Franck Jeveme Panta
email: franck.panta@irit.fr

André Péninou
email: andre.peninou@irit.fr

Florence Sèdes
email: florence.sedes@irit.fr

Negative Filtering of CCTV Content -Forensic Video Analysis Framework

Keywords: Metadata, CCTV Systems, forensic video analysis, video evidence

This paper presents our work on forensic video analysis that aimed to assist videosurveillance operators by reducing the volume of video to analyze during the search for post-evidence in videos. This work is conducted in collaboration with the French National Police and is based on requirements defined in a project related to videos analysis in the context of investigations. Due to the constant increasing volume of video generated by CCTV cameras, one of the investigators' goals is to reduce video analysis time. For this purpose, we propose a negative filtering approach based on quality and usability/utility metadata, enabling to eliminate video sequences that do not satisfy requirements for their analysis through automatic processing. Our approach involves a data model which is able to integrate different levels of video metadata, and an associated query mechanism. Experiments performed using the developed framework demonstrate the utility of our approach in a real-world case. Results show that our approach helps CCTV operators to significantly reduce video analysis times.

INTRODUCTION

Videosurveillance has become a very important security measure in crime prevention [START_REF] Gill | Assessing the impact of CCTV[END_REF]. Recent studies [START_REF] Fletcher | Is CCTV effective in reducing anti-social behaviour[END_REF], [START_REF] Brandon | Effects of closed circuit television surveillance on crime[END_REF] illustrate the relevance of videosurveillance that helps store owners, business owners and police to deter and respond to criminal incidents detected by this technology. One of the main functions of videosurveillance is to store images of criminal incidents and non-social behaviour to facilitate post-event analysis during investigations. The current method used by investigators (in France), consists of applying automatic processing (face detection, vehicle detection, license plate recognition...) to all video sequences collected upstream and previously indexed (conversion to the right format, camera geolocation, management of timestamps...). Automatic processing are applied to all the videos or only to a geographical or temporal subset. After these processing and data extraction, investigators conduct researches (vehicles, plates, people, faces...), view the sequences of interest and launch new processing. Recent investigations ( robbery, terrorism, incivility, homicide) have required the analysis of several tens of terabytes of video data, corresponding to several tens of thousands of video hours. The use of automatic processing in these investigations enabled a time saving of a factor of 3 on average ( which still too low in an operational context) compared to manual analysis. However, many videos were unusable for automatic processing (brightness due to night, optical conditions, etc.). The processing time could have been reduced if unsuitable video sequences for automatic processing could have been discarded (what we call "negative filtering"). In this context, negative filtering is therefore defined as a set of processes enabling elimination of video sequences that are not compatible with a given automatic processing, among a mass of available videos.

In this paper we focus on reducing the volume of video to be exploited (implicitly the reduction of operating time) for the search of video evidence during an investigation through the negative filtering. The goal is to improve the automatic processing speed by discarding video sequences that do not satisfy automatic processing requirements. So, it means determining whether a video sequence is able to give results with respect to a given automatic processing, in which case the automatic processing will be applied to this sequence. In the contrary case, it is useless to carry out the automatic processing, if it is already sure that no result will be obtained. Three automatic processing have been selected for this study: (i) face detection, (ii) vehicle detection, and (iii) plate detection and recognition. These automatic processing are the most commonly filters used by Scientific Technical Police in in criminal investigations which are generally done in two modes: urgent investigation and deep investigation. The first mode requires a very fast analysis of the videos. It occurs when one or more dangerous and wanted individuals are running away. The need for quick results leads to focus only on very good quality sources in the geographical and temporal area where the chances of finding the target are high. It is better to discard videos that results are approximate compared to very good quality videos that could bring significant elements to the investigation. The second mode enables an in-depth and less urgent analysis. The aim here is to get the most accurate and comprehensive possible results. The research can involve video sequences with lower quality, but whose processing is still able to provide results.

We propose a negative filtering approach that takes into account the three automatic processing methods considered and that provides results for the two investigation modes described. Negative filtering is based on features that evaluate the quality and usability/utility of videos. It is then necessary to define for each automatic processing the criteria of quality and usability/utility of video that will allow to filter the video sequences according to the two modes of investigation (urgent and deep). More concretely, it consists of developing metrics that express the quality and usability/utility of videos based on a combination of technical metadata, metadata describing the movement and field of view of the camera (e.g. camera speed, orientation in relation to objects that could obstruct the field of view) and metadata from content analysis algorithms (e.g. describing the movement or number of people in the scene). These metadata can be represented according to different levels of semantics and granularity. Collaboration between the different levels of metadata is a challenge for this study. Therefore, we propose a generic data model to integrate all these metadata and a and supporting mechanisms for filtering large collections of video related to the research of a posteriori evidence.

To sum up, the main contributions of this paper are summarized as follows:

• We propose a generic and scalable data model enabling integration and interoperability of metadata (quality and usability/utility of the videos) required for negative filtering implementation. • We provide a robust querying mechanism to filter out video segments that processing will be useless for the search of digital evidence. • We conduct experimental evaluations demonstrating the usability of our approach in a real-world scenario of searching for a posteriori evidence in videos.

The rest of the paper is organized as follows. Section 2 reviews the related works; Section 3 presents a description of our approach; Section 4 shows an real-case experimentation that we performed to evaluate our methods for relevant video retrieval and content filtering. Finally, in section 5, we discuss and conclude with suggestions for future research.

RELATED WORK

Interest for a posteriori video analysis motivated many researchers to propose solutions for the problem of searching for "digital evidence" in video surveillance collections. Most of the proposed work focuses on the development of tools for video content analysis in order to detect and/or track objects [START_REF] Edelman | Tracking people and cars using 3D modeling and CCTV[END_REF], [START_REF] Chen | Intelligent urban video surveillance system for automatic vehicle detection and tracking in clouds[END_REF], to recognize actions [START_REF] Carlos Niebles | Unsupervised learning of human action categories using spatial-temporal words[END_REF], events [START_REF] Gerónimo | Unsupervised surveillance video retrieval based on human action and appearance[END_REF] or scenes [START_REF] Hc Lee | Forensic evidence and crime scene investigation[END_REF], [START_REF] Van Den Eeden | Forensic expectations: Investigating a crime scene with prior information[END_REF], and to analyze human crowd behavior [START_REF] Yogameena | Synoptic video based human crowd behavior analysis for forensic video surveillance[END_REF], etc. During the last few years, many solutions have been proposed and many collaborative projects have been set up both at national and European level.

CARETAKER [START_REF] Carincotte | Toward generic intelligent knowledge extraction from video and audio: the EU-funded CARETAKER project[END_REF] is a European project which was part of the context of the surveillance of metro stations via the exploitation of video and audio streams. The project enabled the development of techniques for automatically extracting relevant semantic metadata from video content. However, no filtering was performed before extracting the knowledge from the video streams.

VANAHEIM project (Video/Audio Networked surveillance system enhAncement through Human-cEntered adaptIve Monitoring) enabled the development of a technique for real-time automatic filtering of videos using algorithms to detect abnormal activity. But the implementation of the learning algorithms used in the filtering process seems complex for large volumes of data.

In [START_REF] Deng | Fast forensic video event retrieval using geospatial computing[END_REF], authors present a video event analysis and recovery system using geospatial computer techniques. Based on target tracking and analysis of video streams from distributed camera networks, the system generates video tracking metadata for each video, represents them on a map, and merges them into a uniform geospatial coordinate. The combined metadata are stored in a spatial database where target trajectories are represented in geometry and geographic data type. The spatial database provides the system with a stable, fast, and easyto-manage platform, which is essential for managing large amounts of video data. The spatial index provided by the database allows online querying by quickly removing unrelated data and work on data of interest. On the other hand, there is no filtering before the generation of video tracking metadata for each video, which can be very time consuming.

One of the recent works of our team [START_REF] Codreanu | Modélisation des métadonnées spatio-temporelles associées aux contenus vidéos et interrogation de ces métadonnées à partir des trajectoires hybrides : Application dans le contexte de la vidéosurveillance[END_REF] was on the modeling of spatio-temporal metadata associated with video content and the querying of these metadata using hybrid trajectories. This work is applicable in outdoor environments. An extension to indoor environments has been proposed in [START_REF] Sèdes | Meta-) data modelling: gathering spatio-temporal data for indoor-outdoor queries[END_REF]. One of the perspectives of this work was to rely on relevant metadata in the context of videosurveillance to reduce space and consequently research time, and other measures that can be developed based on the metadata or on images features (e.g. image quality).

PROPOSED APPROACH

This section develops our negative filtering approach that helps investigators to facilitate the post-event research of evidence in videos by eliminating video sequences based on their non-eligibility for the selected automatic processing. The main goal is to speed up the process of forensic video analysis that we define as the offline analysis of video aimed at finding video or digital evidence during an investigation. The proposed approach consists of two main steps:

• step 1 -Metadata modeling: Since filtering criteria are based on metadata describing the quality and usability/utility of videos, it is necessary to provide uniform modelling of this metadata to facilitate their usage. • step 2 -Querying mechanism development: the idea is to provide algorithms based on the proposed metadata model in order to implement filtering.

Metadata modeling for negative filtering

The value of digital information depends on how easily it can be located, searched and retrieved. Metadata describing the content of digital information are essential for these tasks, and without them, some digital information are considered as useless. Metadata modeled in this section describe the quality and usability/utility of videos. Image quality can refer either to the degree/level of accuracy of images (viewed as a set of signals) during acquisition, processing, storage and restitution, or to a set of visually significant attributes of the image. Usability/utility of video refers to a set of features that determine the suitability of a video for a given situation.

Metadata describing the video quality.

Image quality depends on the optics of the sensor, the electronics (amplification, quantification and sequencing), as well as the environment in which the image was captured and the lighting conditions. In order to evaluate video quality, it is necessary to define a set of quality metrics by using or developing spatial image quality descriptors to describe the visible and preponderant degradations in the visual rendering of an image. Defining quality metrics is generally based on two types of approaches [START_REF] Saad | A DCT statistics-based blind image quality index[END_REF]: (i) quality measurement approaches with reference, which aim to evaluate the compliance of the target (degraded) image with respect to an original or reference image,and (ii) non-referenced quality measurement approaches based on statistical learning, natural scene statistics, or specific distortions. Video quality metadata used in this study are related to non-referenced measurement approaches. In these approaches, video-quality metadata are provided as feature vectors extracted from images.

Examples of metrics without references G-BLIINDS2 and BIQI have been developed by in [START_REF] Charrier | Modélisation statistique et classification par apprentissage pour la qualité des images[END_REF]. As shown in Figure 1, these metrics are used to evaluate the quality of three images extracted from the TID2008 database [START_REF] Ponomarenko | Color image database for evaluation of image quality metrics[END_REF], and degraded from left to right respectively by JPEG compression, JPEG2000 transmission error and noise due to the insertion of blocks of different color and intensity. MOS values (Mean Opinion Score) are provided by human observations and represent the ground truth of the image quality assessment. These values are calculated on a scale from 0 (very poor quality) to 9 (excellent quality).

Metadata describing the usability/utility of the video.

Usability/utility of video content can be defined based on features related to low-level image information. Features related to various acquisition artifacts such as blur, brightness, capture noise, etc. are parameters that are taken into account when defining the usability/utility criteria of the video.

The usability/utility of the video takes into account the ability to detect, recognize or identify objects in the videos. Using the "Johnson's criteria" is a basis for defining metrics to evaluate the usability/utility of videos. Johnson has defined thresholds, known as "Johnson's criteria", as the effective resolutions for detecting, recognizing or identifying targets captured by the cameras. Let's remember that "detect" is the ability to distinguish an object from the background, recognize is the ability to classify objects (people, vehicle, etc.), identify is the ability to describe the object in detail (person with a hat, reading a license plate, etc.). Thresholds defined by Johnson's criteria can be affected by factors such as field of view, spatial resolution, scene occultation, etc. This study proposes to make a subjective evaluation of detection, recognition and identification, then to introduce the performed scores into a machine learning algorithm in order to propose metadata of usability/utility of the videos.

Proposed data model.

Figure 2 represents a generic metadata model of video quality and usability/utility metadata proposed for negative filtering of videosurveillance content. This metadata model highlights all the entities taken into account in the modeled system, as well as the relationships between the different entities. The definition of the classes VIDEO and FRAME is essential for the subsequent definition of the other classes. In conventional video analysis, videos are divided into scenes, each one related to a different aspect of the entire video, and the scenes are subdivided into shots, each one is a single contiguous series of frames derived from one shot. Video features are computed per frame or group of frames, so the video can be divided directly into frames without having to define video segments. Video features for each frame are represented by the class FEATURE and each descriptor is linked to a specific processing (class PROCESSING). Functions FeatureValue() and Confidence() are respectively used to compute the global value and global confidence based on the quality (class QUAL-ITY) or usability (class USABILITY) metadata attributes of the videos. New attributes (ATTRIBUTE_QUALITY, AT-TRIBUTE_USEABILITY) can be defined for the metadata at any time. Thresholds (class THRESHOLD) are defined for each investigation mode (class INVESTIGATION MODE), in order to determine the compatibility of a processing to the chosen investigation mode. Although the required metadata for different types of video analytics could differ, the proposed metadata model is designed to be generic, enabling new metadata (inherited from FEATURE) to be easily integrated so that new requirements can be taken into account.

Filtering mechanism

Negative filtering is a pre-analysis module that will be integrated upstream in the overall process of massive video analysis. At the end of its computations, the negative filtering module provides two types of information:

• Urgent analysis: the result of the filtering will indicate for each video segment and for each automatic processing if an urgent investigation is relevant or not. The result will be displayed a two-level colour code: green if video sequence is compatible with an automatic processing in the urgent investigation mode, red if not. • Deep analysis: the result of the filtering will show for each video sequence and each automatic processing a compatibility score with the deep investigation mode. The result will be presented as a three-level colour code based on predefined thresholds: Green is defined for perfect compatibility, orange for medium compatibility and red for incompatibility. Investigators will then choose whether to process the video sequences in orange or not depending on their needs and time resources.

Example: Figure 3 shows the results of negative filtering for a given automatic processing (e.g. vehicle detection) on the video "file_001.mp4". Color coding shows that the selected automatic processing can be applied to the video sequences "U 2 " and "U 4 " in the urgent analysis mode, as well as to the Algorithms 1 and 2 provide negative filtering results for both analysis modes. For these two algorithms, function getVide-oFrames(𝑣 𝑖 ) retrieves in a list all the frames of the video 𝑣 𝑖 , and function getFeatureValue(𝑓 𝑘 , 𝑡 𝑗 ) retrieves for each frame 𝑓 𝑘 of this list the global feature value corresponding to the automatic processing 𝑡 𝑗 . This global features value is then compared to the different thresholds defined for each analysis mode in order to determine the compatibility of the frame with automatic processing. Algorithms run in two main steps which are frame filtering and segment composition.

Algorithm 1: Negative filtering algorithm for urgent analysis

Input: a set of processing tasks: 𝑇 and a set of videos: 𝑉 Output: a list of compatible video segments for each type of processing task Frame filtering step: is the step that consists of comparing each frame of a video to the different thresholds defined in order to determine its eligibility for a given automatic processing according to an analysis mode.

Video segment composition step: since a video segment is defined as a consecutive sequence of frames, this step groups together the frames of a video chronologically and according to the classification (eligibility for a given processing in a given analysis mode) made in the filtering step, in order to build indexed video segments, i.e. eligible or not eligible for a given processing according to a chosen analysis mode.

Example of a negative filtering application case.

Let's consider as inputs for our algorithms:

• video "video_001.mp4" shown in figure 4. This video is composed of 20 frames (𝑓 1 , 𝑓 2 , 𝑓 3 , ..., 𝑓 20 ); • automatic processing 𝑡 1 , 𝑡 2 , and 𝑡 3 whose compatibility thresholds for each analysis mode are defined in the table of Figure 5. The global features values for each frame of the video and related automatic processing are presented in the table 1.

Algorithm 2: Negative filtering algorithm for deep analysis

Input: a set of processing tasks: 𝑇 and a set of videos: 𝑉 Output: a compatible list and an optional list of video segments for each type of processing task

Example of urgent analysis

The two steps of algorithm 1 are presented in Figure 6. At step 1, the global feature value associated to each frame and related to an automatic processing is retrieved and compared to the threshold defined for this automatic processing. For example automatic processing 𝑡 1 is applicable to a frame if the global features value for the frame is in interval [0.85, 1] (see Figure 5). The global features value for frame 𝑓 1 for automatic processing 𝑡 1 is 0.71 (see table 1), so processing 𝑡 1 is not applicable to frame 𝑓 1 in urgent mode. Therefore, on Figure 6, frame 𝑓 1 is represented in red color for processing 𝑡 1 . However, automatic processing 𝑡 2 is applicable to frame 𝑓 1 in urgent Figure 7 shows the 2 running steps of algorithm 2. At step 1 of this algorithm, a new threshold is taken into account in the comparison of global feature values associated to each frame for a given automatic processing. This is the medium compatibility threshold. At step 1 of the urgent analysis mode, a frame could have either the "compatible" state (shown in green) or the "incompatible" state (shown in red) for a given automatic processing. With the deep analysis mode, a new "medium compatible" or "optional" state (shown in orange) is taken into account. For example, for the deep analysis mode, automatic processing 𝑡 1 is optional for a frame if the global feature value of the frame is in the range [0.15, 0.5] (see Figure 5). The global feature value of frame 𝑓 12 for automatic processing 𝑡 1 is 0.16 (see table 1), so automatic processing 𝑡 1 is optional for frame 𝑓 12 in the deep analysis mode. Therefore, on Figure 7, frame 𝑓 12 is shown in orange color for automatic processing 𝑡 1 .

At step 2, video segments that are medium compatible or optional for an automatic processing can be constructed. For example, video segment 𝑈 4 (composed of frames 𝑓 12 , 𝑓 13 , 𝑓 14 , 𝑓 15 , 𝑓 16 , 𝑓 17 ) is medium compatible with processing 𝑡 1 (or optional) for a deep analysis mode of video "video_oo1.mp4".

Negative filtering in deep analysis mode for our example consist of two sets:

• the set composed of video segments compatible with deep analysis mode: {(𝑡 1 , video_001. prototype has been developed in Java and communicates with an Oracle database that integrates spatial extension to store spatial data and perform spatial queries. This framework is composed of three modules: metadata collection module, user interface module, and metadata management and processing module.

Metadata collection module. Metadata sources considered in this work are multiple can be classified into two main groups: metadata from sensors, metadata from video analytics tools.

User interface module. User interface enables to define user's queries or to use queries already defined in JSON format files, to view the data stored in the database and to view the results.

Metadata management and processing module. This is the most important part of the framework. It has three components: metadata storage, query interpreter, and negative filtering. Component Metadata repository enables to store metadata collected for our experiments based on the proposed data model. Component Query interpreter interprets the user's query to make it usable by the framework. It takes as input a JSON file containing the different elements of the query such as location, time, analysis mode, etc. Component Negative filtering implements the proposed negative filtering algorithms and returns the results to the user through User interface module.

Data set and experiments

Data set presentation.

Experiments were performed on the ToCaDa dataset [START_REF] Thierry Malon | Toulouse campus surveillance dataset: scenarios, soundtracks, synchronized videos with overlapping and disjoint views[END_REF], which contains a collection of videos recorded on the campus of the University of Toulouse III -Paul Sabatier. A detailed description of the ToCaDa dataset (Toulouse Campus surveillance Dataset) is presented in the work of our team and the laboratory [START_REF] Thierry Malon | Toulouse campus surveillance dataset: scenarios, soundtracks, synchronized videos with overlapping and disjoint views[END_REF]. Here we provide a useful summary for understanding our experiments. This dataset contains two sets of 25 time-synchronized videos corresponding to two predefined scenarios. The videos were recorded on July 17, 2017 at 9:50 a.m. for the first scenario and at 11:04 a.m. for the second scenario. Cameras were installed as follows:

• 9 cameras were located inside the main building and were shooting from the windows of the different floors. All these cameras were focused on the parking and the path leading to the main entrance of the building with large overlapping fields of view.

• 8 cameras were located in front of the building, with large overlapping fields of view also ( these 9+8=17 cameras with overlapping fields of view are visible in Figure 9 ). • 8 cameras were placed further away, scattered across the university campus (see Figure 10). The fields of view of these cameras are disjointed.

About 20 actors were invited to follow two realistic scenarios by performing predefined actions, such as driving a car, walking, entering or leaving a building, or holding an object in their hands during filming. In addition to ordinary actions, some suspicious behaviour are present. Specifically:

• In the first scenario, a suspicious car (C) with two men inside (D the driver and P the passenger) arrives and parks in front of the building (in view of the overlapping cameras). P gets out of car C and enters the building. Two minutes later, P leaves the building holding a package and goes into C. C leaves the parking lot and drives away from the university campus (passing some of the cameras with disjointed fields of view). • In the second scenario, the situation is similar with a suspicious car (C) and two men inside (D the driver and P the passenger) arriving and parking in front of the building (again in view of the overlapping cameras). P gets out of C and enters the building. A minute later, a woman complains to D about her poor parking. C moves away quickly and stops in the field of view of camera 8. About a minute later, P leaves the main building holding a package and runs away. P meets C a little further away (in the field of view of camera 8), enters C, and C quickly leaves the university campus (passing within the fields of view of most cameras).

In our experiments, we do not take into account all the cameras located in front of and inside the main building, as they were deployed for the purpose of reconstructing 4D scenes, which explains the overlapping of their fields of view. Among these cameras, we have selected three (cameras 2, 5 and 25 in Figure 9) whose fields of view allow maximum coverage of the desired area. All cameras in Figure 10 are included in the experiments. Cameras 2, 5, 25 of Figure 9 have respectively for identifier 𝑐𝑎𝑚𝐴, 𝑐𝑎𝑚𝐵, 𝑐𝑎𝑚𝐶, and cameras 6, 8, 9, 10, 11, 12, 13, 14 of Figure 10 have respectively for identifier 𝑐𝑎𝑚𝐷, 𝑐𝑎𝑚𝐸, 𝑐𝑎𝑚𝐹 , 𝑐𝑎𝑚𝐺, 𝑐𝑎𝑚𝐻 , 𝑐𝑎𝑚𝐼 , 𝑐𝑎𝑚𝐽 , 𝑐𝑎𝑚𝐾. Each camera filmed for a total of 10 minutes 28 seconds (4 minutes 48 seconds for Scenario 1 and 5 minutes 40 seconds for Scenario 2). The videos from the 11 cameras (𝑐𝑎𝑚𝐴 to 𝑐𝑎𝑚𝐾) are respectively identified by 𝑉 1 , 𝑉 2 , 𝑉 3 , 𝑉 4 , 𝑉 5 , 𝑉 6 , 𝑉 7 , 𝑉 8 , 𝑉 9 , 𝑉 10 , 𝑉 11 .

Tests were conducted to measure the impact of our proposition on video processing times. In this experiment we run our negative filtering algorithms on videos from the eleven cameras selected for the experiments. As the quality of the videos from the selected cameras was perfect, we randomly deteriorated some video segments in order to filter based on quality criteria.

Quality of each frame was evaluated using the BRISQUE (Blind Referenceless Image Spatial Quality Evaluator) metric [START_REF] Mittal | Blind/referenceless image spatial quality evaluator[END_REF]. BRISQUE metric is the most commonly used metric in Figure 10: Camera positions on the campus of the Université Paul Sabatier. These 8 cameras have disjointed views [START_REF] Thierry Malon | Toulouse campus surveillance dataset: scenarios, soundtracks, synchronized videos with overlapping and disjoint views[END_REF]. La zone rouge correspond à la Figure 9 Image Quality Assessment (IQA) without a reference [START_REF] Charrier | Comparison of no-reference image quality assessment machine learning-based algorithms on compressed images[END_REF], i.e. not requiring a reference image with good quality. Extracting this metric for each frame of the degraded video has been implemented in Python using the "pybrisque" module proposed by Kushashwa Ravi Shrimali (under MIT license) 1 . Extracted quality metadata were saved in the database.

Results

Negative filtering for a given video, returns for each frame of the video its compatibility (compatible, optional, incompatible) with each processing (face detection, vehicle detection, plate detection and recognition) according to the different analysis modes (urgent, deep). Figures 11,12, and 13 represent the negative filtering of video 𝑉 1 for the three automatic processing according to each analysis mode. On these figures, green frames are compatible, orange frames are optional, and red frames are incompatible with the automatic processing chosen in the given analysis mode.

Negative filtering results are returned as video segments consisting of successive frames of same color. For example, for automatic processing "Face Detection", result for video 𝑉 1 is:

Evaluation

We evaluated the time savings gained using the proposed approach. This time saving is evaluated for each automatic processing in different analysis modes.

The time savings 𝐺 𝑡𝑖𝑚𝑒 for a given video is the ratio of the total processing time for the non-filtered video 𝑇 𝑡𝑜𝑡𝑎𝑙 over the total processing time for the filtered video 𝑇 𝑎𝑝𝑝𝑟𝑜𝑎𝑐ℎ . where:

𝐺 𝑡𝑖𝑚𝑒 = 𝑇 𝑡𝑜𝑡𝑎𝑙 𝑇 𝑎𝑝𝑝𝑟𝑜𝑎𝑐ℎ (1)
• 𝐺 𝑓 𝑖𝑙𝑡𝑟𝑎𝑔𝑒 = 𝑡 𝑡𝑟𝑎𝑖𝑡𝑒𝑚𝑒𝑛𝑡 𝑡 𝑓 𝑖𝑙𝑡𝑟𝑎𝑔𝑒 is a saving of filtering time (to be distinguished from the total time saving 𝐺 𝑡𝑖𝑚𝑒 , • 𝐺 𝑓 𝑟𝑎𝑚𝑒 = 𝑛 𝑡𝑜𝑡𝑎𝑙 𝑛 𝑟𝑒𝑠𝑡𝑒 is a saving of frame. Evaluation of the time saving for automatic processing "face detection", "vehicle detection", and "plate detection and recognition" corresponding to the 11 videos taken into account in this experiment is illustrated respectively by the figures 14, 15, and 16.

CONCLUSION AND FUTURE WORK

In this paper, we proposed a so-called "negative" filtering approach enabling, in the context of a posteriori video analysis, to save processing time by eliminating, among the mass of videos to be analysed, video sequences that are unusable based on the quality and usability/utility of the videos. The defined filtering algorithms are based on a generic metadata modeling of video quality and usability/utility. The proposed approach has been validated in the French project ANR FILTER2 and experimental results achieved with the developed framework shown the relevance of our approach and its feasibility in a real case. Although it is functional, improvements can still be added to the proposed framework. In order to improve the negative filtering of large video collections related to postresearch of evidence, a perspective of this work is to into account contextual information (open data, mobility, social media, etc.) in order to filter according to new parameters or to enrich videos.

Figure 1 :

 1 Figure 1: Examples of image quality scores performed using G-BLINDS2 and BIQI non-reference metrics.

Figure 2 :

 2 Figure 2: Generic model for video quality and usability/utility metadata.

Figure 3 :

 3 Figure 3: Example of negative filtering results.

3. 2 . 1

 21 Negative filtering algorithms. The proposed negative filtering is based on the metadata modelling presented earlier. The goal is to define metadata-based query algorithms to automatically discard unusable video segments based on quality and video utility/usability criteria. Filtering algorithms have as parameters a video list, an automatic processing list, and customizable thresholds. Thresholds are defined for each analysis mode (urgent or deep analysis) in order to determine the compatibility of the video sequences with the different automatic processing (face detection, vehicle detection, plate detection and recognition). Compatibility to an analysis mode is determined by comparing the global features value for each frame (or group of frames) of video to the compatibility thresholds defined for different automatic processing. Then, the results of the comparisons are used to build (frame grouping) video segments. Given a set of videos 𝑉 = {𝑣 1 , 𝑣 2 , ..., 𝑣 𝑖 } (each video 𝑣 𝑖 composed of a set of frames 𝐹 𝑖 = {𝑓 𝑖 1 , 𝑓 𝑖 2 , ..., 𝑓 𝑖 𝑛 }) and a set of automatic processing 𝑇 = (𝑡 1 , 𝑡 2 , ..., 𝑡 𝑗 ), the result of negative filtering for each analysis mode is a set of triplets: 𝑅 = {𝑟 = (𝑡 𝑗 , 𝑣 𝑖 , [𝑓 𝑖 𝑠𝑡𝑎𝑟𝑡 , 𝑓 𝑖 𝑒𝑛𝑑 ])}, where 𝑡 𝑗 ∈ 𝑇 , 𝑣 𝑖 ∈ 𝑉 , and 𝑓 𝑖 𝑠𝑡𝑎𝑟𝑡 , 𝑓 𝑖 𝑒𝑛𝑑 ∈ 𝐹 𝑖 |𝑓 𝑖 𝑠𝑡𝑎𝑟𝑡 ≤ 𝑓 𝑖 𝑒𝑛𝑑 . For deep analysis mode, there are compatible video segments and medium compatible (optional) video segments with automatic processing.

Figure 4 :

 4 Figure 4: Example of video input for negative filtering.

Figure 5 :

 5 Figure 5: Examples of compatibility thresholds for different automatic processing.

Figure 6 :

 6 Figure 6: Example of negative filtering in urgent analysis mode.

  Figure7shows the 2 running steps of algorithm 2. At step 1 of this algorithm, a new threshold is taken into account in the comparison of global feature values associated to each frame for a given automatic processing. This is the medium compatibility threshold. At step 1 of the urgent analysis mode, a frame could have either the "compatible" state (shown in green) or the "incompatible" state (shown in red) for a given automatic processing. With the deep analysis mode, a new "medium compatible" or "optional" state (shown in orange) is taken into account. For example, for the deep analysis mode, automatic processing 𝑡 1 is optional for a frame if the global feature value of the frame is in the range [0.15, 0.5] (see Figure5). The global feature value of frame 𝑓 12 for automatic processing 𝑡 1 is 0.16 (see table1), so automatic processing 𝑡 1 is optional for frame 𝑓 12 in the deep analysis mode. Therefore, on Figure7, frame 𝑓 12 is shown in orange color for automatic processing 𝑡 1 .At step 2, video segments that are medium compatible or optional for an automatic processing can be constructed. For example, video segment 𝑈 4 (composed of frames 𝑓 12 , 𝑓 13 , 𝑓 14 , 𝑓 15 , 𝑓 16 , 𝑓 17 ) is medium compatible with processing 𝑡 1 (or optional) for a deep analysis mode of video "video_oo1.mp4".Negative filtering in deep analysis mode for our example consist of two sets:• the set composed of video segments compatible with deep analysis mode: {(𝑡 1 , video_001.mp4, [𝑓 1 , 𝑓 3 ]), (𝑡 1 , video_001.mp4, [𝑓 8 , 𝑓 11 ]), (𝑡 1 , video_001.mp4, [𝑓 18 , 𝑓 20 ]), (𝑡 2 , video_001.mp4, [𝑓 1 , 𝑓 4 ]), (𝑡 2 , video_001.mp4, [𝑓 13 , 𝑓 20 ]), (𝑡 3 , video_001.mp4, [𝑓 1 , 𝑓 9 ]), (𝑡 3 , video_001.mp4, [𝑓 14 , 𝑓 20 ])}. • the set composed of video segments that are mediumcompatible or optional for deep analysis mode: {(𝑡 1 , video_001.mp4, [𝑓 12 , 𝑓 17 ]), (𝑡 2 , video_001.mp4, [𝑓 9 , 𝑓 12 ])}.

Figure 7 :

 7 Figure 7: Example of negative filtering in deep analysis mode.

Figure 8 :

 8 Figure 8: Architecture of the proposed framework.

Figure 9 :

 9 Figure 9: Main building with 17 cameras with overlapping fields of view [12].

  (a) Urgent analysis mode. (b) Deep analysis mode.

Figure 11 :

 11 Figure 11: Face detection for video 𝑉 1 .

Figure 12 :

 12 Figure 12: Vehicle detection for video 𝑉 1 .

  (a) Urgent analysis mode. (b) Deep analysis mode.

Figure 13 :

 13 Figure 13: Plate detection and recognition for video 𝑉 1 .

Figure 14 :

 14 Figure 14: Time saving for automatic processing "face detection".

Figure 15 :

 15 Figure 15: Time saving for automatic processing "vehicle detection".

Figure 16 :

 16 Figure 16: Time saving for automatic processing "plate detection and recognition".

  1 foreach 𝑡 𝑗 in 𝑇 do 𝑔𝑒𝑡 𝐹𝑒𝑎𝑡𝑢𝑟𝑒𝑉 𝑎𝑙𝑢𝑒 (𝑓 𝑘 , 𝑡 𝑗 );

	2	foreach 𝑣 𝑖 in 𝑉 do
	3	𝑓 𝑟𝑎𝑚𝑒𝐿𝑖𝑠𝑡 ← 𝑔𝑒𝑡𝑉 𝑖𝑑𝑒𝑜𝐹𝑟𝑎𝑚𝑒𝑠 (𝑣 𝑖 );
	4	foreach 𝑓 𝑘 in 𝑓 𝑟𝑎𝑚𝑒𝐿𝑖𝑠𝑡 do
	6	if 𝑣𝑎𝑙 ≥ 𝑡 𝑗 .𝑠 (𝑢).𝑝𝑎𝑟𝑎𝑚1 and 𝑣𝑎𝑙 ≤
		𝑡 𝑗 .𝑠 (𝑢).𝑝𝑎𝑟𝑎𝑚2 then
	7	𝑎𝑑𝑑 (𝑢𝑟𝑔𝑒𝑛𝑡𝑆𝑒𝑔𝑚𝑒𝑛𝑡, 𝑓 𝑘 );
	8	𝑓 𝑖 𝑠𝑡𝑎𝑟𝑡 ← 𝑑𝑒𝑏𝑆𝑒𝑔 (𝑢𝑟𝑔𝑒𝑛𝑡𝑆𝑒𝑔𝑚𝑒𝑛𝑡 );
	9	𝑓 𝑖 𝑒𝑛𝑑 ← 𝑓 𝑖𝑛𝑆𝑒𝑔 (𝑢𝑟𝑔𝑒𝑛𝑡𝑆𝑒𝑔𝑚𝑒𝑛𝑡 );
	10	else if 𝑢𝑟𝑔𝑒𝑛𝑡𝑆𝑒𝑔𝑚𝑒𝑛𝑡 𝑖𝑠 𝑛𝑜𝑡 𝑒𝑚𝑝𝑡 𝑦 then
	11	𝑎𝑑𝑑𝑅𝑒𝑠𝑢𝑙𝑡 (𝑡 𝑗 , 𝑣 𝑖 , [𝑓 𝑖 𝑠𝑡𝑎𝑟𝑡 , 𝑓 𝑖 𝑒𝑛𝑑 ]);
	12	𝑐𝑙𝑒𝑎𝑟 (𝑢𝑟𝑔𝑒𝑛𝑡𝑆𝑒𝑔𝑚𝑒𝑛𝑡 );
	13	else
	14	𝑐𝑙𝑒𝑎𝑟 (𝑢𝑟𝑔𝑒𝑛𝑡𝑆𝑒𝑔𝑚𝑒𝑛𝑡 );
	15	end if
	16	end foreach
	17	if 𝑢𝑟𝑔𝑒𝑛𝑡𝑆𝑒𝑔𝑚𝑒𝑛𝑡 𝑖𝑠 𝑛𝑜𝑡 𝑒𝑚𝑝𝑡 𝑦 then
	20	end if
	21	end foreach
	22 end foreach

5 𝑣𝑎𝑙 ← 18 𝑎𝑑𝑑𝑅𝑒𝑠𝑢𝑙𝑡 (𝑡 𝑗 , 𝑣 𝑖 , [𝑓 𝑖 𝑠𝑡𝑎𝑟𝑡 , 𝑓 𝑖 𝑒𝑛𝑑 ]); 19 𝑐𝑙𝑒𝑎𝑟 (𝑢𝑟𝑔𝑒𝑛𝑡𝑆𝑒𝑔𝑚𝑒𝑛𝑡 );

  1 foreach 𝑡 𝑗 in 𝑇 do 𝑔𝑒𝑡 𝐹𝑒𝑎𝑡𝑢𝑟𝑒𝑉 𝑎𝑙𝑢𝑒 (𝑓 𝑘 , 𝑡 𝑗 );

	2	foreach 𝑣 𝑖 in 𝑉 do
	3	𝑓 𝑟𝑎𝑚𝑒𝐿𝑖𝑠𝑡 ← 𝑔𝑒𝑡𝑉 𝑖𝑑𝑒𝑜𝐹𝑟𝑎𝑚𝑒𝑠 (𝑣 𝑖 );
	4	foreach 𝑓 𝑘 in 𝑓 𝑟𝑎𝑚𝑒𝐿𝑖𝑠𝑡 do
	6	if 𝑣𝑎𝑙 ≥ 𝑡 𝑗 .𝑠 (𝑎).𝑝𝑎𝑟𝑎𝑚1 and 𝑣𝑎𝑙 ≤
		𝑡 𝑗 .𝑠 (𝑎).𝑝𝑎𝑟𝑎𝑚2 then
	7	𝑎𝑑𝑑 (𝑖𝑛𝑑𝑒𝑝𝑡ℎ𝑆𝑒𝑔𝑚𝑒𝑛𝑡, 𝑓 𝑘 );
	8	𝑓 𝑖 𝑠𝑡𝑎𝑟𝑡 ← 𝑑𝑒𝑏𝑆𝑒𝑔 (𝑖𝑛𝑑𝑒𝑝𝑡ℎ𝑆𝑒𝑔𝑚𝑒𝑛𝑡 );
	9	𝑓 𝑖 𝑒𝑛𝑑 ← 𝑓 𝑖𝑛𝑆𝑒𝑔 (𝑖𝑛𝑑𝑒𝑝𝑡ℎ𝑆𝑒𝑔𝑚𝑒𝑛𝑡 );
	10	else if 𝑣𝑎𝑙 ≥ 𝑡 𝑗 .𝑠 (𝑜).𝑝𝑎𝑟𝑎𝑚1 and 𝑣𝑎𝑙 ≤
		𝑡 𝑗 .𝑠 (𝑜).𝑝𝑎𝑟𝑎𝑚2 then
	13	𝑓 𝑖 𝑒𝑛𝑑 ← 𝑓 𝑖𝑛𝑆𝑒𝑔 (𝑂𝑝𝑡𝑖𝑜𝑛𝑎𝑙𝑆𝑒𝑔𝑚𝑒𝑛𝑡 );
	14	else
	15	if 𝑖𝑛𝑑𝑒𝑝𝑡ℎ𝑆𝑒𝑔𝑚𝑒𝑛𝑡 𝑖𝑠 𝑛𝑜𝑡 𝑒𝑚𝑝𝑡 𝑦 then
	18	else
	19	𝑐𝑙𝑒𝑎𝑟 (𝑖𝑛𝑑𝑒𝑝𝑡ℎ𝑆𝑒𝑔𝑚𝑒𝑛𝑡 );
	20	end if
	21	if 𝑂𝑝𝑡𝑖𝑜𝑛𝑎𝑙𝑆𝑒𝑔𝑚𝑒𝑛𝑡 𝑖𝑠 𝑛𝑜𝑡 𝑒𝑚𝑝𝑡 𝑦 then
	24	else
	25	𝑐𝑙𝑒𝑎𝑟 (𝑂𝑝𝑡𝑖𝑜𝑛𝑎𝑙𝑆𝑒𝑔𝑚𝑒𝑛𝑡 );
	26	end if
	27	end if
	28	end foreach
	29	if 𝑖𝑛𝑑𝑒𝑝𝑡ℎ𝑆𝑒𝑔𝑚𝑒𝑛𝑡 𝑖𝑠 𝑛𝑜𝑡 𝑒𝑚𝑝𝑡 𝑦 then
	32	end if
	33	if 𝑂𝑝𝑡𝑖𝑜𝑛𝑎𝑙𝑆𝑒𝑔𝑚𝑒𝑛𝑡 𝑖𝑠 𝑛𝑜𝑡 𝑒𝑚𝑝𝑡 𝑦 then
	36	end if
	37	end foreach
	38 end foreach

5 𝑣𝑎𝑙 ← 11 𝑎𝑑𝑑 (𝑂𝑝𝑡𝑖𝑜𝑛𝑎𝑙𝑆𝑒𝑔𝑚𝑒𝑛𝑡, 𝑓 𝑘 ); 12 𝑓 𝑖 𝑠𝑡𝑎𝑟𝑡 ← 𝑑𝑒𝑏𝑆𝑒𝑔 (𝑂𝑝𝑡𝑖𝑜𝑛𝑎𝑙𝑆𝑒𝑔𝑚𝑒𝑛𝑡 ); 16 𝑎𝑑𝑑𝑅𝑒𝑠𝑢𝑙𝑡𝐴(𝑡 𝑗 , 𝑣 𝑖 , [𝑓 𝑖 𝑠𝑡𝑎𝑟𝑡 , 𝑓 𝑖 𝑒𝑛𝑑 ]); 17 𝑐𝑙𝑒𝑎𝑟 (𝑖𝑛𝑑𝑒𝑝𝑡ℎ𝑆𝑒𝑔𝑚𝑒𝑛𝑡 ); 22 𝑎𝑑𝑑𝑅𝑒𝑠𝑢𝑙𝑡𝑂 (𝑡 𝑗 , 𝑣 𝑖 , [𝑓 𝑖 𝑠𝑡𝑎𝑟𝑡 , 𝑓 𝑖 𝑒𝑛𝑑 ]); 23 𝑐𝑙𝑒𝑎𝑟 (𝑂𝑝𝑡𝑖𝑜𝑛𝑎𝑙𝑆𝑒𝑔𝑚𝑒𝑛𝑡 ); 30 𝑎𝑑𝑑𝑅𝑒𝑠𝑢𝑙𝑡𝐴(𝑡 𝑗 , 𝑣 𝑖 , [𝑓 𝑖 𝑠𝑡𝑎𝑟𝑡 , 𝑓 𝑖 𝑒𝑛𝑑 ]); 31 𝑐𝑙𝑒𝑎𝑟 (𝑖𝑛𝑑𝑒𝑝𝑡ℎ𝑆𝑒𝑔𝑚𝑒𝑛𝑡 ); 34 𝑎𝑑𝑑𝑅𝑒𝑠𝑢𝑙𝑡𝑂 (𝑡 𝑗 , 𝑣 𝑖 , [𝑓 𝑖 𝑠𝑡𝑎𝑟𝑡 , 𝑓 𝑖 𝑒𝑛𝑑 ]); 35 𝑐𝑙𝑒𝑎𝑟 (𝑂𝑝𝑡𝑖𝑜𝑛𝑎𝑙𝑆𝑒𝑔𝑚𝑒𝑛𝑡 );

Table 1 :

 1 Global feature values for each automatic processing.AUTOMATIC PROCESSING FRAMES processing 𝑡 1 processing 𝑡 2 processing 𝑡 3 ) for compatibility in urgent mode. This is illustrated at Figure6by the representation of frame 𝑓 1 in green color for automatic processing 𝑡 2 .At step 2, frames are grouped together to create video segments, while distinguishing for each processing the video segments that are compatible or not with the urgent analysis mode. For example, processing 𝑡 2 can be applied to video segments 𝑉 1 (composed of frames 𝑓 1 , 𝑓 2 , 𝑓 3 , 𝑓 4 ) and 𝑉 3 (composed of frames 𝑓 13 , 𝑓 14 , 𝑓 15 , 𝑓 16 , 𝑓 17 , 𝑓 18 , 𝑓 19 , 𝑓 20 ) for an urgent analysis of the video "video_oo1.mp4".Negative filtering result in urgent mode for our example is the set: {(𝑡 1 , video_001.mp4, [𝑓 8 , 𝑓 11 ]), (𝑡 2 , video_001.mp4, [𝑓 1 , 𝑓 4 ]), (𝑡 2 , video_001.mp4, [𝑓 13 , 𝑓 20 ]), (𝑡 3 , video_001.mp4, [𝑓 1 , 𝑓 9 ])}.

	𝑓 1	0.71	0.76	0.67
	𝑓 2	0.68	0.80	0.71
	𝑓 3	0.74	0.83	0.74
	𝑓 4	0.11	0.79	0.68
	𝑓 5	0.12	0.32	0.76
	𝑓 6	0.14	0.29	0.82
	𝑓 7	0.13	0.30	0.74
	𝑓 8	0.87	0.24	0.91
	𝑓 9	0.91	0.41	0.89
	𝑓 10	0.94	0.52	0.21
	𝑓 11	0.98	0.49	0.23
	𝑓 12	0.16	0.61	0.19
	𝑓 13	0.18	0.83	0.24
	𝑓 14	0.14	0.78	0.53
	𝑓 15	0.19	0.84	0.61
	𝑓 16	0.25	0.90	0.51
	𝑓 17	0.35	0.87	0.55
	𝑓 18	0.56	0.79	0.62
	𝑓 19	0.67	0.87	0.59
	𝑓 20	0.78	0.93	0.64
	mode, because the global feature value of 𝑓 1 for this automatic
	processing (𝑣𝑎𝑙𝑢𝑒 = 0.76) fits the defined threshold (range
	[0.75, 1]Example of deep analysis

  𝐹 9275 , 𝑉 1 𝐹 11561 ], and [𝑉 1 𝐹 16532 , 𝑉 1 𝐹 18840 ]. -Optional video segments: [𝑉 1 𝐹 14242 , 𝑉 1 𝐹 16531 ]. -Incompatible video segments: [𝑉 1 𝐹 4928 , 𝑉 1 𝐹 9274 ], and [𝑉 1 𝐹 11562 , 𝑉 1 𝐹 14241 ].

• Urgent analysis mode -Compatible video segments: [𝑉 1 𝐹 1 , 𝑉 1 𝐹 1963 ], [𝑉 1 𝐹 2747 , 𝑉 1 𝐹 5031 ], and [𝑉 1 𝐹 9274 , 𝑉 1 𝐹 11383 ]. -Incompatible video segments: [𝑉 1 𝐹 1964 , 𝑉 1 𝐹 2746 ], [𝑉 1 𝐹 5032 , 𝑉 1 𝐹 9274 ], and [𝑉 1 𝐹 11384 , 𝑉 1 𝐹 18840 ]. • Deep analysis mode -Compatible video segments: [𝑉 1 𝐹 1 , 𝑉 1 𝐹 4927 ], [𝑉 1

https://github.com/krshrimali/No-Reference-Image-Quality-Assessmentusing-BRISQUE-Model


Benoît Richard
email: benoit.richard@cea.fr

Xavier Le Pivert
email: xavier.lepivert@cea.fr

Yves-Marie Bourien
email: yves-marie.bourien@cea.fr

BESS Optimal Sizing Methodology -Degree of Impact of Several Influencing Factors

Keywords: battery energy storage system, optimal sizing, hybrid microgrid

Battery Energy Storage Systems (BESS) are more and more competitive due to their increasing performances and decreasing costs. Although certain battery storage technologies may be mature and reliable from a technological perspective, with further cost reductions expected, the economic concern of battery systems is still a major barrier to be overcome before BESS can be fully utilized as a mainstream storage solution in the energy sector. Since the investment costs for deploying BESS are significant, one of the most crucial issues is to optimally size the battery system to balance the trade-off between using BESS to improve energy system performance and to achieve profitable investment. Determining the optimal BESS size for a specific application is a complex task because it relies on many factors, depending on the application itself, on the technical characteristics of the battery system and on the business model framework. This paper describes a generic simulation-based analytical method which has been developed to determine the BESS optimal size by taking into account both the application and the storage performance over its lifetime. Its implementation and the associated results are presented for two different BESS use cases: A smoothing and peak shaving application for PV injection and an off-grid hybrid microgrid case. In order to provide a better understanding of the most influencing drivers to consider during a BESS sizing procedure, several sensitivity analyses have been carried out on these two illustrative cases. The use of comparative scenarios led to quantify the degree of impact on optimal sizing results of several factors among the following topics: control strategy, forecast quality, degradation of battery performance due to ageing, precision of technical modelling.

I. INTRODUCTION

Due to the number and variety of services they can provide, energy storage is likely to play a significant role in the optimal mix of flexibility solutions for the European power system. Of the various type of energy storage technology available, battery energy storage systems (BESS) have attracted considerable attention with clear advantages like fast response, controllability, and geographical independence [START_REF]Energy storage study -funding and knowledge sharing priorities[END_REF][START_REF] Irena | Battery storage for renewables: market status and technology outlook[END_REF]. Besides the advantages mentioned, BESS also have a wide scope of applications ranging from short-time power quality enhancement to long-term energy management, as well as reliability enhancement, uninterrupted power supply and transmission upgrade deferral. BESS thus mitigate some of the current and future challenges that grid operators face to improve the overall economics of the infrastructure while reducing the overall carbon footprint and providing reliable services. Specifically, the challenges include managing peak demand, resolving transmission line congestion, and integrating renewable energy technology in a climate of financial risk adversity that will limit new transmission construction.

Over the last decades, significant research and development has been conducted to improve cost and reliability of battery energy storage systems. Although certain battery storage technologies may be mature and reliable from a technological perspective [START_REF] Irena | Battery storage for renewables: market status and technology outlook[END_REF], with further cost reductions expected [START_REF] Irena | REmap 2030 -Renewable energy prospects[END_REF], the economic concern of battery systems is still a major barrier to be overcome before BESS can be fully utilized as a mainstream storage solution in the energy sector. The investment costs for deploying a BESS can be significant. That is the reason why, during the implementation of battery energy storage systems, one of the most crucial issues is to optimally determine the size of the battery to define the appropriate balance between the technical improvements brought by the battery and the additional overall cost. Determining the optimal BESS size for a specific application is a complex task because it directly or indirectly depends on a lot of factors, parameters and uncertainties such as:  Application control strategy, which determines how the storage system is used for the considered application,  Energy and power application needs over the project lifetime,  BESS efficiency,  Degradation of the performances of the battery over its lifetime (capacity and/or power degradation due to battery ageing),  Uncertainties related to renewable energy sources / forecast errors / load demands / energy prices,  Realistic economical assessments to correctly evaluate investment as well as operation costs and incomes throughout the project lifetime.

This paper describes a generic method which has been developed to determine the optimal size of a BESS involved in a specific power application. To assess the degree of impact of some influencing factors among those listed above, this method has been used to carry out several sensitivity analyses.

II. ANALYTICAL METHOD IMPLEMENTED

One of the major objectives of this study is to provide useful synthetic information on the most influencing factors to consider during the BESS sizing procedure. For this purpose, some sensitivity analyses need to be performed to assess how the value of BESS sizing criteria (financial and/or technical metrics) may be affected by a change of influencing parameter, potentially leading to a different optimal size determination. To conduct this survey, an analytical method has been implemented, based on numerical simulation. Although this type of deterministic technique involves significant computational resources to repeat simulations with different combinations of BESS sizes and influencing factors parameters, it provides the necessary flexibility for all criteria and parameter settings required by the sensitivity analysis. Due to deterministic calculation on user-specified intervals, it also enables a better control and visualization of the impact of the factors variation.

A. Numerical simulation platfom

The method implemented for BESS optimal sizing relies on a numerical simulation platform called SPIDER (Simulation Platform for the Integration of Distributed Energy Resources), which has been developed at CEA in a Matlab / Simulink environment. The main advantages of using this simulation tool both to carry out some techno-economic assessments as required by the BESS optimal size determination and to perform a sensitivity analysis are listed below:

 The Simulink graphic-modelling environment enables to reproduce the functional architecture of the study cases by hierarchical blocks and diagrams and to interface the energy system components models with the control algorithms.

 This platform environment offers a high-level of modularity, enabling to run some similar operation scenarios with different control algorithms and/or different degrees of technical modelling for a same energy component, just by switching the corresponding block model in the Simulink use-case diagram.

 The SPIDER platform benefits from an already existing library of energy component models (PV plants, wind turbines, energy storage systems, battery cells, converters, fuel generators,…) and control algorithm templates developed by CEA.

 The SPIDER platform provides a generic structure and a ready-to-use set of templates, functions and tools for configuring simulations, launching some sensitivity analysis scenarios and customizing postprocessing calculations, as well as instantiating the models with some specific set of parameters of the case study.

 The ability to run simulations at different time steps, specified by the user as a configuration parameter.

B. Simulation-based method for optimal sizing

The general synoptic implemented for the calculation of the optimal sizing indicator of a given configuration (i.e. one particular size of BESS) is depicted on Fig. 1. By repeating this procedure for different BESS configuration sizes, it becomes possible to identify which configuration size leads to the best value of the performance indicator, determining thus the optimal size.

In practice, the optimal sizing tool developed into the SPIDER platform enables to define a range of BESS size values for launching the automatic processing of the defined sizing indicators on the entire search area. At the end of this processing, an overview graphic is produced to visualize the variation of the sizing indicator along with the BESS size, as well as synthetic tables containing all values of intermediate and final indicators for each of the simulated configurations.

C. Post-processing calculations

The purpose of post-processing for optimal size determination is to associate a performance value to each simulated configuration, enabling to have a common comparison criteria and identify which configuration, i.e. which size of BESS is the best solution.

Among the different categories of sizing criteria [START_REF] Yang | Battery energy storage system size determination in renewable energy systems: A review[END_REF], financial indicators are the most commonly used [START_REF] Chen | Optimal allocation and economic analysis of energy storage system in microgrids[END_REF][START_REF] Shang | An improved particle swarm optimisation algorithm applied to batterysizing for stand-alone hybrid power systems[END_REF]. They have the advantage of easily enabling the comparison of different alternatives through a common unit, and can be directly used in discussions with project investors for evaluating financial return and making decisions.

BESS sizing criteria used in the present methodology are based on financial indicators, with the setting of a comprehensive techno-economic assessment to balance the economic value of the rendered service and the total system costs. It relies on the calculation of total system expenses and incomes. Incomes are application dependent since they may come from sales on energy markets, green certificates, feed-in tariffs, etc. For each component, expenses are obtained by summing up investment, total O&M and total replacement costs. O&M costs applied each year and replacement costs applied when equipment estimated life span is expired. The total system expenses are obtained by summing up expenses of all components.

The most appropriate financial indicator for BESS sizing should then be chosen in regards to the purpose of the application. For standalone systems or generation units, LCOE (Levelized Cost of Energy, expressed in €/MWh) is generally well suited as it estimates the average cost of produced energy [START_REF] Shang | An improved particle swarm optimisation algorithm applied to batterysizing for stand-alone hybrid power systems[END_REF]. However, when the energy application is designed for more complex market rules where variable feed-in tariffs may be applied or ancillary services may be remunerated, other financial indicators like NPV (Net Present Value) or IRR (Internal Rate of Return) may be more suitable [START_REF] Chen | Optimal allocation and economic analysis of energy storage system in microgrids[END_REF].

Table I lists the implemented BESS sizing criteria and their definitions. To be able to compute these final key performance indicators according to the formula presented, Fig. 1. Overview of the generic method used for BESS optimal sizing some annual intermediate indicators need to be calculated from the simulation output time series results, such as the amount of yearly electrical energy generated, annual incomes, total operation costs including replacement costs when necessary, etc. Furthermore, this financial evaluation requires a set of economic assumptions that allows realistic estimates of investment, O&M and replacement costs for each component and that include a discount rate value close to the WACC (Weighted Average Cost of Capital) generally observed in the business field of activity of the project. It is worth mentioning that all financial indicators values computed in this study are highly dependent on this set of economic assumptions.

III. ILLUSTRATIVE APPLICATION USE CASES

The method implemented and the sensitivity study have been carried out for two different illustrative BESS application use cases.

A. BESS application #1: PV smoothing and peak shaving 1) Application description

This application case corresponds to the call for tenders issued by the French Energy Regulatory Commission in 2015 for installing PV solar plants in French Non-Interconnected Islands. The full description of the call for tenders can be found on the French Energy Regulatory Commission website [START_REF]CDC_AO_PV_100Plus_ZNI[END_REF].

For these grid-connected PV power plants, an energy storage system must be installed in order to control the power injection to the grid.

A minimal capacity of the storage system is imposed by the call for tenders, set 0.5MWh useful capacity per MW of installed PV peak power, at any time of the project life. To respect this constraint, the battery nameplate capacity must be chosen a little higher, to take into account both the deep of discharge (DoD) range and the capacity degradation due to ageing. In our study case, with a DoD of 90% and a capacity degradation up to 30% before battery replacement, the minimal nominal capacity should be set to:

𝑟𝑎𝑡𝑒𝑑 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑚𝑖𝑛 =
𝑢𝑠𝑒𝑓𝑢𝑙 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑚𝑖𝑛 0.9 * (1 -0.3) = 0.5 0.9 * 0.7 ≈ 0.8 𝑀𝑊ℎ 𝑝𝑒𝑟 𝑀𝑊 𝑜𝑓 𝑃𝑉 In order to sell the injected energy at the agreed feed-in tariff, the following main constraints must be respected:  Power injection profile must be announced in advance: the daily injection profile must be known the day before by the grid operator and the producer shall respect it: outside a tolerance range of ±5% of the installed PV power, some financial penalties are applied.

 PV smoothing: PV fluctuations must be limited to specific ramp rates in the resulting grid injection.

 Power injection during peak period: In order to contribute at the mitigation of the daily peak power demand, the plant must inject energy every day during the two hours of the peak period (19h00 -21h00) at a minimum power output of 20% of the PV installed capacity. For the energy injected to the grid during the peak period, a bonus equal to 200€/MWh is added to the agreed feed-in tariff.

Fig. 2 provides an illustration of the requested operation for a typical clear day.

2) BESS optimal sizing a) Sizing criteria

The economic model of this application, for which the income arises from the sale of electricity at a specified feed-in tariff reduced by any penalties applied when the announced power profile is not respected, leads to choose NPV (Net Present Value) as the sizing indicator. b) Optimal sizing reference curve Fig. 3 details the system setup used in simulation and Fig. 4 depicts the NPV values obtained along the BESS sizes range explored for the baseline scenario. It shows that the evolution of the sizing indicator as a function of the BESS size has not an optimum curve shape, but is rather quite linear, with the minimum battery size imposed being the most profitable configuration. It can indeed be demonstrated that, because of the economic framework defined by the call of tenders, additional battery capacity costs are always higher than the additional incomes generated by a larger storage system. As the optimal size is always the smallest for this application, this will unfortunately prevent the sensitivity study from identifying when an influencing factor has an impact strong enough to change the value of the optimal size. Nevertheless the impact on the sizing criteria (Net Present Value) could be quantified.

B. BESS application #2: hybrid microgrid 1) Application description

The second application is related to a standalone hybrid microgrid, which is composed of a load to supply for the demand (industrial power profile), and of a diesel generator with the addition of solar PV for the generation, as represented on Fig. 5. This use case is typical of remote areas where electricity consumption is too low to justify the investment to connect them to the main grid. In the past, fossil fuel generators such as diesel generators have been heavily used for power supply in those areas. However, the rising cost of fuel for the generators, the decreasing cost of renewable energy technologies, as well as the environmental concerns, has led to standalone hybrid energy systems as an attractive solution for remote area power supply.

The key objective of employing a BESS in a standalone hybrid system is to match the imbalance between renewable energy generation and electricity demand to ensure continuity of power supply. In this sense, the functions of diesel generators can be partially or completely replaced by renewable energy and BESS.

2) BESS optimal sizing a) Sizing criteria For this standalone application case, LCOE is a well suited sizing indicator as it will enable to estimate the average cost of the energy produced to supply the industrial load. The optimal BESS size will be determined by the configuration for which the LCOE is the lowest. b) Optimal sizing reference curve Fig. 6 details the system setup used in simulation and Fig. 7 depicts the LCOE values obtained along the BESS sizes range explored for the baseline scenario. For this application case, the evolution of LCOE as a function of the BESS size reveals an optimum curve shape. The high LCOE for the smallest BESS configurations [100 -300 kWh] is mainly composed of OPEX costs, due to the intense use of the fuel generator, and few CAPEX. On the opposite side, the LCOE for the largest BESS configurations [> 700 kWh] contains a strong proportion of CAPEX due to the high initial investment for the storage system procurement, and low fuel costs. Between the two ends of the curve, the optimal trade-off between BESS investment cost and fuel consumption reduction is obtained for a battery size of 440 kWh with the lowest LCOE value, here at 360€/MWh.

IV. SENSITIVITY ANALYSIS

A. Sensitivity study scope

To provide some better understanding on the most influencing drivers to consider during a BESS sizing procedure, a sensitivity analysis has been carried out for assessing the impact on BESS optimal sizing of several factors. This study has been performed through the simulation method described in section II, using the two illustrative usecases described in section III.

To sum up the different areas explored by the sensitivity analysis, Table II lists the different factors which have been investigated with their comparative simulation scenarios.

B. Illustration of detailed results obtained when assessing the influence of control strategy

In this section is discussed the influence on optimal sizing of the control algorithms which manage the whole energy system in regards to the purpose of the application. For a same application case, different control strategy may be implemented, according to the degree of complexity of the control algorithms which have been developed.

For the hybrid microgrid illustrative case, comparison of sizing results is made by separately processing the simulations with two different sets of control algorithms:

 The basic control strategy has the main function of starting and stopping the diesel generator according to the SOC level of the storage system:

o When the battery is almost empty (SOC threshold has been set to 10%), the generator is started.

o When there is a certain quantity of energy in the battery (SOC threshold has been set to 30%), the generator is stopped.

Its secondary function is to regulate the constant balance between the power generation and the electrical consumption of the load. To fulfil this objective, battery capacity is primarily used as a buffer to compensate for any potential imbalances. In the event of excessive generation and a full battery, the PV production may also be reduced.

 The advanced control strategy is more complex as the generator start and stop operations are no longer managed through SOC thresholds but through an optimisation logic which has been implemented thanks to the interface with GAMS software. This optimisation logic aims at minimizing the genset operation costs on a daily horizon. To achieve this objective, the optimisation problem is fed both with a load consumption prediction and a PV forecast, enabling to determine the minimal quantity of additional energy that will be needed from the diesel generator and when it should be produced. As a result, both fuel consumption and genset startup numbers are minimized, leading thus to an operation cost reduction. Concerning the prediction inputs, a real day-ahead forecast has been used for PV and a persistent D+7 prediction has been built for the load consumption as it presents a weekly profile.

As an illustration, Fig. 8 compares the resulting operation for a 3-day simulation period between the two different control strategies: it can be observed that the fuel generator is started less frequently with the advanced control strategy. Fig. 9 and Fig. 10 show that optimal sizing results are strongly affected by the choice of the control strategy, up to the point of changing the optimal BESS size.

For small BESS configurations where the LCOE is mainly composed of OPEX costs, the reduction in operating costs induced by the advanced control strategy is so substantial that it moves the optimum of the LCOE curve from the BESS size of 440 kWh (LCOE value of 357 € / MWh) to a smallest BESS

Forecast quality when predictive control is facing forecast errors

Baseline PV: standard day-1 forecast Load: persistence day+7

Comparative #1 PV: perfect forecast (actual PV production) Load: perfect forecast (actual consumption)

Comparative #2 PV: enhanced forecast with 50% fewer errors Load: enhanced forecast with 50% fewer errors (average between baseline and perfect forecasts)

Precision of the BESS efficiency behaviour

Baseline BESS model parameters include tables of precise efficiency values varying according to temperature, current and SOC Comparative BESS efficiency is set up as a constant value (average efficiency)

Degradation of battery capacity due to ageing

Baseline BESS model parameters include ageing data enabling the simulation to take into account the battery capacity degradation over time Comparative Battery capacity remains constant over time

Degree of technical modelling of the BESS component

Baseline

In-depth performances battery modelling based on equivalent-circuit equations (EC_model)

Comparative

Simplified modelling of the energy/power behaviour of the BESS (E/P_model)

Simulation time-step

Baseline

Time-step of 1 mn

Comparative #1 Time-step of 10 mn Comparative #2 Time-step of 1 hour size of 330 kWh (LCOE value of 344 € / MWh). Consequently, thanks to a higher degree of complexity of control algorithms, not only can a smaller BESS be installed, but also a decrease of the LCOE of 3.64% is achieved.

For large BESS configurations where the LCOE is mainly composed on CAPEX costs, the enhanced control strategy doesn't bring any advantage since the operating costs are already very low. LCOE is even a little higher: where the basic control can start the diesel generator to charge largest battery capacities (between SOC 10% and SOC 30%) for a period of several days, the optimised control restarts the generator more frequently because of the daily optimisation horizon setup. Some improvements may still be achievable in the advanced control algorithms by fine-tuning the optimisation horizon parameters.

C. Summary of results obtained for all investigated factors

For each influencing factor listed in the scope of the sensitivity study, some detailed analyzes similar to the comparison performed in the previous chapter have been carried out for the two different BESS application cases, in accordance with the provided comparative scenarios. The conclusions of the sensitivity study for each factor investigated are summarized in Table III.

V. CONCLUSION Among the wide range of techniques which can be used to achieve optimal sizing of BESS [START_REF] Yang | Battery energy storage system size determination in renewable energy systems: A review[END_REF], the present document described a deterministic simulation-based methodology which can be applied for any type of energy system application. Since the main objective of the study was to provide a better understanding of the most influencing factors to consider when determining the optimal size of a BESS, this method was particularly well suited as it offers the adequate level of flexibility to perform various sensitivity analyses.

By using two very different illustrative BESS use cases, the study enabled to:  illustrate how this generic methodology can be applied to different use cases, for systems composed of various energy components and/or different energy application purposes leading to define different sizing criteria,  discriminate, among the influencing factors investigated through sensitivity analysis, those whose impact has the same magnitude regardless to the application from those whose impact is applicationdependent.

At the stage of modelling or collecting data for optimal sizing purpose, the conclusions provided by this study should help to concentrate the effort on the crucial factors which have the strongest influence on the optimal size determination. In addition, these sensitivity study results enable to identify how calculation time can be significantly reduced within an acceptable trade-off between the accuracy of the result and the computing time. As an illustration, by putting together into practice the conclusions related to the use of a simplified BESS model, to the setting of a time-step of 10 minutes and to the ageing estimation by extrapolating a single year simulation, computation time is divided by 840 compared to the baseline scenario, with an average error below 2%. Fig. 11 illustrates the resulting optimal sizing curve superimposed to the baseline reference for application #2 and Fig. 12 compares the LCOE values obtained in both cases as well as the calculation time required for each of the BESS configurations. While each configuration required 1h10mn of computing time with the baseline scenario, it only takes 5 seconds when the conclusions of the study are combined together.

Influencing factor Conclusions

Control strategy

Strong impact: different control strategies may lead to a different optimal BESS size, as illustrated with the hybrid microgrid application. It is therefore recommended to clearly define the control strategy before determining the optimal size.

Forecast quality when predictive control is facing forecast errors

Highly depends on the application purpose: if the main function of BESS is to compensate for forecasting errors in the RE sources, as for illustrative application #1, forecast quality is of the highest importance for optimal sizing: a 50% improvement of the forecast quality induced a difference of 15% of the sizing indicator value for application #1.

Precision of the BESS efficiency behaviour

A variable efficiency behaviour can be approximated by an average efficiency single value without any impact on optimal sizing. However, the average efficiency value must be set precisely since the sizing indicator value is strongly affected by this parameter. An error on BESS efficiency value causes an error bordering on the same magnitude on the sizing indicator.

Degradation of battery capacity due to ageing

Ageing must be taken into account in optimal sizing. In case of limited availability to precise ageing parameters, an estimation of average degradation is sufficient to obtain appropriate confidence levels on sizing indicators.

Degree of technical modelling of the BESS component

Optimal sizing does not require a high degree of technical modelling: a simplified model of BESS directly handling power and energy quantities from global efficiency parameters is adapted and leads to the same sizing indicator values, within a one percent interval, as an in-depth performances model based on equivalent-circuit equations.

Simulation time-step

The influence of the simulation time-step on optimal sizing strongly depends on the application time constants related to the events impacting the operation costs or incomes. An hourly time-step should in general not be recommended as it could lead to an important loss of information about these events. When such events are related to PV fluctuation or fuel generator operation, like on the two illustrative cases, a time-step of 10mn is suitable. Despite the fact that computing time can be significantly reduced with relevant approximations, this optimal sizing method, well suited for sensitivity analysis, has certain drawbacks related to its deterministic nature:  it requires to collect a large amount of data,  it doesn't take into account the uncertainties of some variables, like production or consumption forecasts,  a key concern is the need for a large number of simulations with varying battery capacities to reach the optimum solution.

These inherent weaknesses could however be mitigated by further enhancements which could take advantage of the strengths of other techniques such as probabilistic methods or direct search algorithms involving mathematical optimisation or heuristic approach [START_REF] Yang | Battery energy storage system size determination in renewable energy systems: A review[END_REF].

At last, it should be pointed out that the optimal BESS sizing performed through this study was related to singlefunction applications. A further way to make the energy capacity (and by extension the physical size of the BESS) a less critical component is the use of advanced dispatch strategies to achieve multiple functions, allowing an existing BESS to be used more effectively and for system design to more effectively use the energy and power capacity of a BESS.

Fig. 2 .

 2 Fig. 2. Application #1 -Daily injection profile (illustration)

Fig. 8 .

 8 Fig. 8. Comparison of simulated operation with different control strategies

Fig. 11 .

 11 Fig. 11. Conclusive approximation with a time reduction factor of 840 Fig. 12. Detailed results for the conclusive approximation

TABLE I .

 I DEFINITION OF SIZING INDICATORS USED IN THE STUDY : total investment costs of year 𝑛 𝑂𝑃𝐸𝑋 𝑛 : total O&M costs of year 𝑛 𝐸 𝑛 : total electrical energy generated in the year 𝑛 𝑟 : discount rate 𝑁 : project lifetime

	Performance indicator		Formula		Details
	Levelized Cost of Energy It determines the average net present cost of electricity generation over the project lifetime 𝐶𝐴𝑃𝐸𝑋 Net Present Value 𝑳𝑪𝑶𝑬 = ∑ 𝐶𝐴𝑃𝐸𝑋 𝑛 + 𝑂𝑃𝐸𝑋 𝑛 (1 + 𝑟) 𝑛 𝑁 𝑛=0 ∑ 𝐸 𝑛 (1 + 𝑟) 𝑛 𝑁 𝑛=0 It determines the present value of all future cash flows generated by a project, including the initial capital investment 𝑵𝑷𝑽 = ∑ 𝑁 𝐶𝐹 𝑛 : cash flow of year 𝑛 𝐶𝐹 𝑛 𝑟 : discount rate (1 + 𝑟) 𝑛 𝑛=0 𝑁 : project lifetime
	Internal Rate of Return IRR is defined as the discount rate that makes the NPV equal to zero	∑ 𝑁 𝑛=0	𝐶𝐹 𝑛 (1 + 𝑰𝑹𝑹) 𝑛	= 0	𝐶𝐹 𝑛 : cash flow of year 𝑛 𝐼𝑅𝑅 : internal rate of return 𝑁 : project lifetime

𝑛

TABLE II

 II

			.	SENSITIVITY ANALYSIS SCENARIOS
	Influencing factor			Face to face scenarios
	Control strategy	Baseline Comparative	Basic control algorithms Advanced control algorithms (including optimisation)

TABLE III .

 III SENSITIVITY ANALYSIS CONCLUSIONS

ACKNOWLEDGMENT

The work presented in this paper is part of the results from OSMOSE project, which has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 773406.


M Bourgain

T Provot

C Sauret

L Valdes-Tamayo

O Rouillon

P Thoreux

P Rouch

Variability of motor moment during golf swing: study of a female professional player

Introduction

Golf swing performance has been widely studied. Performance parameters based on various mechanical concepts were developed such as X-factor [START_REF] Kwon | Validity of the X-factor computation methods and relationship between the X-factor parameters and clubhead velocity in skilled golfers[END_REF], or ground reaction forces [START_REF] Mcnitt-Gray | Regulation of reaction forces during the golf swing[END_REF], for instance. More recently, parameters based on the capacity to generate motor moments were introduced [START_REF] Bourgain | Contribution of vertical and horizontal components of ground reaction forces on global motor moment during a golf swing: a preliminary study[END_REF] to better describe performance.

However, this parameter is a composition of the ground reaction forces, body position and club positions. So, its control requires to control each element and to reduce their variabilities.

Thus the aim of this publication was to estimate the intra-subject variability of the motor moment and its contributors during a golf swing.

Methods

Experimentations

One female professional golfer participated to this study, which had received ethical agreement from an external ethical committee (2015-A01760-49, Ile de France X). After giving her written consent, she performed her personal warm-up routine, and then performed 10 swings with her own driver, in a motion analysis laboratory. It was equipped with a 12-cameras optoelectronic motion capture system (Vicon system, Oxford metrics, UK; 200 Hz), coupled with 2 force plateforms (OR6, AMTI; 1200 Hz), one under each foot, allowing the measurement of ground reaction forces under each foot during the swing. The global reference frame was defined with x-axis mediolateral, pointing toward the right, y-axis antero-posterior pointing forward and z-axis vertical pointing upward. The swing performance was assessed with a dedicated ball launch radar (TrackMan 3, Trackman, USA) and defined as the clubhead speed at impact.

Processing

The instants of the downswing were visually estimated (top of backswing and ball impact). The beginning was defined when the clubhead changed its direction when behind the golfer, and the end (corresponding to impact) when the club was at the same position than at the address.

The segments position amont time was estimated with a multibody kinematic approach performed on OpenSim [START_REF] Delp | OpenSim opensource software to create and analyze dynamic simulations of movement[END_REF]), with the model described by [START_REF] Bourgain | Effect of shoulder model complexity in upper-body kinematics analysis of the golf swing[END_REF]. The global centre of mass (CoM) was calculated by the barycentre of all the body segments centre of mass, among time.

The clubhead marker positions were used to compute the swing plane. It was computed as the plane minimizing the squarre distance with all the positions from mid-downswing to impact, according to [START_REF] Morrison | The relationship between the golf swing plane and ball impact characteristics using trajectory ellipse fitting[END_REF].

Motor moment was defined as the sum of the moments produced by each component of the ground reaction forces (GRF) at the CoM, according to the vector perpendicular to the swing plane.

Variabilities assessment

For all parameters, the variability was assessed over the 10 swings, by computing its standard deviation (SD) and coefficient of variation (CV). The instant T max was defined when the motor moment reached its maximum and DT max corresponded to the duration between T max and impact. GRF variabilities were assessed at the instant T max .

Results and discussion

The performance varied from 44.7.s À1 to 46.3 m.s À1 , with a mean value of 45.2 m.s À1 and a SD of 0.4 m.s À1 corresponding to 1% of variation. The duration of the downswing was on average of 0.28 s with a SD of 0.01 s, which is in accordance with the study of [START_REF] Egret | Kinematic analysis of the golf swing in men and women experienced golfers[END_REF]. The time to impact, DT max , was of 0.21 s and had a variation of about 7% with a SD of 0.01 s, however, this value is close to the limit of sensitivity of the method as the acquisition frequency of the kinematics data was 200 Hz.

The mean values and variations at T max , of the motor moment and the GRF were written in the Table 1. Vertical ground reactions forces had a lower CV than horizontal ones, but had a higher SD. Horizontal ground reaction force had a higher variability, however their absolute were lower. The motor moment had a higher CV than vertical ground reaction forces, thus, horizontal ground reaction forces variation may induce a part of its variability.

The evolution of the mean value of the motor moment and its variation among the downswing were reported in the Figure 1.

Conclusions

The duration of the downswing was the more reproducible parameter, with a variation close to the limit of measurement. As the reproducibility is needed to perform in golf, the reduction of variability is essential for professional golf players. This professional golfer had a range of clubhead speed of 1.59 m.s À1 and this variability may be induced by a variation of motor moment. Thus the control of all the element to produce the motor moment such as GRF seemed essential. However, this study only focus on GRF but CoM position and plane inclination variations should also be investigated.

Figure 1 .

 1 Figure 1. Evolution of the motor moment during the downswing, mean value in red, corridor of þ/-1 SD in grey.

Table 1 .

 1 mean values, standard deviation and coefficient of variation of motor moment and GRF at the instant T max .

	Values at T max	Mean	SD	CV[%]
	Mmot [N.m]	58.24	8.56	14.69
	Trailed FX [N]	À35.11	3.32	9.45
	Trailed FY [N]	À9.39	4.04	42.99
	Trailed FZ [N]	296.04	10.09	3.41
	Lead FX [N]	48.85	3.77	7.72
	Lead FY [N]	14.74	4.21	28.54
	Lead FZ [N]	281.04	8.93	3.18

maxime.bourgain@ensam.eu

Acknowledgements

Authors would like to thank the volunteer for his time. But also TrackMan and Titleist companies which borrow respectively a radar and balls for the experiments.

Disclosure statement

No potential conflict of interest was reported by the authors.