Methods for Linear Electronic Analog Circuits Diagnosis. Carles Pous, Joan .... specific for circuit analysis can be used instead, such as. PSPICE, PCAD ...
Improving Fault Dictionary Techniques with Artificial Intelligence Methods for Linear Electronic Analog Circuits Diagnosis Carles Pous, Joan Colomer, Joaquim Melendez Institut d’Inform` atica i Aplicacions. Universitat de Girona Avda. Llu´ıs Santal´ o s/n. Edifici P-4. 17071 GIRONA (Spain) e-mail: {carles, colomer, quimmel}@eia.udg.es
Abstract Testing circuits is a stage of the production process that is becoming more and more important when a new product is developed. Test and diagnosis techniques for digital circuits have been successfully developed and automated. But, this is not yet the case for analog circuits. Even though there are plenty of methods proposed for diagnosing analog electronic circuits, the most popular are the fault dictionary techniques. But during these last decades automating fault diagnosis using Artificial Intelligence (AI) techniques has become an important research field. This paper describes the main work done for testing analog electronic circuits focusing on AI methods. In particular, taking fault dictionaries as a starting point two of these AI techniques are developed in order to fill in some gaps of the standard methods. The first proposal is to build a fuzzy system as an identification tool. The second proposal improves a fault dictionary diagnosis by means of adding and adapting new cases to develop a Case Based Reasoning system. Examples showing how these methods work are given using a biquadratic filter as a benchmark.
1 Introduction In this section we summarize major works that have paved the way of analog electronic circuit diagnosis. Further details on the related literature are given in [1]. In 1978 Schreiber [2] made the first Automatic Test Generation Techniques classification. But it was in 1979 when P. Duhamel and J.C.Rault [3] published a more exhaustive categorization of the known analog circuit testing methods. The types of tests and faults to diagnose were given and classified. The methods were grouped into estimation techniques, topological methods, taxonomical methods and methods for linear circuits. In 1985 J.W. Bandler and A.E. Salama [4] reported another excellent classification, including methods that had just appeared and the improvements obtained from
them. This is one of the most referenced reviews for analog electronic circuit testing. They classify the methods into two main groups: techniques that need a simulation before the test, and the ones that need the simulation after the test. In this report AI techniques are briefly mentioned, basically because in 1985 they were not very developed and poor results were obtained. While digital circuits are normally characterized by a very limited number of fault categories, the nature of analog circuits makes this universe of fault discretization more difficult, since this universe is continuous. The type of measures taken and the circuit topology define the degree of solvability of the circuit, and can be quantified by means of a testability measure. The most useful degree of testability calculation is the one suggested by [5]. It proposes the use of the column-rank of the system sensitivity matrix as a testability measure for parametric faults in linear analog circuits. The problem still remains far from being solved. It is a field that has a lot of literature, and a good summary of the techniques for deriving the testability is given in [6]. It has to be said that the majority of the proposed methods are for linear circuits. As it could seem an important drawback, for mixed-signal circuits almost all the analog modules compounding the circuit are of this nature, while the non linear parts are moved to the digital part [7]. As the complexity of the circuits increases, development of new Designs For Testability (DFT) is getting more important. DFT techniques try to provide accessibility to internal nodes with the minimum addition of extra components or pins. In [8], a classification of these techniques into two groups is made. The first one is based on the circuit reconfiguration in order to improve the testability. The second one relies on the insertion of test points to increase the controllability and observability of the circuit’s internal nodes. [9] presents a tutorial that reinforces the classification of [4] and extends it by incorporating how the most recent DFT techniques, and in particular Built-In Self Test (BIST), can be matched . [10] also makes a good review of the evolution of BIST
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techniques to the present day and a new testability measure is given. Among all the Design For Testability techniques the standard IEEE1149.x, and in particular the IEEE1149.4 for mixed-signal testing have to be cited. Its main objective is to incorporate in the digital standard IEEE1149.1 characteristics to be used for analog and mixed signal circuits. The standard is described in detail in [11]. Although there are several studies on this subject trying to analyze the impact of adding the analog blocks and how the standard performs in particular circuits [12], [13], [14] or [15], it is important to mention that, to date, it is not clear if the industry is going to accept and incorporate the standard, as is discussed in the editor’s note of [15]. About using AI techniques for electronic circuit diagnosis, in [16] the importance of intelligent tools for electronic circuit fault diagnosis is highlighted. A classification of these methods for electronic circuits is given. Basically, they are grouped into rule-based approaches, model-based approaches, learning approaches, other approaches and hybrid combinations of the previous ones. In this domain, there is plenty of work done using expert systems, neural networks, Fuzzy Logic or a combination of them. Concerning expert systems, [17] proposes an expert system based on interval propagation in order to diagnose an astable multivibrator circuit. Also, [18] describes the expert system that Hewlett-Packard used for testing a processor board during its production step. In [19] a Neural network for fault detection in a SallenKey filter is described. The acquired data is previously processed using wavelet decomposition and principal component analysis to generate optimal features for training the neural network. [20] treats analog circuit diagnosis as pattern recognition. After a review of AI techniques applied to analog circuit diagnosis, they propose to train a neural network obtaining data from a circuit simulation SPICE environment. Also, several feature extraction techniques and their impact on the final diagnosis are shown. In particular a DC motor driver is tested. Analyzing the fuzzy techniques applied to analog circuit diagnosis, the work done in [21] can be cited. The effect of treating the circuit parameter intervals as fuzzy sets for propagation considerations is studied. On the other hand [22] proposes a fuzzy system where the inputs are based on a fault dictionary and the outputs are crisp or singleton functions from a Sugeno fuzzy system. [23] provides a similar fuzzy system but applied to the Hybrid Combustion Facility at the NASA Ames Research Center. Therefore, these systems can detect the incorrect component, but not its actual deviation. In [24], a fuzzy system is developed that uses information from the fault dictionary to build the input membership functions. A Mandami fuzzy system with Gaussian shaped membership functions is utilized for each output.
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Case-Based Reasoning systems (CBR) is another powerful tool that can be applied to the analog circuit diagnosis. [25] presents a CBR system acting as a help-desk that makes the right questions in order to isolate the possible fault in the circuit. In [26] an incremental case retrieval mechanism is designed for minimizing the number of initial cases necessary to initiates case retrieval with a brief case description, it is not necessary to have all the features available at the first steps. The CBR system is applied to diagnose a switching power supply module by guiding the appropriate questions to the user. As the CBR system’s core is a base of cases that can be very large, it has a lot in common with the data mining methodologies for data processing. In [27] data mining is used for generating databases for CBR applications. In particular, [28] propose CBR systems as an extension of the fault dictionaries. They study the case applied to digital circuits and discuss the appropriateness of using the Nearest Neighbor criterion. Also, the paper [29] has to be cited, which was proposed by the authors of the present work. It uses the DROP algorithm for maintaining a case base for diagnosing a biquadratic filter, after defining the adequate case memory (case structure and hierarchy) and introducing the conflictive cases into another case base, where a different metric is used for retrieval. To finish with this brief summary of related works, the standard IEEE1232 AI-ESTATE has to be taken into account; it stands for Artificial Intelligence Exchange and Service Tie to All Test Environments [30]. The purpose of this standard is ”to standardize interfaces between functional elements of an intelligent diagnostic reasoner and representations of diagnostic knowledge and data for use by such diagnostic reasoners”, as described in its abstract. Hence, the importance of the Artificial Intelligence applied to circuit diagnosis is emphasized. Next sections of the paper are structured as follows: First, the biquadratic circuit under test and the faults to diagnose are briefly described; then, fault dictionary techniques and their main drawbacks are introduced in Section 3; section 4 gives a classification of the main AI based methods used for diagnosing electronic circuits and two of them are described in more detail in Section 5 and Section 6. The former describes a fuzzy logic technique while the latter proposed a CBR system for diagnosing analog circuits. To finish, some conclusions are made in last section.
2 The Circuit Under Test In order to show the performance of the methodologies proposed in the present paper, a particular circuit has been chosen. The circuit proposed is a biquadratic filter widely cited in the bibliography as a benchmark for analog circuits [31], [32]. This benchmark is a linear system that can be found applied in several electronic schemes.
Improving FD with AI Methods for Linear Electronic Analog Circuits Diagnosis
It can be used itself or as part of the leap-frog filter. The structure of the biquadratic filter is shown in Fig. 1, with the component values given in Table 1. The circuit is linear and only parametric faults (soft deviations from the nominal value) of the passive components are considered.
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Fig. 1 Biquadratic filter under test
In our case, the component values are given in Table 1. They all are taken with a tolerance of 10%.
Table 1 Biquadratic filter component values Component R1 R2 R3 R4
Value 2.7K 1K 10K 1.5K
Component R5 R6 C1 C2
Value 12K 2.7K 10nF 10nF
Since the circuit is linear, it is not difficult to derive its transfer functions at the output V0 with respect to the input Vi . The transfer function of the circuit in Matlab software is used for simulations, although other packages specific for circuit analysis can be used instead, such as PSPICE, PCAD, ORCAD and so forth. On the other hand, the real circuit is specifically designed for test purposes, allowing the universe of considered faults to be generated in an easy manner. To facilitate fault generation, digital potentiometers are used for resistors fault simulation. Capacitors are simulated using an electronic switch and a bank of discrete capacitors. The integrated circuit TL074 is used for the operational amplifiers. The data acquisition board for taking the measures is a PCI 6071-E from National Instruments. the diagnosis methods proposed in this paper are tested with a set of 100 new faults for each component, uniformly distributed between ±70% of the nominal value. A diagnostic is considered incorrect when the proposed fault is given with an error estimating the component deviation bigger than 10%. When there are deviations of the components smaller than the tolerance, the circuit is considered to be not faulty. This is known as the nominal case.
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3 Fault Dictionary Techniques Fault dictionaries are techniques completely based on quantitative calculations. Once the universe of faults to be detected is defined (Fault 1, Fault 2, ..., Fault m), selected characteristics of the measured or simulated output are obtained from the system for each considered fault and stored in a table. This set of output characteristics is known as Fault signature. The groups of fault signatures considered constitute the Fault dictionary. The method has two steps: the first one is based on simulation in order to built the dictionary; the second one consists in comparing the measures from the unknown faulty system with the stored fault signatures. The advantage of these techniques is their simplicity. But they have an important drawback: The only faults detected and located will be the ones that have been previously simulated and stored in the dictionary. So, the more faults to locate, the longer the dictionary should be. Therefore, these techniques are a compromise between fault coverage and dictionary length. Non previously simulated situations can be produced by the tolerances that electronic components have or simply by non considered faults. In the first situation, the tolerances effect can be seen as non considered cases since the dictionary is obtained by simulating the faults only considering the nominal values of the parameters. In order to find the possible cases produced by the tolerances for a particular measure, several simulation runs have to be carried out. One of the most commonly used methods is the Monte-Carlo. The second situation, the non previously considered deviations, can cause limitations on the fault dictionary diagnostics. For example, if the dictionary is built considering faults corresponding to deviations of ±50% from nominal, a fault corresponding to a deviation of 70% could not be diagnosed with precision. Despite this important limitation, Fault Dictionaries are the most extensively used technique for detecting and locating faults. There are a lot of Fault Dictionary methods that can be found in the literature, but we have selected the saturated ramp method described in [31] that is based on time response for our purposes. This is because the method has shown to be as good as a frequency based ones and, in general, it needs to keep less measures, while maintains the performance. Also, the results show that in spite of taking only measures at the output node, the percentage of faults located at the output is high, even when tolerances are considered. The main parameters used by the method are displayed in Figure 2 for a better understanding. 4 Artificial Intelligence Techniques Due to the increase in circuit complexity, system malfunction detection and isolation are becoming more difficult. Artificial Intelligence (AI) techniques have been a
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Amplitude
Output Input SP
0,9 Vest Vest
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the attributes of acquiring and scaling input variables and their fuzzification. The universe of each considered variable has to be partitioned. This partition is carried out by defining fuzzy sets with a particular membership function shape for each input variable. Fuzzy sets can be built from Monte-Carlo simulations and the dictionary instances can be compacted in fuzzy rules. The system includes tolerance effects and its output is an estimation of each parameter value. In the inference step, the individually fuzzy sets that result have to be combined. The decision fuzzy set obtained as output is the result of the union of the singular fuzzy sets derived for each particular rule.
Fig. 2 Circuit response to a ramp input
5.1 Defining Linguistic Variables major research topic over the last decades. In [33] a good review of AI techniques is shown. In this work, AI techniques are classified in Traditional Approaches, ModelBased Approaches, Machine Learning Approaches, Other Approaches and Hybrid Approaches. The first ones are the most common techniques used in the industry, and are based on heuristics. The expert experience is collected in a IF-THEN rule base or as a decision tree. Faults that are not predicted in advance will not be detected. Hence, the methods have no learning capability. Model-Based Approaches make use of the model to predict faults in the real circuit. Its main disadvantage is its inability to deal with unsimulated faults and the expert knowledge acquisition when causal models are needed. Also, they are not able to learn from new situations. Fault Dictionaries are included in this group. Concerning to Machine Learning Approaches, they take advantage of previous successful or failed diagnoses, and they use this knowledge in order to improve the system’s performance. Case-Based reasoning (CBR) systems can be classified in this group. The main advantage of these techniques is that they have learning capability. Fuzzy and Neural Network techniques can be cited in the group of other approaches, while hybrid approaches propose a combination of models and cases to solve particular situations. Two of these AI techniques developed by the authors of the present work are explained in the following sections. The results obtained when these techniques are applied to the biquadratic filter are given in Section 8.
5 Diagnosis Using Fuzzy Logic Fuzzy logic usually perform well in systems with imprecision or uncertainty, such as electronic circuits. This technique has three main decision making steps: fuzzification, inference and defuzzification. The fuzzification unit is the interface between input variables (measures from the circuit in our case) and the inference unit. It has
Each measure is considered as the fuzzy system input. For the saturated ramp method, the system will have 4 inputs (SP ,td , tr , Vest ). The number of membership functions belonging to each input is given by the previously considered universe of faults and the nominal case. That is, if the circuit is composed of N parameters and each of them has a deviation of ±X% to be considered as desirable identifiable faults, each fuzzy input will have 2N +1 membership functions. Figure 3 shows a possible appearance of the measure i input. Each membership function is related to a possible considered fault (P arameter1 + X%, P arameter1 − X%, N ominal,...). In general, membership functions are not symmetric. Certainty Param.1 - X% Param.1 + X% Param.2 + X%
Nominal
....
Param.N - X% Param.N + X%
....
Measure i
Fig. 3 Measure i appearance
The membership function shape has been selected taking advantage of the Monte-Carlo simulation results. An analysis of the M easure i faults distribution is carried out. For example, M easure i for F ault j can have the distribution shown in Figure 4, after a Monte-Carlo simulation of L runs. This distribution could be approximated, for example, by a Gaussian or triangular shape as it is depicted in Figure 4. On the other hand, the outputs of the system are the estimated parameter values. Therefore, there will be as many outputs as components. Each output will have a membership function for each considered deviation. The membership function shape will be taken according to the parameter value distribution. For resistors and capacitors, it is well known that these components have
Improving FD with AI Methods for Linear Electronic Analog Circuits Diagnosis
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5.2 The Fuzzy Inference Model
Number of cases
Figure 6 displays how the inputs, outputs and rules are combined for the ramp method. The example shows that taking the measures SP1 , td1 , tr1 and Vest1 , rules 1 and 3 are activated. The corresponding consequents are derived giving an estimation of the present value for each component. Antecedents R1+20%
R1+20%
AND
Rule 1. IF
Measure Value
Fig. 4 Measure i input distribution for fault j
td
R1 +50%
R1+50%
... Rule 3. IF
a Gaussian distribution probability function [34], [35]. For example, if deviations of ±X% are considered, the parameter param i output can exhibit a membership distribution as shown in Figure 5.
AND
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1 0.9
Fig. 6 Fuzzy inference model
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The defuzzification procedure combine the consequents of the activated rules by means of the centroid method. The result is an estimated value for each component. Further details on this method can be found in [24].
0.6 0.5 0.4 0.3 0.2
6 The CBR-System
0.1 0
Component value
Fig. 5 Gaussian output membership functions
Once the inputs and outputs are defined, they have to be connected by means of rules. The rule structure for the fault P arameter1 + X% is if (Meas. 1 is Param. 1+X%)&(Meas. 2 is Param 1+X%)&....(Meas. M is Param. 1+X%) then (Param. 1 is Param. 1+ X%)&(Param. 2 is nominal)&(Param. 3 is nominal)&... (Param. N is nominal).
Hence, there are as many rules as considered faults. The advantage of this method is that it is not necessary to store all the cases, only the rules and membership functions for the inputs and the outputs. The operator selected to combine antecedents is the product. The main reason is to penalize measures falling outside the membership’s scope. If one of the M measures falls outside of at least one of the sets defined by the rule antecedents, the final product will be 0, and the rule will not be fired. Otherwise, the rule will be triggered with a value corresponding to the product of the belonging coefficients.
Case Based Reasoning is an approach to problem solving that is able to use specific knowledge of previous experiences [36]. A new problem will be solved by matching it with a similar past situation. If the problem is solved, it is not necessary to retain the new situation. In case of diagnosis, solving the problem means that the CBRsystem proposes a solution satisfactory enough to identify the new fault. The methodology proposed here focuses on the knowledge contained in the case base, where learning is performed keeping new cases, when necessary, and forgetting noisy exemplars. The method could be classified as a multi-edit technique, since is a mixture and modification of two existing ones. The case memory structure is chosen to be the same as the one used in the fault dictionary techniques with a slight difference in the information considered about the fault. The proposed structure is shown in Figure 7. Observe that one part of the case is directly related with the measures taken from the circuit at one or several nodes. This numeric part will be used to retrieve the most similar cases. The second part of the case contains information about the fault diagnosis.
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Carles Pous et al. Case Num Case i
Meas. 1 M1i
Meas. 2 M2i
… …
Measures. Numeric Part
Meas. n Mni
Class Class i
Compo Compo i
Devi X%
Hierarchy Li.Mj
Fault. Qualitative Part
Fig. 7 Case Structure
As a reference, the classes associated with the faults considered in the classical dictionary (±20% and ±50%) are taken. When a fault has a deviation that does not correspond exactly to one of the original ones, the associated class will be the same given to the closest possible deviations considered as references. For example, if a fault is R + 40%, its associated class will be the same as R + 50%. But if a fault is R + 35%, its corresponding class will be the same as R + 20%. This Class field is not used for classification purposes. It is only used in particular steps to help in the maintenance. Concerning the other three qualitative fields, one of them has the faulty component location (Compo); the second contains the characterization of the fault (Devi ) corresponding to the % of deviation from the Compo nominal value.
The solution to the new presented case has to be revised. If the solution is considered to be correct and accurate enough, it is not necessary to retain the new case. On the other hand, if it is considered to be incorrect or with poor accuracy, the new case will be retained in the case memory. The revision analyzes how the cases that constitute the adapted solution are performing the diagnosis. Hence there are two possibilities: a)It is supposed that the new case diagnosis is known by the user for its revision, which allows a decision to be made about when it should be retained. b) The decision can be made automatically, using a threshold as proposed in [40]. When the CBR-system is testing circuits with unknown faults, there is no revision task, since the proposed diagnosis can not be contrasted with the correct one. The new case should be retained if the selected learning algorithm applied decides so. The algorithm can be any one used in the machine learning schemes, although the best results obtained by the authors from several tested algorithms were performed by the DROP and the All-KNN algorithms. The revision procedure is given in Figure 8. A detailed explanation of how it works can be found in [29].
The third field (Hierarchy) has additional information about the component, for example at level Li and the module Mj to which the component belongs. Case base hierarchy is defined considering several levels depending on circuit complexity as it is done in [37]. It is necessary to have certain knowledge on the circuit topology in order to build the case base hierarchy. For small circuits it can be done simply by inspection. For large circuits the method proposed in [38] can be used. Since the proposed CBR-system uses numerical data corresponding to the measures, we deal with continuous linear attributes; that is, attributes that can be any real number. Therefore, from among all possible distance functions [39], the normalized Euclidean distance has been chosen. Attributes Normalization is necessary because of their different order of magnitude. The number of cases k to retrieve from the case base will be related to the value of k that produces the best diagnosis results. Normally it is a small odd number. In general, the more noisy the data is, the greater the optimal value of k. In our experiments, a value of k = 3 produces the best results. Taking a bigger value produces confusion in the diagnosis because of the extraction of cases corresponding to other different faults to be diagnosed. Once k − nearest cases are extracted, they are used to propose a possible diagnosis. The proposal is to use the qualitative part of the extracted cases to derive a possible solution. Several situations can be given that are described in [29]. The case adaptation is carried out completely in the reuse task. It uses the past case solution instead of the past method that constructed the solution (transformational reuse).
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One of the main drawbacks when training a CBRsystem is to know when to stop. If the case base is oversized, its efficiency falls. This is known as the utility prob-
Improving FD with AI Methods for Linear Electronic Analog Circuits Diagnosis
lem. Hence, a good policy for the training and maintenance tasks is necessary. In order to keep new cases on the case base, the All-KNN algorithm [41] is the one that produces the best results for the biquadratic filter. To avoid the utility problem, the way to maintain the case base memory is very similar to the IB3 ([42]) algorithm used when dropping cases. In fact, it uses the same criterion for removing cases, that is, when the performance of a particular case drops below a certain established value with a certain confidence index, the case is considered to be spoiling the diagnosis and it will be deleted. The confidence limit used is the one defined by the success probability of a Bernoulli process [43]. IB3 normally takes a confidence index Cmax = z = 0.9 for acceptance and Cmin = z = 0.7 for rejecting. In the present paper the algorithm is used only for removing noisy cases. Several values of confidence, from 0.3 to 0.9 have been tested. The maximum performance is obtained for C = z = 0.9 as a confidence level to forget cases. Hence it is better for our system to forget irrelevant cases faster.
6.1 The training process The process of training is extremely sensitive to how the new presented cases are sorted. Hence, a method like the well-known ten-fold cross-validation has to be applied. In our case, we have decided to build several independent sets {S1 , S2 , ...., Sn } of randomly generated exemplars corresponding to a N number of cases for each component, with faults uniformly distributed between ±70% as the maximum component deviation considered to be diagnosed. The CBR-system is trained with several series {T1 , T2 , ..., Tm } of these sets randomly sorted in order to obtain a case base that performs better.
7 Effects When Using Real Data According to [44], several errors can be given when using measures instead of data from simulation. These errors can be produced by controllable or uncontrollable factors. Since the circuit is well isolated (physically) and insulated (electrically), there is no electromagnetic interference and the circuit is not submitted to any air flow that can change its working temperature. Also, the power supply offers great protection from the electrical net fluctuations. Hence, the uncontrollable errors are negligible and the only errors considered are the controllable ones. In our case, the main controllable factors that can influence the measurements are due to: Sampling time, Relative accuracy and Noise. Let us particularize the previous effects on the measures corresponding to the saturated ramp response method. Concerning the sample time, the error affects the parameters td and tr , since the overshoot and steady state calculations has given a negligible error. It is demonstrated
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in [1], that the highest dispersion is produced by the parameter SP for the biquadratic example. Also it can be seen that after averaging 60 measures the error is below the acquisition card resolution, and these derived real parameters are very close to the simulated ones. Hence, when considering real data, great differences from the simulated results are not expected. 8 Results on the Biquadratic Filter First of all, the Fault Dictionary (FD) based on the saturated ramp method and the fuzzy logic system proposed are tested for checking their behavior with the tolerance effect. The circuit under diagnosis is the biquadratic filter given in Section 2. For the Fuzzy logic system each input attribute is divided into 33 triangular shaped membership functions corresponding to component deviations of ±20% and ±50% for each component, and there are 8 outputs (one per circuit component), each of them constituted by five sets (±20%, ±50% and nominal). Therefore, 33 rules are necessary to relate the inputs and the outputs of the system. In some situations, signatures cause the fired rules to point to an incorrect diagnosis. For example, a random simulation of the fault R5 − 20% while other components stay at their tolerance margin from a nominal of 10%, produces the following component values: R1 = 2.6966K, R2 = 1.0170K, R3 = 9.9316K, R4 = 1.4443K, R5 = 9.6000K, R6 = 2.6995K, C1 = 9.8752 nF and C2 = 9.8169 nF . Simulating the circuit with these values, the corresponding temporal signature activates several rules at the same time producing an error estimating R2 , R3 , R5 and C1 . The fuzzy logic system is tested using a file constituted by 100 instances corresponding to deviations in the interval of ±70% for a component, while the other stay in its 10% of tolerance margin. This gives us a set of 800 (8 components x 100 faults/component) new cases to test. A comparison with the results obtained is given in Table 2. Table 2 Diagnosis success FD versus fuzzy for ±70% faults Fault dictionary Fuzzy Logic Diag. Component Incorrect Diag. Component Incorrect Success Success R1 19% 57% 16% 14 41 45 R2 20% 25% 42% 29 49 22 R3 5% 44% 37% 10 83 7 R4 15% 65% 17% 11 52 37 R5 15% 24% 50% 9 48 43 R6 20% 62% 12% 13 67 20 C1 12% 42% 35% 27 37 36 C2 30% 52% 7% 4 51 45 Average 17% 46.375% 27% 14,62% 53,5% 31,88% Fault
In this situation, the Fuzzy logic system can locate better the components than the fault dictionary, but it performs worse when predicting the component deviation. As a conclusion, the proposed fuzzy approach can
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help in locating wrong components, but care must be taken when using it for estimating the component deviation. Neither the proposed Fault Dictionary nor the Fuzzy Logic system give a good percentage of success when diagnosing non previously predicted faults, because these methods are not able to learn from new situations. This is the reason why the CBR system of Section 6 has been developed. This system can be trained and so, it can learn from previously unseen situations. Figure 9 shows the results obtained on the biquadratic filter while the CBR system is trained. Observe that the number of cases diagnosed with precision has increased up to 50%. From these graphics, taking the situation after 63 trainings as an example, the case base has a size of 742 cases with a reasonable percentage of success diagnosing component deviations. Using the same test set of 100 faults per component corresponding to deviations in the range of ±70% from nominal, the results obtained by the CBR-system are compared with the ones given by the previous methods. The comparison is shown in Table 3, demonstrating how useful is to provide the diagnosis system with a learning capability. Table 3 Comparison FD-FL-CBR for deviations compressed in the range of ±70% Method Classic FD Fuzzy CBR
OK diagnosed 17% 14.62% 49.40%
Component OK 46.375% 53.50% 20.25%
Wrong 27% 31.88% 10.37%
The advantage of the proposed methodology for building a CBR-system is that the CBR can be trained by means of simulated instances. Thousands of new cases can be generated easily and very fast. So, the CBR case base is obtained by simulation. Then, when the CBR is used with real data, if the effects described in Section 7 are taken into account, and the parameters given to the CBR are derived from the real signals after an averaging of 60 measures, it has been demonstrated that the diagnosis do not differ significantly when using real circuits or simulated ones. In particular, 10 new sets of real data and 10 new sets of simulated data are taken for comparing the performance of the case base constructed. These sets represent instances corresponding to any fault compressed in the range of ±70% of deviation from nominal. A hundred cases uniformly distributed for each component are generated, so each set has a total of 800 new instances (8 components x 100 faults). The diagnosis results given for each one of these test sets is given in Table 4. Observe that with the appropriate average of the real data, there are small differences when using the case base obtained with simulation for testing new simulated or real data. Hence, as a conclusion, the methodology
proposed for filtering the noise contained in the measures has proven to be quite effective. 9 Conclusions This paper deals with the diagnosis of analog electronic circuits. A review of the literature, shows that in recent years diagnosis of analog electronic circuits has taken on importance once again, after having been pushed aside by digital circuits. Even though circuits are becoming more and more digitalized every day, there is still a small part of analog circuits that makes the process of testing difficult and expensive. The integration of circuits dramatically increases the expectations of the electronic world, but it also makes the test stage extremely complicated. DFT techniques, including the standard IEEE 1149.4, attempt to simplify the problem but, despite the effort, it is far from solved. Also, the literature shows that in recent years, the interest in AI techniques for diagnosing analog electronic circuits has increased. The appearance of a standard, the IEEE 1232, reinforces that idea. Therefore, the design of a new methodology for analog circuit diagnosis makes sense. In this paper two examples of AI techniques are given. The first proposal uses an AI technique based on fuzzy logic. After applying fuzzy modeling to the saturated ramp method, an improvement in the diagnostic is obtained if compared with the classic dictionary. The fuzzy system performs quite well when locating faulty components, but not when estimating the real value of the components. Also, the problem of diagnosing non previously considered faults still remains to be solved. At last a methodology to built a CBR from a fault dictionary is given in section 6. The percentage of success obtained by the proposed CBR method provide improvement on the results with a case base of relatively moderate size, and with the advantage that the system can learn from new situations. This is the case of the biquadratic filter. It is supposed that larger circuits will need more training and the retention of more cases, while for small circuits less trainings will be enough to describe the circuit behavior. But, a good measurement system has to be ensured. For the biquadratic filter and the PCI 6071-E acquisition board, it has been found that by averaging 60 acquired signals, the results are quite similar to those obtained by simulation. For other analog circuits, a similar analysis has to be done in order to derive the minimum number of measures necessary that have to be averaged to eliminate the effect of noise. References 1. C. Pous Sabadi, Case-Based Reasoning as an Extension of Fault Dictionary Methods for Linear Electronic Analog Circuits Diagnosis, ser. Thesis. Universitat de Girona.
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OK 48,75 47,37 48,00 49,25 46,00 46,00 45,62 50,50 45,12 47,12 47,37
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Compo 20,13 24,50 24,12 22,37 25,00 21,87 24,62 22,25 24,62 23,75 23,32
Module 14,13 10,25 10,12 10,25 11,50 15,50 13,25 11,12 11,37 11,37 11,89
Wrong 10,25 10,75 11,12 11,37 11,12 11,25 10,37 10,37 12,62 12,50 11,17
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