- Email: [email protected]
Using Artificial Neural Networks (ANNs) in Detection Methodologies. First Detection Results Concerning a DMDP Antenna Structure
Copyright eEl IF AC Intelligent Components and Instruments for Control Applications, Buenos Aires, Argentina, 2000
USING ARTIFICIAL NEURAL NETWORKS (ANNS) IN DETECTION METHODOLOGIES. FIRST DETECTION RESULTS CONCERNING A DMDP ANTENNA STRUCTURE N. Hernandez-Gress ,.1 A. Kimon" N. Karakatsanis ••• A. Bekiaris ••• .2
• LAAS/CNRS 7, Avenue du Colonel Roche 31077 Toulouse , Cedex 4 France •• CASA Av. de Arag6n, 404 28022 Madrid, Spain ••• TRD International, 28, Alexandras Avenue GR-10683 Athens, Greece
Abstract: The objective of this paper is to present detection results , produced from experiments in a Dual Mode Dual Polarity (DMDP) antenna structure, using a general detection methodology based on Statistics and Artificial Neural Networks (ANNs), in order to detect possible abnormalities within the structure. The antenna is supposed in three states (healthy, minus2bolts , minus1mass) . Several experiments, both on healthy and damaged DMDP antenna structure, were carried out in a free configuration space i.e. the structure is suspended with elastic strings , so that it has rigid body suspension frequencies. Frequency Response Functions (FRFs) were recorded and used to detect the abnormalities. A simple identifier for all frequencies is proposed and statistically studied . This identifier is then used by the proposed methodology to compute the diagnosis . The diagnosis performance is 100% for all the treated experiments (in laboratory). Copyright@2000IFAC Keywords: Diagnosis,Real-time supervision, Artificial Neural Networks, Fuzzy Logic , Structure Systems.
diagnosis based on Statistics and Artificial Neural Networks (Hernandez-Gress 1998) to a system in which inputs and outputs are known . This methodology has the following characteristics (shown in figure 1) : firstly the original signals are processed in order to creat a reduced number of new variables while keeping the most important information . These variables, are then learned by the Support Vectors Machine algorithm (Vapnik 1998) .
1. INTRODUCTION This paper presents detection results concerning a DMDP antenna which is part of the work within AMADEUS project (BE-97-5103), partly financed by DG XII of the European Commission. The aim of this work is to detect the state (healthy, minus2bolts , minus1mass) of the antenna through the analysis of the frequency response functions (FRFs) and then to apply the detection methodology described on (Bekiaris and Hernandez-Gress June 1999) The methodology, propose a real time
The work presented in this paper focuses several objectives: • To observe if the frfs are different from the normal state to another.
mail to : [email protected] This work has been carried out under the AMADEUS (BE-97-5103) project
1
2
95
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Punctual
Synthetic
Diagnosr-is~-,..,,,----,-~.,.,.,.....,...,......,
NellralNetwl1rks Co/ISITUctioa by SVM : '" . 1eamlng method "_' ~~
Diagnosis Filtering by statistical methods
Synthetic Components choice by visual and correlation analysis Data Filtering
Fig. l. General diagnosis methodology. • To use the frfs directly to train a system and detect the abnormalities. • To construct an identifier of the frfs , having the needed information able to distinguish the normal and abnormal states of the antenna. • To observe if this identifier is discriminating in all the experiments. • To detect which are the most important sensors and information from a correlation study. • To train the system with this identifier and observe its performance .
only lasts for a percentage of the excitation window , in order to aid in a leakage free signal derivation. The burst random excitation is further defined by the frequency range in which the energy of the signal will be contained. Typically a range of 128, 256 , 512 , 1024 Hz is chosen. The response of the structure will then have a frequency content similar to that of the excitation and depending on its dynamics . Considering excitation at point i and response measurement at point j then all frequencies ar excite and respond at the same time due to the random nature of the excitation signal. Hence the excitation autopower spectrum C i ; is calculated along with the cross power spectrum of each response point, i.e. C ji with reference to the excitation point i. Assuming a single excitation at point i and say 30 responses at j = 1,2, ... 30, then we will have one G i ; and thirty C j ;.
Firstly, a description of the experiments is commented, while secondly, the frfs were used directly to train an ANN . Then, we are presenting an identifier , which is based on the mean value of the frfs spectrum energy and its statistical study. Furthermore , the proposed identifier has been used to train an ANN . Finally, some conclusions and perspectives of this work are discussed.
2.3 Derivation of the Transfer functions
Once all the Gs are calculated then the H 1 transfer function (also called frequency response functions) , for example , at points ji , i.e. Hji is given by: Hji = Cj;/Cii and similarly for all the other 30 response points.The H2 for points ji is similarly calculated as: Hji = Cjj/C ij , where Cjj and C ij correspond to the autopower of the response point j and cross power of the response point j with reference to the excitation point i respectively. Finally, the coherence is calculated as the ratio of Hl/ H2.
2. GENERAL BACKGROUND INFORMATION : THE FRFS COMPUTATION 2.1 Instrumentation
The structure is instrumented with accelerometers at pre-selected locations/ directions and a number of electrodynamic exciters is then connected at selected locations. The latter are determined via a preliminary hammer excitation. The exciter is connected via a push rod and has a force cell included in between so that the applied forces can be measured.
2.4 Formation Transfer Function matrix
The transfer [unction matrix is calculated at each frequency step, within the frequency range selected i.e. if the frequency step is 0.5 Hz and the range 256 Hz then we will have the transfer function matrix defined at 512 frequency points . The frequency step is calculated by the software given the frequency range and the blocksize for the data
2.2 Excitation
Burst random is used in the modal tests, meaning that the signal is of random nature and that it
96
acquisition. Assuming a single excitation point then the transfer function matrix will consist of a single column, i.e. will be a vector. If how~yer we use more than one excitation point, say n, then the transfer function matrix will have n columns.
(2) Test 2:Abnormal minus2bolts. Two (of the four) small bolts that attach one small mass of about 400gr of one corner of the antenna are loosened, as if they were not there. The same 10 triaxial sensor locations were repeated 5 times. Thirty frfs are available per experiment. (3) Test 3:Abnormal minuslmass. For this experiment, the four bolts and the mass were completely removed from the antenna and the same measurements at the same sensor locations were done. Experiments were repeated 5 times. Thirty frequency response functions (frfs) are available per experiment.
2.5 Modal parameter extraction
There are various methods for extracting modal parameters from the transfer function matrix. The simplest one is the Nyquist one operating on a single H j ; and obtaining the parameters operating on Nyquists circle. This assumes that the modes are far apart from each other in frequency . With realistic structures with many close modes though this technique does not work and one has to resort to more advanced techniques like for e.g. the Polyreference one used in AMADEUS . This method uses more than one column at a time. The user selects a sub range of the frequency to do the curve fitting and then the Polyreference fits a multi degree offreedom mathematical model to reproduce the measured curves. When this is achieved then the modes in this sub range are extracted. The next sub range is then done till the whole frequency range is covered .
The frequency of the frfs is between 0-256Hz with a step of 0.25Hz. Practically, for each frf, 1024 points are available.
3. THE FRFS IN NORMAL , MINUS2BOLTS AND MINUS1MASS Figure 2 shows the frfs for sensor 1 in all three directions. As we can observe , the amplitude and frequency response functions are different . The same response has been derived for the ten sensors sensors placed on the DMDP antenna in all experiments. These differecies in the response function is important because detection is feasible .
2.6 Quality checking of extracted modal parameters
The first experiment has consisted to train a system having as inputs the 30 frfs in all the frequency spectrum (1024*30 = 30720) and 20 (all the experiments) sample vectors. The output is 0 for normal and 1 for abnormal (minus2bolts , minus1mass) experiments. All the experiments were used to train this system (training data base 20 vectors x 30720 variables). The system used to train is the SVM (Support Vector Machine) algorithm . The result is that this system didnt diagnose well, due to the very big number of variables, with respect to the number of sample vectors (experiments) . This approach can continue having a most important number of different experiments.
There are some checks of the quality of the extracted modal parameters. The most efficient uses the extracted modal parameters to reproduce or synthesise the measured transfer functions . By then overlaying the measured and synthesised functions, if they coincide, then one knows that the extraction has been successful.
2.7 Experiment definition
Three tests were made on the DMDP antenna for which 10 locations were chosen . These 10 locations are a sub-set of the complete set of locations used for the complete modal test and, were chosen because they are representative and possibly sensitive to changes on the structure. On each location, triaxial accelerometers (z,x,y axes) were positioned to obtain measurements. For each of the experiments, the autopower spectrum of the force (the excitation energy) and the coherence function are available. on the antenna, where. The tests are as follows:
4. THE MEAN VALUE OF THE FRFS The main idea of this section, is to extract some characteristics from the frfs and then to use them instead of the frfs , to train an SVM based system. Some ideas were then tested, the one presented here is based on the use of the statistical mean value of the frfs. The physical representation of this approach is to keep the mean value of the spectral energy as identifier characteristic of the frfs . A statistical study of this identifier is proposed in the following paragraphs. Figure 2 shows the mean value ofthe 30 (10 sensors, 3 directions) frfs per experiment for the three different states
(1) Test I:Normal. The antenna is in a healthy state. The experiments were repeated 10 times . Thirty frfs are available per experiment. 97
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Fig. 2. The frequency response functions of the triaxial accelerometer 1 in directions z, y and x respectively. Light-gray =normal, black = minus2bolts , gray = minus1mass. of the antenna. In light-gray are presented the 10 experiments for the normal state , in black the 5 experiments of the minus2bolts state and in gray the 5 experiments of the minus1mass experiment.
has constructed only 3 important components, as it can be seen in figure 4. The correlation between the 30 initial variables and the synthetic components is given by:
As we can observe from figure 3, the mean value can be used as an identifier due to that:
• Synthetic Component No . 1 (1 ,+0.9) ; (4,+1.0); (6 ,+0.9); (7,+1.0); (8,+1.0) ; (9,+1.0); (10,1.0) ; (11,+1.0); (12 ,+0.9); (13,+0.9); (14,+1.0) ; (15 ,+1.0); (16,+1.0) ; (17 ,+1.0); (18,+0 .9); (19,+1.0); (20,+0.9); (21,+0 .9); (22 ,+1.0); (23 ,+1.0); (24,+1.0); (25,+1.0); (26 ,+1.0); (28,+1.0); (29 ,+1.0); (30,+1.0); • Synthetic Component No . 2 (2,-0 .8); (3,-0.9); • Synthetic Component No . 3 (5 ,-0.7); (27 ,0.8) ;
• The mean standard deviation of the mean is 0.328 for the normal experiments , 0.18 for the minus2bolts experiments and 0.2005 for the minuslmass experiments , • The mean maximal values of the mean are between 0 and 5.63 for the normal experiments , 5.54 for the minus2bolts experiments and 5.93 for the minuslmass experiments. • There exists a very important graphical differentiation between the 3 states of the antenna. • In the abnormal states not always a conclusion was derived, regarding sensors and directions , while in the normal is always very well separated.
Where 1,2,3, .. . are the initial variables; 1,2 and 3 are the three directions z, y, x of the first sensor, . .. 28, 29,30 are the three directions z, y, x of the 10th sensor. The real numbers between (-1.0 to 1.0) are the correlation between the initial variable and the synthetic component. From this analysis , some important conclusions can be presented:
It seems that the mean value can be used as an identifying characteristic , in order to train the state system. A database has been constructed having dimensions of 20 vectors x 30 variables , and two analyses were applied to the database, in order to observe the separation characteristics of the mean values of the frfs.
(1) From the graphical analysis in figure 3, it is important to note that: • The 3 classes are very well grouped and form a well compact class. • It seems that detection by classification is possible. (2) From the correlation analysis , it is clear that a lot of sensors are correlated and that they could be reduced. (3) The most important sensors are number 1, 2 and 9.
5. INDEPENDENT COMPONENT ANALYSIS The ICA has been applied in order to study the correlation and dependence between initial variables. From the 30 initial variables , the method
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Fig. 5. Decision regions of the response of the SVM algorithm to the detection problem.
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have more precision in the localisation of the most important frequencies. • Change from the mean to another parameter, which explains better the spectrum as the cumulated sum. (3) The SVM method was used because the classes are well separated and do not overlap. If overlapping is presented, then the general Neuro-Fuzzy methodology can be then used.
6. TRAINING BY SUPPORT VECTOR MACHINES We have trained a system by Support Vector Machine method using the 3 most important synthetic components . Figure 4 shows the decision regions for this system. The total number of support vectors is 5. The general performance of this SVM system is 100%.The decision regions are shown in figure 5.
8. REFERENCES Bekiaris, A. and N. Hernandez-Gress (June 1999) . Towards developping tool of damage detection of safety and high value structures . In: COMADEM. Sunderland University. p. 6. Hernandez-Gress, Neil (1998). Systeme de Diagnostic par Reseaux de Neurones et Statistiques : Application a la Detection d 'hypovigilancedu conducteur Automobile. PhD thesis. Institut National Poly technique de Toulouse, LAAS/CNRS . Toulouse. Vapnik, V.N. (1998) . Statistical Learning Theory. John Wiley & Son. New York.
7. CONCLUSION AND PERSPECTIVES The goal of this work was to find out whether the frfs do constitute a good means for detecting problems in a DMDP antenna. The experiments carried out do form the basis of this work . First, the frfs were used to train a general system, which seems not very well adapted due to the number of information available . The idea was to extract some characteristics from the frfs . We have used the mean of the frfs , which seems to have all the needed characteristics to make the diagnosis by the appropriate system. The physical representation ofthe identifier is the mean value of the total energy between 0-256Hz. This hypothesis has been tested by some visual and statistical tests . The ICA has been applied to this identifier and it was found that: • All the 30 frfs can be reduced to 3 important components, forming 3 classes, which are compact and different in the space between them. • A lot of sensors are correlated between them. Using these 3 components , we have applied the SVM (Support Vector Machine) algorithms to train an ANN based system , the generalisation performance is of 100%. The system that has been deduced has the following characteristics: An identifier consisting of the mean value of the frfs is first extracted, corresponding to the mean value of the total spectrum . Using the ICA method , the 3 most important components are kept and used , in order to train a system based on the SVM method . The perspectives that this study opens up are multiple: (1) More experiments are needed in order to simulate the system and be sure of the method , under several states of the antenna. (2) If the mean value of the spectrum appears not to be well adapted for localisation , some perspectives are to: • Compute the mean value of the spectrum in reduced windows (50Hz) , in order to
100
USING ARTIFICIAL NEURAL NETWORKS (ANNS) IN DETECTION METHODOLOGIES. FIRST DETECTION RESULTS CONCERNING A DMDP ANTENNA STRUCTURE N. Hernandez-Gress ,.1 A. Kimon" N. Karakatsanis ••• A. Bekiaris ••• .2
• LAAS/CNRS 7, Avenue du Colonel Roche 31077 Toulouse , Cedex 4 France •• CASA Av. de Arag6n, 404 28022 Madrid, Spain ••• TRD International, 28, Alexandras Avenue GR-10683 Athens, Greece
Abstract: The objective of this paper is to present detection results , produced from experiments in a Dual Mode Dual Polarity (DMDP) antenna structure, using a general detection methodology based on Statistics and Artificial Neural Networks (ANNs), in order to detect possible abnormalities within the structure. The antenna is supposed in three states (healthy, minus2bolts , minus1mass) . Several experiments, both on healthy and damaged DMDP antenna structure, were carried out in a free configuration space i.e. the structure is suspended with elastic strings , so that it has rigid body suspension frequencies. Frequency Response Functions (FRFs) were recorded and used to detect the abnormalities. A simple identifier for all frequencies is proposed and statistically studied . This identifier is then used by the proposed methodology to compute the diagnosis . The diagnosis performance is 100% for all the treated experiments (in laboratory). Copyright@2000IFAC Keywords: Diagnosis,Real-time supervision, Artificial Neural Networks, Fuzzy Logic , Structure Systems.
diagnosis based on Statistics and Artificial Neural Networks (Hernandez-Gress 1998) to a system in which inputs and outputs are known . This methodology has the following characteristics (shown in figure 1) : firstly the original signals are processed in order to creat a reduced number of new variables while keeping the most important information . These variables, are then learned by the Support Vectors Machine algorithm (Vapnik 1998) .
1. INTRODUCTION This paper presents detection results concerning a DMDP antenna which is part of the work within AMADEUS project (BE-97-5103), partly financed by DG XII of the European Commission. The aim of this work is to detect the state (healthy, minus2bolts , minus1mass) of the antenna through the analysis of the frequency response functions (FRFs) and then to apply the detection methodology described on (Bekiaris and Hernandez-Gress June 1999) The methodology, propose a real time
The work presented in this paper focuses several objectives: • To observe if the frfs are different from the normal state to another.
mail to : [email protected] This work has been carried out under the AMADEUS (BE-97-5103) project
1
2
95
Final
Punctual
Synthetic
Diagnosr-is~-,..,,,----,-~.,.,.,.....,...,......,
NellralNetwl1rks Co/ISITUctioa by SVM : '" . 1eamlng method "_' ~~
Diagnosis Filtering by statistical methods
Synthetic Components choice by visual and correlation analysis Data Filtering
Fig. l. General diagnosis methodology. • To use the frfs directly to train a system and detect the abnormalities. • To construct an identifier of the frfs , having the needed information able to distinguish the normal and abnormal states of the antenna. • To observe if this identifier is discriminating in all the experiments. • To detect which are the most important sensors and information from a correlation study. • To train the system with this identifier and observe its performance .
only lasts for a percentage of the excitation window , in order to aid in a leakage free signal derivation. The burst random excitation is further defined by the frequency range in which the energy of the signal will be contained. Typically a range of 128, 256 , 512 , 1024 Hz is chosen. The response of the structure will then have a frequency content similar to that of the excitation and depending on its dynamics . Considering excitation at point i and response measurement at point j then all frequencies ar excite and respond at the same time due to the random nature of the excitation signal. Hence the excitation autopower spectrum C i ; is calculated along with the cross power spectrum of each response point, i.e. C ji with reference to the excitation point i. Assuming a single excitation at point i and say 30 responses at j = 1,2, ... 30, then we will have one G i ; and thirty C j ;.
Firstly, a description of the experiments is commented, while secondly, the frfs were used directly to train an ANN . Then, we are presenting an identifier , which is based on the mean value of the frfs spectrum energy and its statistical study. Furthermore , the proposed identifier has been used to train an ANN . Finally, some conclusions and perspectives of this work are discussed.
2.3 Derivation of the Transfer functions
Once all the Gs are calculated then the H 1 transfer function (also called frequency response functions) , for example , at points ji , i.e. Hji is given by: Hji = Cj;/Cii and similarly for all the other 30 response points.The H2 for points ji is similarly calculated as: Hji = Cjj/C ij , where Cjj and C ij correspond to the autopower of the response point j and cross power of the response point j with reference to the excitation point i respectively. Finally, the coherence is calculated as the ratio of Hl/ H2.
2. GENERAL BACKGROUND INFORMATION : THE FRFS COMPUTATION 2.1 Instrumentation
The structure is instrumented with accelerometers at pre-selected locations/ directions and a number of electrodynamic exciters is then connected at selected locations. The latter are determined via a preliminary hammer excitation. The exciter is connected via a push rod and has a force cell included in between so that the applied forces can be measured.
2.4 Formation Transfer Function matrix
The transfer [unction matrix is calculated at each frequency step, within the frequency range selected i.e. if the frequency step is 0.5 Hz and the range 256 Hz then we will have the transfer function matrix defined at 512 frequency points . The frequency step is calculated by the software given the frequency range and the blocksize for the data
2.2 Excitation
Burst random is used in the modal tests, meaning that the signal is of random nature and that it
96
acquisition. Assuming a single excitation point then the transfer function matrix will consist of a single column, i.e. will be a vector. If how~yer we use more than one excitation point, say n, then the transfer function matrix will have n columns.
(2) Test 2:Abnormal minus2bolts. Two (of the four) small bolts that attach one small mass of about 400gr of one corner of the antenna are loosened, as if they were not there. The same 10 triaxial sensor locations were repeated 5 times. Thirty frfs are available per experiment. (3) Test 3:Abnormal minuslmass. For this experiment, the four bolts and the mass were completely removed from the antenna and the same measurements at the same sensor locations were done. Experiments were repeated 5 times. Thirty frequency response functions (frfs) are available per experiment.
2.5 Modal parameter extraction
There are various methods for extracting modal parameters from the transfer function matrix. The simplest one is the Nyquist one operating on a single H j ; and obtaining the parameters operating on Nyquists circle. This assumes that the modes are far apart from each other in frequency . With realistic structures with many close modes though this technique does not work and one has to resort to more advanced techniques like for e.g. the Polyreference one used in AMADEUS . This method uses more than one column at a time. The user selects a sub range of the frequency to do the curve fitting and then the Polyreference fits a multi degree offreedom mathematical model to reproduce the measured curves. When this is achieved then the modes in this sub range are extracted. The next sub range is then done till the whole frequency range is covered .
The frequency of the frfs is between 0-256Hz with a step of 0.25Hz. Practically, for each frf, 1024 points are available.
3. THE FRFS IN NORMAL , MINUS2BOLTS AND MINUS1MASS Figure 2 shows the frfs for sensor 1 in all three directions. As we can observe , the amplitude and frequency response functions are different . The same response has been derived for the ten sensors sensors placed on the DMDP antenna in all experiments. These differecies in the response function is important because detection is feasible .
2.6 Quality checking of extracted modal parameters
The first experiment has consisted to train a system having as inputs the 30 frfs in all the frequency spectrum (1024*30 = 30720) and 20 (all the experiments) sample vectors. The output is 0 for normal and 1 for abnormal (minus2bolts , minus1mass) experiments. All the experiments were used to train this system (training data base 20 vectors x 30720 variables). The system used to train is the SVM (Support Vector Machine) algorithm . The result is that this system didnt diagnose well, due to the very big number of variables, with respect to the number of sample vectors (experiments) . This approach can continue having a most important number of different experiments.
There are some checks of the quality of the extracted modal parameters. The most efficient uses the extracted modal parameters to reproduce or synthesise the measured transfer functions . By then overlaying the measured and synthesised functions, if they coincide, then one knows that the extraction has been successful.
2.7 Experiment definition
Three tests were made on the DMDP antenna for which 10 locations were chosen . These 10 locations are a sub-set of the complete set of locations used for the complete modal test and, were chosen because they are representative and possibly sensitive to changes on the structure. On each location, triaxial accelerometers (z,x,y axes) were positioned to obtain measurements. For each of the experiments, the autopower spectrum of the force (the excitation energy) and the coherence function are available. on the antenna, where. The tests are as follows:
4. THE MEAN VALUE OF THE FRFS The main idea of this section, is to extract some characteristics from the frfs and then to use them instead of the frfs , to train an SVM based system. Some ideas were then tested, the one presented here is based on the use of the statistical mean value of the frfs. The physical representation of this approach is to keep the mean value of the spectral energy as identifier characteristic of the frfs . A statistical study of this identifier is proposed in the following paragraphs. Figure 2 shows the mean value ofthe 30 (10 sensors, 3 directions) frfs per experiment for the three different states
(1) Test I:Normal. The antenna is in a healthy state. The experiments were repeated 10 times . Thirty frfs are available per experiment. 97
Irl sensor 1 ; directions z,y.x
'~l~i j o
50
100
150
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300
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Fig. 2. The frequency response functions of the triaxial accelerometer 1 in directions z, y and x respectively. Light-gray =normal, black = minus2bolts , gray = minus1mass. of the antenna. In light-gray are presented the 10 experiments for the normal state , in black the 5 experiments of the minus2bolts state and in gray the 5 experiments of the minus1mass experiment.
has constructed only 3 important components, as it can be seen in figure 4. The correlation between the 30 initial variables and the synthetic components is given by:
As we can observe from figure 3, the mean value can be used as an identifier due to that:
• Synthetic Component No . 1 (1 ,+0.9) ; (4,+1.0); (6 ,+0.9); (7,+1.0); (8,+1.0) ; (9,+1.0); (10,1.0) ; (11,+1.0); (12 ,+0.9); (13,+0.9); (14,+1.0) ; (15 ,+1.0); (16,+1.0) ; (17 ,+1.0); (18,+0 .9); (19,+1.0); (20,+0.9); (21,+0 .9); (22 ,+1.0); (23 ,+1.0); (24,+1.0); (25,+1.0); (26 ,+1.0); (28,+1.0); (29 ,+1.0); (30,+1.0); • Synthetic Component No . 2 (2,-0 .8); (3,-0.9); • Synthetic Component No . 3 (5 ,-0.7); (27 ,0.8) ;
• The mean standard deviation of the mean is 0.328 for the normal experiments , 0.18 for the minus2bolts experiments and 0.2005 for the minuslmass experiments , • The mean maximal values of the mean are between 0 and 5.63 for the normal experiments , 5.54 for the minus2bolts experiments and 5.93 for the minuslmass experiments. • There exists a very important graphical differentiation between the 3 states of the antenna. • In the abnormal states not always a conclusion was derived, regarding sensors and directions , while in the normal is always very well separated.
Where 1,2,3, .. . are the initial variables; 1,2 and 3 are the three directions z, y, x of the first sensor, . .. 28, 29,30 are the three directions z, y, x of the 10th sensor. The real numbers between (-1.0 to 1.0) are the correlation between the initial variable and the synthetic component. From this analysis , some important conclusions can be presented:
It seems that the mean value can be used as an identifying characteristic , in order to train the state system. A database has been constructed having dimensions of 20 vectors x 30 variables , and two analyses were applied to the database, in order to observe the separation characteristics of the mean values of the frfs.
(1) From the graphical analysis in figure 3, it is important to note that: • The 3 classes are very well grouped and form a well compact class. • It seems that detection by classification is possible. (2) From the correlation analysis , it is clear that a lot of sensors are correlated and that they could be reduced. (3) The most important sensors are number 1, 2 and 9.
5. INDEPENDENT COMPONENT ANALYSIS The ICA has been applied in order to study the correlation and dependence between initial variables. From the 30 initial variables , the method
98
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Fig. 5. Decision regions of the response of the SVM algorithm to the detection problem.
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have more precision in the localisation of the most important frequencies. • Change from the mean to another parameter, which explains better the spectrum as the cumulated sum. (3) The SVM method was used because the classes are well separated and do not overlap. If overlapping is presented, then the general Neuro-Fuzzy methodology can be then used.
6. TRAINING BY SUPPORT VECTOR MACHINES We have trained a system by Support Vector Machine method using the 3 most important synthetic components . Figure 4 shows the decision regions for this system. The total number of support vectors is 5. The general performance of this SVM system is 100%.The decision regions are shown in figure 5.
8. REFERENCES Bekiaris, A. and N. Hernandez-Gress (June 1999) . Towards developping tool of damage detection of safety and high value structures . In: COMADEM. Sunderland University. p. 6. Hernandez-Gress, Neil (1998). Systeme de Diagnostic par Reseaux de Neurones et Statistiques : Application a la Detection d 'hypovigilancedu conducteur Automobile. PhD thesis. Institut National Poly technique de Toulouse, LAAS/CNRS . Toulouse. Vapnik, V.N. (1998) . Statistical Learning Theory. John Wiley & Son. New York.
7. CONCLUSION AND PERSPECTIVES The goal of this work was to find out whether the frfs do constitute a good means for detecting problems in a DMDP antenna. The experiments carried out do form the basis of this work . First, the frfs were used to train a general system, which seems not very well adapted due to the number of information available . The idea was to extract some characteristics from the frfs . We have used the mean of the frfs , which seems to have all the needed characteristics to make the diagnosis by the appropriate system. The physical representation ofthe identifier is the mean value of the total energy between 0-256Hz. This hypothesis has been tested by some visual and statistical tests . The ICA has been applied to this identifier and it was found that: • All the 30 frfs can be reduced to 3 important components, forming 3 classes, which are compact and different in the space between them. • A lot of sensors are correlated between them. Using these 3 components , we have applied the SVM (Support Vector Machine) algorithms to train an ANN based system , the generalisation performance is of 100%. The system that has been deduced has the following characteristics: An identifier consisting of the mean value of the frfs is first extracted, corresponding to the mean value of the total spectrum . Using the ICA method , the 3 most important components are kept and used , in order to train a system based on the SVM method . The perspectives that this study opens up are multiple: (1) More experiments are needed in order to simulate the system and be sure of the method , under several states of the antenna. (2) If the mean value of the spectrum appears not to be well adapted for localisation , some perspectives are to: • Compute the mean value of the spectrum in reduced windows (50Hz) , in order to
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