A robustness analysis method for aviation relay fault diagnosis expert system based on IBRB

Abstract

The present invention relates to the technical field of aviation relay fault diagnosis, and in particular to a robustness analysis method of an aviation relay fault diagnosis expert system based on IBRB. The method comprises step 1: constructing a robustness judgment criterion of an IBRB expert system for aviation relay fault diagnosis under Lipschitz conditions; steps 2-5 are respectively determining the Lipschitz constants of the IBRB expert system input information conversion process, matching degree calculation process, matching degree normalization process and rule fusion process; step 6: determining the overall Lipschitz constant of the IBRB expert system, constructing a robustness analysis model of the utility output of the IBRB expert system, determining the Lipschitz constant of the utility output of the IBRB expert system through the overall Lipschitz constant, and realizing robustness analysis of the aviation relay fault diagnosis expert system. The present invention innovatively provides a robustness quantitative analysis method of an interpretable confidence rule base expert system from a theoretical perspective, which can realize a specific analysis of the robustness of its key reasoning links and has good engineering application value.

Description

Technical Field

[0001] The invention relates to the technical field of aviation relay fault diagnosis, and in particular to an IBRB-based robustness analysis method for an aviation relay fault diagnosis expert system. Background Art

[0002] Robustness refers to the ability of a model to resist disturbances. When diagnosing faults in risk-sensitive systems such as aviation relays, different forms of disturbances will be reflected in the input fault feature information as changes in the input value, which will lead to deviations in the output results of the fault diagnosis model. The robustness analysis of the model studies the impact of disturbances on the model, which is helpful in identifying the weak links of the model for further improvement.

[0003] Many scholars have studied fuzzy rule-based systems (FRBS). For example, Ying defined the maximum perturbation and average perturbation of fuzzy sets and used them as criteria for model selection. Xu et al. listed several cases of slight perturbations of fuzzy rules and further studied the influence of fuzzy implication operators on the robustness of various fuzzy reasoning methods. On this basis, Chen et al. defined the fuzzy Lipschitz aggregation operator and pointed out that the 1-Lipschitz operator can effectively suppress the fuzzy reasoning output perturbations caused by input and rule perturbations. Cheng and Fu estimated the upper and lower limits of the FRBS output error caused by input perturbations. In addition, some other studies mainly focus on the measurement methods of fuzzy set perturbations. Jin et al. defined fuzzy set perturbations using logic-oriented equivalence measures and further gave the robustness analysis results of fuzzy sets.

[0004] As an extension of FRBS, the robustness of Interpretability Belief Rule Base (IBRB) is crucial to its modeling performance. On the one hand, it can make IBRB's sensitivity to input information at an appropriate level to ensure modeling accuracy. On the other hand, it can make the reasoning process more repeatable, which is conducive to understanding IBRB output. In the past few years, some studies have analyzed the sensitivity of IBRB parameters, which can only partially demonstrate the robustness of IBRB. For example, Feng et al. conducted a sensitivity analysis on the reliability of IBRB; Wang et al. explored the changing relationship between IBRB's weight and its output. Tang et al. proposed a method to estimate the robustness of IBRB inference machine by simulating input perturbations. This method is relatively easy to operate, but its effectiveness depends on the effectiveness of input perturbation simulation and has certain limitations.

[0005] In order to better understand and use the IBRB model in aviation relay fault diagnosis, it is urgent to understand what changes will occur in the various reasoning parts of the IBRB when disturbances occur. Therefore, it is necessary to propose a robustness analysis method for the IBRB expert system to provide efficient theoretical guidance for users to establish, adjust and improve the IBRB expert system for aviation relay fault diagnosis. Summary of the invention

[0006] In view of the above-mentioned problems, the present invention aims at the unclear performance of the IBRB expert system in aviation relay fault diagnosis when it is disturbed. Based on the Lipschitz stability condition of the model, the robustness of the IBRB expert system is explored in four steps: input conversion, matching degree calculation, matching degree normalization and rule fusion. This provides technical support for the application of the IBRB expert system in high reliability requirements and high risk sensitivity fields such as aviation relay fault diagnosis.

[0007] In order to achieve the above object, the technical solution of the present invention is as follows:

[0008] A robustness analysis method for aviation relay fault diagnosis expert system based on IBRB, including:

[0009] Step 1: Construct the robustness judgment criteria of the IBRB expert system for aviation relay fault diagnosis under Lipschitz conditions;

[0010] Step 2: Based on step 1, determine the Lipschitz constant of the input information conversion process of the IBRB expert system;

[0011] Step 3: Based on step 1, determine the Lipschitz constant of the IBRB expert system matching degree calculation process;

[0012] Step 4: Based on step 3, determine the Lipschitz constant of the normalization process of the matching degree of the IBRB expert system;

[0013] Step 5: Based on step 4, determine the Lipschitz constant of the IBRB expert system rule fusion process;

[0014] Step 6: Based on steps 2-5, determine the overall Lipschitz constant of the IBRB expert system, build a robustness analysis model for the utility output of the IBRB expert system, determine the Lipschitz constant of the utility output of the IBRB expert system through the overall Lipschitz constant, and realize the robustness analysis of the aviation relay fault diagnosis expert system.

[0015] Preferably, the robustness determination criterion of the IBRB expert system in step 1 is specifically:

[0016]

[0017] in, It represents the confidence of the nth conclusion in the output of the IBRB expert system. express The value after disturbance, x i (i=1,...,T) represents the i-th input of the IBRB expert system, x′ represents the value of x after being disturbed, is the overall Lipschitz constant of the IBRB expert system, It is obtained by aggregating the Lipschitz constants of each reasoning step of the IBRB expert system. The reasoning steps of IBRB include input conversion, matching degree calculation, matching degree normalization and rule fusion.

[0018] Preferably, the determination process of the Lipschitz constant of the IBRB expert system input information conversion process in step 2 is:

[0019] Step 2.1: Assume that x and x′ represent the fault characteristic input value and the disturbed fault characteristic input value of the aviation relay, respectively, where the reference value of the fault characteristic input is

[0020] {u(A1),...,u(A j ),u(A j+1 ),...,u(A j′ ),u(A j′+1 ),...,u(A J )}, where u(A j ) is the reference level A of the fault characteristic input j The utility of

[0021] Step 2.2: When u(A j )≤x,x′≤u(A j+1 )hour,

[0022] x is converted to: {(A1,0),...,(A j ,a j ),(A j+1 ,a j+1 ),...,(A J ,0)},

[0023] x′ is converted to: {(A1,0),...,(A j ,a′ j ),(A j+1 ,a′ j+1 ),...,(A J ,0)};

[0024] At this point, the Lipschitz constant is calculated as:

[0025]

[0026] a j represents the matching degree of the input x to the jth reference level after being transformed, a′ j for a j The disturbed value of j =1,a j+1 =0,a′ j =0,a′ j+1 =1 or a j =0,a j+1 =1,a′ j =1,a′ j+1 = 0, Get the maximum value |2 / (u(A j+1 )-u(A j ))|;

[0027] Step 2.3: When u(A j )≤x≤u(A j+1 ),u(A j′ )≤x′≤u(A j′+1 )hour,

[0028] The perturbed input x′ is transformed into: {(A1,0),...,(A j′ ,a′ j′ ),(A j′+1 ,a′ j′+1 ),...,(A J ,0)};

[0029] At this point, the Lipschitz constant is calculated as:

[0030]

[0031] but Get the maximum value |2 / (u(A j′ )-u(A j ))|;

[0032] Step 2.4: In the case of step 2.3, the value of |x′-x| is greater than or equal to the value in the case of step 2.2, then Therefore, the Lipschitz constant for the input transformation is given by Sure.

[0033] Preferably, the Lipschitz constant of the matching degree calculation process in step 3 is:

[0034]

[0035] Among them, f MDC is the rule matching calculation function, Indicates the reference value matching degree.

[0036] Preferably, the Lipschitz constant of the matching degree normalization process in step 4 is:

[0037]

[0038] Among them, w k represents the activation weight of the kth rule, and α1, α2, and α3 represent the matching degrees of the 1st, 2nd, and 3rd rules, respectively.

[0039] Preferably, the Lipschitz constant of the rule fusion process in step 5 is:

[0040]

[0041] Among them, β n,k (n=1,...,N) represents the conclusion D in the kth rule n The confidence level, Indicates the output result pair D n confidence level.

[0042] Preferably, the overall Lipschitz constant of the IBRB expert system in step 6 is:

[0043]

[0044] Preferably, the robustness analysis model of the utility output of the IBRB expert system in step 6 is:

[0045]

[0046] in, is the fluctuation value of the nth output confidence, u′(S(A * )) is the disturbed u(S(A * )),u(S(A * )) represents the utility of fault characteristic input information;

[0047] When the IBRB expert system outputs utility, the overall Lipschitz constant is expressed as:

[0048]

[0049] Among them, u(D n ) is the reference value of the fault result output by the IBRB expert system. Based on this, the Lipschitz constant of the utility output of the IBRB expert system is Determined by the following formula:

[0050]

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] Theoretically, a quantitative analysis method for the robustness of the aviation relay fault diagnosis expert system based on IBRB is given, which can realize the specific analysis of the robustness of the key reasoning links of IBRB, provide technical support for IBRB to solve the aviation relay fault diagnosis in the disturbed environment, and effectively improve the reliability of the aviation relay fault diagnosis process and the credibility of the results. First, the IBRB robustness judgment criterion under the Manhattan distance measure is constructed based on the Lipschitz stability condition of the function; second, the Lipschitz constant acquisition method of IBRB is given by distinguishing the four steps of input information conversion, matching degree calculation, matching degree normalization and rule fusion of IBRB; third, based on the above results, the overall Lipschitz constant determination method of the IBRB expert system is given, realizing the quantitative analysis of the robustness of the IBRB expert system. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0054] In the attached picture:

[0055] Figure 1 An analytical framework for the robustness of the IBRB model.

[0056] Figure 2 N is the number of rule consequent conclusions and φ n,k The relationship between the maximum values.

[0057] Figure 3 is the number of rule consequent conclusions N and and The relationship between the maximum values.

[0058] Figure 4 To verify the main idea of ​​the experiment.

[0059] Figure 5 is the fault state utility when the input is disturbed.

[0060] Figure 6 is the difference between the perturbed confidence and the original confidence.

[0061] Figure 7 For 300 rounds of experiments The estimated value of .

[0062] Figure 8 The present invention is a flow chart of the method. DETAILED DESCRIPTION

[0063] The following combination Figure 1-Figure 8 The preferred embodiments of the present invention are described. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0064] A robustness analysis method for aviation relay fault diagnosis expert system based on IBRB, including:

[0065] Step 1: Construct the robustness judgment criteria of the IBRB expert system for aviation relay fault diagnosis under Lipschitz conditions. Specifically include:

[0066] In order to discuss the robustness of the IBRB expert system, the Lipschitz condition of the function is briefly explained here.

[0067] Lipschitz condition for a function: there exists a constant So that the function f:X→Y satisfies the Lipschitz condition, then:

[0068]

[0069] Where x′ represents the value of x after being disturbed. X and d Y denote the distance measure of variable space X and Y respectively. If is the smallest constant that satisfies the inequality, then f satisfies the Lipschitz condition and is the Lipschitz constant of the function.

[0070] A function that satisfies the Lipschitz condition means that the function is Lipschitz stable. Specifically, a perturbation ε in the function input produces a perturbation on the function output that is less than or equal to in, The smaller it is, the more robust the function is. Manhattan distance is usually regarded as a standard distance measure. The Lipschitz condition of the function under the Manhattan distance measure can be defined as follows:

[0071] for Manhattan distance Given by the following formula

[0072] d r ((x1,...,x T ),(x′1,...,x′ T ))=|x1-x′1|+...+x T -x′T | (2)

[0073] For function The condition for Lipschitz stability is that

[0074]

[0075] Based on the above analysis, the robustness judgment criterion of the IBRB expert system for aviation relay fault diagnosis under Lipschitz conditions is constructed as follows:

[0076] for If there is a minimum constant Make the model It is Lipschitz stable if the following conditions are met:

[0077]

[0078] in, and d(·) represents the distance measure. And under the Manhattan distance measure, the robustness criterion of IBRB can be rewritten as

[0079]

[0080] in, It represents the confidence of the nth conclusion in the output of the IBRB expert system. express The value after disturbance. i (i=1,...,T) represents the i-th input of the IBRB expert system, and x′ represents the value of x after being disturbed.

[0081] is the overall Lipschitz constant of the IBRB expert system, It needs to be obtained by aggregating the Lipschitz constants of each reasoning step of the IBRB expert system. The reasoning steps of IBRB include input conversion, matching degree calculation, matching degree normalization and rule fusion, etc., to obtain the Lipschitz constant of the IBRB model. One approach is to estimate the Lipschitz constant for each step separately and then aggregate them. The analytical framework for IBRB robustness is as follows Figure 1 As shown, the Lipschitz constants of each IBRB reasoning step are expressed as and

[0082] Combined with the above analysis, we need to determine and Then calculate Right now:

[0083]

[0084] Step 2: Based on step 1, determine the Lipschitz constant of the IBRB expert system input information conversion process. Specifically, for the quantitative attributes described by IBRB in semantic terms, the input can be in the following forms: a single deterministic value, a closed interval, a triangular distribution, or a trapezoidal distribution. They are usually transformed based on different fuzzy membership functions. Here, the transformation of a single deterministic value is taken as an example.

[0085] Step 2.1: Assume that x and x′ represent the fault characteristic input value and the disturbed fault characteristic input value of the aviation relay, respectively, where the reference value of the fault characteristic input is

[0086] {u(A1),...,u(A j ),u(A j+1 ),...,u(A j′ ),u(A j′+1 ),...,u(A J )}, where u(A j ) is the reference level A of the fault characteristic input j The utility of

[0087] Step 2.2: When u(A j )≤x,x′≤u(A j+1 )hour,

[0088] x is converted to: {(A1,0),...,(A j ,a j ),(A j+1 ,a j+1 ),...,(A J ,0)},

[0089] x′ is converted to: {(A1,0),...,(A j ,a′ j ),(A j+1 ,a′ j+1 ),...,(A J ,0)};

[0090] At this point, the Lipschitz constant is calculated as:

[0091]

[0092] a j represents the matching degree of the input x to the jth reference level after being transformed, a′ j for aj The disturbed value of j =1,a j+1 =0,a′ j =0,a′ j+1 =1 or a j =0,a j+1 =1,a′ j =1,a′ j+1 = 0, Get the maximum value |2 / (u(A j+1 )-u(A j ))|;

[0093] Step 2.3: When u(A j )≤x≤u(A j+1 ),u(A j′ )≤x′≤u(A j′+1 )hour,

[0094] The perturbed input x′ is transformed into: {(A1,0),...,(A j′ ,a′ j′ ),(A j′+1 ,a′ j′+1 ),...,(A J ,0)};

[0095] At this point, the Lipschitz constant is calculated as:

[0096]

[0097] but Get the maximum value |2 / (u(A j′ )-u(A j ))|;

[0098] Step 2.4: In the case of step 2.3, the value of |x′-x| is greater than or equal to the value in the case of step 2.2, then Therefore, the Lipschitz constant for the input transformation is given by Sure.

[0099] Step 3: Based on step 1, determine the Lipschitz constant of the IBRB expert system matching degree calculation process. Specifically:

[0100] The matching degree of the input vector to the activation rule is calculated by aggregating the matching degree of the corresponding input to the reference value. The aggregation process is as follows:

[0101]

[0102] According to the total differential theorem, we can deduce that f MDC The total differential formula is as follows:

[0103]

[0104] in, Indicates the matching degree of the disturbed reference value The Lipschitz constant of the rule matching degree calculation process can be determined by the following formula:

[0105]

[0106] f MDC is the rule matching calculation function, Indicates the reference value matching degree.

[0107] Among them, the i-th partial derivative function is expressed as:

[0108]

[0109] When the i-th attribute is absolutely important, the corresponding weight is equal to 1. The above formula can be expressed as follows:

[0110]

[0111] It can be seen that it is a It is easy to get that the maximum value of formula (12) is equal to 1, that is

[0112] when When, in formula (12) The maximum value of is 1, then formula (12) is derived as:

[0113]

[0114] Step 4: Based on step 3, determine the Lipschitz constant of the IBRB expert system matching degree normalization process. Specifically:

[0115] The matching degree normalization process is performed using the following formula:

[0116]

[0117] Among them, α k Calculated by formula (9). When IBRB has information input, the number of activated rules can be 1, 2 or 4. Generally speaking, activating 1 or 2 rules is a special case of activating 4 rules. Therefore, the following discussion focuses on the case where 4 rules are activated. The activation weight of the kth rule is calculated by the following formula:

[0118] w k =f MDN =θk α k / (θ1α1+θ2α2+θ3α3+θ4α4) (16)

[0119] Among them, k = 1, 2, 3, 4, α4 = 1-(α1+α2+α3). From this we can get:

[0120]

[0121] Among them, w′ k represents the perturbed w k .f MDN The Lipschitz constant can be expressed as

[0122]

[0123] Among them, w k represents the activation weight of the kth rule, and α1, α2, and α3 represent the matching degrees of the 1st, 2nd, and 3rd rules, respectively.

[0124] make If i = k, then g i＝k It can be expressed as:

[0125]

[0126] If i≠k, then g i≠k It can be expressed as

[0127]

[0128] From equations (19)-(20), we can see that g i＝k The maximum value is always greater than g i≠k The maximum value of Lipschitz constant θ MDN Generally take g i＝k The maximum value of .

[0129] Step 5: Based on step 4, determine the Lipschitz constant of the IBRB expert system rule fusion process. Specifically:

[0130] Assume that m n,I(k) It means that the first k rules are combined using the Evidential Reasoning (ER) algorithm, and the result is relative to D n The basic probability mass of Let m n，I(1) =m n，1 , m D，I(1) =m D，1 , the following iterative ER algorithm is used to fuse the activation rules:

[0131]

[0132]

[0133]

[0134]

[0135]

[0136]

[0137] in, Indicates the output result pair D n The confidence level, Denotes the pair D = {D1, D2, ..., D N}confidence.

[0138] Assume that all rules are complete, that is and k=1,...,L. In general, when IBRB has information input, 4 rules will be activated. The following formula can be used to calculate the nth conclusion D n Confidence of:

[0139]

[0140] Among them, the number of rules L = 4. k is the activation weight of the kth rule, and β n,k (n=1,...,N) represents the conclusion D in the kth rule n Confidence

[0141] In order to explore the robustness of formula (27), the following formula is given

[0142]

[0143] in, is disturbed The Lipschitz constant can be expressed as

[0144]

[0145] Among them, β n,k (n=1,...,N) represents the conclusion D in the kth rule n The confidence level, Indicates the output result pair D n confidence level.

[0146] To discuss the weight w k right The influence of can be derived as follows:

[0147]

[0148] Use the MATLAB Optimization Toolbox to optimize the following objective function:

[0149]

[0150] φ n,k The maximum value of Figure 2 As shown. It can be seen that φ n,k The maximum value of increases with the number of conclusions N, but the increase is small. When N is less than 10, φ n,k The maximum value is less than 1.043 and close to 1.

[0151] When building the IBRB model, determine and optimize the confidence level β n,k Such interference may further affect the generation of To address this, right It can be expressed as the partial derivative of Then we have:

[0152] when hour,

[0153]

[0154] when hour,

[0155]

[0156] Then the objective function of finding its maximum value can be expressed as follows:

[0157]

[0158] Where ρ(·) represents or Using the MATLAB optimization toolbox to find the optimal value, the maximum value of ρ(·) is as follows Figure 3 As shown. It can be seen that and The maximum value of is close to 1.11, and they are not affected by the number of conclusions. Based on the above analysis, the Lipschitz constant is close to 1, which indicates that the ER method does not significantly amplify the interference from the input, which is an important property for its successful application in information fusion.

[0159] Step 6 includes:

[0160] Step 6.1: Based on the analysis of steps 2 to 5, determine the overall Lipschitz constant of the IBRB expert system

[0161]

[0162] in, if The input disturbance may be amplified by the IBRB. Then the IBRB will not amplify the input disturbance. An important goal of constructing the IBRB is to obtain the smallest possible

[0163] Step 6.2: Construct a robustness analysis model for the utility output of the IBRB expert system:

[0164]

[0165] in, is the fluctuation value of the nth output confidence, u′(S(A * )) is the disturbed u(S(A * )),u(S(A * )) represents the utility of fault characteristic input information;

[0166] Step 6.3: When the IBRB expert system outputs utility, its overall Lipschitz constant is expressed as:

[0167]

[0168] Among them, u(D n ) is the reference value of the fault result output by the IBRB expert system. Based on this, the Lipschitz constant of the utility output of the IBRB expert system is Determined by the following formula:

[0169]

[0170] Finally, the robustness analysis of aviation relay fault diagnosis expert system is realized.

[0171] Embodiment 1:

[0172] Taking the IBRB expert system for aviation relay fault diagnosis as the object, its parameter values ​​are shown in Table 1, Table 2 and Table 3, where X1 and X2 represent the winding resistance and normally open contact resistance of the aviation relay respectively.

[0173] Table 1 Attribute weights and reference values

[0174]

[0175] Table 2 Reference levels and reference values ​​for aviation relay fault states

[0176]

[0177] Table 3 IBRB expert system parameters

[0178]

[0179] According to step 2, the information transformation process of the above IBRB expert system is analyzed, and the obtained Lipschitz constant is given in Table 4. Among them, Indicates that the input value satisfies A i,j ≤x i ≤A i,j+1 The Lipschitz constant when . is the Lipschitz constant for the transformation of input information.

[0180] Table 4 Lipschitz constants of the input transformation process of the IBRB expert system

[0181]

[0182] The weights of attributes X1 and X2 in IBRB are 1 and 0.998 respectively. According to step 3, the Lipschitz constant of the matching degree calculation process is equal to The maximum value of is shown in Table 5. As it approaches 0, the value of g increases. However, when When it is less than a certain tolerance threshold, for example When the value is less than 0.05, it is difficult for people to judge whether the input data belongs to the corresponding reference value. At this time, the maximum value g is 1.004. Lipschitz constant for matching degree calculation It is 1.004.

[0183] Table 5 Lipschitz constants in the IBRB rule matching degree calculation process

[0184]

[0185] According to step 4, the Lipschitz constant of the IBRB rule matching degree normalization process is The value of is associated with the weight and matching degree of the activation rule, where The maximum values ​​are shown in Table 6.

[0186] Available

[0187] Table 6 Lipschitz constant of IBRB rule matching degree normalization process

[0188]

[0189] According to step 5, the robustness of the rule fusion process based on the ER method is related to the confidence of the rules and the activation weight of the rules. After the IBRB expert system is established, the confidence in the rules has been determined, and the activation weight is mainly affected by the input information. Therefore, the robustness of the IBRB rule fusion process can be analyzed by analyzing the rule activation weight. Assume that the activation weights of the four activated rules are represented by w1, w2, w3 and w4, and the activation weight w k Confidence in output Impact Given in Table 7, we can get

[0190] Table 7 Lipschitz constants of IBRB rule fusion process

[0191]

[0192] According to step 6, the overall Lipschitz constant of the IBRB expert system can be calculated as 9.753. It can also be seen from Table 8 that the robustness of the information conversion process has a greater impact on the robustness of IBRB. In addition, combined with the Lipschitz constants listed in Table 4, it can be seen that technicians should pay more attention to avoid interference with the test value of X2.

[0193] Table 8 Lipschitz constant of the IBRB expert system as a whole

[0194]

[0195] In order to further verify the effectiveness of the proposed method, random interference χ is added to the IBRB expert system input X1 and X2. The random interference χ is defined as follows:

[0196] χ=ε·Δ (39)

[0197] Among them, ε represents the random factor, which is a random value between -1 and 1. Δ represents the upper bound of the perturbation. Therefore, the perturbed input can be expressed as:

[0198] x i ′=x i +χ (40)

[0199] Among them, x i Represents X i The specific value of x i ′ represents the perturbed x i .

[0200] Figure 4The main idea of ​​the verification experiment is presented, which is to use the input and output calculation of the IBRB expert system. The basic parameters of the input disturbance are set as follows: the upper limit of the disturbance Δ is set to 0.8, and the random factor ε is a random value that satisfies -1≤ε≤1. When there is no disturbance, X1 is disturbed, X2 is disturbed, and both are disturbed, the fault state utility value is as follows: Figure 5 As shown. It can be seen that the impact of X1 disturbance on the fault state utility is smaller than the impact of X2 disturbance on the fault state utility. In addition, it can be seen that when X2 is disturbed, the IBRB output utility cannot accurately distinguish the state of the fault (see the green box mark).

[0201] Figure 6 The difference between the disturbed confidence and the original confidence is shown. It can be seen that when X2 is disturbed, the perturbation of the confidence is more obvious, which is consistent with the previous analysis. In addition, Figure 6 -(c) It can be seen that the disturbance of X1 has a smaller impact on the confidence of the "minor fault" state, and the change in confidence caused by the disturbance of X2 is independent of the value of X2. Figure 5 and Figure 6 Together, it is shown that the interference of X2 has a greater impact on the results. This shows that in order to improve the robustness of IBRB, the interference of X2 should be suppressed first.

[0202] according to Figure 4 300 replicates were performed to estimate The perturbation upper limit Δ varies randomly from 0.2 to 1.8. The value of Figure 7 As shown, most are close to 8, and The maximum estimated value is 9.684, which is less than 9.753 (the Lipschitz constant calculated in Table 8). This means that the Lipschitz constant obtained by using the proposed method is valid.

[0203] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A robustness analysis method for aviation relay fault diagnosis expert system based on IBRB, characterized by: include: Step 1: Construct the robustness judgment criterion of the IBRB expert system for aviation relay fault diagnosis under Lipschitz conditions; the robustness judgment criterion of the IBRB expert system in step 1 is specifically as follows: in, It represents the confidence of the nth conclusion in the output of the IBRB expert system. express The value after disturbance, x i (i=1,...,T) represents the i-th input of the IBRB expert system, x′ represents the value of x after being disturbed, θ IBRB is the overall Lipschitz constant of the IBRB expert system, θ IBRB It is obtained by aggregating the Lipschitz constants of each reasoning step of the IBRB expert system. The reasoning steps of IBRB include input conversion, matching degree calculation, matching degree normalization and rule fusion; Step 2: Based on step 1, determine the Lipschitz constant of the IBRB expert system input information conversion process; the determination process of the Lipschitz constant of the IBRB expert system input information conversion process in step 2 is: Step 2.1: Assume that x and x′ represent the fault characteristic input value and the disturbed fault characteristic input value of the aviation relay, respectively, where the reference value of the fault characteristic input is {u(A1),...,u(A j ),u(A j+1 ),...,u(A j′ ),u(A j′+1 ),...,u(A J )}, where u(A j ) is the reference level A of the fault characteristic input j The utility of Step 2.2: When u(A j )≤x,x′≤u(A j+1 )hour, x is converted to: {(A1,0),...,(A j ,a j ),(A j+1 ,a j+1 ),...,(A J ,0)}, x′ is converted to: {(A1,0),...,(A j ,a′ j ),(A j+1 ,a′ j+1 ),...,(A J ,0)}; At this point, the Lipschitz constant is calculated as: Among them, a j represents the matching degree of the input x to the jth reference level after being transformed, a′ j for a j The disturbed value of j =1,a j+1 =0,a′ j =0,a′ j+1 =1 or a j =0,a j+1 =1,a′ j =1,a′ j+1 =0, θ IT-1 Get the maximum value |2 / (u(A j+1 )-u(A j ))|; Step 2.3: Tou(A j )≤x≤u(A j+1 ),u(A j′ )≤x′≤u(A j′+1 ) time, The perturbed input x′ is transformed into: {(A1,0),...,(A j′ ,a′ j′ ),(A j′+1 ,a′ j′+1 ),...,(A J ,0)}; At this point, the Lipschitz constant is calculated as: Then θ IT-2 Get the maximum value |2 / (u(A j′ )-u(A j ))|; Step 2.4: In the case of step 2.3, the value of |x′-x| is greater than or equal to the value in the case of step 2.2, then θ IT-1 ≥θ IT-2 ; Therefore, the Lipschitz constant of the input transformation is given by θ IT =maxθ IT-1 Sure; Step 3: Based on step 1, determine the Lipschitz constant of the IBRB expert system matching degree calculation process; Step 4: Based on step 3, determine the Lipschitz constant of the normalization process of the matching degree of the IBRB expert system; Step 5: Based on step 4, determine the Lipschitz constant of the IBRB expert system rule fusion process; Step 6: Based on steps 2 to 5, determine the overall Lipschitz constant of the IBRB expert system, build a robustness analysis model for the utility output of the IBRB expert system, determine the Lipschitz constant of the utility output of the IBRB expert system through the overall Lipschitz constant, and implement robustness analysis of the aviation relay fault diagnosis expert system.

2. A robustness analysis method for aviation relay fault diagnosis expert system based on IBRB according to claim 1, characterized in that: The Lipschitz constant of the matching degree calculation process in step 3 is: Among them, f MDC is the rule matching calculation function, Indicates the reference value matching degree.

3. A robustness analysis method for aviation relay fault diagnosis expert system based on IBRB according to claim 2, characterized in that: The Lipschitz constant of the matching degree normalization process in step 4 is: Among them, w k represents the activation weight of the kth rule, and α1, α2, and α3 represent the matching degrees of the 1st, 2nd, and 3rd rules, respectively.

4. The robustness analysis method of an aviation relay fault diagnosis expert system based on IBRB according to claim 3 is characterized in that: Step 5 The Lipschitz constant of the rule fusion process is: Among them, β n,k (n=1,...,N) represents the conclusion D in the kth rule n The confidence level, Indicates the output result pair D n confidence level.

5. The robustness analysis method of an aviation relay fault diagnosis expert system based on IBRB according to claim 4 is characterized in that: The overall Lipschitz constant of the IBRB expert system in step 6 is: i IBRB =Γ(θ IT ,i MDC ,i MDN ,i ER )=θ IT ·i MDC ·i MDN ·i ER 。 6. The robustness analysis method of an aviation relay fault diagnosis expert system based on IBRB according to claim 5 is characterized in that: The robustness analysis model of the utility output of the IBRB expert system in step 6 is: in, is the fluctuation value of the nth output confidence, u′(S(A * )) is the disturbed u(S(A * )),u(S(A * )) represents the utility of fault characteristic input information; When the IBRB expert system outputs utility, the overall Lipschitz constant is expressed as: θ Utility =max{|u(D1)|,...,|u(D n )|,...,|u(D N )|} Among them, u(D n ) is the reference value of the fault result output by the IBRB expert system. Based on this, the Lipschitz constant θ of the utility output of the IBRB expert system IBRB-utility Determined by the following formula:

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