Application of Extension Neural Network Type-1 to Fault Diagnosis of Electronic Circuits

The values of electronic components are always deviated, but the functions of the modern circuits are more and more precise, which makes the automatic fault diagnosis of analog circuits very complex and difficult. This paper presents an extension-neural-network-type-1ENN-1based method for fault diagnosis of analog circuits. This proposed method combines the extension theory and neural networks to create a novel neural network. Using the matter-element models of fault types and a correlation function, can be calculated the correlation degree between the tested pattern and every fault type; then, the cause of the circuit malfunction can be directly diagnosed by the analysis of the correlation degree. The experimental results show that the proposedmethod has a high diagnostic accuracy and is more fault tolerant than the multilayer neural network MNN and the k-means based methods.


Introduction
In the real situation, there are certain errors in the electronic components.For example, the last color ring of electronic resistance is used to specify the range of errors.Therefore, every component would have errors when they are produced by the factory.This would result the shift of the circuit.As long as the errors are still in the acceptable range, the circuit is still normal.But when the value of the component is out of the error range, there would be faults.Therefore, the faults of circuit include two types: hard fault and soft fault 1 .Generally speaking, hard fault happens when the circuit is burned and cannot be operated, while soft fault happens when the value of the circuit is out of the acceptable range but can still work.The result of output is wrong and may destroy the output of the circuit.Compared with hard fault, soft fault is harder to detect 2, 3 .The value of the component which shifts less than 5% is normal and acceptable in the range of errors.The value of the component shifting from

Extension Neural Network Type-1
The extension neural network type-1 ENN-1 introduced by this author is a new pattern classification system based on concepts from extension theory and neural networks.ENN-1 permits that clustering problems have a range of features, supervised learning, continuous input, and discrete output.This new neural network is the first combination of extension set theory and neural network.The extension theory provides a novel distance measurement for classification, and the neural network can embed the salient features of parallel computation power and learning capability.The ENN-1 is a relatively new neural network model and has been shown to be successful as a classifier using the well-known Iris dataset and the more complex problems 9, 10 .

Structure of the ENN-1
ENN-1 has been successfully applied to fault diagnosis of 12 actual cases, the schematic structure of the ENN-1 is depicted in Figure 1.It comprises both the input layer and the output layer.The nodes in the input layer receive an input feature pattern and use a set of weight parameters to generate an image of the input pattern.In this network, there are two connection values weights between input nodes and an output node; one weight w L kj represent the lower bound for this classical domain of the features and the other weights w U kj represents the upper bound.This image is further enhanced in the process characterized by the output layer.Only one output node in the output layer remains active to indicate a classification of the input pattern.The learning algorithm of the ENN-1 is discussed in the next section.

Learning Algorithm of the ENN-1
The learning of the ENN-1 is a supervised learning.Before the learning, several variables have to be defined.number of the feature of patterns and the category of the ith pattern is p.To evaluate the clustering performance, the total error number is set as N m , and the total error rate E T is defined below: The detailed supervised learning algorithm can be described as follows.
Step  Step 4. Use the extension distance ED, Figure 2 to calculate the distance between the input pattern X p i and the kth cluster as follows: Step 5. Find the k, such that ED ik = min{ED ik }.If k p, then go to Step 7, otherwise go to Step 6.
Step 6. Update the weights of the pth and the kth clusters as follows: where η is a learning rate, set to 0.1 in this paper.From this step, we can clearly see that the learning process is only to adjust the weights of the pth and the mth clusters.
Step 7. Repeat Step 3 to Step 6; if all patterns have been classified, then a learning epoch is finished.
The second-order high-pass filter.
Step 8. Stop if the clustering process has converged, or the total error rate has arrived at a preset value, otherwise, return to Step 3.

ENN-1 Recognition Stage
After finishing learning ENN-1, we can classify or distinguish the fault types by the following steps.
Step 1. Read the weight matrix which is learned by extension neural network.
Step 2. Calculate each middle value, just like function 2.3 .

2.7
Step 4. Calculate distance between test sample and each group by extension distance if 2.5 .
Step 5. Find out k * , using ED ik * min ED ik , and set O ik * 1 of the cluster categories.
Step 6.If all test samples have been classified completely, it stops; otherwise, turn back to Step 3.

The Proposed Fault Diagnosis Method
The tested circuit of this paper was the second-order high-pass filter as shown in Figure 3. Second-order high-pass filter is a signal filter that passes high frequencies well but attenuates frequencies lower than the filter cutoff frequency.The actual amount of attenuation for each frequency is a design parameter of the filter.For different filters, the attenuation level of each frequency signal is different.It is called a low-cut filter when it used in audio applications.In this paper, the DC gain of the filter is set to 1.586 and the cutoff frequency is set to 7.96 kHz.Nodes 1 and 2 are the testing node where voltage can be measured or simulated.A list of the nominal values of components is presented in Table 1.

The Various Situations of Analog Circuits
The circuit under test was simulated both at normal and all faulty conditions by using PSPICE software; the tolerance normal range was selected with deviation of about ±5% of the nominal values, and soft fault was deviation of about ±20%.By analyzing sensitivity of the circuit under test, R 1 , R 2 , R 3 , R 4 , C 1 , and C 2 are selected to be the fault components; the preselected set of single faults of the test circuit are presented in Table 2.
The measurement point in the study is node 1 and node 2 which are transient voltage and phase spectrum as four test signals and simulate normal and various fault condition.Figures 4, 5, 6 and 7 show the RMS value of transient voltage and phase spectrum by R 1 as the fault components to simulate the correct and soft fault on the node 1 and node 2. Using the Monte-Carlo needle produces 30 training sets for each fault type in training phase; in addition, every fault type can build 11 matter element models.Figure 8 in this paper designs a user interface of fault diagnosis for this analog circuit by the LabVIEW, and Figure 9 shows a diagnostic fault in R 2 and also shows in the fault-displayed window a twinkling green light to alert user to in which the circuit element fault was happening.

ENN1-Based Fault Diagnosis Method
If the circuit components have fault, that can cause the function to change in a circuit.In this study, the circuit faults can be divided into 11 types 1 for normal, 10 for the soft fault , and using PSPICE software simulates various faults, and then we used the ENN-1 to diagnose the Frequency (kHz) Phase angle (deg.)Fault diagnosis of electronic circuit   fault conditions of the testing circuit.The proposed fault has been successfully implemented using LabVIEW software for fault diagnosis of electronic circuit.The overall operation flowchart is shown in Figure 10.Using the proposed method can be simply described as follows.
Step 1. Set up the training pattern.
Step 2. Set up the structure of the ENN-1 that has 4 input nodes and 11 output nodes in this paper.
Step 3. Train the ENN-1 using the proposed learning algorithm in Section 2.2.
Step 4. Go to Step 3 if training process is not finished; otherwise go to Step 5.
Step 5. Save the weight vector of the trained ENN-1.
Step 6. Use the trained ENN-1 to diagnose the fault types of the electronic circuit.
Basically, the learning time of the proposed method is shorter than the traditional neural-based methods due to the fact that initial weights of ENN-1 can be directly determined from training data according to the upper bound and lower bound of input features of pattern.

Experimental Results and Discussion
The fault types are divided into 11 categories in this paper, every fault type has 30 sets and total 390 sets of the training data for the training stage.After completing the training stage, this diagnosis system can carry out the fault diagnosis.Table 3 shows the typical circuit signal  4 is the smallest, so the circuit neither has a fault nor is normal.The proposed method cannot only diagnose the circuit fault type but also know the circuit potential failure factors by the correlation index and then in the future can early maintain the circuit to prevent more serious faults.
Table 5 shows the accuracy by using the multilayer neural network MNN , k-means, and the proposed ENN-1-based method to diagnose the soft fault of tested circuit.There are total 390 sets of the new data for the testing diagnosis.The maximum testing accuracy is 89% in the MNN and 85% in the k-means-based method.The testing accuracy of proposed method is 97%.It is clearly shown that the proposed ENN-1 diagnosis method is better than the other methods in both the training and testing stages.The accuracy rates of the proposed ENN-1 based method are 99% and 97% in training and testing stages, respectively.It is obvious that the ENN has strong generalized capability.Moreover, the training times of proposed method are also less than the MNN.The input data of a diagnosis system would unavoidably contain some noise and uncertainties.The sources of error include environmental noise, transducers, human mistakes, and so forth, which could lead to data uncertainties.To take into account the noise and uncertainties, 390 sets of testing data were created by adding ±5 to ±15 of random, uniformly distributed error to the training data to appraise the fault-tolerant abilities of the proposed method.The test results using different amounts of errors added are given in Table 6.Usually, the error-containing data indeed degrade the diagnosis capabilities in proportion to the amounts of error added.Table 6 shows that the proposed methods all bear remarkable tolerance to the errors contained in the data.The proposed methods show good tolerance to added errors and have high accuracy rate of 71% in extreme error of ±15.Contrarily, the accuracy of the MNN-based method is only 39%, and the k-mean method is only 30% under the same conditions.

Conclusions
This paper presents a novel fault diagnosis method based on ENN-1 for analog circuits.Compared with other traditional AI methods, the proposed ENN-1-based method can achieve the higher accuracy.The calculation of the proposed diagnosis algorithm is also fast and simple.According to the simulation results, the proposed method has a significantly high degree of diagnosis accuracy and shows good tolerance to the errors added.This new approach merits more attention, because the ENN-1 deserves serious consideration as a tool in fault diagnosis or pattern recognition.We hope this paper will lead to further investigation for industrial applications.

Figure 2 :
Figure 2: The proposed extension distance ED .

Figure 4 :
Figure 4: The phase spectrum between normal and soft fault at node 1.

Figure 5 :
Figure 5: The phase spectrum between normal and soft fault at node 2.

Figure 6 :
Figure 6: The RMS value of voltage between normal and soft fault at node 1.

Figure 7 :
Figure 7: The RMS value of voltage between normal and soft fault at node 2.

Figure 8 :
Figure 8: The window of the fault diagnosis system.
Let training pattern set be X {x 1 , x 2 , . . ., x N p }, where N p is the total number of training patterns.The ith pattern is X

Table 1 :
The nominal value of high-pass filter.

Table 2 :
The tolerance ranges of normal and soft faults for the circuit components.

Table 3 :
The circuit data with different fault types partial samples .The partial relation indexes of soft faults are shown in Table4, the relation indexes of using ENN-1 to diagnose training sample.For example, the correlation index of the third data and first type in Table

Table 4 :
Correlation indexes of the ENN-1 after diagnosis partial results .

Table 5 :
Diagnosis performances of different methods.

Table 6 :
Diagnosis performances of errors added.