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Acoustical Surveillance of Industrial Plants: an Approach Using Neural Networks
Copyright
ACOUSTICAL SURVEILLANCE OF INDUSTRIAL PLANTS: AN APPROACH USING NEURAL NETWORKS P. Degoul and A. Lemer Thomson SinJra ASM. 1 avenue Aristide Briand. 94117 Arcueil Cedex, France
Abstract: The exploitation of industrial processes makes more and more frequently use of on-line surveillance techniques in order to early detect any malfunction and to give a diagnosis . A general surveillance approach which can be used for acoustical or vibratory signatures is proposed. This approac h is decomposed into two stages, the preprocessing stage and the decision stage, and makes use of advanced signal processing techniques, neural networks , and knowledge based system . As an illustration, the acoustical surveillance of transient noises of an industrial process is presen ted . Key words: Acoustical surveillance, industrial production proce ss, failure detection, diagnosis, signal processing, neural nets, artificial intelligence.
1. INTRODUCTION: The exploitation of industrial processes makes more and more frequently use of on-line surveillance techniques in order to maintain the service safety of production devices. The objective of the surveillance systems is to control a machine or a set of machines, in order to early detect any malfunction or incident, and sometimes to give a diagnosis . Generally, sensors are disposed on the system to be controlled, and provide data which hold the information on the state of the system. Various types of sensors are used depending on the system to be controlled. Quite often, measurements are: temperature, pressure, delivery ... Presently, vibratory measurements are commonly used, and more recently, surveillance relying on acoustical measurements is the subject of a significant number of research works. Unfortunately, it is often difficult to detect a malfunction from the raw behaviour of physical measurement such as pressure, vibrations, acoustics ... Moreover, the measurement evolution can be due to the possible coming out of an incident, but also to the natural evolution of the process . So, natural evolution of the process can provide a significant rate of false alarms. In order to perform a reliable surveillance system, it is necessary to develop new concepts.
ral networks or knowledge based systems in order to take the decision: the detection of the incident, and, if necessary, the diagnosis of the malfunction. In this paper, we first describe how signal processing methods can provide relevant descriptors from raw signals . Secondly, advanced tools which allow to reach a decision are described , with emphasis on neural networks . Finally, as an illustration of the use of these tools, recent researchs on the specific subject of acoustical surveillance of industrial system are presented .
2. PREPROCESSING STAGE: It is now well known that signals from physical measurements like vibrations , or acoustics, have to be processed to give relevant informations on the state of the physical system. In the field of surveillance, the objective of signal processing methods is double. On the first hand, these methods should be able to enhance specific features or parameters that can be efficiently used to take the decision . On the other hand, signal processing methods should be able to reduce the input data flow, the raw signal being replaced by a few number of parameters. So, providing a reduced number of relevant parameters is the dual condition to reach in the preprocessing stage, in order to achieve good results in the decision stage.
The general approach that is proposed to realize the surveillance can be decomposed into two stages (see Fig. 1). The first one is the preprocessing stage which performs a parameters extraction from the raw signal. Relying on the underlying signal nature and on the malfunction to be detected, advanced signal processing methods are used to extract from the raw signal a relevant set of parameters or descriptors . In the second stage, called the decision stage, the previous set of parameters is processed through decision tools such as neu-
In order to realize such a parameter extraction, it is necessary to use signal processing methods dedicated to the expected nature of the signal and to the malfunction to be detected . So, we have developed an easy-to-use library of specialized signal processing methods. These methods enable to describe the signal by different representations: - the time representation by the amplitude evolution or energy evolution of the signal (or evolution of higher order statistics);
357
can be translated into rules which are used by a knowledge based system in order to automatically take the decision .
- the frequency representation by Fourier analysis, - the time-frequency representation with long time analysis (LOFAR analysis), short time analysis (short time Fourier transformation, Wigner- Vi lie transformation) , or with octave frequency decomposition (constant Q analysis); - the time-scale representation by Morlet wavelet decomposition, or the orthogonal wavelet decomposition; - the modulation representation by cesptral analysis, envelop analysis, or spectral correlation method . Although these techniques, called non-parametric methods, do not reduce directly the input data flow, they give rise to representations where a few specific features can be easily measured: for example, broad or narrow band energy, time vs frequency shape, time vs scale energy distribution, modulation rates . .. Other techniques, called parametric methods, enable through modelling, direct measurements of a few model parameters, thus efficiently reduce the data flow. We currently use time or frequency representations by AR (autoregressive) modelling, Pisarenko modelling, or Prony modelling, and time-frequency representations by adaptative or evolutive AR modelling.
However, it is often difficult to model by a conscious reasoning the way to provide a decision from the different parameters. In this case, an elegant solution is to process the set of parameters by means of supervised methods of classification or discrimination. The use of these methods implies that a great amount of data has been recorded from the sensor, both data recorded in a normal working of the industrial process and data recorded during a malfunction or a failure of a machine. The usual approach in supervised classification is to partition the available set of patterns into a learning subset and a generalization (or testing) subset. The learning subset is used to fit a classification function (i.e. a function associating a given example to its belonging class) by the means of an algorithm. The efficiency of this estimated function is tested on the generalization subset examples leading to a a confusion matrix. There exist a lot of supervised methods including both classical statistical methods or neural networks. In order to easily compare the main discrimination techniques on a given application, we have developed an evaluation software which includes both classical methods such as main composant analysis, Fisher discriminant analysis, dynamic clouds, k-nearest neighbours, linear gaussian discrimination, and neural networks such as multilayered perceptron with gradient backpropagation, second order networks, high-order-of-polynomialinput network, Copper algorithm, Kohonen maps, Parzen windows . . .
Efficient use of these techniques implies an a priori knowledge of the underlying signal nature. For example: - stationary spectral lines can be processed by Fourier analysis or Pisarenko modelling; - stationary wide-band noises by Fourier analysis, or AR modelling; - non-stationary spectral lines (spectral lines evolving in time) by LOFAR analysis; - harmonic spectral lines due to modulations by cepstral analysis, - wide-band modulated noises by spectral correlation method; - short duration or transient sounds such as shocks , clicks , by time-frequency analysis, timescale decomposition , AR modelling (both in adaptative or evolutive versions), or by Prony modelling for resonant shocks.
4. AN APPLICATION: As an illustration of the use of these tools, we describe now an example of acoustical analysis of transient noises recorded in an industrial process (Degoul et al, 1992). The considered process is a vacuum pump system with different equipments: electric motors, water pump, fan system .. . In such an industrial process, various transient noises can be heard, both in correct working conditions (water gate openings , modifications of the working state .. . ), and during malfunctions (cavitation and loose parts in pipes, unexpected working of rotating machineries or of driving belts ... ). In order to control the various transient noises, it is necessary to automatically detect and classify each noise. The energy of transient sounds is often insufficient to identify their nature. Relying on the fact that a human person can recognize transient noises simply by listening them, we have developed a system using the previous tools . The system works in two successive stages: - a preprocessing stage which performs both an
Lastly, efficient use of these techniques also implies a good knowledge of their robustness vs signal to noise ratio.
3. DECISION STAGE: Once a relevant set of parameters, called a pattern, has been extracted from the raw signal, it is necessary to come to a decision: to detect or not a malfunction, and eventually to give diagnosis elements. Sometimes, it is possible to make a simple reasoning based on the different parameters of the set in order to come to a decision . The reasoning
358
ceptron with gradient backpropagation algorithm (Rumelhart and Mac Clelland, 1986).
early detection of the transient sound from the noise, and a parameters extraction on each isolated transient, - a classification of the transient which enable to take a decision. Three shocks classes have been considered. Firstly, two classes have been simulated, which can occur during an incident: shocks from the vacuum pump (class 1), shocks from the protection carter of a belt system (class 2). A third class is composed of shocks recorded during the normal working of the water pump (class 3). The last class corresponds to the ambient noise (class 4), and is useful to invalidate false alarms of the early detection stage. The system decision can be: there is no transient noise (no detection or class 4), or there is a transient noise, but it is typical of the normal working of the process (class 3), or there is a transient noise typical of a specific malfunction (classes 1 and 2).
Obviously, classification performances depend on the patterns used for the training phase and those used for the testing phase. In order to obtain reliable results, we have carried out, for each classification method, 50 experiments with random selections of the training and testing subsets. Results from various methods are presented on Fig. 2. Performances are good on the whole, and neural nets show better performances than classical methods. In order to give more details, the confusion matrices of the multilayered perceptron, which is the best performing method, are presented (see Fig. 3) . Results are good for each class (recognition rate between 89% and 100%). The class of the" clicks" recorded on the water pump is the most difficult to identify, probably because this class is less homogeneous.
The early detection is realized in two steps. Firstly, a noise cancelling is performed on the raw signal. The AR filter modelling the ambient noise is estimated, and the raw signal is filtered by the MA (moving average) filter equal to the inverse of the previous AR filter. Secondly, the early detection is based on an energy detection which first makes a rough estimation of the residual surrounding noise and according to a signal to noise ratio threshold, locates the impulse occurences . After the early detection, signal parts corresponding to impulse locations are processed in order to describe each transient sound by a limited set of relevant parameters. To do so, two complementary signal processing techniques have been chosen: the AR modelling and the Daubechies wavelet decomposition. AR analysis is performed by the Levinson algorithm (Kay, 1988) with a filter order equal to 10, and provides 10 predictor coefficients (or partial correlation coefficients). The wavelet analysis is done using the Daubechies orthogonal wavelets (Daubechies, 1988), and according to the Mallat algorithm (with a decomposition depth of 5)(Mallat, 1989), which supplies 10 parameters related to the energy of the analysed signal at different steps of the multiscale decomposition. Four parameters corresponding to a rough histogram of the wavelet decomposition coefficients are also used. By the end of the preprocessing stage, each transient sound is described by a pattern of 24 parameters.
5. CONCLUSION: In the field of surveillance of industrial plants, we propose a general approach which is composed of two stages: the preprocessing stage, and the decision stage. In order to realize these two stages, different classes of tools can be used, such as advanced signal processing methods, neural nets, and knowledge based system. It is obvious that the efficiency of future surveillance systems should rely on the complementary use of these various techniques.
Acknowledgement: This work has been partly supported by ELECTRICITE DE FRANCE under contract EDF P65L01/1F8221/EP 507.
Reference: - Barron, R.L. (1975). Learning network improve computer-aided prediction and control. Computer Design, 65-70. - Daubechies, I. (1988). Orthonormal bases of compactly supported wavelets. Comm. Pure and Applied Math., 41,909-996. - Degoul, P., A. Lemer, L. Schwab, P. Bernard, and C. Duvermy (1992). Surveillance acoustique en milieu industriel: une approche par classification hierarchisee. In: Recent Advances in Surveillance using Acoustical and Vibratory Methods (Ed. Societe Fran~aise des Mecaniciens), pp. 409-419. - Kay, S.M. (1988). Modern Spectral Estimation: Theory and Application. Prentice Hall, Englewood Cliffs . - Mallat, S.G. (1989). A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Analysis and Machine Intelligence, 11(7) ,674-693. - Rumelhart, D.E. and J .L. Mac Clelland (1986). Parallel Distibuted Processing. MIT press, London .
In the decison stage, various classification algorithms have been tested, both classical techniques such as dynamic clouds, k-nearest neighbours, and neural nets such as the HOPI (High Order of Polynomial Input) which is a multiclass version of a discrimination method called ALN (Adaline like network)(Barron, 1975), and the multilayered per-
359
-
Raw Signal
Preprocessmg Stage
Set of Parameters
Dec l Slon Stage
~
Incldent detection or Diagnos;s
Figure 1 : General surveillance approach
~Iethod
Training phase
Testing phase
MultilayerecLPerceptron
99 .6% (± 0 .2%)
97.3% (± 0.5%)
High_Order_PolynomiaUnput
99.8% (± 0.1%)
96.7% (± 0.7%)
K-NearesLNeighbours
D69% (± 0.4%)
94 .6% (± 0.6%)
DynamicClouds
!liA% (± 0.6%)
93.8% (± 0.7%)
Figure 2 : C lassification results
Class
Confusion matrix
Size
1
20
(25 .0%)
100.0
(± 0.0)
0 .0
(± 0.0)
0.0
(± 0.0)
0.0
(± 0.0)
2
20
(25.0%)
0.0
(± 0.0)
100.0
(± 0.0)
0.0
(± 0 .0)
0.0
(± 0.0)
3
20
(25.0%)
0.2
(± 0.3)
l.3
(± 0.6)
98 .2
(± 0.7)
0.3
(± 0.3)
4
20
(25 .0%)
0.0
(± 0.0)
0.0
(± 0.0)
0.0
(± 0.0)
100.0
(± 0.0)
Training mean rate : 09.6% (± 0.2%) Class
Size
(50 trials)
Confusion matrix 100 .0
(± 0 .0)
0.0
(± 0.0)
0.0
(± 0.0)
0.0
(± 0.0)
(36.0%)
lA
(± 1.0)
08 .2
(±l.l)
0.4
(± 0.3)
0.0
(± 0 .0)
20
(18.0%)
0.0
(± 0.0)
1.0
(± 1.2)
89 .2
(± 1.9)
6.8
(± 1.5)
20
(18 .0%)
0.0
(± 00)
0.0
(± 0.0)
0.6
(± 0.5)
99,4
(± 0 .5)
1
31
(27 .9%)
2
40
3 ·1
Testing mean rate : 07.3% (± 0.5%)
(50 trials)
Figure 3 : Confusion matrices fo r the multilayered perceptron method
360
ACOUSTICAL SURVEILLANCE OF INDUSTRIAL PLANTS: AN APPROACH USING NEURAL NETWORKS P. Degoul and A. Lemer Thomson SinJra ASM. 1 avenue Aristide Briand. 94117 Arcueil Cedex, France
Abstract: The exploitation of industrial processes makes more and more frequently use of on-line surveillance techniques in order to early detect any malfunction and to give a diagnosis . A general surveillance approach which can be used for acoustical or vibratory signatures is proposed. This approac h is decomposed into two stages, the preprocessing stage and the decision stage, and makes use of advanced signal processing techniques, neural networks , and knowledge based system . As an illustration, the acoustical surveillance of transient noises of an industrial process is presen ted . Key words: Acoustical surveillance, industrial production proce ss, failure detection, diagnosis, signal processing, neural nets, artificial intelligence.
1. INTRODUCTION: The exploitation of industrial processes makes more and more frequently use of on-line surveillance techniques in order to maintain the service safety of production devices. The objective of the surveillance systems is to control a machine or a set of machines, in order to early detect any malfunction or incident, and sometimes to give a diagnosis . Generally, sensors are disposed on the system to be controlled, and provide data which hold the information on the state of the system. Various types of sensors are used depending on the system to be controlled. Quite often, measurements are: temperature, pressure, delivery ... Presently, vibratory measurements are commonly used, and more recently, surveillance relying on acoustical measurements is the subject of a significant number of research works. Unfortunately, it is often difficult to detect a malfunction from the raw behaviour of physical measurement such as pressure, vibrations, acoustics ... Moreover, the measurement evolution can be due to the possible coming out of an incident, but also to the natural evolution of the process . So, natural evolution of the process can provide a significant rate of false alarms. In order to perform a reliable surveillance system, it is necessary to develop new concepts.
ral networks or knowledge based systems in order to take the decision: the detection of the incident, and, if necessary, the diagnosis of the malfunction. In this paper, we first describe how signal processing methods can provide relevant descriptors from raw signals . Secondly, advanced tools which allow to reach a decision are described , with emphasis on neural networks . Finally, as an illustration of the use of these tools, recent researchs on the specific subject of acoustical surveillance of industrial system are presented .
2. PREPROCESSING STAGE: It is now well known that signals from physical measurements like vibrations , or acoustics, have to be processed to give relevant informations on the state of the physical system. In the field of surveillance, the objective of signal processing methods is double. On the first hand, these methods should be able to enhance specific features or parameters that can be efficiently used to take the decision . On the other hand, signal processing methods should be able to reduce the input data flow, the raw signal being replaced by a few number of parameters. So, providing a reduced number of relevant parameters is the dual condition to reach in the preprocessing stage, in order to achieve good results in the decision stage.
The general approach that is proposed to realize the surveillance can be decomposed into two stages (see Fig. 1). The first one is the preprocessing stage which performs a parameters extraction from the raw signal. Relying on the underlying signal nature and on the malfunction to be detected, advanced signal processing methods are used to extract from the raw signal a relevant set of parameters or descriptors . In the second stage, called the decision stage, the previous set of parameters is processed through decision tools such as neu-
In order to realize such a parameter extraction, it is necessary to use signal processing methods dedicated to the expected nature of the signal and to the malfunction to be detected . So, we have developed an easy-to-use library of specialized signal processing methods. These methods enable to describe the signal by different representations: - the time representation by the amplitude evolution or energy evolution of the signal (or evolution of higher order statistics);
357
can be translated into rules which are used by a knowledge based system in order to automatically take the decision .
- the frequency representation by Fourier analysis, - the time-frequency representation with long time analysis (LOFAR analysis), short time analysis (short time Fourier transformation, Wigner- Vi lie transformation) , or with octave frequency decomposition (constant Q analysis); - the time-scale representation by Morlet wavelet decomposition, or the orthogonal wavelet decomposition; - the modulation representation by cesptral analysis, envelop analysis, or spectral correlation method . Although these techniques, called non-parametric methods, do not reduce directly the input data flow, they give rise to representations where a few specific features can be easily measured: for example, broad or narrow band energy, time vs frequency shape, time vs scale energy distribution, modulation rates . .. Other techniques, called parametric methods, enable through modelling, direct measurements of a few model parameters, thus efficiently reduce the data flow. We currently use time or frequency representations by AR (autoregressive) modelling, Pisarenko modelling, or Prony modelling, and time-frequency representations by adaptative or evolutive AR modelling.
However, it is often difficult to model by a conscious reasoning the way to provide a decision from the different parameters. In this case, an elegant solution is to process the set of parameters by means of supervised methods of classification or discrimination. The use of these methods implies that a great amount of data has been recorded from the sensor, both data recorded in a normal working of the industrial process and data recorded during a malfunction or a failure of a machine. The usual approach in supervised classification is to partition the available set of patterns into a learning subset and a generalization (or testing) subset. The learning subset is used to fit a classification function (i.e. a function associating a given example to its belonging class) by the means of an algorithm. The efficiency of this estimated function is tested on the generalization subset examples leading to a a confusion matrix. There exist a lot of supervised methods including both classical statistical methods or neural networks. In order to easily compare the main discrimination techniques on a given application, we have developed an evaluation software which includes both classical methods such as main composant analysis, Fisher discriminant analysis, dynamic clouds, k-nearest neighbours, linear gaussian discrimination, and neural networks such as multilayered perceptron with gradient backpropagation, second order networks, high-order-of-polynomialinput network, Copper algorithm, Kohonen maps, Parzen windows . . .
Efficient use of these techniques implies an a priori knowledge of the underlying signal nature. For example: - stationary spectral lines can be processed by Fourier analysis or Pisarenko modelling; - stationary wide-band noises by Fourier analysis, or AR modelling; - non-stationary spectral lines (spectral lines evolving in time) by LOFAR analysis; - harmonic spectral lines due to modulations by cepstral analysis, - wide-band modulated noises by spectral correlation method; - short duration or transient sounds such as shocks , clicks , by time-frequency analysis, timescale decomposition , AR modelling (both in adaptative or evolutive versions), or by Prony modelling for resonant shocks.
4. AN APPLICATION: As an illustration of the use of these tools, we describe now an example of acoustical analysis of transient noises recorded in an industrial process (Degoul et al, 1992). The considered process is a vacuum pump system with different equipments: electric motors, water pump, fan system .. . In such an industrial process, various transient noises can be heard, both in correct working conditions (water gate openings , modifications of the working state .. . ), and during malfunctions (cavitation and loose parts in pipes, unexpected working of rotating machineries or of driving belts ... ). In order to control the various transient noises, it is necessary to automatically detect and classify each noise. The energy of transient sounds is often insufficient to identify their nature. Relying on the fact that a human person can recognize transient noises simply by listening them, we have developed a system using the previous tools . The system works in two successive stages: - a preprocessing stage which performs both an
Lastly, efficient use of these techniques also implies a good knowledge of their robustness vs signal to noise ratio.
3. DECISION STAGE: Once a relevant set of parameters, called a pattern, has been extracted from the raw signal, it is necessary to come to a decision: to detect or not a malfunction, and eventually to give diagnosis elements. Sometimes, it is possible to make a simple reasoning based on the different parameters of the set in order to come to a decision . The reasoning
358
ceptron with gradient backpropagation algorithm (Rumelhart and Mac Clelland, 1986).
early detection of the transient sound from the noise, and a parameters extraction on each isolated transient, - a classification of the transient which enable to take a decision. Three shocks classes have been considered. Firstly, two classes have been simulated, which can occur during an incident: shocks from the vacuum pump (class 1), shocks from the protection carter of a belt system (class 2). A third class is composed of shocks recorded during the normal working of the water pump (class 3). The last class corresponds to the ambient noise (class 4), and is useful to invalidate false alarms of the early detection stage. The system decision can be: there is no transient noise (no detection or class 4), or there is a transient noise, but it is typical of the normal working of the process (class 3), or there is a transient noise typical of a specific malfunction (classes 1 and 2).
Obviously, classification performances depend on the patterns used for the training phase and those used for the testing phase. In order to obtain reliable results, we have carried out, for each classification method, 50 experiments with random selections of the training and testing subsets. Results from various methods are presented on Fig. 2. Performances are good on the whole, and neural nets show better performances than classical methods. In order to give more details, the confusion matrices of the multilayered perceptron, which is the best performing method, are presented (see Fig. 3) . Results are good for each class (recognition rate between 89% and 100%). The class of the" clicks" recorded on the water pump is the most difficult to identify, probably because this class is less homogeneous.
The early detection is realized in two steps. Firstly, a noise cancelling is performed on the raw signal. The AR filter modelling the ambient noise is estimated, and the raw signal is filtered by the MA (moving average) filter equal to the inverse of the previous AR filter. Secondly, the early detection is based on an energy detection which first makes a rough estimation of the residual surrounding noise and according to a signal to noise ratio threshold, locates the impulse occurences . After the early detection, signal parts corresponding to impulse locations are processed in order to describe each transient sound by a limited set of relevant parameters. To do so, two complementary signal processing techniques have been chosen: the AR modelling and the Daubechies wavelet decomposition. AR analysis is performed by the Levinson algorithm (Kay, 1988) with a filter order equal to 10, and provides 10 predictor coefficients (or partial correlation coefficients). The wavelet analysis is done using the Daubechies orthogonal wavelets (Daubechies, 1988), and according to the Mallat algorithm (with a decomposition depth of 5)(Mallat, 1989), which supplies 10 parameters related to the energy of the analysed signal at different steps of the multiscale decomposition. Four parameters corresponding to a rough histogram of the wavelet decomposition coefficients are also used. By the end of the preprocessing stage, each transient sound is described by a pattern of 24 parameters.
5. CONCLUSION: In the field of surveillance of industrial plants, we propose a general approach which is composed of two stages: the preprocessing stage, and the decision stage. In order to realize these two stages, different classes of tools can be used, such as advanced signal processing methods, neural nets, and knowledge based system. It is obvious that the efficiency of future surveillance systems should rely on the complementary use of these various techniques.
Acknowledgement: This work has been partly supported by ELECTRICITE DE FRANCE under contract EDF P65L01/1F8221/EP 507.
Reference: - Barron, R.L. (1975). Learning network improve computer-aided prediction and control. Computer Design, 65-70. - Daubechies, I. (1988). Orthonormal bases of compactly supported wavelets. Comm. Pure and Applied Math., 41,909-996. - Degoul, P., A. Lemer, L. Schwab, P. Bernard, and C. Duvermy (1992). Surveillance acoustique en milieu industriel: une approche par classification hierarchisee. In: Recent Advances in Surveillance using Acoustical and Vibratory Methods (Ed. Societe Fran~aise des Mecaniciens), pp. 409-419. - Kay, S.M. (1988). Modern Spectral Estimation: Theory and Application. Prentice Hall, Englewood Cliffs . - Mallat, S.G. (1989). A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Analysis and Machine Intelligence, 11(7) ,674-693. - Rumelhart, D.E. and J .L. Mac Clelland (1986). Parallel Distibuted Processing. MIT press, London .
In the decison stage, various classification algorithms have been tested, both classical techniques such as dynamic clouds, k-nearest neighbours, and neural nets such as the HOPI (High Order of Polynomial Input) which is a multiclass version of a discrimination method called ALN (Adaline like network)(Barron, 1975), and the multilayered per-
359
-
Raw Signal
Preprocessmg Stage
Set of Parameters
Dec l Slon Stage
~
Incldent detection or Diagnos;s
Figure 1 : General surveillance approach
~Iethod
Training phase
Testing phase
MultilayerecLPerceptron
99 .6% (± 0 .2%)
97.3% (± 0.5%)
High_Order_PolynomiaUnput
99.8% (± 0.1%)
96.7% (± 0.7%)
K-NearesLNeighbours
D69% (± 0.4%)
94 .6% (± 0.6%)
DynamicClouds
!liA% (± 0.6%)
93.8% (± 0.7%)
Figure 2 : C lassification results
Class
Confusion matrix
Size
1
20
(25 .0%)
100.0
(± 0.0)
0 .0
(± 0.0)
0.0
(± 0.0)
0.0
(± 0.0)
2
20
(25.0%)
0.0
(± 0.0)
100.0
(± 0.0)
0.0
(± 0 .0)
0.0
(± 0.0)
3
20
(25.0%)
0.2
(± 0.3)
l.3
(± 0.6)
98 .2
(± 0.7)
0.3
(± 0.3)
4
20
(25 .0%)
0.0
(± 0.0)
0.0
(± 0.0)
0.0
(± 0.0)
100.0
(± 0.0)
Training mean rate : 09.6% (± 0.2%) Class
Size
(50 trials)
Confusion matrix 100 .0
(± 0 .0)
0.0
(± 0.0)
0.0
(± 0.0)
0.0
(± 0.0)
(36.0%)
lA
(± 1.0)
08 .2
(±l.l)
0.4
(± 0.3)
0.0
(± 0 .0)
20
(18.0%)
0.0
(± 0.0)
1.0
(± 1.2)
89 .2
(± 1.9)
6.8
(± 1.5)
20
(18 .0%)
0.0
(± 00)
0.0
(± 0.0)
0.6
(± 0.5)
99,4
(± 0 .5)
1
31
(27 .9%)
2
40
3 ·1
Testing mean rate : 07.3% (± 0.5%)
(50 trials)
Figure 3 : Confusion matrices fo r the multilayered perceptron method
360