André Lage Freitas

Nikos Parlavantzas
email: nikos.parlavantzas@irisa.fr

Jean-Louis Pazat
email: jean-louis.pazat@irisa.fr

An Integrated Approach for Specifying and Enforcing SLAs for Cloud Services

Cloud computing has evolved from the provisioning of virtual machines to the provisioning of complex services, delivered to customers under the terms of Service-Level Agreements (SLAs). SLAs specify the Quality of Service (QoS) that should be provided to customers as well as the billing model. A main concern for cloud service providers is to maintain the agreed SLA terms in order to avoid losses and penalties. Maintaining the SLA in turn requires translating the QoS to configurations of low-level mechanisms, able to enforce the agreed terms. Current systems provide no integrated support for SLA specification, translation, and enforcement. In this paper, we propose an approach for specifying and enforcing SLAs for cloud service providers. The approach covers the creation of SLA templates under a billing model, the design of performance and faulttolerance QoS assurance mechanisms as well as the translation of QoS to appropriate configurations of those mechanisms. We demonstrate the feasibility of our approach by using the Qu4DS framework for PaaS cloud providers. Moreover, we evaluate the impact of failures on the provider profit. The experiments were carried out on the Grid5000 testbed and demonstrate the effectiveness of ensuring fault tolerance in different scenarios.

I. INTRODUCTION

The cloud computing paradigm has evolved from the provisioning of virtual machines to the provisioning of complex services. Higher-level services are built on top of distributed infrastructures in a layered fashion as proposed by the common cloud architecture [START_REF] Schubert | The Future Of Cloud Computing, Opportunities for European Cloud Computing Beyond[END_REF], [START_REF] Chohan | AppScale: Scalable and Open AppEngine Application Development and Deployment[END_REF], [START_REF] Mell | The NIST Definition of Cloud Computing[END_REF]. The cloud architecture decomposes resources, platforms, and the final software in three layers: IaaS (Infrastructure as a Service), PaaS (Platform as a Service), and SaaS (Software as a Service). Example services at each layer include Amazon EC2 [START_REF]Amazon Elastic Compute Cloud (Amazon EC2)[END_REF], SalesForce [START_REF]Salesforce.com[END_REF], and Google Maps [START_REF] Google | Google maps[END_REF] respectively.

The interactions between customers and cloud service providers are typically specified in Service-Level Agreements (SLAs). SLAs cover customer and provider obligations and further details about the service, such as functional requirements as well as the Quality of Service (QoS) that should be delivered along with the service. Moreover, SLAs should include billing details which describe the pricing model and how penalties are computed in case of SLA violations. For instance, Zencoder [START_REF] Zencoder | Zencoder -Cloud Video Encoding/Transcoding Software as a Service[END_REF] offers video and audio encoding services and charges customers based on each minute of encoded video output. Regarding SLA violations, if Zencoder services are not available at least 99.9% in a month, Zencoder fully refunds customers by means of service credits. Similarly, Amazon EC2 [START_REF]Amazon Elastic Compute Cloud (Amazon EC2)[END_REF] also pays service credits to customers if virtual machines are available less than 99.95% in a month.

Although SLAs are useful for describing the service along with its QoS and billing aspects, SLAs are not enough to ensure QoS. SLAs serve as guidelines to which the service execution should comply in order to prevent losses. Therefore, QoS assurance mechanisms should be integrated with the service execution in order to ensure that the service will be delivered as agreed. Moreover, the employment of QoS assurance mechanisms requires translating high-level SLA objectives to system-level configurations.

Current work fails to integrate SLA description, translation and enforcement. Indeed, some approaches describe SLAs and their pricing model but do not address QoS assurance [START_REF]Amazon Elastic Compute Cloud (Amazon EC2)[END_REF], [START_REF] Zencoder | Zencoder -Cloud Video Encoding/Transcoding Software as a Service[END_REF], [START_REF] Macías | Rule-based SLA management for revenue maximisation in Cloud Computing Markets[END_REF], [START_REF] Genaud | Cost-wait trade-offs in client-side resource provisioning with elastic clouds[END_REF]. These approaches also fail to include fines into their pricing model. Other approaches deal with QoS assurance but describe neither details about SLA nor billing concerns [START_REF] Kecskemeti | An Approach for Virtual Appliance Distribution for Service Deployment[END_REF], [START_REF] Huedo | A framework for Adaptive Execution in Grids[END_REF], [START_REF] Klein | An RMS Architecture for Efficiently Supporting Complex-Moldable Applications[END_REF], [START_REF] Luckow | SAGA BigJob: An Extensible and Interoperable Pilot-Job Abstraction for Distributed Applications and Systems[END_REF]. Finally, other approaches focus on translating SLA to low-level configurations [START_REF] Hasselmeyer | Towards SLA-Supported Resource Management[END_REF], [START_REF] Stantchev | Negotiating and Enforcing QoS and SLAs in Grid and Cloud Computing[END_REF], [START_REF] Li | SLA Translation in Multi-layered Service Oriented Architectures: Status and Challenges[END_REF] but they neither specify how QoS can be ensured nor apply QoS under a pricing model.

In this paper, we propose an integrated approach for SLA management. Firstly, we introduce the context of our approach in Section II. Section III discusses the creation and translation of SLA templates based on the customization of performance and fault-tolerance QoS. We also include into the SLA description a pricing model which considers operational expenses and currency fines in a pay-per-use fashion. In Section IV, we present two QoS assurance mechanisms which ensure performance and fault-tolerance QoS along with the translation of QoS to low-level mechanism configurations. Section V explains how the Qu4DS framework [START_REF] Freitas | Cost Reduction Through SLA-driven Self-Management[END_REF] is used as proof of concept for our approach. Qu4DS provides automatic SLA management functionalities which include service negotiation, resource booking, instantiation, billing, SLA translation, and QoS assurance in a transparent fashion. Furthermore, experiments were performed on Grid'5000 in order to analyze the impact on the service profit for different scenarios. The results of these experiments are presented in Section VI.

II. THE PROBLEM

The Figure 1 introduces the context of this work by describing a fictitious example based on real cloud services. A music group wants to publish its album in an audio sharing service such as Jamendo [START_REF] Jamendo | Jamendo[END_REF]. The group uploads their songs to Jamendo in a lossless audio format, e.g., FLAC [START_REF]Free Lossless Audio Codec[END_REF], as required by Jamendo. In order to save storage space, Jamendo asks the Zencoder [START_REF] Zencoder | Zencoder -Cloud Video Encoding/Transcoding Software as a Service[END_REF] audio encoder service to compress the FLAC songs to the lossy OGG [START_REF]The Xith Open Source Community[END_REF] format. In turn, Zencoder books virtual machines from a cloud provider such as Amazon EC2 [START_REF]Amazon Elastic Compute Cloud (Amazon EC2)[END_REF] in order to encode the songs. After encoding the songs, Zencoder forwards them to Jamendo which publishes the album along with the OGG songs for streaming and downloading. The example depicted by Figure 1 can be realized using current cloud services -in fact, Zencoder uses Amazon EC2. However, the challenge is to provide QoS in this context, e.g., to define which level of QoS Zencoder can offer to Jamendo in order to ensure that the songs will be encoded successfully and that the encoding process will not take longer than an agreed timeout. The SLA agreed between Zencoder and Jamendo should include QoS metrics and the penalties that should be applied if Zencoder does not guarantee QoS. In order to address this problem, the first issue is to define which QoS metrics can be provided in such a dynamic, unpredictable, and distributed environment. Secondly, it is necessary to design and implement QoS assurance mechanisms able to ensure the defined QoS. Thirdly, a mapping between high-level QoS metrics and low-level means is necessary in order to configure QoS assurance mechanisms. Finally, the SLA should also include a complete billing model which includes pricing, infrastructure costs and fine payments.

This work provides a solution for the stated problem by focusing on supporting cloud service providers in guaranteeing SLA terms. The approach integrates SLA description, negotiation and enforcement in a transparent way. In the following, we explain how SLA templates are created, the description of the billing model, the design of QoS assurance mechanisms, and the translation of QoS to system-level configurations.

III. CREATING SERVICE-LEVEL AGREEMENTS

A. SLA Templates SLA templates are useful for enabling service negotiation. This work assumes that SLA templates are provided by the service provider. Figure 2 depicts a contract establishment followed by a request treatment. First, costumers choose an SLA template based on the desired level of QoS. Once chosen, they set the contract duration and propose the customized template to the service provider. The provider may reject the contract proposal, otherwise it is accepted and a contract is established. Following that, customers are able to send requests. The idea is to rely on a simple SLA negotiation protocol based on contract templates which include the description of the involved parties, the terms as well as the QoS that should be met by the provider. For instance, the aforementioned negotiation requirements are supported by complete negotiation specifications and protocols such as WSLA [START_REF] Ludwig | Web Service Level Agreement (WSLA) Language Specification[END_REF] and WS-Agreement [START_REF] Andrieux | Web Services Agreement Specification (WS-Agreement)[END_REF]. This approach includes SLA templates which describe performance and fault-tolerance QoS. Performance is addressed by defining the response time QoS metric, which specifies the maximum amount of time that a request treatment can take. The fault tolerance QoS metric is reliability which specifies the degree of dependability. Moreover, both response time and reliability are quantified by the high-level constraints strong, medium, and weak [START_REF] Rosa | An Approach for Reasoning and Refining Non-Functional Requirements[END_REF].

Finally, SLA templates are created based on the customization of QoS constraints. In order to ease the identification of SLA templates, labels are used to name them according to their main quality characteristic. The Table I depicts four SLA templates whose labels are fast, safe, classic and standard. Setting SLA templates labels involves defining the degree of performance and fault tolerance of each SLA template. Because providing fault tolerance capabilities adds operational overhead, performance and fault tolerance cannot be prioritized simultaneously. Therefore, SLA templates are customized by prioritizing one QoS metric at a time or none of them. For instance, the fast SLA template prioritizes performance, while the safe SLA template prioritizes fault tolerance. On the other hand, the classic and standard SLA templates prioritize neither performance nor fault tolerance.

B. Pricing

It is important to set the price as a function of the expenses in order to prevent losses. Thereby the targeted profit margin is guaranteed as the price fluctuates according to the expenses. The service price is set based on operational costs as depicted by Equation 1. The price is represented by ρ where l is the SLA template label and t is the contract duration. The expenses for providing the service are represented by ǫ which quantifies the costs of resource acquisition; however, expenses may include software licenses as well as further required services. Finally, π represents how much the provider wants to profit from the given SLA template label and contract duration.

ρ(l, t) = ǫ(l, t) + π(l, t) (1)
Customer billing is assumed to be computed according to service usage, i.e., in a pay-per-use fashion [START_REF] Lehmann | Pricing Strategies of Software Vendors[END_REF], [START_REF] Lehmann | Pricing Models of Software as a Service Providers: Usage-Dependent Versus Usage-Independent Pricing Models[END_REF]. Service usage is measured based on the chosen contract template and on the contract duration. In other words, each contract template has its own cost per time unit (cf. Equation 1). Moreover, the time metric is used for generality as it is suitable for most type of services, e.g., monthly installments. However, further metrics such as number of requests, concurrent usage and key performance indicators can be added in order to support specific services. Note that this work is not limited to the pay-per-use model. For instance, subscription-based models are often employed by current cloud providers. They rely on a predefined amount of billing metrics to be consumed given a billing time unit (e.g., ten gigabytes per month). In this example, pay-per-use would assess how many megabytes were consumed given a time interval. However, if we impose to customers a predefined amount of data (i.e., ten gigabytes) given a time period (i.e., month), then pay-per-use is transformed in a subscription model. This work assumes that penalties owing to SLA violations are payed in monetary terms. An SLA violation means the unsuccessful request treatment and implies the payment of the fine ψ as depicted in Equation 2; where f ψ is a constant which is used to adjust ψ as a function of the cost of treating the request q k , and resp time q k is the response time of q k . In contrast, current cloud providers [START_REF]Amazon Elastic Compute Cloud (Amazon EC2)[END_REF], [START_REF]Google Application Engine[END_REF], [START_REF]Salesforce.com[END_REF], [START_REF] Zencoder | Zencoder -Cloud Video Encoding/Transcoding Software as a Service[END_REF] rely on service credits as fine payments in order to prevent losses since it is very hard to ensure any QoS in a dynamic and distributed environment. However, providing QoS assurance mechanisms encourages cloud service providers to rely on monetary fines. The advantage of paying fines in monetary terms is that it allows the cloud service provider to positively differentiate itself from its competitors which rely on service credits.

ψ(l, q k ) = f ψ • ρ(l, resp time q k ) (2)
Ultimately, the provider profit P is calculated as depicted by Equation 3. Given the provisioning time interval [t, t ′ ], the provider held n contracts in such a way that ρ i is the price of the contract c i and ǫ i represents the expense of c i . The term ψ i,j represents fine cost of the j-th request that belongs to c i and will be taken into account if such a request could not be treated.

P [t,t ′ ] = n i=0 ρ i - n i=0 ǫ i - n i=0 m j=0 ψ i,j (3)

IV. QOS ASSURANCE MECHANISMS

A. QoS Translation

QoS translation refers to mapping QoS constraints to the right configuration which enables the system to deliver the targeted QoS level. The QoS translation is represented by the generic function τ as Equation 4 depicts where qos is a QoS constraint and sys conf ig is a system configuration.

τ (qos) = sys conf ig (4)
This work describes two QoS assurance mechanisms which handle performance and fault tolerance. The configuration of the performance QoS assurance mechanism uses the resource requirements able to meet a given response time; hence the translation is done by τ (resp time cons ) = res req cons where cons is a QoS constraint. Moreover, the mapping between response time and resource requirements is done by profiling the service provider. The configuration of the faulttolerance QoS assurance mechanism uses replacement threshold parameters as it relies on a job replacement algorithms. Thus the translation of the reliability QoS constraints is done by τ (reliability cons ) = (f ailure th cons , delay th cons ) where f ailure th and delay th are replacement thresholds for failed and delayed jobs respectively.

B. Performance

The response time QoS is ensured by booking resources, configuring the service instance, and deploying the instance based on the minimal resource requirements 1 able to meet the given response time. The performance QoS assurance mechanism is described by the sequence diagram depicted by Figure 3. When a customer proposes a contract, the service provider translates the response time to its respective resource requirements based on profiling data. Then the service provider acquires resources from the infrastructure according to the previous resource requirements until the end of the contract duration. The translated resource requirements are also used to configure and deploy the service instance. When the service instance is operational, the customer can send requests which are forwarded to the right service instance. Thus, requests are then treated by the service instance according to the resource requirements to which the service instance is configured.

C. Fault Tolerance

The goal of the fault-tolerance QoS assurance mechanism is to improve the provider ability of overcoming malfunctions during request treatment. In this context, malfunctions can be either job failures or job delays. While a failed job is considered to be an unsuccessful job execution (e.g., an I/O error), identifying job delays requires information regarding the provider profiling, i.e., job execution time and request response time. 1 Minimal resource requirements are preferred to others that achieve the same response time but imply a greater operational cost.

The fault-tolerance QoS assurance mechanism relies on job replacement algorithms. The basic idea is to replace failed and delayed jobs in order to not compromise the request treatment. The Algorithm 1 replaces failed jobs up to the failed replacement threshold (f ailure th ji ); where n indicates how many times the job was already replaced, J q k is the set of all jobs belonged to q k , J F is the set of failed jobs, J R is the set of running jobs, elapsed time q k is the request elapsed time, and adapt th ji is the adaptation threshold, i.e., the time for triggering an adaptation action. Similarly, the Algorithm 2 replaces delayed jobs up to its replacement threshold (delay th ji ) where J C is the set of canceled jobs. In addition, diagnosing a delayed job requires comparing its elapsed time (elapsed time ji ) with its execution time (exec time ji gathered from the provider profiling.

Algorithm 1 Job Failure Tolerance Require: abort q k , j n i ∈ J q k 6: end if Algorithm 2 Job Delay Tolerance Require: abort q k , j n i ∈ J q k 7: end if Moreover, further fault-tolerance techniques can be used by the aforementioned Algorithms 1 and 2 such as including job replication, migration, or checkpointing.

j n i ∈ J q k ∧ j n i ∈ J F Ensure: j n+1 i ∈ J q k ∧ j n+1 i ∈ J R 1: if elapsed time q k < adapt
j n i ∈ J q k ∧ j n i is delayed Ensure: j n i ∈ J C ∧ j n+1 i ∈ J q k ∧ j n+1 i ∈ J R 1: if elapsed time q k < adapt

V. PROOF OF CONCEPT

We use the Qu4DS (Quality Assurance for Distributed Services) framework [START_REF] Freitas | Cost Reduction Through SLA-driven Self-Management[END_REF] to validate the approach proposed in this paper. Qu4DS is a research prototype for supporting the development and management of cloud services. The Qu4DS architecture abstracts over distributed infrastructures as depicted by Figure 4. Qu4DS creates SLA templates under a pricing model as described in Section III. Then Qu4DS manages SLAs which includes service negotiation, instantiation and provisioning. Qu4DS also implements the QoS assurance mechanisms presented in Section IV whose configurations are generated by translating QoS constraints. Thereby, performance is ensured by booking resources and configuring the service instance according to the right resources requirements. Fault tolerance is ensured by replacing failed and delayed jobs during the request treatment. As case study, we implemented the flac2ogg service provider by using Qu4DS. The flac2ogg provider compresses FLAC audio files to the OGG format. In relation to the example introduced in Section II, the flac2ogg provider represents Zencoder whose customer is Jamendo. In order to improve performance, the flac2ogg provider leverages the Master/Worker pattern to compress the FLAC file in parallel. Qu4DS supports the development and management of the flac2ogg service as Figure 5 illustrates. At development time, the developer imports the Qu4DS library which requires implementing two methods. The first method is treatRequest(args) which is used to call the instance when the customer sends a request. The second method is workerResults(args) which notifies the instance that the workers were executed. Secondly, the service developer exports a Java jar file which is used by the Qu4DS framework to deploy service instances on the infrastructure which is similar, for instance, to the way Amazon MapReduce [START_REF]Amazon Elastic MapReduce[END_REF] works. Lastly, Qu4DS profiles the flac2ogg provider and creates SLA templates which are used for negotiating SLAs.

With respect to service execution management at runtime, SLA negotiation is delegated to Qu4DS (arrow 1 in Figure 5) which triggers resource acquisition and service instantiation on the infrastructure (arrow 2). When a customer sends a request (arrow 3), Qu4DS forwards the request to the right service instance (arrow 4) by calling its treatRequest(args) method. The service instance splits the FLAC file according to its configuration (i.e., n number of workers), prepares the workers, and sends them to Qu4DS (arrow 5). Following that, Qu4DS executes the workers on the infrastructure in accordance to the agreed QoS, i.e., it reacts to job failures and delays according to replacement thresholds. When all the FLAC file parts are compressed to the OGG format, Qu4DS sends the result files to the service instance by calling the workerResults(args) method (arrow 6). Then the instance merges the OGG files to a single OGG file and sends it to Qu4DS (arrow 7) which forwards the response to the customer (arrow 8). Finally, Qu4DS destroys the service instance when the contract ends; thus releasing the previously booked resources. The Table II depicts the QoS translation of QoS constraints to the configurations of QoS assurance mechanisms. The flac2ogg service provider was profiled in order to map the translation of response time to resources requirements, i.e., number of workers necessary to reach a given response time. The reliability QoS constraints were statically set with greater replacement thresholds for constraints which express stronger reliability.

VI. EVALUATION

A. Scenarios

In order to validate that the proof-of-concept of the approach can effectively ensure QoS, we evaluated the efficiency of the fault-tolerance mechanism in the previously-mentioned case study. The goal is to analyze the impact on the provider profit in the presence of job malfunctions for different fine values. The rate of job misbehaviors varies from zero to forty percent of the total amount of jobs. The misbehaved jobs were randomly chosen 2 where half of the given percentage was set to fail and the other half was set to be delayed. The fines were set by assuming that they can cost half of the price to treat the request (f ψ = 0.5), the same price (f ψ = 1.0) or two times the price to treat the request (f ψ = 2.0). The experiments were performed on the Grid'5000 [START_REF] Cappello | Grid'5000: A large scale and highly reconfigurable grid experimental testbed[END_REF] testbed which served as the IaaS resource provider. An operating system image was customized and used to deploy Qu4DS 3 . In addition, a total of fifty-one nodes of the paradent cluster at the Rennes site were used.

Three scenarios were created in order to represent different customer profiles. All scenarios rely on fixed contract duration set to the experimentation time. SLA templates were used to customize the scenarios as explained next.

• high-FT: composed of ten customers whose contract template label is fast. • hybrid: composed of twelve customers, three customers of each contract template label (fast, safe, classic, standard). • high-RR: composed of ten customers whose contract template label is safe.

B. Results

The Figures 6,7, and 8 depict the results of the experimental evaluation. Each dot represent a different experiment configuration whose experimentation time is nine-hundred seconds (i.e., 15 minutes). The Y-axis shows the provider profit (cf. Equation 3) in currency units while the X-axis shows the rate of misbehaved jobs in percentage. The curves represent different configurations concerning the value of the fine ψ which depends on the fine constant f ψ (cf. Equation 2). The experiments were performed by disabling Qu4DS fault tolerance mechanism whose curves are name as FT-off ; except for the high-RR scenario as it holds no SLA template which requires fault tolerance. Finally, the loss horizontal line represents the limit when the profit starts getting negative values, i.e., losses.

The first general observation is that the greater the misbehavior rate is, the lower the profit is. This expected behavior 2 Only jobs used to deploy the workers were candidate to be failed or delayed. 3 The details of this image is available on-line: https://www.grid5000.fr/ mediawiki/index.php/Lenny-x64-quads happens because increasing misbehaved jobs increases the chances of implying SLA violations. Regarding the different scenarios, the more a scenario holds contract template labels which require fault tolerance capabilities, the more moderately the profit drops. For instance, the curves of the high-RR scenario in Figure 8 (i.e., no fault tolerance is required) decrease sharper than the other scenarios. Specifically, the high-FT scenario was able to keep a moderate decrease of profit curves (cf. Figure 6). Secondly, we can observe the difference between profits with same fine value when the fault tolerance is disabled. In Scenarios high-FT and hybrid (cf. Figures 6 and7), all the full line curves are plotted above the dashed lines (i.e., FT-off ). This means that disabling the QoS assurance mechanism negatively influences the profit. Hence, for the experimented situation, the fault-tolerance QoS assurance mechanism showed to be effective.

Finally, the greater the fine is, the sharper the profit decreases. An interesting aspect to note is how the fault-tolerance QoS assurance mechanism smooths the profit drop for significant job misbehavior rates. For instance, even when the job misbehavior rate is 40% (cf. Figure 6), Qu4DS prevented the profit to reach negative values.

VII. RELATED WORK

Considering work related to SLA management, the SLA@SOI project [START_REF] Theilmann | A Reference Architecture for Multi-Level SLA Management[END_REF] proposes a hierarchical and integrated architecture for services. The SLA@SOI architecture wraps software and resources as services and separates service management from SLA management. The SOA4ALL [START_REF] Krummenacher | Final SOA4All Reference Architecture Specification[END_REF] project proposes an architecture for service composition driven by quality aspects. It includes comprehensive service discovery and bindings based on semantics. However, these architectures define neither QoS assurance mechanisms nor pricing models.

In the context of SLA description and pricing, some approaches well describe SLAs and pricing models such as Amazon EC2 [START_REF]Amazon Elastic Compute Cloud (Amazon EC2)[END_REF] and Zencoder [START_REF] Zencoder | Zencoder -Cloud Video Encoding/Transcoding Software as a Service[END_REF]. Other approaches such as Macías et al. [START_REF] Macías | Rule-based SLA management for revenue maximisation in Cloud Computing Markets[END_REF] and Genaud and Gossa [START_REF] Genaud | Cost-wait trade-offs in client-side resource provisioning with elastic clouds[END_REF] address profit concerns under a pricing model. Nevertheless, these approaches do not address QoS assurance. Moreover, these approaches fail in including currency fines into their pricing model.

With regard to SLA translation, in [START_REF] Kotsokalis | Translation of Service Level Agreements: A Generic Problem Definition[END_REF], Kotsokalis and Winkler model the translation of SLA based to service dependency properties. In [START_REF] Chen | Translating service level objectives to lower level policies for multi-tier services[END_REF], Chen et al. translate response time metrics to CPU requirements. In [START_REF] Stantchev | Negotiating and Enforcing QoS and SLAs in Grid and Cloud Computing[END_REF], Stantchev and Schröpfer use service replication in order to improve and ensure performance and fault-tolerance QoS. The authors translate QoS to infrastructure-level by setting the service replication degree. Hasselmeyer et al. [START_REF] Hasselmeyer | Towards SLA-Supported Resource Management[END_REF] investigate how SLA objectives are translated to infrastructure configurations in order to enable high-performance computing service providers to meet the agreed QoS. The main drawback of these approaches is that they fail to specify QoS assurance mechanisms and to apply a billing model. Lastly, in [START_REF] Li | SLA Translation in Multi-layered Service Oriented Architectures: Status and Challenges[END_REF], Li et al. investigate various techniques for translating SLA properties to different layers in a tier architecture. Despite the comprehensive study, the authors also consider neither pricing nor QoS assurance aspects.

With regard to QoS assurance, in [START_REF] Kecskemeti | An Approach for Virtual Appliance Distribution for Service Deployment[END_REF], the Kecskemeti et al. address performance by decreasing the virtual machine deployment time. The GridWay [START_REF] Huedo | A framework for Adaptive Execution in Grids[END_REF] project proposes a framework that reschedules jobs in order to improve performance. In [START_REF] Klein | An RMS Architecture for Efficiently Supporting Complex-Moldable Applications[END_REF], Klein and Perez propose to improve performance of distributed applications by prioritizing previously submitted applications. In [START_REF] Luckow | SAGA BigJob: An Extensible and Interoperable Pilot-Job Abstraction for Distributed Applications and Systems[END_REF], Luckow et al. propose the SAGA big-job abstraction to acquire cloud resources, deploy virtual machines and submit grid jobs to the booked resources. SAGA bigjob replaces pilot-jobs which fail to acquire resources from clouds. In [START_REF] Lee | Rescheduling for Reliable Job Completion with the Support of Clouds[END_REF], Lee and Zomaya propose an algorithm for job rescheduling which replaces grid resources by cloud resources if a grid resource is identified as delaying job executions. These previously mentioned approaches concern low-level details; hence they do include neither higher-level SLA aspects nor billing models.

MapReduce Library [START_REF] Dean | Mapreduce: simplified data processing on large clusters[END_REF] handles worker failures by periodically checking if workers are reachable. If a worker fails, their task are re-scheduled to be executed on another idle worker. Moreover, the MapReduce Library relies on a replicating scheme for the remaining jobs since latest jobs are more susceptible to fail. In order to improve performance, the MapReduce library also relies on replication of remaining jobs by statically configuring the number of map and reduce operations as well as the number of workers. Indeed, the replication of remaining jobs is a solution for improving performance and fault-tolerance qualities. However, we propose to rely on dynamic job metrics such as job elapsed time and job state in order to immediately identify malfunctioning jobs. Thus repairing actions are triggered at this very moment instead of postponing them to the end of the computation.

VIII. CONCLUSION

In this work, we address the problem of integrating SLA specification and enforcement for clouds. Firstly, our approach supports creating SLA templates by combining performance and fault-tolerance QoS, represented by response time and reliability QoS metrics. A billing model is also described and integrated into the SLA templates. Secondly, our approach includes the design of two QoS assurance mechanisms, which dynamically ensure response time and reliability. The response time is ensured by booking resources, configuring, and deploying the service instance according to the resource requirements. Reliability is ensured through algorithms that replace failed and delayed jobs. Finally, the approach covers how to translate QoS to appropriate configurations of the QoS assurance mechanisms.

The approach is validated by the Qu4DS framework [START_REF] Freitas | Cost Reduction Through SLA-driven Self-Management[END_REF] which supports the development and management of cloud services on distributed infrastructures. A case study was used to evaluate the impact of faults on the provider profit. The evaluation was carried out on the Grid'5000, which served as an IaaS provider by providing fifty-one resources to run the experiments. The results demonstrated the effectiveness of assuring fault tolerance in different situations.

The contribution proposed by this paper opens up several directions for future work. With respect to billing, a natural first step is to take into account different IaaS clouds and to enable the provider to adjust its expenses based on different resource costs. Further future work involves evaluating the performance of the QoS assurance mechanism by dealing with resource shortages. Finally, another direction is to investigate the augmentation of the cloud provider profit through underprovisioning or prioritizing more profitable contracts during resource shortages.

IX. ACKNOWLEDGMENTS

The research leading to these results has received funding from the European Community's Seventh Framework Programme [FP7/2007-2013] under grant agreement 215483 (S-CUBE). Experiments presented in this paper were carried out using the Grid'5000 experimental testbed, being developed under the INRIA ALADDIN development action with support from CNRS, RENATER and several Universities as well as other funding bodies (see https://www.grid5000.fr).

Fig. 1 .

 1 Fig. 1. An example of how cloud services can be used to support a music sharing service.

Fig. 2 .

 2 Fig. 2. Sequence diagram of an SLA negotiation based on templates defined by the service provider.

Fig. 3 .

 3 Fig. 3. Sequence diagram of the performance QoS assurance mechanism which books resources, configures and deploys service instances based on resource requirements able to meet the agreed response time.

  th ji and n ≤ f ailure th ji then

  th ji and n ≤ delay th ji and elapsed time ji > exec time ji then

Fig. 4 .

 4 Fig. 4. Qu4DS architecture.

Fig. 5 .

 5 Fig. 5. Qu4DS supports service development and execution management automatically and transparently. This figure shows how Qu4DS supports the flac2ogg provider in compressing FLAC files to the OGG format.

Fig. 6 .Fig. 7 .

 67 Fig. 6. Scenario high-FT.

Fig. 8 .

 8 Fig. 8. Scenario high-RR.

TABLE I SLA

 I TEMPLATES, THEIR LABELS AND RESPECTIVE QOS CONSTRAINTS.

	````````L abels	QoS Metrics	Time Response	Reliability
	Fast		strong	weak
	Safe		weak	strong
	Classic		medium	medium
	Standard		weak	weak


C Fuzibet

Desnuelle

Jeandel Py

Rosenthal

Treatment with rituximab in patients with polyneuropathy with anti-MAG antibodies

Keywords:

Treatment with rituximab in patients with polyneuropathy with anti-MAG antibodies.

Efficacy of rituximab (RTX), a monoclonal anti-CD20 antibody, has been suggested in a recent controlled trial in polyneuropathies with antibodies against myelin-associated glycoprotein (PN-MAG) 1. Aims of this study were to evaluate the efficacy and safety of RTX in PN-MAG and to search for predictive factors of response to treatment.

Methods:

Six patients fulfilling diagnosis criteria for PN-MAG 2 received 4 weekly infusions of RTX (375 mg/m 2 ). Clinical status of each patient was evaluated, before treatment (M0) then every 3 months during 9 months, by assessing Overall Neuropathy Limitation Scale (ONLS) 3, INCAT Sensory Score (ISS) 4, and MRC sumscore on 28 muscle groups 5. Anti-MAG titers (Buhlmann ELISA technique) and B cells expressing CD19 blood count were concomitantly quantified. Nerve conduction studies were performed before treatment and 9 months after, on fibular, tibial, median and ulnar nerves 5. Treatment was considered efficient only when ONLS score decreased by at least 1 point at M9. Demographic, clinical, biological and electrophysiological status before RTX, were statistically compared between patients with efficient and non-efficient response to treatment using the Mann-Whitney and Fisher's exact tests. The level of statistical significance was set at p=0.05. Patients were asked to give informed consent for use of data in a journal publication.

Results:

Mean age of patients (70 yo, range 57-86), duration before treatment from onset of the disease (5 years, range 2-10), main clinical manifestations of each patient and previous immunotherapies are detailed in table 1. Before RTX treatment, ONLS score ranged from 2 to 6 (mean 3.7) and ISS score from 2 to 12 (mean 6.2). Nine months after the last RTX infusion, ONLS score improved by 1 point in 2 patients, by 2 points in 1, remained stable in the 3 others. ISS score improved in 5 patients (mean 3.8 points), MRC score improved in 3 patients (mean 2.7 points). Decrease of anti-MAG titers was observed in all the 6 patients at M9 by a mean of 43% (figure 1). By the meantime, IgM monoclonal titers decreased in 5 patients but did not change in one. As expected, CD19 B cells blood count dramatically decreased, after treatment and stayed low at M9 (138x10 9 /l at M0 vs 2.5x10 9 /l at M3 vs 40x10 9 /l at M9). RTX treatment did not modify the mean CD4 and CD8 lymphocytes blood counts (respectively 674x10 9 /l at M0 vs 789x10 9 /l at M9; and 448x10 9 /l at M0 vs 416x10 9 /l at M9) as the mean gammaglobulins titers (9.7g/l at M0 vs 9g/l at M9). No change in individual or overall electrophysiological data was evidenced when comparing examination before treatment and 9 months after treatment. No serious adverse event was reported. Demographic, clinical, biological and electrophysiological data at baseline, including MAG titers and IgM monoclonal titers, were not statistically different in the 3 patients who improved their ONLS score at M9 compared to the 3 patients who did not.

Discussion:

Experimental pathogenicity of anti-MAG antibodies has been established in anti-MAG polyneuropathies 6. RTX is a monoclonal antibody designed to target the B-cells producing anti-MAG antibodies and then expected to reverse the pathogenic process.

In clinical practice, therapeutic benefits of RTX are known to be delayed and are reported to be more evident on sensory deficiency than on functional disability. Our results confirm those of previous studies: improvement of sensory deficiency in half to 2/3 of the treated patients, improvement of the functional disability in less than half of the treated patients, decrease of IgM monoclonal component and of anti-MAG titers respectively by 30 to 74% and by 44 to 87%, as assessed 8 or 12 months after the RTX infusions 1, 7, 8, 9, 10.

In this study, we did not find any predictive factor of response to RTX treatment, including type of the underlying hemopathy and disease duration prior to treatment. Predictive value of anti-MAG antibodies titers is not clear in the literature: RTX is more efficient when anti-MAG antibodies titers are moderately elevated in one study 9 and when titers are high in another 1. Better improvement was reported in patients with more severe sensory deficit at baseline 1.

Treatment with RTX improved functional disability in half of our PN-MAG population.

Treatment was safe, no serious adverse event occurred during the 9 months period of follow up. As no predictive factor of efficacy appears informative, RTX should be reserved to patients impaired in their daily life. Studies in larger cohorts are needed to confirm.


Jean-Jacques Sinou
email: jean-jacques.sinou@ec-lyon.fr

On the use of non-linear vibrations and the anti-resonances of Higher-Order Frequency Response Functions for crack detection in pipeline beam

The identification of new scientific challenges, as well as the increasing high-performance computing support, indicate that the benefits of applying novel nonlinear techniques for crack detection will continue to grow. So, significant effort has been invested in recent years to develop effective techniques to detect crack in mechanical structures. The objective of this paper is to discuss and propose a robust diagnostic of damage based on non-linear vibrational measurements with particular regard to the Higher-Order Frequency Response Functions. An important observation is that the appearances of the non-linear harmonic components and the emerging anti-resonances in Higher-Order Frequency Response Functions can provide useful information on the presence of cracks and may be used on an on-line crack monitoring system for small levels of damage. Efficiency of the proposed methodology is illustrated through numerical examples for a pipeline beam including a breathing crack.

Introduction

The presence of a crack may lead to serious damage and dangerous effect on the dynamic behavior of mechanical structures. In order to avoid severe damage, the detection of a crack in the early stage can be of great interest. In recent years a lot of effort has been devoted to the detection of cracks in mechanical structures and many researchers have proposed various developments of non-destructive techniques based on changes in the structural vibrations [START_REF] Doebling | Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: A literature review[END_REF][START_REF] Doebling | A summary review of vibration-based damage identification methods[END_REF][START_REF] Dimarogonas | Vibration of cracked structures: a state of the art review[END_REF][START_REF] Sinou | A review of damage detection and health monitoring of mechanical systems from changes in the measurement of linear and non-linear vibrations[END_REF]. Basic methods based on linear condition monitoring techniques have been extensively developed by considering not only changes in natural frequencies and modes shapes [START_REF] Salawu | Detection of structural damage through changes in frequency: a review[END_REF], but also the appearances of resonant peaks due to vibration coupling [START_REF] Gounaris | Crack identification in beams by coupled response measurements[END_REF][START_REF] Liu | Crack detection in hollow section structures through coupled response measurements[END_REF], different changes in the measurements of the Frequency Responses Functions and the motion of anti-resonances [START_REF] Bamnios | Crack identification in beam structures using mechanical impedance[END_REF][START_REF] Dharmaraju | Some comments on use of anti-resonance for crack identification in beams[END_REF][START_REF] Dilena | The use of anti-resonances for crack detection in beams[END_REF].

Even if in the case of simple structures, the damage severity can be determined from changes by using various linear analysis previously presented (changes in natural frequencies, modes shapes, Frequency Response Functions, anti-resonances, coupling measurements,...), some researchers have illustrated the fact that the presence of damage can induce more complicated behavior. For example Gudmundson [START_REF] Gudmundson | The dynamic behaviour of slender structures with cross sectional cracks[END_REF] noted that decrease in natural frequencies for a cantilever beam is not always observed during experimental tests due to the closing of the crack. So the linear analysis appears to be insufficient to describe the non-linear behavior of the crack, the so called "'breathing phenomena"' corresponding to the fact that the crack alternately opens and closes during experimental tests. Also, the common use of robust developments based on the presence of the nonlinear components in the vibrational responses of damaged structures has to be taken into account to avoid worse damage identification [START_REF] Sinou | A review of damage detection and health monitoring of mechanical systems from changes in the measurement of linear and non-linear vibrations[END_REF][START_REF] Pugno | Evaluation of the non-linear dynamic response to harmonic excitation of a beam with several breathing cracks[END_REF][START_REF] Sinha | Simulation of the dynamic response of a cracked beam[END_REF].

However few efforts have been dedicated to discuss the main advantages of using the non-linear vibrational signatures and anti-resonances of the Higher-Order Frequency Response Functions for an efficient and robust 1 In order to propose some answers, the present study proposes to show that not only an appropriate use of the super-harmonic frequency components of the non-linear dynamical behaviour but also the anti-resonances of the super-harmonics components can be useful for crack identification in mechanical systems. The paper is organized as follows: firstly, a description of the cracked simply supported pipeline beam and the estimation of the non-linear vibrational response of the mechanical system are discussed. Secondly, explanation is given of the most common uses of the non-linear signatures to detect the presence of damage. Finally, damage detection and detection of the crack location based on the emergence of antiresonances for the super-harmonics components are discussed.

The model of the cracked beam

The system is composed of a beam of length 0.5m with an inner and outer diameters of 0.06m and 0.1m respectively (see Figure 1(a)). The beam is discretized into 20 Timoshenko beam finite elements, with four degrees of freedoms at each node, the axial and torsional degrees of freedom being not considered. The pipeline beam is simply supported at each end, as indicated in Figure 1(a)). The layout of the cracked beam element under consideration is shown in Figure 1(b). All the values of the material properties and dimensions of the beam are given in Table 1.

The equations of the simply supported cracked pipeline beam can be written as

Mẍ + C ẋ + (K + q (t)) x = f (1)
where ẍ, ẋ and x are the acceleration, velocity and displacement vectors. M, C and K are the mass, damping and stiffness matrices of the complete uncracked pipeline beam. f is an external force (periodic excitation of pulsation ω). q (t) defines the breathing behavior of the global stiffness K c at the crack location due to the evolution of the external forces. If we assume the open crack at the i th element, the global stiffness matrix K c defines the global stiffness matrix due to the presence of the crack in the fixed frame (X, Y, Z). It is given by

diag (K c ) = ( 0 • • • 0 K crack 0 • • • 0 ) ↑ i th element (2)
In the present study, it is assumed that the opening and closing of the crack depends on the level of load [START_REF] Elber | Fatigue crack closure under cyclic tension[END_REF][START_REF] Cheng | Dynamics of cracked rotors: Literature survey[END_REF]. The crack breathing phenomenon varies with time due to vibration. Examining the dynamic response of a breathing crack at its first mode, it can be decomposed in the following way [START_REF] Cheng | Dynamics of cracked rotors: Literature survey[END_REF]

q (t) = 1 2 (K c -K) (1 -cosωt) (3)
where ω is equal to the excitation and is defined as the crack breathing frequency. If (1cosωt) = 0 (i.e. ωt = 2nπ with n any integer), the crack is closed and has no effect on the dynamic behaviour: the beam may be treated as uncracked. If (1cosωt) = 1 (i.e. ωt = (2n -1) π with n any integer), the crack is in the fully open state. Otherwise the crack is in a state of partial closure given by the relation [START_REF] Dimarogonas | Vibration of cracked structures: a state of the art review[END_REF]. The modeling of a transverse crack that was described extensively in [START_REF] Sinou | Numerical investigations of a robust identification of crack location and size in beams using only changes in ratio pulsations of the cracked beams[END_REF][START_REF] Sinou | Damage Assessment Based on the Frequencies' Ratio Surfaces Intersection Method for the Identification of the Crack Depth, Location and Orientation[END_REF] is briefly presented here. The model proposed by Mayes and Davies [START_REF] Davies | The vibrational behaviour of a multi-shaft, multi-bearing system in the presence of a propagating transverse crack[END_REF][START_REF] Mayes | Analysis of the response of a multi-rotor-bearing system containing a transverse crack in a rotor[END_REF] is used in order to locally represent the stiffness properties of the crack cross section. Due to strain energy concentration in the vicinity of the tip of the crack under load, the presence of a transverse crack introduces local flexibility. So, this model considers the reduction of the second moment of area ∆I of the element at the location of the crack that may be defined by

∆I = I 0    R l 1 -ν 2 F (µ) 1 + R l 1 -ν 2 F (µ)    (4)
where I 0 , R , l, and ν are the second moments of area, beam external radius, length of the section and Poisson's ratio, respectively. µ is the non-dimensional crack depth and is given by µ = h R where h defines the crack depth of the beam, as shown in Figure 1(b). As indicated in Figure 1(b), the total angle α subtended by the crack is related to the depth of crack by the relation α = 2cos -1 (1µ). F (µ) defines the non-linear compliance as a function of variations in non-dimensional crack depth µ, which can be derived from a series of experiments using chordal cracks (see Mayes and Davies [START_REF] Davies | The vibrational behaviour of a multi-shaft, multi-bearing system in the presence of a propagating transverse crack[END_REF][START_REF] Mayes | Analysis of the response of a multi-rotor-bearing system containing a transverse crack in a rotor[END_REF]). Considering the finite element formulation and the local reduction of the second moments of area that are given in Equation ( 4), the stiffness contribution K η,ξ

crack of an open crack about the centroidal axes η and ξ for a two nodes Timoshenko beam element of length l and Young's modulus E (corresponding to the flexible degree-of-freedom [u 1 ; v 1 ; θ 1 ; ψ 1 ; u 2 ; v 2 ; θ 2 ; ψ 2 ], see Figure 1(c)) can be defined at the crack location

K η,ξ crack = E l 3             12I η 0 0 6lI η -12I η 0 0 6lI η 12I ξ -6lI ξ 0 0 -12I ξ -6lI ξ 0 4l 2 I ξ 0 0 6lI ξ 2l 2 I ξ 0 4l 2 I η -6lI η 0 0 2l 2 I η 12lI η 0 0 -6lI η 12lI ξ 6lI ξ 0 4l 2 I ξ 0 4l 2 I η             (5)
Finally, K crack that is defined in Equation ( 2) is obtained by passing from the fixed frames (η, ξ, Z) to (X, Y, Z) via the rotation χ (see Figure 1

Determination of the nonlinear response of the cracked beam

As previously indicated, the above equations of the cracked pipeline beam have a time-dependent coefficient due to the fact that the crack breathes when the excitation force changes. The non-linear dynamic response of the system can be approximated by finite Fourier series

x (t) = m k=1 (A k cos (kωt) + B k sin (kωt)) (6)
where ω defines the crack breathing frequency. A k and B k (with k = 1, • • • , m) define the unknown coefficients of the finite Fourier series. The number of harmonic coefficients m is selected on the basis of the number of significant harmonics expected in the dynamical response of the cracked beam. The excitation force f can be exactly defined by finite Fourier series with first-order periodic components in the frequency domain.

Expressions are given by f = C 1 cos (ωt) + S 1 sin (ωt) with C 1 and S 1 the first-order periodic components in the frequency domain.

As previously explained, the amount of open part of the crack constantly varies with the excitation force, thereby changing the stiffness q (t) of the cracked beam. So, by considering the approximated nonlinear solution of the cracked beam (see Equation ( 6)) and the global mechanism of the time dependent part for the crack breathing phenomenon (see Equation (3)), the expression q (t) x (t) can be approximated by the following expression

q (t) x (t) = 1 2 (K c -K) (1 -cosωt) m k=1 (A k cos (kωt) + B k sin (kωt)) (7)
By substituting expressions ( 6) and [START_REF] Liu | Crack detection in hollow section structures through coupled response measurements[END_REF] in Equation ( 1), the unknown coefficients of the finite Fourier series A k and B k (with k = 1, • • • , m) can be found solving the following equations

K -k 2 ω 2 M A k -kωCB k + (K c -K) A k-1 4 + A k 2 + A k+1 4 = δ k=1 C 1 ( 8
)
kωCA k + K -k 2 ω 2 M B k + (K c -K) B k-1 4 + B k 2 + B k+1 4 = δ k=1 S 1 (9)
with A n = 0 and B n = 0 if n < 1. The complete algorithm and process of the computation is given in Figure 2.

Numerical results

In this section, the effects of a breathing crack on the nonlinear dynamic response of the beam are quantified.

The basic deterministic parameters used in all cases are given in Table 1. For each case, the location of the external force, the position, orientation and depth of the crack are given in Table 2. First of all, the detection of the presence of one crack by using the appearance of the non-linear components will be investigated. Secondly, we undertake the determination of the crack location based on the appearances of anti-resonances in the signature of the non-linear components.

Crack detection based on the non-linear response

First of all, we consider a horizontal crack (χ = 0 degree) with a crack severity µ = 0.3 at the 7 th element (case 1 given in Table 2). Figure 3(a) shows the non-linear response for the pipeline beam with the breathing crack. It clearly appears that the global response is composed by not only the first harmonic component but also by the components of higher order. For example, the second, third and fourth orders are predicted when the crack breathing frequency is approximately one-half, one-third and one-fourth of the first resonance frequency, as indicated in Figure 3(a). Moreover, due to the presence of the crack, the n th orders increase when the frequency of the excitation force is near 1 m of the first resonance frequency (with m < n or any m positive integer). It is recalled that the response will be composed by only the first harmonic component (i.e. a linear response) for the uncracked beam. Then, Figure 3(b) shows the non-linear response for a small crack that is situated at the 10 th element with χ = 0 degree (see case 2 in Table 2). It is observed that the global nonlinear response has a significant peak at one-half of the first frequency of the cracked system. However, only small changes in the vibration amplitude are observed at one-third or one-fourth of the first frequency. So, it may be concluded that the non-linear behavior for a small crack is mainly due to the predominance of the first and second harmonic components. Therefore it should be considered that contributions of the third and fourth harmonic components are too small to allow the detection of crack in realistic cases. Now, we consider case 3 given in Table 2. Compared to the previous case 1, the crack orientation χ that defines the angle between the orientation of the crack front and the vertical axis (see Figure 1(b)) has changed. Figures 4(a) and 4(b) show some interesting features for the coupling measurements (i.e. horizontal and vertical directions) of the nonlinear components due to the presence of the crack. Indeed, the presence of the crack introduces excitation on the principal X-axis (i.e. horizontal displacement) even if the external force is only on the principal Y-axis (i.e. vertical displacement). The appearance of nonlinear vibrations in the horizontal direction is only due to the breathing behavior of the crack and the fact that the crack front is not in the same direction than the external force (i.e. χ = 0). In the two previous cases (i.e. cases 1 and 2), there is no coupling between the two lateral vibrations due to the fact that the external force is on the same direction than the crack front (i.e. χ = 0). Thereby, the crack does not induce excitation on the principal horizontal axis. So no vibration on the X-axis exists.

Crack location based on the anti-resonances of the non-linear components

In this part of the paper, we propose to use evolutions of anti-resonances of the Higher-order Frequency Response Functions for detecting the damage location.

Indeed, it is well known that the breathing behavior of the crack induces an additional internal force for the linear and non-linear components at the crack location [START_REF] Sinou | Detection of cracks in rotor based on the 2X and 3X super-harmonic frequency components and the crack-unbalance interactions[END_REF]. Due to the fact that the external force f given in Equation ( 1) only induces first-order periodic components in the frequency domain, it can be concluded that only the presence of the breathing crack adds an excitation for higher orders. So, the position of the crack can be identified by considering the evolution of anti-resonances of the super-harmonic components.

To illustrate this, Figures 5(a), 5(b) and 5(c) give the evolutions of the second, third and fourth harmonic components of the cracked beam in the vertical axis for case 2. First of all, the appearances of peak amplitudes for the second, third and fourth harmonic components that form the signature of the presence of a crack are visible for all the positions of the pipeline beam. Secondly, it appears that the emerging and location of some new anti-resonances and the variation in the anti-resonance frequency along the beam depend on the crack location. For example, it can be observed that the anti-resonance frequency decrease from 3300Hz to 2200Hz for the variations of the beam location from 0m to 0.25m. Then increased values of anti-resonance frequency is observed along the beam (from 0.25m to 0.5m). The minimum of anti-resonances (in frequency) for the second order harmonic components of the cracked system appears at the crack location (see the red circle in Figure 5(a)). The same conclusions can be made for the third and fourth harmonic components, as indicated in Figures 5(b) and 5(c). Here again, the red circle indicated the minimum of anti-resonance frequency for the third and fourth-order Frequency Response Functions. So it can be concluded that the beam position where the minimum value of anti-resonance frequency is observed for all the non-linear harmonic components corresponds to the location of the crack.

Then, Figures 6(a), 6(b), 6(c), 6(d), 6(e) and 6(f) give the evolutions of all harmonic components in the vertical and horizontal directions for case 3. It is recalled that the presence of horizontal responses of the system is due to the coupling measurements via excitation of the crack in the horizontal axis and the breathing behavior. In both directions and for all harmonic components, the minimum value of anti-resonance frequency is detected at the position of the crack (see the red circle for all Figures 6).

Now, we consider case 4 that is concerns with a different position for both the crack location and the external excitation. The same behavior for the variation of the anti-resonance frequency is observed in case 4, Considering all these results, it can be concluded that one of the main advantage of using the anti-resonances for the Higher-order Frequency Response Functions is that the detection of the crack location is not sensitive to the excitation position and can be easily applied for the detection of small cracks.

Finally, Figure 8 gives the first harmonic component in the horizontal direction for case 4. Due to the fact that the external excitation is in the vertical direction, the appearance of the first harmonic component in the horizontal direction is only due to the crack. So, the position of the minimum of anti-resonance frequency gives the crack location (indicated by the red circle in Figure8). For all the present study, it is also remained that the breathing behavior given in Equation ( 3) is only valuable around the first frequency. So all the previous comments discussed in the present section are limited to the non-linear dynamic behavior of the cracked system around its first frequency.

Conclusion

This paper highlights the possibility of crack detection through the observation of the non-linear dynamic behaviour of a simply supported cracked pipeline beam. This study has demonstrated that the introduction of

  (a) Description of the pipeline beam system (b) Crack element (c) Description of the degrees of freedom in η and ξ-axes

Figure 1 :

 1 Figure 1: Finite-element model of the pipeline beam and the crack section

Figure 2 :

 2 Figure 2: Process of the numerical computation for the calculation of the non-linear displacements of the simply supported cracked pipeline beam

Figure 3 :

 3 Figure 3: Non-linear vertical amplitudes for cases 1 and 2 at the middle of the beam (blue=global non-linear response, black=order 1, red=order 2, magenta=order 3, green=order 4)

Figure 4 :

 4 Figure 4: Non-linear vertical and horizontal amplitudes for case 3 at the middle of the beam (blue=global non-linear response, black=order 1, red=order 2, magenta=order 3, green=order 4)

Figure 5 :

 5 Figure 5: Vertical displacement for all the beam positions -Case 2

Table 1 :

 1 (b) for more details). Value of the physical parameters

	Notation	Description	Value
	R e	outer radius of the beam	0.1m
	R i	inner radius of the beam	0.06m
	L	length of the rotor shaft	0.5m
	E	Young's modulus of elasticity 2.1 10 11 N.m -2
	ρ	density	7800kg.m -3
	ν	Poisson ratio	0.3
	ζ	modal damping	10 -3

Table 2 :

 2 Description of cases

a crack breathing phenomenon that varies with time due to vibration induces the emerging of the n th superharmonic frequency components. The appearances of non-linear components can be considered as one of the most practical indicators of the presence of a crack for health monitoring purposes.

The localization of anti-resonances for Higher-Order Frequency Response Functionsn provides useful information on the location of a crack and can be used on an on-line robust crack monitoring system.