The increasing adoption of renewable energy has accelerated the deployment of photovoltaic infrastructure, introducing new challenges for fault diagnosis systems. Among these, classification-based diagnosis holds considerable practical significance. However, relying solely on classification accuracy to evaluate model effectiveness proves insufficient, particularly in the context of fault data scarcity commonly observed in commercial applications. While models may exhibit accuracy degradation under real-world constraints. This discrepancy reveals that accuracy alone fails to reflect performance deterioration under boundary scenarios, whereas the proposed indicators can expose potential reliability risks. To address this limitation, this work introduces two complementary evaluation metrics: inference-weighted accuracy and coverage-weighted accuracy. Inference-weighted accuracy is defined as the product of classification accuracy and the normalized inference scope, penalizing models that perform well but operate on only a limited subset of data. Coverage-weighted accuracy is defined as the product of classification accuracy and the overall scenario coverage, highlighting models capable of maintaining consistent performance across diverse and complex operating conditions. These metrics offer a more comprehensive and practically meaningful evaluation framework for photovoltaic fault diagnosis systems.

Accurate prediction of Remaining Useful Life (RUL) is critical for ensuring the reliability and safety of Lithium-ion Batteries (LiBs) in applications ranging from portable electronics to electric vehicles. However, capacity fading and complex aging mechanisms make RUL estimation challenging. This work presents a hybrid model based on Particle Swarm Optimization (PSO) and Variational Mode Decomposition (VMD) to evaluate the RUL of LiBs. The optimal hyperparameters of the VMD are determined with PSO, before the decomposition of the capacity data into Intrinsic Mode Functions (IMFs). Then, each IMF is input to a Transformer model for time-series forecasting and RUL estimation. The performance of the methodology is assessed with the NASA B0018 and CALCE C37 datasets with a 50%-50% training–testing split. The results show that this proposed hybrid model achieves superior accuracy and robustness compared to other state-of-the-art models.

It has been shown that an analytical model including amplitude, phase shift, and the mean value of the phase currents in seven-phase electrical machines can be used as relevant information for fault detection, isolation, and estimation. However, this model fails to estimate the fault severity accurately under noisy conditions, especially for faults affecting the mean value. Therefore, the model is extended with the noise as the fourth parameter. Two approaches are considered before the estimation performance is evaluated: the noise level is estimated, or the currents are first denoised. The simulation results with different combinations of noise level and fault severity show that both approaches are efficient and enhance the fault severity estimation, even under high-noise conditions (SNR as low as 5dB). Besides, the analytical model, including the noise, agrees well with the numerical model.

Among the data-driven techniques for abnormalities detection in complex systems, Principal Component Analysis (PCA) is popular because of its simplicity and it does not require prior knowledge. However, the used of PCA is limited to stationary data. This work proposes a methodology to address this limitation. It consists of applying Nuisance Attribute Projection (NAP) in the preprocessing stage before the fault features are transformed with PCA to remove the nonstationarity effects due to the variable operating conditions. The proposal is evaluated to detect inter-turn short-circuits in the stator of a Permanent Magnet Assisted Synchronous Reluctance Motor (PMaSynRM) used in the powertrain of electric vehicles. The variances of the phase currents, computed in moving windows, are used as fault features. The results, obtained with seven fault severities and three load conditions, show that monitoring the Hotelling$T^{2}$in the principal subspace leads to good performance, with probabilities of missed detection and false alarms lower than 0.02 and 0.05, respectively. To provide a safety metric, an estimate of the fault level is obtained with an analytical model of the evolution of the slope of the CUmulative SUM decision function with an accuracy greater than 97%.

This paper presents a fast and efficient fault isolation method in 7-phase electrical machines based on the phase currents projections in the stationary reference frames. The study considers both non incipient faults with 15% to 30% fault severities, and incipient ones whose severities vary 1% to 6%. The noise level effect on the fault isolation is also considered. The fault features are extracted from the transformed currents in the frequency domain. The features are processed with a multi-step classification methodology based on usual techniques (principal component analysis, linear discriminant analysis and support vector machine). The simulation results show that the fault classification under low noise level conditions is effective with an accuracy higher than 98%. However, when the noise level increases, the proposal fails to classify incipient faults.

Recently, the Local Mahalanobis Distance (LMD) technique was proposed for incipient fault detection, which was shown to be sensitive, robust and distribution assumption-free. Further, this paper explicitly establishes the relation between fault severity and LMD index to take advantage of those excellent characteristics for fault severity estimation. The performance of the estimation model is evaluated based on a benchmark case of Continuous-flow Stirred Tank Reactor (CSTR) process, which shows a high accuracy even for tiny deviation of signal and large signal-to-noise ratio.

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This work proposes a diagnosis method based on mutual dimensionless indices (MDIs) and receiver operating characteristic (ROC) analysis for the detection of rolling bearing faults, which is of great importance to maintain the functionality of rotating machines. The proposed method consists of five steps. Firstly, the mutual dimensionless technique is used to extract five MDIs from the raw vibration signal. Secondly, the principal components analysis (PCA) is employed to reduce the five MDIs to a one-dimensional feature. Thirdly, we obtain the areas under the ROC curve (AUC) and associated variances using two sliding windows along the one-dimensional feature sequence. Fourthly, the potential fault occurring time is estimated via comparing the AUC and the associated variances with the corresponding detection thresholds. Finally, a parameter K is introduced to delete the false alarms, and then the predicting fault occurring time is chosen from the local extrema of the potential fault occurring times. Experimental results demonstrate that our proposed approach is capable to detect fault occurring time with high accuracy and a low false-positive rate.

Demand for power quality analysis in industrial networks has increased in recent years. Voltage sags are the most frequent and impactful disturbances, with especially high financial implications for industrial clients. Understanding the underlying causes behind voltage sags is a first step towards a mitigation solution. In this paper, we propose a voltage sag cause identification algorithm based on instantaneous symmetrical components and dynamic time warping applied to voltage and current measurements. Short-Time Fourier Transform and Fortescue transform are implemented in the pre-processing stage, obtaining a four-dimension time series signature. Then, a simple but effective multivariate time series classification approach is used. It is based on 1-Nearest Neighbor classifier and dependent Dynamic Time Warping as distance measure (1NN-DTWD). The main advantages of the proposed method are the electrical interpretability of the signatures and the reduced size of the training data. A classification accuracy of 100% is reached with synthetic data, representing seven voltage sag sources. The method reaches a classification accuracy ratio higher than 98% with a reduced real dataset representing five event classes.

Incipient fault diagnosis is an important and challenging issue in academic and industrial communities but got insufficient attention. Recently, the local Mahalanobis distance was proposed and applied to incipient fault detection, which is shown to be effective for non-linear data and sensitive to incipient faults. However, this method's performance degenerates when training samples contain outliers. To cope with this issue, we propose robust healthy domain approximation based on a specific anchors-generating algorithm to improve the local Mahalanobis distance calculation. Simulation results show that the new proposed anchors-generating algorithm can significantly avoid the interference caused by outliers and then develop a performed healthy domain approximation for a more accurate fault detection procedure. The comparison result between our proposal and other one-class classification methods highlights the efficiency of the proposed solution for incipient fault detection.

Interleaved DC-DC converters are prevalent in many applications like wind turbine systems, photovoltaic energy systems, and hybrid electric vehicles, for their characteristics of high conversion efficiency and low current ripple. Motivated by the increasing requirement of system reliability, fault diagnosis and tolerant strategies for this topology have become a topic of concern. Throughout the present works in this topic, single-phase fault is mainly discussed, which does not cover all the potential scenarios of a system. Furthermore, most methods are based on a certain number of phases structure, leading to a restricted generality. To solve the above problems, this paper proposes an open-circuit fault diagnosis method for interleaved DC-DC converters with any phases number. Without using additional sensors, the method sharing signals with a control unit can detect faults and locate more than one faulty phases. Simulation and experimental results based on a four-phases interleaved DC-DC converter confirm the effectiveness of the method.

Incipient fault detection plays an essential role in the system's health monitoring and condition maintenance. However, incipient faults will not cause obvious changes in the system parametric information, they tend to cause slight modifications in their data distributions. In high noise level environment, the slight changes caused in the fault features can be masked by the noise information. Thus, obtaining an efficient incipient fault detection in high noise level environments is more tricky. In the literature, it is proved that the traditional statistics methods such as the four statistical moments, the Hotelling's T2and Square Prediction Error (SPE) which focus on detecting the changes in the parameters of the data distribution can't well address the incipient fault detection problem in a high noise level environment. These last years, the Probability Density Functions (PDF)-based distance measure algorithms and the Cumulative Density Functions (CDF)-based ones with good advantages in measuring slight differences of data distributions have shown their potential in fault detection for incipient fault. In this paper, addressing the incipient fault detection of the multivariate system in a high noise level environment, we evaluate the detection performances of several widely used PDF-based and CDF-based methods in the principal component analysis (PCA) framework. Their advantages and limitations are shown and comparatively discussed.

The diagnosis (Detection, Estimation and Isolation) of incipient faults, i.e. faults with severity variation2statistics. The fault estimation performances validates the theoretical modeling for incipient faults in noisy environments. An estimation error lower than 3% is obtained even for a Signal to Noise Ratio (SNR) as low as 25dB.

Bearing early fault detection and diagnosis (classification, estimation, ...) is a key issue in Condition Monitoring (CM) of rotating machinery. In this context, we propose in this paper a multi-fault classification comparison between traditional Support Vector Machine (SVM) solutions and wavelet SVM (WSVM). For this work several kernel and wavelet functions were considered in the Kullback Leibler Divergence (KLD) framework. First, Empirical Mode Decomposition (EMD) is employed to preprocess vibration signals acquired from the rolling bearings elements. Second, a specific statistical analysis study is performed to select the most salient components from the different obtained Intrinsic Mode Functions (IMFs). Then, the KLD of the retained IMFs is calculated to carry out the classification of three bearing ball fault severities for several operating conditions. Thanks to four criteria, namely the classification accuracy rate average (ARA), the support vector average (SVA), the training time (Trt) and testing time (Tst), our results are derived to highlight the technique allowing to obtain the better results.

The nondestructive crack detection is an important issue in industrial engineering. However, the detection of incipient cracks that can cause non obvious changes in the conductive material impedance map is difficult. In our paper, we propose a new method based on wavelet and Jensen-Shannon divergence in the framework of Noisy Independent Component Analysis (NICA) to address this problem. The source signals with fault features are obtained by the application of the Independent Component Analysis regarding the noise. Then, the wavelet decomposition is considered as the denoising method to partially reduce the noise influence. The Jensen-Shannon divergence(JSD) which has been proved as an efficient incipient fault detection algorithm in previous works is used here for incipient crack detection. The detection performances of the proposed method is compared with the ones obtained with the Kullback-Leibler divergence often proposed in the literature.

The high penetration of Wind Turbine (WT) in the grid is a promising solution to increase the electricity production with renewable energies. In this work, we propose a data-driven methodology for dip voltage fault detection and diagnosis. From experimental measurements the current vector trajectory deformation in the (αβ) reference frame is derived and a statistical-based analysis (first four statistical moments) of two relevant features are extracted (the ratio between the two axis and the rotation angle) is conducted. Thanks to this ratio, the method is robust to load variations. The fault isolation is done accurately with the analysis of the shift angle. The fault detection performances are evaluated with the ROC curves that reveal a probability of detection equal to 1 and a null probability of false alarm.

In this paper we develop a fault detection and isolation method based on data-driven approach. Data-driven methods are effective for feature extraction and feature analysis using statistical techniques. In the proposal, the Cumulated Sum (CUSUM) efficiency is explored for incipient fault detection. The fault is assumed to be a Gain variation, an Offset evolution, a Phase shifting or one of the multiple possible combination of such faults. A first preprocessing stage is proposed for this study and using some statistical other features we proceed to the operations of a Fault Detection and Diagnosis process: Detection, and Isolation. For the detection, the CUSUM efficiency is proved. For the isolation, we propose a specific algorithm based on the combination of several multivariate statistical techniques such as Support Vector Machines (SVM) and Linear Discriminant Analysis (LDA). The classification of each fault or one of their combination is accurately obtained. The results show that for incipient faults (<;10%), the fault detection and isolation is accurate with a relative classification error lower than 3%.

In this paper, we propose line current sensor fault detection for AC drives. The method is based on the measured currents and the features are extracted either in the natural reference frame or in the transformed Park synchronous rotating frame. The features are the first four statistical moments or the Kullback Leibler Divergence (KLD) of the Probability Density Functions (PDF). For offset fault, we show that if the offset is higher than 3% of the current amplitude, the mean value is the most relevant value among the first four statistical moments that leads to good detection performances (low probability of false alarm and low probability of miss detection). But for incipient faults (offset ranging from 1 to 2%), even the projection in the transformed Park reference frame cannot improve the fault detection. For these cases, we show that the fault information can be retrieved using the PDF and the KLD. This is confirmed by the results showing that the fault is detected with 100% probability of detection.

This paper addresses the estimation of a permanent magnet synchronous machine mechanical position and speed estimation at low speed and standstill. The method is based on the injection of an additive voltage at High Frequency (HF), which exploits the position dependency to the magnetic saliency. Unlike the usual HFI method, this estimator has a simple structure with only one filter. The simulation results prove the efficacy of the estimation under no load and with a load torque in the low speed region and at standstill. The mechanical position estimation errors are lower than 0.035rad (2°).

This paper proposes a data driven approach for dip voltage fault detection and identification using the grid current vector trajectory in the stationary reference frame. Three features are extracted for the different operating conditions to build the database and analysed using Linear Discriminant Analysis to identify the fault type and subtype. In the subspaces spanned by the factorial components the four faults and eight out of nine faults subtype are successfully identified and isolated with an error rate less than 5%. Simulation results prove the efficiency of the proposed algorithm.

Due to the increasing requirements of safety and reliability in more electrified applications (transportation for example), fault detection and diagnosis (FDD) of electrical systems has become a hot research topic. In the process of FDD, there are three steps: fault detection, fault isolation and fault estimation. The first two items are the commonly addressed while the last one is less tackled as it requires the development of a fault model which parameters are relevant of the fault. In this paper, we propose an analytical model of multiple fault effects on a three phases electrical system. The model is based on the expressions of the currents in the (d,q) or Park synchronous rotating reference frame. We prove through simulation results the efficiency of the model for fault combination of gain, offset and phase shift. The results show also the accuracy of the model that could be used for fault estimation purpose.

In this paper, a current sensor fault estimation using the transformed currents in the Park synchronous rotating frame is proposed. We show that from an analytical model, the fault characteristics can be retrieved. From experimental raw data collected from a Permanent Magnet Synchronous Machine drive, the gain or offset fault characteristics (amplitude and frequency) have been estimated with an average error of 10%. For incipient fault, despite the analytical model, the estimation might be tedious because the fault is concealed by the noise. In this case the Kullback-Leibler Divergence between two Probability Density Functions can be computed and the fault estimated from the value of the divergence. If the distributions are Gaussian, the closed form of the divergence allows the fault estimation. However even if the data are not perfectly Gaussian-distributed, the closed form can still be used despite an overestimation of the fault characteristics that is preferable as it is a safety margin.

This paper is a contribution to the detection and characterisation of small cracks using Eddy Current Testing in the Non Destructive Evaluation framework. Small cracks are considered as incipient faults defined as gradual faults whose signature is weak and concealed by the noise. They are characterized by high signal to noise ratio and low fault to noise ratio. The detection and diagnosis of such faults is still an open challenge. For complex systems, model-based incipient fault detection and diagnosis (FDD) methods usually fail because of the inaccuracy of the model to describe all the phenomena and their interactions. Data-driven methods using statistical features are very promising as long as historical data are available. However in the case of incipient faults, there is not a significant variation of a single feature. The fault signature lies in the global variation of the signal properties. The proposed method relies on the Kullback-Leibler Divergence (KLD) as a nonparametric fault indicator. It measures the slight dissimilarities between the probability density functions of the current signal compared to the faultless or healthy one. Through experimental results, the KLD exhibits a higher sensitivity than the usual statistical features for the detection of small cracks (with dimensions in the order of 0.1 mm) realized in a nickel-based superalloy plate. Moreover, the detection is done with zero missed detection probability. Furthermore, the fault severity is assessed through the characteristics of the crack (surface, length, and depth). In the principal component analysis framework, the analysis of four statistical features (KLD, mean, variance, and maximum) dependency to the excitation frequency allows to discriminating among the cracks.

This paper proposes a new method based on multiple thresholds for automatic extraction of blood vessels specially from a low contrast and non-uniformly illuminated background of retina. Curvelet transform is used to extract the finest details along the vessels since it can represent the lines, the edges and the curvatures very well. Next matched filtering is done to intensify the blood vessels' response in the enhanced image. The multiple threshold values for the maximum matched filter response that maximize the fuzzy entropy are considered to be the optimal thresholds to extract the different types of vessel silhouettes from the background. Differential Evolution algorithm is used to specify the optimal combination of the fuzzy parameters. Performance is evaluated on publicly available DRIVE database and is compared with the existing blood vessel extraction methods. Simulation results demonstrate that the proposed method outperforms the existing methods in detecting the long and the thick as well as the short and the thin vessels.

Usually, bearing faults are diagnosed by the search of bearing characteristic frequencies in the spectrum of current or vibration signals. This local approach, even efficient, has the drawback of requiring the a prior knowledge of these frequencies. Moreover, characteristic bearing frequencies are only a part of the global spectral signature induced by natural bearing damages. In real situations, a fault on a particular bearing element may not produce the corresponding characteristic frequency. Several multiple harmonics of this frequency and sidebands related to their modulations by rotational frequencies can be quite dominant. An effective diagnosis should rather consider the global fault signature. Based on the fact that the global information encoded in the frequency domain is usually descriptive enough to diagnose and classify bearing faults, the present work proposes a classification scheme for bearing conditions which does not require the characteristic frequencies to be known or estimated. The method combines the envelope analysis, the sliding Fast Fourier Transform (FFT) technique and Principal Component Analysis (PCA). The application on experimental data shows that bearing faults can be diagnosed and classified accurately and without overlapping, irrespective of the system operating point. The extracted spectral features are informative enough to discriminate between different conditions of bearing.

Process-history based methods are very commonly used for fault diagnosis and detection. However their efficiency is closely related to the quality of the measured data. In noisy environments, they usually fail particularly for incipient faults. This paper is an attempt to determine an analytical model allowing to estimate a theoretical threshold for fault detection based on the Fault to Noise Ratio (FNR). This model is developed using the Kullback-Leibler Divergence (KLD). For feature extraction, the used data are previously processed through Principal Component Analysis (PCA). The model is validated with simulated data and the results are so far very encouraging.

This paper proposes an optimal algorithm that minimizes watermark power (hence embedding distortion) subject to meeting the strict data hiding rate constraint in presence of joint additive noise and random gain attack. The proposed algorithm approaches such problem using convex optimization framework and gets the solution for watermark power and host sample allocation. This offers an optimality in terms of embedding distortion-robustness-data hiding capacity with polynomial computation complexity. Simulation carried over convolution coded integer wavelet coefficients on compressed host image show that ~ 4.5 to ~ 3 times less normalized watermark power is required in the proposed system. This leads to an improvement of ~ 10 dB in document- to-watermark ratio over direct embedding on entropy coded data. Simulation results also show that an improvement in bit error rate of 10-2is achieved over fixed memoryless attack channel.

In fault diagnosis studies two main approaches are mostly used. The first one consists in designing the full physical or empirical model of the system in healthy and faulty conditions. The major drawback of this approach is the difficulty to obtain an accurate model reflecting all the operating conditions and phenomena. The second approach, used in this work, consists in using signal processing techniques for the characterization of the healthy and faulty behaviors. This paper deals with the study of a fault detection and isolation procedure on a three phase inverter feeding an induction machine drive using pattern recognition techniques. The diagnosis procedure relies on the use of classifiers after the collection of the output currents of the inverter flowing in the machine windings. The proposed classifiers are based on Support Vector Machines (SVM). We show in this paper how it is possible to tune the SVM and also the influence of the data normalisation to perform an effective diagnosis with experimental data.

Fault Detection and Isolation (FDI) based on Principal Component Analysis (PCA) is achieved through the construction of control charts. Control charts differ, primarily, by the subspace into which they were defined, namely, the principle and the residual subspaces. Abnormalities are detected in the plotted monitoring chart if the confidence limit is violated. Often, the Hotelling's T2control chart, defined in the principal subspace, is applied for process monitoring. But to detect a fault with the T2chart, it must cause significant changes in the principal subspace, because little disturbances may be hidden by the large amount of variabilities present in the principal subspace. In this paper, we propose to use the Kullback-Leibler divergence, a probabilistic measure taken from information theory, as a diagnosis criterion. We show the efficiency of this criterion for which we find that small faults which might not be detected by the Hostelling test, become detectable without ambiguity. The simulation results show a significant improvement in the fault detection.

This paper proposes a data hiding scheme to serve dual purpose of quality access control and error concealment of digital images. This is accomplished by projecting host image first on N-mutually orthogonal sample sets followed by embedding of an encoded binary watermark (host digest) using quantization index modulation (QIM) but without complete self-noise suppression. It is well known that due to insertion of external information, there would be degradation in visual quality of the host image. This has been used here to play the key role in access control through reversible process and error concealment using the extracted image digest. Decision variable for each bit of watermark decoding is formed from the weighted average of N-decision statistics that increases the correctness of extracted watermark bits. This improved detection enables self-noise suppression by authorized user, error concealment in fading radio mobile channel and thus leads to avail better quality image. Simulation results have shown the validity of our claims along with relative comparative results for other existing works.

The Spread Transform (ST) robustness facing a Temporal Frame Averaging (TFA) is studied in this paper. Our analysis provides new insights on the effect of the TFA attack in the context of video watermarking when the ST is used. To remove the interferences and the attenuation of the watermark caused by the TFA attack, an adaptation of the Spread Transform is proposed. Our solution is based on the embedding of the watermark thanks to different orthogonal directions and by exploiting the temporal diversity of the video signal, i.e. the message is spread over several video frames. Finally, we show that the robustness and decoding performances are close to the ones before the attack.

In this paper, security evaluation of an important watermarking class based on quantization is given. Theoretical developments and practical simulations are used to measure the security level of watermarking techniques. We give the contribution of each observation available to the attacker on the total gathered information about the watermarking secrecy. By leading on watermarking technique weaknesses, we find that using the Quantization Index Modulation (QIM) with continuous secret key is equivalent to using a secret key with two states. The latter is easier to estimate than a continuous key. Then, we propose a secure version of a classical trellis coded quantization watermarking. The security is guaranteed thanks to the trellis path generated from the discrete key and the message. We show that the spread transform can represent a second or alternative security level for watermarking systems. It allows to increase the watermarking security level and to keep the embedded message hard to read for unauthorise user.

The quantization based embedding systems are usually used in the information hiding domain, thanks to their efficiency and simplicity. In other hand, they are known to be insecure in steganography context (according to Cachins' security definition) because they distort the stego-signal density function. In this paper, we show that an important kind of quantization based systems (those resulting from the combination with the spread transform and classical data hiding schemes based on quantization ) preserve the probability density function of the stego-signal. We prove the undetectability theoretically and show how the spread transform makes the stego-message statistically non-dectectable in the real case.

The steganographic security in the Cachin's work is defined as the statistical invisibility between the host signal and its marked version. At contrary, the robustness to an attack is not a prime goal. In robust watermarking, this is exactly the inverse. The scalar costa scheme (SCS) is a typical example of this fact. Indeed, this scheme is robust to additive white Gaussian noise (AWGN) attack but is drastically insecure since its probability density function for Gaussian host signal is severely discontinuous. An improved scheme has been proposed by Guillon et al. which increases the security to the detriment of the robustness. In this paper, we propose a new watermarking scheme, based on the combination of the spread transform (ST) and the trellis coded quantization (TCQ) which is secure and robust to AWGN attack.

Several authors have studied stego-systems based on Costa scheme, but just a few ones gave both theoretical and experimental justifications of these schemes performance in an active warden context. We provide in this paper a steganographic and comparative study of three informed stego-systems in active warden context: scalar Costa scheme, trellis-coded quantization and spread transform scalar sosta Scheme. By leading on analytical formulations and on experimental evaluations, we show the advantages and limits of each scheme in term of statistical undetectability and capacity in the case of active warden. Such as the undetectability is given by the distance between the stego-signal and the cover distance. It is measured by the Kullback-Leibler distance.

In this paper, we propose an audio watermarking scheme based on the scalar Costa scheme specifically calibrated with a perceptual model allowing to increase the embedding power. For our study, this scheme is designed to be efficient for low bit-rate embedding with sufficient robustness to channel degradations. We present here the main characteristics of our scheme and the way for introducing perceptual models in such a Costa based watermarking scheme without introducing any noticeable artifacts. An evaluation of the robustness of the embedding system is also theoretically discussed by the way of the main channel attack : additive noise from low to high level. We illustrate its relevance in practice using Monte Carlo simulations.

Using electronic watermarks as copyright protection for still images requires robustness against attacks. In this paper we propose a watermarking scheme that is robust to rotation, scaling and translation (RST) distortions. The watermark is embedded in a 1D invariant domain that is a projection of the polar Fourier transform. Roc curves depicting false positives versus detection probability of the watermark are provided, under various geometrical attacks and JPEG coding.

In the field of smart sensors new applications named electronic noses are now developed and used for environmental air quality control. In our case we are developing such an application based on a tin oxide gas sensor array for the main detection of two gases : a refrigerant gas Forane 134a (Hydro fluorocarbon) and a carbonic gas. Due to the high sensitivity to humidity observed for these types of sensors, we study here the ability of our system to well discriminate the target gases and also their concentrations whatever the relative humidity rate in a wide range. By using a multidimensional pattern recognition method (Discriminant Factorial Analysis) these learning process results are presented and the created decisive laws are used to successfully identify unknown cases.