Measurement point selection method for analog circuit fault diagnosis based on amplitude-phase aliasing degree

Abstract

The invention discloses a measuring point selection method for analog circuit fault diagnosis based on amplitude-phase aliasing degree, and the method comprises the steps: collecting the amplitude-frequency and phase-frequency data of a detected circuit, and constructing a Gaussian probability density curve based on the amplitude and phase sample distribution on a frequency point; the minimum value of the amplitude and phase aliasing region area between different fault modes is used as an amplitude-phase aliasing degree evaluation index; an integer coding table is generated according to a preset threshold value, the fault isolation degree is calculated, iterative optimization is conducted on the test point and test frequency combination through a heuristic graph search algorithm till the fault isolation degree tends to be in a stable state, and at the moment, the corresponding test point set and the corresponding frequency set are optimal solutions. According to the optimal solution, the coverage range of the analog circuit fault can be remarkably expanded, the defects existing in a traditional measuring point selection method are effectively overcome, and a more efficient and reliable solution is provided for measuring point selection of analog circuit fault diagnosis.

Description

Technical Field

[0001] The present invention relates to the field of analog circuit fault diagnosis, including the selection of measurement points for analog circuit fault diagnosis and heuristic search methods, and particularly relates to a method for selecting measurement points for analog circuit fault diagnosis based on amplitude-phase aliasing degree. Background Art

[0002] In modern electronic systems, the integration degree of digital-analog hybrid circuits is getting higher and higher, and the analog circuit fault diagnosis and testing technology has gradually become a research hotspot. To improve the efficiency of analog circuit fault diagnosis and reduce the testing cost, researchers usually select as few measurement points as possible to test the circuit without affecting the test results.

[0003] The goal of measuring point selection for analog circuit fault diagnosis is to find a set of optimal measurement point combinations in all optional measurement points of the circuit under test that can cover the most fault modes. The measurement point combination is also called a measurement point set. As the number of measurement points increases, the solution space grows exponentially. Therefore, redundant measurement points will cause excessive overhead and do not significantly improve the test effect.

[0004] The measurement point selection for analog circuit fault diagnosis mainly consists of two parts: a fault fuzzy group and a measurement point selection algorithm. Fault modes in different fuzzy groups can achieve fault isolation, while fault modes within the same fuzzy group cannot be distinguished. The ability of a set of measurement points to isolate fault modes is characterized by the fault isolation degree. The larger the isolation degree, the more fault fuzzy groups there are under this measurement point set, the fewer fault modes there are under the fault fuzzy group, the more fault modes that can be isolated, and the more extensive the covered fault modes.

[0005] Components in the circuit will have different degrees of parameter offset during long-term operation. The situation where the circuit malfunctions due to the parameter offset of a certain component is called a fault mode. Since the circuit consists of multiple components, there are multiple different fault modes in a circuit. The core goal of measuring point selection in analog circuit fault diagnosis is to maximize fault coverage, and its essence is to minimize the confusion degree between different fault modes by optimizing the test strategy. To achieve this goal, a fault group analysis strategy is usually adopted, that is, all possible fault modes are combined in pairs, and the distinguishable characteristics of each fault group are quantitatively analyzed, and then the selection of test points is optimized. Specifically, this method aims to reduce the confusion degree index of the fault group, thereby significantly improving the identification ability of the fault diagnosis system for different fault modes, and finally effectively improving the fault coverage rate.

[0006] The fault dictionary method is one of the most commonly used technical means. This method stores the voltage response characteristics under different fault modes by constructing a fault dictionary. In the specific implementation process, specific voltage thresholds are usually set based on engineering experience to divide the fault feature space. When the output signals of the fault group at the same test node all fall within the set voltage threshold range, it can be determined that the fault group is indistinguishable at this measurement point. Based on this principle, the system classifies all fault modes with similar voltage responses into the same fault fuzzy group and stores and represents them in the form of an integer coding table. In this coding representation method, different fault modes belonging to the same fault fuzzy group will be assigned the same integer code. This representation method not only facilitates computer processing and analysis but also effectively improves the efficiency of fault diagnosis. By optimizing the setting of voltage thresholds and the selection of test points, the scale of the fault fuzzy group can be minimized, thereby improving the accuracy of fault diagnosis. However, when there are many types of faults, it is unreasonable to use only one voltage threshold to divide all faults with this method, and the integer coding table cannot evaluate the faults that have not been isolated more carefully. At the same time, when using the rule algorithm to select test points, when the number of test points is large, the calculation efficiency is low, and the results are also random.

[0007] In recent years, clustering methods have emerged to replace the traditional fault dictionary method. The aliasing degree under different fault modes is characterized by the accuracy rate of the clustering results, that is, the fault aliasing degree. When the fault aliasing degree is higher than the threshold set according to expert experience, it is judged that the two fault modes are indistinguishable. Based on the fault aliasing degree and the threshold, an integer coding table can be obtained. If the two fault modes in the fault group are indistinguishable, they are coded as 0, otherwise as 1. And based on the integer coding table and the fault aliasing degree, the fault isolation degree of this measurement point set can be obtained.

[0008] The fault aliasing degree introduced here can more intuitively characterize the distinguishable degree of the fault pair, overcoming the unreasonableness of using only one voltage threshold to divide all faults in the traditional method, and effectively evaluating the faults that have not been isolated. However, the clustering method often has randomness; in addition, the traditional fault dictionary method and the clustering method in recent years ignore the selection of the test signal frequency, that is, the frequency measurement selection. The response characteristics of circuit components to test signals with different frequencies are different. The frequency selection of the test signal directly affects the extraction effect of fault features. An appropriate frequency range can amplify the fault features and improve the detectability of faults; while improper frequency selection may cause the fault features to be masked or distorted. Summary of the Invention

[0009] In view of the deficiencies of the prior art, the present invention proposes a method for selecting measurement points for analog circuit fault diagnosis based on the amplitude-phase aliasing degree, so as to solve the randomness of the fault aliasing degree in the prior art, as well as the low efficiency and uncertainty of the measurement point selection algorithm, and introduce the frequency selection of the test signal to improve the effect of measurement point selection.

[0010] According to the phenomenon that different component parameter offsets in the circuit lead to slight differences in the output signal of the circuit, but the fault resolution capabilities of different measurement points are also different. Selecting poor measurement points will not only mislead the test results but also increase the test cost. A measurement point refers to a physical position node specifically set in the circuit system for signal acquisition and status monitoring. These nodes, as the key elements of circuit observability, undertake the important function of obtaining circuit operation status information. From a technical perspective, the selection of measurement points needs to comprehensively consider multiple factors such as circuit topology, fault feature distribution, and measurement feasibility. An ideal measurement point should have good accessibility, be able to accurately reflect the operating state of the circuit, and have significant diagnostic value for fault location. In practical applications, measurement points are usually set at key node positions of the circuit, such as the output end of an amplifier, filter nodes, or power supply access points, etc., in order to obtain the most representative circuit status information. Through scientific and reasonable selection of measurement points, the accuracy and efficiency of fault diagnosis can be effectively improved, providing reliable data support for the maintenance and troubleshooting of the circuit system.

[0011] In order to improve the test effect of measurement point selection, that is, to maximize fault coverage, the present invention adds the selection of test excitation frequency, namely frequency measurement selection, during the measurement point selection process. Frequency measurement selection is a key technical link, which refers to a technical method for further optimizing the selection of test signal frequencies on the basis of determining the test node positions. This selection process needs to comprehensively consider the working characteristics of the circuit and the characteristics of fault modes. From a technical principle perspective, different test frequencies will produce different responses to various components in the circuit. Therefore, selecting appropriate test frequencies can effectively improve the significance and detectability of fault features. Reasonable frequency measurement selection can not only improve the accuracy of fault diagnosis but also optimize the test efficiency and reduce the test cost. By combining measurement point selection with frequency measurement selection, a more perfect test scheme can be constructed to improve the overall effect of analog circuit fault diagnosis.

[0012] The present invention only targets soft faults of resistors and capacitors in a circuit, and each fault occurs in only a single component, excluding the special case where multiple components fail simultaneously. A soft fault refers to the situation where the resistance value or capacitance value deviates by ±30% from the nominal value. For example, for a resistor with a nominal value of 100 kΩ, a soft fault would be 70 kΩ or 130 kΩ. The circuit to be diagnosed is collectively referred to as the circuit under test. If there is only 1 resistor-capacitor component in a circuit under test, then there are 3 fault modes for this circuit, namely, deviation to 70% of the nominal value, no fault, and deviation to 130% of the nominal value. If there are 2 resistor-capacitor components, then there are 5 fault modes for this circuit, and no fault is also considered as one of the fault modes.

[0013] In the present invention, the calculation of the fault aliasing degree adopts a strategy based on fault group analysis. This strategy first systematically combines all possible fault modes in the circuit in pairs to form a complete set of fault groups. The fault aliasing degree is used to quantitatively evaluate the distinguishability of a pair of faults at a specific test node. Taking a circuit with 5 fault modes as an example, through the principle of combinatorial mathematics, C5 2 = 10 different fault groups can be generated. The distinguishability characteristics of each fault group are characterized by a quantitatively calculated fault aliasing degree index, which can accurately reflect the similarity degree of the test responses of the two fault modes in the fault group.

[0014] In the present invention, the determination of the distinguishability of each fault mode within a fault group needs to comprehensively consider the fault aliasing degree and a preset discrimination threshold. This threshold is a key parameter for fault isolation determination. Specifically, when the aliasing degree value of a fault group at a certain measurement point is lower than the preset threshold, it can be determined that the fault group is effectively isolated at this measurement point, and the two fault modes in the fault group should be classified into different fault fuzzy groups. On the contrary, if the aliasing degree value is higher than the threshold, it indicates that there is confusion in the fault group at this measurement point, and the two fault modes in the fault group should be classified into the same fault fuzzy group. By reasonably setting and dynamically adjusting this threshold, a balance can be achieved between the accuracy of fault diagnosis and the test cost, thereby optimizing the performance of the entire diagnostic system. At the same time, the determination of this threshold also needs to consider factors such as the noise level and measurement error in the actual application scenario to ensure the reliability of the diagnostic results.

[0015] In the present invention, the construction of the integer coding table depends on the isolation result of the fault group. When the two fault modes in a fault group are effectively isolated, a 1 is marked at the corresponding position in the integer coding table, which indicates that under this test condition, the two fault modes in the fault group have sufficient distinguishability and can be effectively isolated.

[0016] In the present invention, the fault isolation degree is a comprehensive evaluation index, and its calculation takes into account two key parameters, namely the number of fault fuzzy groups and the fault aliasing degree. From a technical principle perspective, the number of fault fuzzy groups directly reflects the number of distinguishable fault modes under the current test conditions, and the larger its value, the stronger the fault isolation ability of the system. On the other hand, the fault aliasing degree quantifies the degree of confusion between the fault modes that cannot be effectively isolated. The lower this index, the better the distinguishability of the remaining fault modes. By organically combining these two parameters, the fault isolation degree can comprehensively evaluate the overall diagnostic performance of the test scheme, providing a reliable quantitative basis for the optimal selection of measurement points. This comprehensive evaluation method not only overcomes the limitations of single indicators but also can effectively guide the improvement of the test scheme, thereby improving the overall performance of the fault diagnosis system.

[0017] In the research on measurement point selection, a simulation software is used to set soft fault parameters for the resistance and capacitance components of the circuit under test, and sweep-frequency simulation analysis is performed for each fault type. Combining with the Monte Carlo method, the frequency response characteristics of each test node under different fault modes are collected, including the amplitude-frequency characteristic and phase-frequency characteristic curves. Based on these frequency response data, Gaussian probability density distribution functions of amplitude and phase are constructed at specific frequency points. By calculating the overlapping area of the Gaussian distribution curves corresponding to two different fault modes in the fault group, the distinguishability of these two fault modes at this frequency point can be quantitatively evaluated. This method for quantifying the fault aliasing degree based on the overlapping analysis of amplitude and phase distributions is defined as the amplitude-phase aliasing degree. This method comprehensively considers the amplitude and phase characteristics of fault modes and can more comprehensively reflect the degree of confusion between fault modes, providing a more accurate quantitative basis for measurement point selection and test frequency optimization. After obtaining the amplitude-phase aliasing degree, an integer coding table is first constructed by comparing the amplitude-phase aliasing degree with a preset threshold. This coding table systematically records the isolation relationships between fault modes, providing basic data support for the division of fault fuzzy groups. Based on the isolation information in the coding table, the system dynamically updates the division results of fault fuzzy groups, classifying distinguishable fault modes into different fuzzy groups. At the same time, combining the aliasing degree data of the fault groups that cannot be effectively isolated, the comprehensive fault isolation degree index under the current test conditions is calculated. Finally, a heuristic graph search algorithm is used to maximize the fault isolation degree. This algorithm is based on a progressive search strategy and gradually approaches the optimal solution by iteratively evaluating the diagnostic performance of candidate measurement point sets. Specifically, the system evaluates the contribution of newly added measurement points and frequencies to the fault isolation degree in each iteration. When it is detected that the expanded measurement point and frequency combination cannot further improve the fault isolation degree index, it is determined that the current combination has reached the optimal. This termination criterion based on performance saturation determination not only ensures the efficiency of the optimization process but also can effectively avoid resource waste caused by overtesting.

[0018] After selecting the measurement points, the present invention uses the selected measurement points and the test frequency signal to obtain the time series data collected from the measurement points, and uses the time series data to complete the analog circuit fault diagnosis. The fault diagnosis method can be completed by using the existing signal processing and pattern recognition technologies.

[0019] The object of the present invention is achieved by the following technical solutions:

[0020] A method for selecting measurement points for analog circuit fault diagnosis based on amplitude-phase aliasing degree, comprising the following steps:

[0021] Simulation data acquisition stage:

[0022] Step 1, after determining the circuit under test, the set of optional measurement points and the set of optional frequencies, soft faults are respectively set for each diagnosable device. For the soft fault conditions of each diagnosable device, which are called fault modes, under the conditions of resistor tolerance of ±5% and capacitor tolerance of ±10%, frequency sweep simulations are performed for each fault mode, and multiple Monte Carlo analyses are respectively carried out to obtain multiple amplitude-frequency curves and phase-frequency curve samples of each fault mode under the set of optional measurement points, thereby obtaining a simulation data set;

[0023] Establishment stage of Gaussian probability density curve:

[0024] Step 2, after obtaining the amplitude-frequency curve and phase-frequency curve samples, there are multiple amplitude and phase distribution points distributed at each frequency. The mean and variance in the amplitude and phase distributions are respectively calculated, and the Gaussian probability density curves of the amplitude and phase distributions are obtained based on the mean and variance;

[0025] Amplitude-phase aliasing degree calculation and integer coding table establishment stage:

[0026] Step 3, after determining all possible fault modes, a complete set of fault groups is generated based on the principle of combinatorial mathematics. For each fault group, the aliasing degree indexes, namely amplitude aliasing degree and phase aliasing degree, are respectively calculated on two independent characteristic dimensions of amplitude and phase;

[0027] Among them, the amplitude aliasing degree reflects the confusion degree of the fault modes in the energy distribution characteristics by quantifying the similarity degree of the fault modes in the signal amplitude response; the phase aliasing degree characterizes the distinguishability of the fault modes in the timing characteristics by evaluating the closeness degree of the fault modes in the phase response characteristics;

[0028] Step 4: Based on the amplitude aliasing and phase aliasing in step 3, considering that the differences in the output signals of different fault modes at the measuring points may be mainly reflected in the amplitude or phase characteristics, an optimized aliasing calculation method is adopted: for the amplitude aliasing and phase aliasing, the smaller value of the two is taken as the amplitude-phase aliasing value of the fault group. The fault aliasing index calculated based on this method is called amplitude-phase aliasing. This minimization selection strategy can effectively capture the most significant distinguishable features between fault modes, thereby realizing the organic combination of amplitude and phase information.

[0029] Step 5: Based on the preset judgment threshold and the amplitude-phase aliasing value calculated in step 4, an integer coding table is constructed:

[0030] When the amplitude-phase aliasing value of a certain fault group is lower than the preset discrimination threshold, it indicates that the two fault modes under the fault group have been effectively isolated under the current test conditions. Based on this judgment criterion, a corresponding integer coding table is constructed, in which the row and column indexes correspond to the fault modes under the fault group respectively. In the integer coding table, if the two fault modes are judged to be isolable, they are marked as 1 at the corresponding position; conversely, if the amplitude-phase aliasing value exceeds the threshold, it is marked as 0. At the same time, based on the isolation information in the coding table, the system dynamically updates the division results of the fault fuzzy group and classifies the distinguishable fault modes into different fuzzy groups.

[0031] Heuristic graph search algorithm to find the optimal frequency set and measurement point set:

[0032] Step six, based on the amplitude-phase aliasing and fault fuzzy group information generated in steps four and five, the fault isolation under the current test conditions is obtained by calculating the mean amplitude-phase aliasing that cannot be effectively isolated and the number of fault fuzzy groups; using the heuristic graph search algorithm, the system gradually searches for the optimal combination from the candidate frequency set and the measurement point set; in each iteration, the algorithm is used to evaluate whether the newly added frequency or measurement point has an improvement effect on the fault isolation, and if the fault isolation is improved, the newly added frequency or measurement point is included in the selected set; during the search process, whenever a new frequency or measurement point is added to the selected set, the system synchronously updates the candidate set and removes the selected elements; when it is detected that the fault isolation index is no longer improved, it is determined that the current selected set has reached the optimal level, and at this point, the measurement point and measurement frequency selection for the fault diagnosis of the circuit under test is completed.

[0033] According to the optimal frequency set and measuring point set obtained in step six, a test signal of a frequency included in the optimal frequency set is input to the circuit under test, and a time series signal is collected at the measuring points included in the optimal measuring point set for subsequent fault diagnosis.

[0034] The present invention proposes innovations based on the amplitude-phase aliasing degree and further incorporating frequency measurement selection into measurement point selection.

[0035] The present invention first performs sweep frequency analysis and Monte Carlo analysis on the circuit under test to obtain the frequency response characteristics of each candidate measurement point. Specifically, the amplitude-frequency characteristics and phase-frequency characteristics curves of the measurement point output are obtained through sweep frequency analysis, and at the same time, the Monte Carlo method is used to simulate the changes in circuit parameters to evaluate the statistical characteristics of the measurement results; based on these analysis data, the system constructs Gaussian probability density distribution curves of amplitude and phase at each frequency point to describe the statistical distribution characteristics of the circuit response; then, based on the relationship between the integral area of the Gaussian probability density curve and the probability distribution, a method for measuring the amplitude-phase aliasing degree is proposed. Combining the amplitude-phase aliasing degree with a preset determination threshold, a corresponding integer coding table is generated; subsequently, the integer coding table is used to update the fault fuzzy group; further, by counting the number of the fault fuzzy group and combining the average value of the amplitude-phase aliasing degree in the case of non-isolation, the specific value of the fault isolation degree is finally calculated; the fault isolation degree can more comprehensively represent the isolation situation of the selected frequency set and measurement point set for the faults in the circuit under test. To reduce the computational overhead, a heuristic graph search algorithm is selected as the measurement point search method, avoiding the disadvantages of low efficiency and random results of the regular algorithm.

[0036] Effects or advantages of the present invention:

[0037] According to the present invention, a set of test signals with specific frequencies is selected to test the circuit under test in different fault modes, which can effectively improve the difference degree of the output signals of the measurement points in amplitude and phase. At the same time, the heuristic graph search algorithm is used to take into account the selection of test frequencies while selecting the measurement points, improving the search efficiency and avoiding the randomness of the results. Since the simulation is carried out under the conditions that the resistor tolerance in the circuit under test is ±5% and the capacitor tolerance is ±10%, it has a certain anti-interference ability. Taking the four-op-amp biquadratic example circuit for simulation verification, the diagnostic accuracy rate in the simulation results is 100%, indicating that the method is feasible and effective and can realize the classification and location of faults. Description of the drawings

[0038] Figure 1 It is the amplitude Gaussian probability density curve graph in the analog circuit measurement point selection method based on the amplitude-phase aliasing degree in the embodiment;

[0039] Figure 2 It is the amplitude sample distribution graph in the analog circuit measurement point selection method based on the amplitude-phase aliasing degree in the embodiment;

[0040] Figure 3 It is the phase sample distribution graph in the analog circuit measurement point selection method based on the amplitude-phase aliasing degree in the embodiment;

[0041] Figure 4 It is the test frequency selection flow chart in the analog circuit measurement point selection method based on the amplitude-phase aliasing degree in the embodiment;

[0042] Figure 5 Schematic diagram of the frequency measurement selection process of the heuristic graph search method in the analog circuit measurement point selection method based on the amplitude-phase aliasing degree in the embodiment;

[0043] Figure 6 Flowchart of the measurement point selection in the analog circuit measurement point selection method based on the amplitude-phase aliasing degree in the embodiment;

[0044] Figure 7 Schematic diagram of the measurement point selection process of the heuristic graph search method in the analog circuit measurement point selection method based on the amplitude-phase aliasing degree in the embodiment;

[0045] Figure 8 Flowchart of the analog circuit measurement point selection method based on the amplitude-phase aliasing degree in the embodiment;

[0046] Figure 9 Circuit diagram of a four-op-amp biquadratic filter. Detailed implementation manners

[0047] The following further elaborates on the content of the present invention in combination with the embodiments and the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention.

[0048] To better understand the present invention, the basic principles and related concepts of the present invention are briefly introduced below.

[0049] Amplitude-phase aliasing degree:

[0050] In order to avoid the inability to carefully evaluate and calculate the uncertainty of the undetected faults caused by using the fault dictionary method and the clustering method to characterize the fault aliasing degree, and to ignore the combined effect of the amplitude and phase at the test frequency, the present invention combines the characteristics of different distributions of the amplitude and phase under different test conditions, where the test conditions are jointly determined by two key parameters, namely the measurement point and the measurement frequency. After obtaining the amplitude-frequency curve and phase-frequency curve samples, at each frequency, the mean and variance of the amplitude and phase distributions are calculated in sequence, and a Gaussian probability density curve is established. The Gaussian density curve equation of the amplitude is shown in Equation (1), and the Gaussian density curve equation of the phase is shown in Equation (2):

[0051]

[0052] In Equation (1) and Equation (2), at a certain frequency, g Amp represents the sample value of the amplitude, and g Pha represents the sample value of the phase; μ Amp represents the sample mean of the amplitude, and μ Pha represents the sample mean of the phase; σ AmpThe sample variance representing the amplitude, σ Pha The sample variance representing the phase; G Amp The Gaussian probability density curve representing the amplitude, G Pha The Gaussian probability density curve representing the phase. The schematic diagram of the amplitude Gaussian probability density curve is as shown in Figure 1 shown. The figure respectively presents the amplitude-frequency characteristic curves of the fault group under two different fault modes and their corresponding amplitude Gaussian distribution density curves G Amp . The establishment process of the phase-frequency curve and the phase Gaussian probability density curve is the same as that of the amplitude and will not be shown.

[0053] According to the principle of the Gaussian probability density curve, the integral area within a certain range is equal to the probability that the sample value falls within that range. Therefore, the overlapping area of the fault group can be expressed as the probability value that the samples cannot be distinguished between different fault modes under the fault group. The overlapping area of the Gaussian probability density curves of the amplitude under different fault modes is as shown in Equation (3), and the overlapping area of the Gaussian probability density curves of the phase under different fault modes is as shown in Equation (4):

[0054]

[0055] In Equation (3) and Equation (4), at a certain frequency, AF Amp represents the overlapping area characterizing the amplitude characteristics of the fault group, that is, the amplitude overlapping degree. Similarly, AF Pha is the phase overlapping degree; G Amp1 and G Amp2 represent the amplitude Gaussian probability density curves under the fault group. Similarly, G Pha1 and G Pha2 represent the phase Gaussian probability density curves; g Amp1 and g Amp2 represent the samples of the amplitude under the fault group, and g Pha1 and g Pha2 represent the samples of the phase; G' Amp represents the intersection point of the amplitude Gaussian probability density curve, and G' Pha represents the intersection point of the phase Gaussian probability density curve; Since the integral of the Gaussian probability density curve over the real number range is 1, the overlapping area is greater than 0 and less than or equal to 1. The size of the overlapping area directly reflects the degree of distinguishability between two different fault modes in the feature space. The amplitude Gaussian probability density curve diagram is as shown in Figure 2 part a in the figure, and the corresponding amplitude sample distribution is as shown in Figure 2 part b in the figure. Similarly, the phase Gaussian probability density curve and the phase sample distribution are as shown in Figure 3 shown; Considering that the differences in the measured point output signals of different fault modes are mainly reflected in the amplitude or phase characteristics, an optimized overlapping degree calculation method is adopted: for AF Amp and AF Pha, take the smaller value of the two as the final aliasing degree value of this fault group. The fault aliasing degree index calculated based on this method is called the amplitude-phase aliasing degree AF, and the calculation is shown in Equation (5):

[0056]

[0057] Integer coding table:

[0058] The distinguishability determination of each fault mode within the fault group needs to comprehensively consider the amplitude-phase aliasing degree and the preset discrimination threshold, which is a key parameter for fault isolation determination. Specifically, when the aliasing degree value of the fault group at a certain measurement point is lower than the preset threshold, it can be determined that the fault group has achieved effective isolation at this measurement point, and the two fault modes in the fault group should be divided into different fault fuzzy groups; on the contrary, if the aliasing degree value is higher than the threshold, it indicates that there is confusion in the fault group at this measurement point, and the two fault modes in the fault group should be classified into the same fault fuzzy group. When the amplitude-phase aliasing degree value of a certain fault group is lower than the preset discrimination threshold, it indicates that the two fault modes under the fault group have achieved effective isolation under the current test conditions. Based on this determination criterion, a corresponding integer coding table is constructed, where the row and column indexes respectively correspond to the fault modes under the fault group. In the integer coding table, if two fault modes are determined to be isolable, they are marked as 1 at the corresponding positions; on the contrary, if they exceed the threshold, they are marked as 0. According to experience, the threshold is set to 0.15. Based on the amplitude-phase aliasing degree numerical values in Table 1, the integer coding table is shown in Table 2.

[0059] Table 1 Amplitude-phase aliasing degree numerical table

[0060] (T,f) <![CDATA[F1]]> <![CDATA[F2]]> <![CDATA[F3]]> <![CDATA[F4]]> <![CDATA[F1]]> Null 0.15 0.51 0.15 <![CDATA[F2]]> Null Null 0.05 0.71 <![CDATA[F3]]> Null Null Null 0.14 <![CDATA[F4]]> Null Null Null Null

[0061] Table 2 Integer coding table

[0062] (T,f) <![CDATA[F1]]> <![CDATA[F2]]> <![CDATA[F3]]> <![CDATA[F4]]> <![CDATA[F1]]> Null 1 0 1 <![CDATA[F2]]> Null Null 1 0 <![CDATA[F3]]> Null Null Null 1 <![CDATA[F4]]> Null Null Null Null

[0063] In Tables 1 and 2, Null represents empty, (T, f) represents the test conditions, that is, the test results under the measurement point set T and the frequency set f, and F1 represents fault mode 1.

[0064] Fault fuzzy group:

[0065] The fault fuzzy group represents a set of fault categories that cannot be distinguished due to similarity in the time - series signals output at the measurement points. Therefore, the fault categories within the fault fuzzy group cannot be effectively distinguished, while the fault modes in different fault fuzzy groups can be effectively isolated for differentiation. During initialization, all fault modes are divided into one fault fuzzy group. During the subsequent process of measurement point selection, the fault fuzzy group is updated synchronously according to the change in the integer coding table. Based on Table 2, the update of the fault fuzzy group can be achieved on the integer coding table, that is, the two fault fuzzy groups {F1,F3} and {F2,F4}. Since the elements of F1 and F3 in the integer coding table are 0, F1 and F3 belong to the same fault fuzzy group, and the same applies to F2 and F4.

[0066] Fault isolation degree:

[0067] The fault isolation degree can better characterize the fault isolation ability of the measurement point and frequency measurement and the aliasing degree within the fuzzy group. The calculation is shown in Equation (6):

[0068] IF (T,f) =ASN (T,f) +ASA (T,f) (6)

[0069] In Equation (6), IF (T,f) represents the fault isolation degree under the measurement point set T and frequency set f. ASN (T,f) represents the number of fault fuzzy groups under (T,f). ASA (T,f) represents, under (T,f), the difference calculated by subtracting the average value of the amplitude - phase aliasing degree in the case where fault isolation is not achieved from 1. Taking Table 1 and Table 2 as examples, ASA (T,f) is calculated as shown in Equation (7):

[0070]

[0071] Therefore, ASN (T,f) under (T,f) is 2, and the value of IF (T,f) is 2.39.

[0072] Heuristic graph search algorithm:

[0073] The heuristic graph search algorithm transforms the measuring point selection problem into a graph search problem. The process of measuring point selection is the process of expanding graph nodes. In the frequency selection stage, after initialization, the selected frequency set is empty, and the set of candidate frequencies contains the frequency values within the swept frequency range. The fault fuzzy group, integer coding table, and fault isolation degree are imported. A frequency is found from the set of candidate frequencies such that the fault isolation degree increases when combined with the selected frequency set. This frequency is deleted from the set of candidate frequencies and added to the selected frequency set. Since the fault isolation degree has changed, the fault fuzzy group needs to be updated, and the next round of frequency search is entered. When the fault isolation degree no longer increases after combining the frequencies in the set of candidate frequencies with the selected frequency set, that is, the current selected frequency set is the optimal frequency set. The flowchart of test frequency selection is as shown in Figure 4 shown below. Figure 5 This is an example process of frequency measurement selection using the heuristic graph search method, where f is the selected frequency set, and the initialized f is an empty set. There are k frequency values within the swept frequency range. The fault isolation degrees IF are calculated for each frequency in the set of candidate frequencies when combined with the selected frequency set. For ease of understanding, Figure 4 taking three rounds of frequency search as an example for demonstration, represents the fault isolation degree under the measuring point set T, when the selected frequency set f is combined with f1. In the first round of search, the fault isolation degree increases when combined with f2. Therefore, f2 is added to the selected frequency set f. After updating the fault fuzzy group and integer coding table, the next round of frequency search is carried out. The fault isolation degree obtained in the third round of frequency search does not increase. Therefore, the optimal frequency set f is as shown in Equation (8):

[0074] f = {f2, f3} (8)

[0075] In the measuring point selection stage, the initialized set of candidate measuring points contains all optional measuring points, and the selected measuring point set is an empty set. The fault fuzzy group, integer coding table, and fault isolation degree are imported. A measuring point is found from the set of candidate measuring points such that the fault isolation degree increases when combined with the selected measuring point set. This measuring point is deleted from the set of candidate measuring points and added to the selected measuring point set. In each iteration of the measuring point search, the calculation of the fault isolation degree is based on the result of the frequency search. Specifically, first, the selected measuring point set is combined with the new measuring point, and then frequency search is carried out on this combination. The finally obtained fault isolation degree is the optimization result of this measuring point combination. Therefore, the measuring point search process follows the same logic as the frequency search, both gradually improving the fault isolation degree through iterative optimization. In each round of measuring point search, the fault fuzzy group needs to be updated. When the fault isolation degree no longer increases, the current selected measuring point set is the optimal measuring point set. The selected measuring point set is the optimal measuring point set. The flowchart of measuring point selection is as shown in Figure 6 shown below. Similarly, Figure 7 taking three rounds of measuring point search as an example for demonstration, there are a total of K optional measuring points, It represents the fault isolation degree under the combined frequency set f, selected measurement point set T and T1. In the first round of search, the fault isolation degree is improved under the combination with T2. Therefore, T2 is added to the selected frequency set T. After updating the fault fuzzy group, the next round of measurement point search is carried out. The fault isolation degree obtained in the third round of measurement point search does not increase. Therefore, the optimal measurement point set T is as shown in Equation (9):

[0076] T = {T2, T3} (9).

[0077] Embodiment:

[0078] As Figure 8 shown, a method for selecting measurement points in analog circuit fault diagnosis based on amplitude-phase aliasing degree includes the following steps:

[0079] Simulation data acquisition stage:

[0080] S1. Determine the circuit under test, the set of optional measurement points and the set of optional frequencies. Set soft faults for each diagnosable device respectively. Under the conditions of 5% resistor tolerance and 10% capacitor tolerance, for each fault mode, 100 Monte Carlo analyses are carried out respectively under sweep frequency simulation to obtain 100 amplitude-frequency curve and phase-frequency curve samples of each fault mode under the set of optional measurement points, and thus a simulation data set is obtained;

[0081] Gaussian probability density curve establishment stage:

[0082] S2. After obtaining the amplitude-frequency curve and phase-frequency curve samples, 100 amplitude and phase distribution points are distributed at each frequency. Calculate the amplitude mean μ Amp , amplitude variance σ Amp , phase mean μ Pha , phase variance σ Pha , and calculate the Gaussian probability density curves G Amp and G Pha . The calculation is as shown in Equation (10) and Equation (11):

[0083]

[0084] In Equation (10) and Equation (11), g Amp represents the sample value of the amplitude at a certain frequency, and g Pha represents the sample value of the phase at a certain frequency;

[0085] Amplitude-phase aliasing degree calculation and integer coding table establishment stage:

[0086] S3. The overlapping area size of the Gaussian probability density curves of two different fault modes in a fault group can represent the overlapping degree of these two fault modes. For each fault group, calculate the aliasing degree index on two independent characteristic dimensions of amplitude and phase respectively: amplitude aliasing degree AFAmp And the phase aliasing degree AF Pha , which is calculated as shown in Equations (12) and (13):

[0087]

[0088] In Equations (12) and (13), G Amp1 and G Amp2 represent the amplitude Gaussian probability density curves under the fault group. Similarly, G Pha1 and G Pha2 represent the phase Gaussian probability density curves; g Amp1 and g Amp2 represent the samples of the amplitude under the fault group, and g Pha1 and g Pha2 represent the samples of the phase; G' Amp represents the intersection point of the amplitude Gaussian probability density curve, and G' Pha represents the intersection point of the phase Gaussian probability density curve;

[0089] S4. Considering that the differences in the output signals of the measuring points for different fault modes are mainly reflected in the amplitude or phase characteristics, the smaller value between AF Amp and AF Pha is taken as the final aliasing degree value of this fault group. The fault aliasing degree index calculated based on this method is called the amplitude-phase aliasing degree AF, which is calculated as shown in Equation (14):

[0090]

[0091] S5. Based on the preset decision threshold and the amplitude-phase aliasing degree value AF calculated in S4, an integer coding table is constructed; when the amplitude-phase aliasing degree value of a certain fault group is lower than the preset discrimination threshold, it indicates that the two fault modes under the fault group are effectively isolated under the current test conditions; based on this decision criterion, the corresponding integer coding table is constructed, where the row and column indices respectively correspond to the fault modes under the fault group; in the integer coding table, if two fault modes are determined to be isolable, they are marked as 1 at the corresponding positions; otherwise, if the aliasing degree exceeds the threshold, they are marked as 0; at the same time, based on the isolation information in the coding table, the system dynamically updates the division result of the fault fuzzy group, classifies the distinguishable fault modes into different fuzzy groups, and sets the threshold to 0.15 according to experience. Taking the amplitude-phase aliasing degree values in Table 3 as an example, the integer coding table is shown in Table 4:

[0092] Table 3 Amplitude-phase aliasing degree value table

[0093] (T,f) <![CDATA[F1]]> <![CDATA[F2]]> <![CDATA[F3]]> <![CDATA[F4]]> <![CDATA[F1]]> Null 0.15 0.51 0.15 <![CDATA[F2]]> Null Null 0.05 0.71 <![CDATA[F3]]> Null Null Null 0.14 <![CDATA[F4]]> Null Null Null Null

[0094] Table 4 Integer coding table

[0095] (T,f) <![CDATA[F1]]> <![CDATA[F2]]> <![CDATA[F3]]> <![CDATA[F4]]> <![CDATA[F1]]> Null 1 0 1 <![CDATA[F2]]> Null Null 1 0 <![CDATA[F3]]> Null Null Null 1 <![CDATA[F4]]> Null Null Null Null

[0096] In Tables 3 and 4, Null represents empty, (T, f) represents the test condition, that is, the test result under the measurement point set T and the frequency set f, and F1 represents the fault mode 1;

[0097] Heuristic graph search algorithm to find the optimal frequency set and measurement point set:

[0098] S6. First, perform initialization. After initialization, the selected frequency set f and the selected measurement point set T are empty. The frequency set to be selected contains the frequency values within the frequency sweep range, and the measurement point set to be selected contains all optional measurement points. When selecting a frequency, find a frequency from the frequency set to be selected that, when combined with the selected frequency set, can improve the fault isolation degree. represents the fault isolation degree under the combination of the measurement point set T, the selected frequency set f, and f1 in the frequency set to be selected. If is greater than IF (T,f) , then f1 is deleted from the frequency set to be selected and added to the selected frequency set. Since the fault isolation degree has changed, the fault fuzzy group and the integer coding table need to be updated; then, re-divide the fault fuzzy group according to the updated integer coding table and enter the next round of frequency search. When the fault isolation degree no longer improves after combining the frequencies in the frequency set to be selected with the selected frequency set, that is, the currently selected frequency set is the optimal frequency set. Taking Figure 5 as an example, f is the selected frequency set, and the initialized f is an empty set. There are k frequency values within the frequency sweep range. Calculate the fault isolation degree IF for each frequency in the frequency set to be selected when combined with the selected frequency set. For ease of understanding, Figure 5 Taking 3 rounds of frequency search as an example for display, in the first round of search, the fault isolation degree improves under the combination with f2. Therefore, f2 is added to the selected frequency set f. After updating the fault fuzzy group and the integer coding table, perform the next round of frequency search. The fault isolation degree obtained in the third round of frequency search does not improve. Therefore, the optimal frequency set f is as shown in Equation (15):

[0099] f = {f2, f3} (15)

[0100] When selecting measurement points, initialize the measurement point set, the fault fuzzy group, the integer coding table, and the fault isolation degree. Find a measurement point from the measurement point set to be selected that, when combined with the selected measurement point set, can improve the fault isolation degree. There are a total of K optional measurement points. represents the fault isolation degree under the combination of the frequency set f, the selected measurement point set T, and T1. When is greater than IF (T,f), then T1 is deleted from the set of candidate measurement points and added to the selected frequency set T. The fault isolation degree of each round of measurement point search is based on the frequency search, that is, after the selected measurement point set is combined with the new measurement point, frequency search is carried out on this basis. The fault isolation degree after frequency search is the fault isolation degree of the combination of the selected measurement point set and the new measurement point. Therefore, the process of measurement point search is the same as that of frequency search. When the fault isolation degree no longer improves, the currently selected measurement point set is the optimal measurement point set. Similarly, Figure 7 Taking 3 rounds of measurement point search as an example for demonstration, the fault isolation degree improves under the combination with T2 in the first round of search. Therefore, after updating the fault fuzzy group, the next round of measurement point search is carried out. The fault isolation degree obtained in the third round of measurement point search does not improve. Therefore, the optimal measurement point set T is as shown in Equation (16):

[0101] T = {T2, T3} (16)

[0102] S7. For the optimal frequency set f and measurement point set T obtained in S6, input the test signals of the frequencies included in the optimal frequency set into the measured circuit, and collect the time series signals at the measurement points included in the optimal measurement point set to carry out subsequent fault diagnosis work.

[0103] Measurement Point Selection and Analysis of Four-Op-Amp Biquadratic Circuit:

[0104] Taking the fault diagnosis model of the four-op-amp biquadratic circuit as an example, it is detailed how to implement measurement point selection by this method, and frequency measurement selection is added on this basis.

[0105] The simulation experiment is carried out on a personal computer with an Intel(R) Core(TM) i5-4210M CPU. PSPICE 24.1 is used for simulation analysis to obtain the simulation data set, and MATLAB 2022a is used for data processing.

[0106] First, set the test signal source for the simulation circuit. For the four-op-amp biquadratic experiment, the frequency range is selected as 1k - 30kHz, and the waveform is a sine wave. The resistor tolerance in the circuit is 5%, and the capacitor tolerance is 10%. When the actual value of the component deviates from the nominal value by ±30%, it can be determined that the component fails. The four-op-amp biquadratic circuit is as Figure 9 shown, where Input in the figure represents the test signal input point.

[0107] Carry out the simulation experiment, and the steps are as follows:

[0108] 1) After drawing the circuit diagram in OrCAD Pspice, set soft faults for all resistor and capacitor components in the four-op-amp biquadratic circuit. The fault settings are shown in Table 5, where NF represents no fault in the measured circuit.

[0109] Table 5 Fault Modes of Four-Op-Amp Biquadratic Circuit

[0110]

[0111]

[0112] Perform 100 sweep Monte Carlo analyses on each mode in Table 5 respectively to obtain samples of amplitude-frequency curves and phase-frequency curves, and thus obtain a simulation data set;

[0113] 2) After obtaining the samples of amplitude-frequency curves and phase-frequency curves, there are 100 amplitude and phase distribution points distributed at each frequency. Calculate the amplitude mean μ Amp , amplitude variance σ Amp , phase mean μ Pha , and phase variance σ Pha . Taking the measuring point T1, test frequency of 1 kHz, and faults F1 and F2 as examples for display, the mean and variance of the amplitude of F1 are 0.0515 and 0.0033 respectively, and the mean and variance of the phase are 0.0515 and 0.0033 respectively. The mean and variance of the amplitude of F2 are 0.0514 and 0.0033 respectively, and the mean and variance of the phase are 0.0515 and 0.0033 respectively. Calculate the Gaussian probability density curves G A mp and G P ha respectively according to Equations (10) and (11);

[0114] 3) After determining all possible fault modes, generate a complete set of fault groups based on the principle of combinatorial mathematics, and calculate the amplitude aliasing degree AF Amp and phase aliasing degree AF Pha of each fault group. According to Equations (12) and (13), the aliasing degrees of both amplitude and phase are 0.9722;

[0115] 4) For the amplitude aliasing degree and phase aliasing degree, take the smaller value of the two as the amplitude-phase aliasing degree AF of this fault group, and the calculation is as shown in Equation (17):

[0116]

[0117] 5) The preset discrimination threshold is 0.15. When the amplitude-phase aliasing degree is lower than the threshold, it means that the two fault modes included in the fault group are isolated from each other. Based on this judgment criterion, the row and column indexes in the constructed integer coding table correspond to the fault modes under the fault group respectively. If the two fault modes are isolated from each other, the corresponding position in the integer coding table is the element 1, otherwise it is 0; at the measuring point T1 and test frequency of 1 kHz, based on the amplitude-phase aliasing degree values in Table 6, the integer coding table is shown in Table 7;

[0118] Table of amplitude-phase aliasing degree values under (T1, 1 kHz)

[0119] <![CDATA[(T1, 1kHz)]]> <![CDATA[F1]]> <![CDATA[F2]]> <![CDATA[F3]]> <![CDATA[F4]]> … <![CDATA[F 25 > <![CDATA[F1]]> Null 0.972 0.970 9.3e-5 … 0.952 <![CDATA[F2]]> Null Null 0.953 1.2e-4 … 0.602 <![CDATA[F3]]> Null Null Null 7.4e-5 … 0.606 <![CDATA[F4]]> Null Null Null Null … 0.073 … Null Null Null Null … … <![CDATA[F 25 > Null Null Null Null … Null

[0120] Integer coding table under Table 7 (T1, 1kHz)

[0121] <![CDATA[(T1, 1kHz)]]> <![CDATA[F1]]> <![CDATA[F2]]> <![CDATA[F3]]> <![CDATA[F4]]> … <![CDATA[F 25 > <![CDATA[F1]]> Null 0 0 1 … 0 <![CDATA[F2]]> Null Null 0 1 … 0 <![CDATA[F3]]> Null Null Null 1 … 0 <![CDATA[F4]]> Null Null Null Null … 1 … Null Null Null Null … … <![CDATA[F 25 > Null Null Null Null … Null

[0122] 6) Before the heuristic graph search algorithm selects the optimal measurement point set, initialization is performed. After initialization, the selected frequency set f and the selected measurement point set T are empty. The set of candidate frequencies contains all frequencies within the swept frequency range, and the set of candidate measurement points contains all measurement points. First, calculate the fault isolation degree at the test frequency of measurement points T1 and 1kHz, and then calculate the fault isolation degrees at the candidate frequencies in sequence. There are 691 frequencies in the swept frequency range, and there are 4 measurement points in the measured circuit. The fault isolation degrees at each frequency under T1 are shown in Table 8.

[0123] Fault isolation degrees at each frequency under T1 in Table 8

[0124]

[0125]

[0126]

[0127]

[0128]

[0129] According to the heuristic graph search algorithm, frequency search is performed under T1, and the search process is shown in Table 9.

[0130] Frequency search process under T1 in Table 9

[0131]

[0132] As can be seen from Table 9, is 7.48, where f = {f 95 , f 205 , f 90}, and the fault isolation degree of each round of measurement point search is based on the frequency search, that is, after the selected measurement point set is combined with the new measurement point, frequency search is performed on this basis. The fault isolation degree after frequency search is the fault isolation degree of the combination of the selected measurement point set and the new measurement point. Therefore, the measurement point search process is the same as the frequency search. When the fault isolation degree no longer increases, the current selected measurement point set is the optimal measurement point set. The measurement point selection process is shown in Table 10.

[0133] Measurement point frequency measurement search process in Table 10

[0134]

[0135] As can be seen from Table 10, the optimal measurement point set T = {T4, T2}, and the optimal frequency set f is {f 45 , f 82 , f 152 , f 458 , f 691}, corresponding to 5.4 kHz, 9.1 kHz, 16.1 kHz, 46.7 kHz, 70 kHz respectively. The fault fuzzy sets under (T, f) are {F1, F 23 , F 24 , F 25}, {F4, F 12}, {F5, F 13}, {F 14 , F 17}, {F 15 , F 16}, {F2}, {F3}, {F6}, {F7}, {F8}, {F9}, {F 10}, {F 11}, {F 18}, {F 19}, {F 20}, {F 21}, {F 22}, a total of 18 fault fuzzy sets;

[0136] 7) Input a sine wave with a frequency within the optimal frequency set f to the circuit under test, and collect time series signals at the measurement points included in the optimal measurement point set T to complete the fault diagnosis. The diagnosis results are shown in Table 11:

[0137] Table 11 Diagnosis Results

[0138]

[0139] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The protection scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for selecting measurement points in analog circuit fault diagnosis based on amplitude-phase aliasing degree, characterized in that By collecting the amplitude-frequency and phase-frequency data of the circuit under test, constructing a Gaussian probability density curve based on the amplitude and phase sample distributions at frequency points, and taking the minimum value of the area of the amplitude-phase aliasing region between different fault modes as the amplitude-phase aliasing degree evaluation index; generating an integer coding table according to a preset threshold, calculating the fault isolation degree, and using a heuristic graph search algorithm to iteratively optimize the combination of measurement points and test frequencies until the fault isolation degree tends to a stable state, and the corresponding measurement point set and frequency set at this time are the optimal solutions.

2. The method for selecting measurement points for analog circuit fault diagnosis based on amplitude-phase aliasing degree according to claim 1, wherein It includes the following steps: Step 1: Determine the circuit under test, the optional measurement point set and the optional frequency set. Set soft faults for each diagnosable device respectively. For the soft fault situation of each diagnosable device, it is called a fault mode. Conduct a frequency sweep simulation for each fault mode, and perform multiple Monte Carlo analyses respectively to obtain multiple amplitude-frequency curves and phase-frequency curve samples of each fault mode under the optional measurement point set, and obtain a simulation data set. Step 2: After obtaining the amplitude-frequency curve and phase-frequency curve samples, there are multiple amplitude and phase distribution points distributed at each frequency. Calculate the mean and variance of the amplitude and phase distribution points respectively, and obtain the Gaussian probability density curve of the amplitude and phase distributions based on the mean and variance. Step 3: After determining all possible fault modes, generate a complete set of fault groups for all fault modes based on the principle of combinatorial mathematics. For each fault group, calculate the aliasing degree index in two independent characteristic dimensions of amplitude and phase respectively to obtain the amplitude aliasing degree and the phase aliasing degree. Step 4: Based on the amplitude aliasing degree and the phase aliasing degree in Step 3, take the smaller value of the two as the amplitude-phase aliasing degree value of this fault group. Step 5: Based on the preset decision threshold and the amplitude-phase aliasing degree value calculated in Step 4, construct an integer coding table: When the amplitude-phase aliasing degree value of a certain fault group is lower than the preset discrimination threshold, it indicates that the two fault modes under the fault group are effectively isolated under the current test conditions; based on this decision criterion, construct the corresponding integer coding table, where the row and column indexes respectively correspond to the fault modes under the fault group; in the integer coding table, if two fault modes are determined to be isolable, mark 1 at the corresponding position. Conversely, if the amplitude-phase aliasing degree exceeds the threshold, mark 0; based on the isolation information in the coding table, the system dynamically updates the division result of the fault fuzzy group, and classifies the distinguishable fault modes into different fuzzy groups. Step 6: Calculate the fault isolation degree under the current test conditions by calculating the mean value of the amplitude-phase aliasing degree that cannot be isolated and the number of fault fuzzy groups; use a heuristic graph search algorithm to gradually find the optimal combination from the candidate frequency set and the measurement point set. In each iteration, the algorithm evaluates whether adding a new frequency or measurement point can improve the fault isolation degree, and decides whether to include it in the selected set accordingly. If the fault isolation degree is improved, the new frequency or measurement point is included in the selected set; during the search process, whenever a new frequency or measurement point is added to the selected set, the system synchronously updates the candidate set and removes the selected elements; when it is detected that the fault isolation degree index no longer improves, it is determined that the current selected set is optimal. Thus, the selection of measurement points for fault diagnosis of the circuit under test is completed.

3. A measuring point selection method for analog circuit fault diagnosis based on amplitude-phase aliasing degree according to claim 2, characterized in that In step 3, the overlapping area of the Gaussian probability density curves of the amplitudes under different fault modes is as shown in Equation (12), and the overlapping area of the Gaussian probability density curves of the phases under different fault modes is as shown in Equation (13): Among them, AF A mp represents the amplitude aliasing degree, AF P ha represents the phase aliasing degree, G Amp1 、G Amp2 represents the amplitude Gaussian probability density curve under the fault group. Similarly, G P ha1, G P ha2 represents the phase Gaussian probability density curve; g A mp1, g A mp2 represents the samples of the amplitude under the fault group, g P ha1, g P ha2 represents the samples of the phase; G' Amp represents the intersection point of the amplitude Gaussian probability density curve, G' Pha represents the intersection point of the phase Gaussian probability density curve.

4. A method for selecting measurement points for analog circuit fault diagnosis based on amplitude-phase aliasing degree according to claim 2, characterized in that In step 4, the amplitude aliasing degree AF A mp and the phase aliasing degree AF P ha, and take the smaller value of the two as the amplitude-phase aliasing degree value AF, as shown in Equation (14):

5. A measuring point selection method for analog circuit fault diagnosis based on amplitude-phase aliasing degree according to claim 2, characterized in that In step 6, the calculation of the fault isolation degree is as shown in Equation (6): IF (T ,f ) = ASN (T ,f ) + ASA (T,f) (6) In formula (6), IF (T , f ) represents the fault isolation degree under the measurement point set T and the frequency set f, and ASN (T , f ) represents the number of fault fuzzy groups under (T, f), and ASA (T , f ) represents the difference between 1 and the average value of the amplitude-phase aliasing degree in the case where fault isolation is not achieved under (T, f).

6. The measuring point selection method for analog circuit fault diagnosis based on the amplitude-phase aliasing degree according to any one of claims 1-5 is used for analog circuit fault diagnosis.

7. The measuring point selection method for analog circuit fault diagnosis based on the amplitude-phase aliasing degree according to any one of claims 1-5 is used for four-op-amp biquadratic circuit fault diagnosis.

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