i u , the elec- tric potential difference ( ) p V constant in each piezoelectric patch, and the fluid pressure p :

 Mechanical equation : i u u C     , ( ) ( ) ( ) 1 2 2 d d d d d p S S p P F ijkl kl ij kij k ij i i p p d i S i i i V c v e n pn u s h u u v F u s t                            (6)
 Electrical equation :

( ) p V R    , ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 d p p P P P p p p p p ikl kl i p p p p V V C V e n V Q h                (7)
where the piezoelectric material permittivity in the direction normal to the electrodes) and ( ) p Q is the global charge in one of the electrodes (see [START_REF] Thomas | Vibrations of an elastic structure with shunted piezoelectric patches: Efficient finite element formulation and electromechanical coupling coefficients[END_REF]).  Acoustic equation :

p p C    , 2 2 2 2 2 1 1 d d d 0 F F F i i i i F F F u p p p v p v n p s c t t                     (8)
The first two equations are directly derived from Eqs. ( 3) and ( 4) using the procedure described in [START_REF] Thomas | Vibrations of an elastic structure with shunted piezoelectric patches: Efficient finite element formulation and electromechanical coupling coefficients[END_REF]. The last equation corresponds to the variational formulation of the Helmholtz equation in the acoustic cavity Thus, the variational formulation of the fluid/structure/piezo-patches coupled problem writes as follows: given ( 6) to [START_REF] Reddy | Mechanics of laminated composite plates and shells: theory and analysis[END_REF] are satisfied. The formulation must be completed by appropriate initial conditions. This formulation, with only a couple of electric variables per patches, is well adapted to practical applications since (i) realistic electrical boundary conditions such that equipotentiality on the electrodes and prescribed global charges naturally appear, (ii) the global charge/voltage variables are intrinsically adapted to include any external electrical circuit into the electromechanical problem and to simulate shunted piezoelectric patches.

d d d F q    ), find ( i u u C   , d C    , p p C  ) such that Eqs. (

Finite element formulation of the fluid/structure/piezo-patches coupled system

Let us introduce U (of length s N ) and P (of length f N ) corresponding to the vectors of nodal values of i u and p respectively, and

(2) ( ) ( )

P T Q Q Q  Q  and (1) (2) ( ) ( ) P T V V V  V 
the column vectors of electric charges and potential differences. The submatrices corresponding to the various linear and bilinear forms involved in Eqs. ( 6) to (8) are defined by

( ) ( ) ( ) ( ) 1 ( ) ( ) 1 2 d d d d 1 d d 1 d d p S p S F F p P T T ijkl kl ij u kij k ij uV p p p P T T T S i i u ikl kl i uV p p T F T i i p i i u p F T F T p i i u p F F V c v e n h V u u v e n h p p v pn u s p p v u n p s c                                                      U K U U C V U M U V C U P K P U C P P M P P C ( ) ( ) ( ) ( ) ( ) 1 1 d T P P p p p T p p T V p p d T i i V C V V Q F u s                 U V K V V Q U F (9)
where u M and u K are the mass and stiffness matrices of the structure; uV C is the electric mechanical coupled stiffness matrix;

(

) (2) ( ) diag P V C C C        K  is a diagonal matrix filled 1
with the P capacitances of the piezoelectric patches; p M and p K are the mass and stiffness matrices of the fluid; up C is the fluid-structure coupled matrix; F is the applied mechanical force vector.

Thus, the variational equations ( 6) to ( 8) for the fluid/structure/piezo-patches coupled problem can be written, in discretized form, as the following unsymmetrical matrix system:

0 0 0 0 0 0 0 0 0 0 u u uV up T uV V T up p p                                                                       M U K C C U F V C K V Q C M P K P    (10)
with appropriate initial conditions.

Structural acoustic problem with piezo patches connected to RL shunt circuit

The above discretized formulation (Eq. ( 10)) can be used for a wide range of applications of mechanicals structure coupled with acoustic domain and associated with piezoelectric patches. It is particularly adapted to the case where the piezoelectric patches are shunted, i.e. connected to a passive electrical network [START_REF] Thomas | Vibrations of an elastic structure with shunted piezoelectric patches: Efficient finite element formulation and electromechanical coupling coefficients[END_REF]. In this case, neither V nor Q are prescribed by the electrical network but the latter imposes only a relation between them. In the case of a resonant shunt connected to the p-th patch and composed of a resistance ( ) p R and an inductance ( ) p L in series (Fig. 1), we have the following relation between electrical potential difference ( ) p V and the electric charge ( )

p Q : 0    LQ RQ V   (11)
where

(1) ( ) diag P R R        R  and (1) ( ) diag P L L        L 
are diagonal matrices filled with the P resistances and inductances of the shunt circuits. Due to the direct piezoelectric effect, the piezoelectric patch converts a fraction of the mechanical energy of the vibrating structure into electrical energy which can be dissipated through the resistive components of the RL circuit. It is well known that the damping effect due to this circuit is maximal when the resonance circular frequency 1 LC  of the shunt circuit is tuned on the circular frequency of the structural-acoustic eigenmode to be controlled. The resistance R and the inductance L can be adjusted and properly chosen so as to maximize the damping effect. Therefore, the optimal resistance and inductance for a series resonant shunt can be calculated by [START_REF] Hagood | Damping of structural vibrations with piezoelectric materials and passive electrical network[END_REF][START_REF] Corr | Comparison of low-frequency piezoelectric switching shunt techniques for structural damping[END_REF] 2 eff opt 2 eff

(1 )

i i i k R C k      (12) opt 2 2 eff 1 (1 ) i i L C k     ( 13
)
where i  is the short circuit natural frequency of the i-th mode and eff i k  is the effective electromechanical coupling coefficient [START_REF] Thomas | Vibrations of an elastic structure with shunted piezoelectric patches: Efficient finite element formulation and electromechanical coupling coefficients[END_REF].

Using the second row of Eq. ( 10), the degrees-of-freedom associated with the electrical potential difference V can be expressed in terms of structural displacements U and electric charge Q as

1 1 T V uV V     V K C U K Q (14)
Thus, after substitution of V into Eq. ( 11) and using Eq. (10), we get the following electro-mechanical-acoustic system:

1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 T u u u V V u V uV V up T V uV V p                                                                                                T up p M U U K C K C C K C U F L Q R Q K C K Q C M P P K P       (15)
Note that this (U, Q, P) formulation is well suited for switch shunting applications.

REDUCED ORDER MODEL

In this section, we introduce a reduced-order formulation of the discretized problem obtained in the previous section. This formulation, based on a modal superposition method, consists in expanding (i) the structural displacement over the in vacuo structure modes in short circuited configuration, (ii) the acoustic pressure over the acoustic modes of the fluid in rigid cavity. This approach is widely used and effective for structural acoustic systems with weak coupling. It can be noted that the acoustic basis is enriched by a static mode ( [START_REF] Morand | Fluid-structure interaction[END_REF]) and that the main motivation of choosing the structural modes with short-circuited patches is that they can be computed using a classical elastic formulation.

Eigenmodes of the structure in vacuo with short-circuited patches

In a first phase, the first s M eigenmodes of the structure in vacuo with all patches shortcircuited are obtained from the following equation

  2 0 for 1 u s i u s i s i M              K M  ( 16
)
where ( )

si s i
   are the natural frequency and eigenvector for the i-th structural mode. These modes verify the following orthogonality properties 2 and

T T si u sj ij si u sj si ij          M K ( 17
)
where si  have been normalized with respect to the structure mass matrix.

Eigenmodes of the internal acoustic cavity with rigid walls

In this second phase, the first f M eigenmodes of the acoustic cavity with rigid boundary conditions are obtained from the following equation 2 0 for 1

p f i p f i f i N                    K M  ( 18
)
where ( )

fi f i
   are the natural frequency and eigenvector for the i-th acoustic mode. These modes verify the following orthogonality properties 2 and

T T fi p fj ij fi p sj fi ij          M K ( 19
)
where fi  have been normalized with respect to the fluid mass matrix.

Modal expansion of the general problem

By introducing the matrices

1 s s s s N              of size s s N M  and 1 f f f f N                of size f f N M 
corresponding to the uncoupled bases, the displacement and pressure are sought as ( ) and ( )

s s f f t t     U q P q (20)
where the vectors

1 s T s s s N q q          q  and 1 f T f f f N q q            q 
are the modal amplitudes of the structure displacement and the fluid pressure respectively. Substituting these relations into Equations (15) and pre-multiplying the first row by T s  and the third one by T f  , we obtain the equation

1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 T T T T s u u V V u V s s uV V s up f s T V uV s V T f p f f T s u s s s f                                                                                                        T T T f up s f p f K C K C C K C q K C K Q K q M q R Q L C M q      0 0 T s f                       F q Q q   (21)
This matrix equation represents the reduced order model of the structural acoustic problem with piezoelectric shunt damping treatments. If only few modes are kept for the projection, the size of this reduced order model (

s f M P M  
) is much smaller than the initial one

( s f N P N   ) (see examples below).
Equation ( 21) can be also written in the following form of coupled differential equations  s N mechanical oscillators

( ) ( ) ( ) 2 ( ) ( ) ( ) 1 1 1 1 2 f s N N p p p P P p i k i i si si si si ij fj i si si p p p k p j q q Q q F q q C C                        (22)
 f N acoustic equations 2 1 0 s N fi fi ij sj fi j q q q         (23)
 P electric equations

( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 0 s N p p p p p i si p p i Q L R q Q Q C C          (24)
where ( ) We can note that modal damping coefficients i  have been added in Equation ( 22) in order to take into account the structural damping which can be measured experimentally. The initial finite element formulation previously introduced has been replaced by the modal formulation of Equations ( 22), ( 23), (24) whose unknowns are the s N structure modal coordinates si q , the f N fluid modal coordinates fi q and the P charges ( ) p Q associated with the piezoelectric patch. Its major interest, and especially the choice of the short-circuit eigenmodes as the expansion basis, is that the above computations of the parameters necessitate only a modal analysis of an elastic problem. This operation can thus be done by any standard finite elements code.

T i s i F t   F

NUMERICTLA EXAMPLES

We consider a 3D acoustic cavity completely filled with air (density = 1.2 kg/m 3 ; speed of sound = 340 m/s). The cavity walls are rigid except the top one which is a flexible aluminium plate of thickness 1 mm clamped at its four edges. The density of the plate is 2700 kg/m 3 the Young modulus 72 GPa and the Poisson ratio 0.34. On the top surface of the plate, two identical piezoelectric patches of thickness 0.5 mm are bounded. For the mechanical characteristics of the piezoelectric material PIC151, the reader can be referred to [START_REF][END_REF]. The geometrical data and mesh are presented in Fig. 3. Concerning the finite element discretization, we have used, for the structural part, 200 four-node plate elements based on Mindlin theory with five degrees-of-freedom per node ( N s =1155). The portions of the plate covered by the PZT patches have been modelled according to the first-order shear deformation laminated theory [START_REF] Reddy | Mechanics of laminated composite plates and shells: theory and analysis[END_REF]. As discussed in the previous sections, only one electrical degree of freedom is used to represent the electrical charge Q in each patch. The acoustic cavity is discretized using 2600 hexahedric elements with one degree-offreedom per node corresponding to the acoustic pressure ( N f =3234). Note that the structural and acoustic meshes are compatible at the interface.

Modal analysis of the acoustic/struc-ture/piezo-patches coupled problem

Table 1 presents the eigenfrequencies in three following cases: (i) the 3D rigid acoustic cavity; (ii) the clamped plate with the two patches short circuited; and (iii) the plate/acousticcavity coupled system in the short circuit case. All coupled frequencies, except the sixth, are associated with the first vibration modes of the structure (lower than 450 Hz), and the sixth coupled frequency corresponds to the first acoustic mode in rigid cavity. It can be confirmed by comparing the mode shapes in case (iii) with those obtained in cases (i) or (ii) which are not shown here for sake of brevity. Moreover, as expected, the natural frequencies of the coupled modes (structure dominated) are lower than those for the structure in vacuum (except for the first mode) due to the "added-mass effect" of the fluid. For illustration purpose, Fig. 4 shows the deformed plate and the pressure field for the first ten vibration modes in the coupled case.

Fluid in rigid cavity

Structure

Transient analysis of the acoustic/structure/piezoelectric-patch coupled problem

In this part, a multiple-mode shunt system with two piezoelectric patches as shown in Fig. 5 is used in order to get an optimal multi-modal damping of the coupled system. The patches are tuned simultaneously on the second and the fourth modes of the plate. For each mode, the optimal values of the shunt electrical parameters are computed using Equations ( 27) and (28) (with R 1  632.73  L 1  9.47 H for the second mode and R 2  735.56  and L 2  3.17 H for the fourth mode). The plate is excited by a mechanical force of intensity 1 N located at (x = 0.14 m, y = 0.06 m, z = 0.3 m). The system vibratory response is obtained with the modal reduction approach defined by Equation (36) with a truncation on the first M s  10 structural modes and the first 10 f M  acoustic modes. Figures 6 and 7 present the frequency response of the system with and without shunt. The mechanical transverse displacement in the plate at the point of coordinates (x = 0.14 m, y = 0.06 m, z = 0.3 m) is presented in Fig. 6 and the sound pressure level in the acoustic cavity at the point of coordinates (x = 0.15 m, y = 0.09 m, z = 0.1 m) in Fig. 7. These Figures show that the modal resonant magnitude for each considered mode have been significantly reduced simultaneously. In fact, the strain energy present in the piezoelectric material is converted into electrical energy and hence dissipated into heat using the RL shunt device.

CONCLUSIONS

In this work, an original finite element formulation of structural acoustic problems with piezoelectric patches is presented. This formulation, involving only a couple of electric variables by patch, allows take into account naturally realistic electric boundary conditions. A reduced-order model, based on a normal mode expansion, is then developed. The proposed methodology requires the computation of the eigenmodes of the structure with short-circuited piezoelectric patches, and the rigid acoustic cavity. It is shown that the projection of the fullorder coupled finite element model on the uncoupled bases, leads to a reduced order model in which the main parameters are the classical fluid-structure and electromechanical modal coupling factors. Despite its reduced size, this model is proved to be very efficient for simulations of steady-state analyses of structural-acoustic coupled systems with shunt damping.

Figure 1 :

 1 Figure 1: Fluid/piezoelectric-structure coupled system.

2. 1 F

 1 Variational formulation of the fluid/structure/piezo-patches coupled system We consider a piezoelectric structure occupying the domain S  filled with an inviscid lin- ear acoustic fluid occupying the domain F  . We denote by  the fluid-structure interface and by S i n and F i n the unit normal external to S  and F  , respectively. The structure is clamped on a part u  and subjected (i) to a given surface force density d i on the complementary part   of its external boundary and (ii) to a pressure field p due to the presence of the fluid on its internal boundary  . The electric boundary conditions are de- fined by a prescribed electric potential d  on   and a surface density of electric charge d q

  on  . This relation expresses the continuity of the normal displacements of the fluid and the structure on  . F c is the constant speed of sound in the fluid and F  the mass density of the fluid. p C is the admissible space of regular functions p defined in F  .

Figure 2 :

 2 Figure 2: Piezoelectric patch connected to RL shunt circuit.

  is the mechanical excitation of the i-th mode; C the electromechanical coupling factors.

Figure 3 :

 3 Figure 3: Acoustic/structure/piezo-patches coupled system: (a) geometrical data (in m) and (b) mesh.

Figure 4 :

 4 Figure 4: First 4 fluid-structure coupled modes: pressure level in the cavity and plate displacement.

Figure 5 :

 5 Figure 5: Vibration plate coupled with an acoustic cavity and connected to RL shunt circuit.

Figure 6 :

 6 Figure 6: Frequency response function: transverse displacement amplitude in dB at the excited point.

Figure 7 :

 7 Figure 7: Frequency response function: pressure level in dB at x = 0.15 m, y = 0.09 m, z = 0.1 m.

without fluid Coupled problem Type of coupled mode

				S: Structure / F: Fluid
	297.94	77.93	85.40	S
	561.56	123.64	122.53	S
	569.00	194.29	192.79	S
	614.82	212.29	211.94	S
	642.29	237.12	236.14	S
	681.94	316.11	298.31	F
	799.44	346.32	315.59	S
	837.71	383.89	346.24	S
	875.22	434.73	382.23	S
	881.62	451.03	433.61	S

Table 1 :

 1 Computed frequencies (in Hz) of the structural-acoustic coupled system.


W Larbi

J.-F Deü

R Ohayon

FINITE ELEMENT FORMULATION OF SMART COMPOSITE STRUCTURE COUPLED TO ACOUSTIC FLUID

Keywords: Composite structures, Structural-acoustic, Piezoelectric patches, Finite element, Noise and vibration attenuation, Shunt damping technique

In the context of noise and vibration reduction techniques by active treatments, this work presents the theoretical formulation and the finite element implementation of the specific problem of piezoelectric adaptive composite structure coupled with acoustic fluid and connected to resonant shunt circuits. The originality of this work lies (i) in the formulation and resolution of the fully coupled electro-mechanical-acoustic system using modal projection techniques, and (ii) in the development of an accurate adaptive laminated plate element.

First, a non-symmetric finite element formulation of the coupled system is derived from a variational principle involving structural displacement, electrical voltage of piezoelectric elements, and acoustic pressure in the acoustic fluid. This formulation, with only one couple of electric variables per piezoelectric layer, is well adapted to practical applications since realistic electrical boundary conditions, such that equipotentiality on the electrodes and prescribed global electric charges, naturally appear. The global charge/voltage variables are intrinsically adapted to include any external electrical circuit into the electromechanical problem and to simulate the effect of resistive or resonant shunt techniques.

The second part of this work is devoted to the introduction of a reduced-order model of the coupled problem. The proposed methodology, based on a normal mode expansion, requires the computation of the eigenmodes of (i) the structure with short-circuited piezoelectric patches, and (ii) the rigid acoustic cavity. It is shown that the projection of the full-order coupled finite element model on the uncoupled bases, leads to a reduced order model in which the main parameters are the classical fluid-structure and electromechanical modal coupling factors. Despite its reduced size, this model is proved to be very efficient for simulations of steady-state and transient analyses of coupled structural-acoustic systems with shunt damping.

In the third part, all the above developments are applied to the simulation of vibration and noise reduction by means of a resonant shunt of a composite plate coupled to a 3D acoustic cavity. We expose in this part the details of a finite element discretization of the laminated composite plate with piezoelectric patches. The considered finite element model is based on an equivalent single layer theory combined with a first order-order shear deformation theory. A nonconforming FE approach is carried out using Lagrange and Hermite interpolations for the mechanical mid-plane displacements and cross-section rotations. For the portion of the plate covered by the piezoelectric patch, only one electrical degree of freedom is used to represent the electrical charge in each patch.

Finally, numerical examples are investigated. They are first analyzed in order (i) to validate and demonstrate the effectiveness of the proposed finite element formulation, (ii) to show that the reduced order model is capable of capturing the main characteristics of the system dynamic behavior, in particular in terms of attenuation. Then, sensitivity analyses concerning the piezoelectric patches (size and position) and the electric circuits (resistance and inductance) are performed in order to highlight the role of each parameter on the performances of the shunt damping techniques.

Figure 1 :

 1 Figure 1: Vibrating composite plate coupled with an acoustic cavity and connected to RL shunt circuit: (a) problem sketch and (b) frequency response function with and without shunt