An Experimental Investigation on Feature Extraction and Fault Detection in Analog Circuits Using Fuzzy Logic and Neural Network

The CUT used in this work is the Sallen-key band pass filter. By using the transfer function of filter, we can extract some features of the circuit, such as gain margin, poles and zeroes and frequency… Based on the characteristics of the feature extracted, fault classification methods can be selected. Double faults are used to create the fault table. In single faults, value of any one particular component is changed at a time. Whereas in double fault values of two components are changed at a time. The feature extracted from the transfer function in this work is the value of the poles. The work flow of the proposed method is shown in Figure 1.

The CUT is simulated under fault-free conditions and its performance has to be tabulated; then faults have to be induced in the circuit by gradually varying the components value in the filter. After changing the component’s value, the circuit has to be simulated, and its performance has to be tabulated. A fault dictionary is created by repeating the above process for all the components.

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Figure 1. Working method of the proposed system with fuzzy logic

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Figure 2. Sallen-key Bandpass filter

FIS is used to classify the faults; triangular membership function is selected in this method for its simplicity. Figure 2 shows the Sallen-Key Bandpass filter, a Voltage-Controlled Voltage-Source (VCVS) filter topology. sallen-key Bandpass filter is used as the CUT in this work because of its simple design with high input impedance and an easily selectable gain.

Transfer function of the filter is

$\mathrm{G}(\mathrm{s})=\frac{\mathrm{SAoG1C1}}{\mathrm{S}^2 \mathrm{C} 1 \mathrm{C} 2+\mathrm{S}\left(\mathrm{G} 3 \mathrm{C} 1+\mathrm{G} 3 \mathrm{C} 2+\mathrm{G} 1 \mathrm{C} 1+\mathrm{C} 1 \mathrm{G} 2\left(1-\mathrm{A}_o\right)\right)+\mathrm{G} 3(\mathrm{G} 1+\mathrm{G} 2)}$

2.1 Feature extraction

Before creating a fault table, feature extraction is very important. In parametric fault detection using the transfer function, one can extract many features such as gain, phase margin, frequency, poles and zeroes is shown in Figure 3. Based on the method used to classify the fault, features are selected. In this paper, poles and zeroes are extracted from the transfer function for each fault.

Table 2. Fault table for R3 & C1

Table 3. Fault table for R3 & C2

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Figure 3. Various features extracted for both faulty and non-fault conditions of Sallen-key band pass filter

Fault table is created by introducing the faults and tabulating their response. In this paper, double faults are introduced, and the corresponding poles and zeros values.

Table 1 shows the Fault index value with corresponding fault conditions of R1 and R2. Similarly Table 2 shows the fault condition of components R3 and C1 and Table 3shows the fault conditions of R3 and C2, Table 4 shows the fault condition of R2 and C2 and Table 5 shows the fault condition of R1 and C1 with corresponding fault index values are tabulated. The step size for each fault is 10% of the original value of the components. This step size covers from -50% to +50% for the actual value of the component.

Table 4. Fault table for R² & C²

2.2 Fault classification

Fuzzy logic has been used to classify the faults. Once the fault table has been generated, based on the fault index and the feature that has been extracted, a suitable fault classification method has to be employed. For double faults with poles and zeros as features extracted from the transfer function, fuzzy logic is the suitable method for fault classification. In fuzzy logic, there are two types: Mamdani FIS and Sugeno FIS, in this paper, for fault classification Mamdani FIS is used. Figure 5 Shows the membership function of the proposed method.

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Figure 4. Fault Percentage of R1 and R2 from Table 1

Figure 4 shows the fault percentage of R1 and R2 from Table 1. Value of R1 and R2 is changed from -50% to +50%.

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Figure 5. FIS of the proposed system

Table 5. Fault table for R1 & C1

2.3 Fuzzy inference system

Once the fault table has been generated successfully, a suitable fault classification method needs to be used. In this paper, Mamdani FIS is used to classify the faults because there is no linear relationship between the inputs and outputs. In the FIS Membership function, the number of inputs is selected based on the feature extracted from the transfer function. In this work, poles are extracted from the transfer function and fault dictionary is created with the values of poles which is a complex number with a real and imaginary part. Figure 6 shows the fuzzy membership functions of the proposed model.

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Figure 6. Fuzzy membership functions

2.4 Fuzzy rule set

?????? are tabulated. The step size for each fault is 10% of the original value of the components. This step size covers from -50% to +50% for the actual value of the component. For inputs and outputs, corresponding membership functions can be selected and connected either using OR operator or AND operator. AND operator is used as a connector. If (MF1 - input) and (MF2 - input) then (MF – output).

2.5 Neural network

Unlike fuzzy, a Neural network can predict the fault by training the network with the values from fault dictionary. This process of selecting the inputs from a dataset and mapping it to the desired output is called neural fitting.

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Figure 7. Neural network model

Based on the fault table, the values are processed using fuzzy logic. Figure 11, shows the rule viewer of the FIS, where pole values from table 1 are entered and their corresponding fault index value is reflected in the rule viewer. Using fuzzy logic, faults are classified, and can be located. The components can be identified with respect to the fault index and how much its value has been deviated from its original value can also be identified. For this problem, Fuzzy logic entirely depends on the fault dictionary; fuzzy cannot locate a fault that is not present in the fault dictionary. In a Neural network, fault dictionary values are trained, and can predict new faults. For the neural network model proposed in the paper, the best validation occurred at the first epoch itself. However, the anticipated model can be improved by analyzing various fault models and optimization algorithms.