A risk assessment method for complex systems based on relevant evidence reasoning rules

Abstract

The present invention discloses a complex system risk assessment method based on relevant evidence reasoning rules, which is used to deal with complex system risk assessment under uncertainty. The present invention constructs a universal risk assessment indicator system, and models and describes the risk indicators as evidence under the framework of identification (FoD). The evidence is unified by a transformation matrix, and the reliability and correlation coefficient of the evidence are clearly measured. The relevant evidence reasoning rule (ERR-DE) model constructs a multi-source information fusion framework, in which multiple pieces of evidence with different weights, reliabilities and correlation coefficients can be aggregated, and the relationship between risk indicators and system risks is established. A parameter optimization model is constructed to optimize all subjective evidence parameters through the idea of ​​expectation maximization.

Description

Technical Field

[0001] The present invention relates to the technical field of risk assessment, and in particular to a complex system risk assessment method based on relevant evidence reasoning rules. Background Art

[0002] Risk assessment aims to quantitatively evaluate the possible impact or loss before or after a risk event occurs. In recent years, risk assessment has developed and been applied rapidly in aerospace, critical infrastructure, industrial automation and control and other fields.

[0003] Existing risk assessment methods can be divided into three categories, including knowledge-based methods, data-driven methods, and hybrid information-based methods. Among them, knowledge-based methods directly establish system risk assessment models through mechanism analysis and expert knowledge, and have strong transparency and interpretability, including hierarchical analysis method, Petri net, fault tree, etc. However, when the system mechanism is very complex, it is difficult to obtain expert knowledge, and the assessment results may have strong subjective uncertainty, which is not conducive to improving the accuracy of the assessment; data-driven methods do not need to accurately obtain the analytical model of the system, and can establish risk assessment models based on statistical data, including artificial neural networks, TOPSIS methods, deep learning, etc. However, this method requires accurate data and relies on large samples, lacking interpretability and traceability; in contrast, hybrid information-based methods can combine qualitative knowledge and quantitative data, and use small samples to effectively assess the risk level of complex systems, including Bayesian networks, fuzzy comprehensive evaluation, trust rule base, and Evidential Reasoning Rule (ERR).

[0004] As a typical method based on mixed information, ERR forms a generalized probabilistic reasoning mechanism to achieve multi-source information fusion, extending the traditional Bayesian rule and Dempster-Shafer rule. It constructs a so-called Framework of Discernment (FoD) to model various uncertainties, in which evidence can be described as a confidence distribution. By using ERR, system input can be transformed into multiple pieces of evidence with weights and reliability, which can be aggregated to build a bridge between system input and output. With the development of evidence theory, ERR has been widely used in risk assessment of complex systems. However, in ERR, the FoD of evidence should strictly correspond to the FoD of reasoning results. Therefore, when assessing system risk, all risk indicators and risk assessment results should be restricted to the same FoD. But this is extremely difficult because different experts can provide different types and numbers of evaluation levels according to system design principles and standards. In addition, from a theoretical point of view, ERR requires that all evidence be independent of each other, which is often idealized because of the coupling of system structure. Although the maximum likelihood evidence reasoning framework has been proposed in the prior art to aggregate relevant evidence, it requires the calculation of joint probabilities and marginal probabilities under all combinations, which in turn leads to exponential computational complexity. Moreover, as the number of risk indicators increases, experts find it difficult to accurately give all evidence parameters due to incomplete or limited knowledge. This greatly increases the subjective uncertainty of risk assessment. Summary of the invention

[0005] The purpose of the present invention is to provide a complex system risk assessment method based on relevant evidence reasoning rules, which can be used for risk assessment of laser gyroscopes. It can improve the accuracy of risk assessment by constructing a new complex system risk assessment model - Evidential Reasoning Rule with Dependent Evidence (ERR-DE).

[0006] To achieve the above object, the present invention provides a complex system risk assessment method based on relevant evidence reasoning rules, which is characterized by comprising the following steps:

[0007] Step 1: Construct a risk assessment indicator system for complex systems and determine risk indicators;

[0008] Step 2: Determine the reference level and reference value of each risk indicator;

[0009] Step 3: Use rule / utility-based input information conversion technology to convert the observed data of risk indicators at each moment into evidence;

[0010] Step 4: Introduce the conversion matrix to convert the evidence obtained in step 3 into evidence under the evaluation result FoD;

[0011] Step 5: Use intervals to describe the weights assigned by experts to risk indicators and calculate the reliability of the evidence obtained in step 4;

[0012] Step 6: According to the reliability of evidence obtained in step 5, determine the fusion order of risk indicators and calculate the correlation coefficient of all evidence;

[0013] Step 7: Establish a parameter optimization model, determine the optimization parameters, and obtain the optimal parameter set;

[0014] Step 8: Based on the optimal parameters, construct a risk assessment model based on relevant evidence reasoning rules and calculate the system risk level.

[0015] Furthermore, the specific steps of obtaining evidence in step 3 include:

[0016] Step 31: Set the risk indicator x i The FoD is defined as Θ i ={H i,1 ,H i,2 ,…,H i,n(i)}, where H i,k is x i The k-th risk level of , and i∈[1,L], k∈[1,n(i)];

[0017] Step 32: Obtain the observed data x according to formula (1)-formula (3) i (t) are H respectively corresponding to the risk level. i,k and H i,k+1 Confidence of:

[0018]

[0019] β i,k+1 (t) = 1-β i,k (t) (2)

[0020] β i,j (t)=0;j≠k,k+1 and j∈[1,n(i)] (3)

[0021] Among them, x i (t) represents the i-th risk indicator x i Observation data at time t; h i,k Indicates risk level H i,k Reference value of β i,k (t), β i,k+1 (t) and β i,j (t) represents x i(t)Assessed as risk level H i,k , H i,k+1 and H i,j Confidence level when

[0022] Step 34: According to the following formula, we can get i The risk indicator x i The confidence distribution of the evidence provided at time t takes the form:

[0023] e i (t) = {(H i,j ,β i,j (t)); j∈[1,n(i)]} (4)

[0024] Among them, e i (t) represents the evidence provided at time t.

[0025] Furthermore, the specific steps of step 4 include:

[0026] Step 41: Define the identification framework of risk assessment results as Θ = {H1, H2, …, H n}, the evidence under Θ is obtained according to the following formula:

[0027] e(t)={(H p ,β p (t)); p∈[1,n]} (5)

[0028] Among them, β p (t) represents the evidence relative to the risk level H p confidence level;

[0029] Step 42: Establish Θ and Θ i The transformation matrix A between i :

[0030]

[0031] Among them, A i All elements in are obtained based on expert knowledge;

[0032] Step 43: According to formula (7), Θ i All evidence under θ is transformed into evidence under θ:

[0033] B=β i A i (7)

[0034] Among them, β i Indicates e i (t) in Θ i The confidence matrix under , and β i =[β i,1 ,βi,2 ,…,β i,n(i) ]; B represents e i (t) The confidence matrix under Θ, and Β = [β1,β2,…,β n ].

[0035] Furthermore, the specific steps of step 5 include:

[0036] Step 51: M experts give risk indicator x i Assign different weights of evidence w i,1 ,w i,2 ,…,w i,M , and sort all weights in ascending order to get w i,1 <w i,2 <… <w 1,M-1 <w i,M , determine x i The weight of evidence interval is [w i,2 ,w 1,M-1 ];

[0037] Step 52: Calculate the reliability of evidence according to formula (8):

[0038] r i (t) = αr i s +(1-α)r i d (t) (8)

[0039] Among them, r i s Represents the static reliability, r i d (t) represents dynamic reliability, and α∈[0,1] represents the discount factor.

[0040] Furthermore, the specific steps of step 6 include:

[0041] Step 61: Determine the two pieces of evidence e at time t according to equation (9): i (t) and e j The relative order Seq of (t) i,j (t):

[0042]

[0043] Among them, Seq i (t) and Seq. j (t) respectively represent e i (t) and e j (t) the fusion order;

[0044] Step 62: For the observation data matrix Z i(t) and Z j (t), calculate e according to the following formula i (t) and e j (t) distance correlation coefficient:

[0045]

[0046] Among them, v 2 (Z i (t),Z j (t)) represents Z i (t) and Z j The empirical distance covariance of (t); v 2 (Z i (t)) and v 2 (Z j (t)) respectively represent Z i (t) and Z j The autocovariance of (t);

[0047] Step 63: Based on Seq i,j (t) determine the evidence e1(t), e2(t),…,e L The fusion order of (t) is as follows:

[0048]

[0049] Step 64: Calculate e based on the correlation matrix C i The overall correlation coefficient Tdd of (t) i (t):

[0050]

[0051] Step 65: According to Tdd i (t) Calculate e i The correlation coefficient d between (t) and all evidence i (t):

[0052]

[0053]

[0054] Among them, d i (t)∈[0,1], and d i The larger the value of (t), the greater the i (t) is less relevant than all the evidence.

[0055] Furthermore, the specific steps of step 7 include:

[0056] Step 71: Construct parameter optimization objective function:

[0057]

[0058] st

[0059]

[0060] Where, Γ represents the objective function; and Represent the weight of evidence w i The upper and lower bounds of and Respectively represent h i,k The upper and lower bounds of the reference value at the initial FoD;

[0061] Step 72: Solve equation (22) to obtain the optimal evidence weight, reference value of risk level and conversion matrix.

[0062] Furthermore, step 8 of constructing a risk assessment model based on ERR-DE includes:

[0063] Step 81: Obtain the evidence e under Θ according to the optimized evidence weight and evidence reliability i The mixing probability mass of (t) is:

[0064]

[0065] in, Represents an empty set; is the mixing weight, and P(Θ) is the power set of Θ, and

[0066]

[0067] Step 82: For evidence e under Θ i (t) and e j (t), the confidence β of the combination of the two relative to the risk level θ e(2),θ (t) and the unnormalized combined probability mass m assigned to θ e(2),θ (t) are:

[0068]

[0069]

[0070] Among them, m i,φ (t) and m j,ψ (t) respectively represent e i (t) and e j (t) the mixed probability mass assigned to risk levels φ and ψ;

[0071] Step 83: For L pieces of evidence e1(t), e2(t),…,e L (t), iterate equations (17)-(18) L-1 times to obtain the final risk assessment result S e(L) (t), its confidence distribution is:

[0072]

[0073] Among them, β e(L),θ (t) is the confidence level of risk level θ,

[0074] Step 84: Substitute S by equation (20) e(L) (t) is mapped to risk level H p The actual probability of

[0075]

[0076] in, The system is at risk level H at time t p The probability of

[0077] Step 85: Calculate the expected utility of the system using equation (21):

[0078]

[0079] Among them, RD(t)∈[0,1] represents the expected utility of the system, that is, the risk of the system. The closer the value of RD(t) is to 1, the higher the risk; and the closer RD(t) is to 0, the lower the risk.

[0080] Therefore, the present invention adopts the above-mentioned complex system risk assessment method based on relevant evidence reasoning rules, which has the following beneficial effects:

[0081] First, the present invention uses rule / utility-based input information conversion technology to convert all risk indicators into evidence under different FoDs, introduces the concept of conversion matrix, and unifies different FoDs of evidence according to the "IF-THEN rule", thereby overcoming the inconsistency between evidence and evaluation results;

[0082] Second, the present invention constructs a risk assessment model based on ERR-DE, through which all evidence information can be aggregated, in which the risk probability and risk degree can be used to measure system risk from discrete and continuous perspectives, respectively, solving the problem of distributed quantitative expression and comprehensive quantitative expression of risk assessment results;

[0083] Third, the present invention constructs a parameter optimization model that can reduce the subjective uncertainty brought by experts and help improve the accuracy of risk assessment.

[0084] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 It is a typical risk assessment indicator system.

[0086] Figure 2 This is the laser gyroscope risk assessment indicator system constructed in the embodiment.

[0087] Figure 3 It is the observation data of K0, K1 and LT in the risk assessment index system of laser gyroscope.

[0088] Figure 4 is the reliability of the evidence calculated in the example.

[0089] Figure 5 is the risk probability of the laser gyroscope relative to different risk levels in the embodiment.

[0090] Figure 6 It is the comparison result between the ERR-DE model in the embodiment and the expected result.

[0091] Figure 7 Comparative results of risk assessment results generated for different ER models. DETAILED DESCRIPTION

[0092] In the description of the present invention, it is also necessary to explain that, unless otherwise clearly specified and limited, these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art make various changes or modifications to the present invention, and these equivalent forms also fall within the scope limited by the claims attached to the application.

[0093] 1. Typical risk assessment model

[0094] For a certain system, the risk level is measured by risk indicators, and the corresponding observation data is monitored by sensors. Assume that there are L risk indicators, represented as x1, x2, …, x L , which is monitored by L different sensors. The typical risk assessment indicator system constructed is as follows Figure 1 shown.

[0095] exist Figure 1 In the example, the number of sub-indicators is m(l), which can be refined according to the actual scenario, where l∈[1,m(L)] and m(L) depends on L. In the time window T, the indicator x i The observation data matrix at different times t is represented as Z i (t) = [xi (tT) x i (t-T+1) … x i (t)]. Each indicator can provide a piece of evidence at time t, denoted as e i (t). Accordingly, the weight of evidence and reliability can be expressed as w i and r i (t), 0≤w i ,r i (t)≤1. Moreover, the reliability of evidence is time-varying, which is determined by the static reliability r i s and dynamic reliability r i d (t) composition. i The correlation coefficient between (t) and all evidence is denoted as d i (t). Therefore, a risk assessment model based on ERR-DE can be constructed.

[0096] 2. Evidence acquisition methods and unified expression methods

[0097] Assume that the risk indicator x i The FoD is Θ i ={H i,1 ,H i,2 ,…,H i,n(i)}, where H i,k is x i The kth risk level of H, and i∈[1,L] and k∈[1,n(i)], n(i) is related to i. i,k The reference value is h i,k , if x i is a benefit-based indicator, then h i,1 <h i,2 <… <h i,n(i) ; if x i is a cost-type indicator, then h i,1 >h i,2 >…>h i,n(i) .

[0098] Assume x i The observed data at time t is x i (t), without loss of generality, assuming h i,k <x i (t) <h i,k+1 , where k, k+1∈[1,n(i)]. The utility / rule-based input information transformation technique can be used to obtain evidence, as follows:

[0099]

[0100] βi,k+1 (t) = 1-β i,k (t) (2)

[0101] β i,j (t)=0;j≠k,k+1 and j∈[1,n(i)] (3)

[0102] Among them, β i,k (t), β i,k+1 (t) and β i,j (t) represents x i (t)Assessed as risk level H i,k , H i,k+1 and H i,j Confidence level when

[0103] Obviously, there are Based on the above method, a piece of evidence can be expressed as the following confidence distribution form:

[0104] e i (t) = {(H i,j ,β i,j (t)); j∈[1,n(i)]} (4)

[0105] Assume that the FoD of the risk assessment result is Θ={H1,H2,…,H n}, a piece of evidence under Θ can be expressed as:

[0106] e(t)={(H p ,β p (t)); p∈[1,n]} (5)

[0107] Among them, β p (t) is the evidence relative to the risk level H p confidence level.

[0108] Since the FoD of evidence may be different from the FoD of evaluation results, this means that Θ i The number and type of evaluation levels are not exactly the same as Θ. Therefore, in order to uniformly express different FoDs, the present invention introduces the concept of conversion matrix to establish Θ i The relationship between and Θ is as follows:

[0109]

[0110] Among them, A i is a transformation matrix with dimension n(i)×n; A i Each row represents an "IF-THEN rule" R i,k , R i,k It means "IF x i is Hi,k ,THEN{(H1,α 1,k ),(H2,α 2,k ),…,(H n ,α n,k ),},with ”; Here, A i All the elements are given by experts.

[0111] Assume e i (t) in Θ i The confidence matrix under i =[β i,1 ,β i,2 ,…,β i,n(i) ],e i (t) The confidence matrix under Θ is Β = [β1,β2,…,β n ], according to formula (6):

[0112] B=β i A i (7)

[0113] At this point, Θ can be expressed as i All the evidence under i (t) are unified as evidence e(t) under Θ.

[0114] 3. Weight of evidence and reliability calculation method

[0115] Since different experts may assign different weights to risk indicators, in order to effectively deal with this subjective uncertainty and give full play to the role of experts in weighting, this paper uses intervals to describe the weight of evidence. For example, if there are M experts, denoted as E1, E2, …, E M , assign different evidence weights w i,1 ,w i,2 ,…,w i,M Give x i , then all weights can be sorted in ascending order. Without loss of generality, if w i,1 <w i,2 <… <w 1,M-1 <w i,M , then x i The interval weights of can be obtained by removing the maximum and minimum weights and i,2 ,w 1,M-1 ]Sure.

[0116] Since the observed data of risk indicators may be affected by environmental noise, in order to measure the data quality, the present invention introduces the reliability of evidence. In the context of sensors, the reliability of evidence consists of the static reliability and dynamic reliability of the sensor. is It is an objective property of the sensor and a fixed value, which can be determined by the factory parameters of the sensor or evaluated by experts. In contrast, dynamic reliability r i d (t) is a subjective attribute of the sensor, which can be obtained by the consistency-based method disclosed in the prior art. Therefore, the reliability of evidence is calculated according to the following formula:

[0117] r i (t) = αr i s +(1-α)r i d (t) (8)

[0118] Among them, α∈[0,1] is a discount factor that measures the role of the two reliability in sensor reliability and is usually given by experts.

[0119] 4. Calculation method of correlation coefficient

[0120] Affected by factors such as system structure coupling and mechanism correlation, risk indicators may not be strictly independent. Therefore, the correlation between indicators should be considered. Since the reliability of different risk indicators is different, the reliability of evidence can be used to determine the fusion order. The higher the reliability of the indicator, the higher its fusion order. The present invention defines the correlation coefficient of evidence as RTDC using the distance correlation method.

[0121] For two pieces of evidence e at time t i (t) and e j (t), and their reliability are r i (t) and r j (t), its relative order Seq i,j (t) is determined by the following formula:

[0122]

[0123] Among them, Seq i (t) and Seq. j (t) respectively represent e i (t) and e j (t) the fusion order;

[0124] Given two data matrices Z i (t) and Z j (t), calculate e according to the following formula i (t) and e j (t) distance correlation coefficient:

[0125]

[0126] Among them, v2 (Z i (t),Z j (t)) represents Z i (t) and Z j The empirical distance covariance of (t); v 2 (Z i (t)) and v 2 (Z j (t)) respectively represent Z i (t) and Z j The autocovariance of (t).

[0127] According to the relative order Seq i,j (t) determine the evidence e1(t), e2(t),…,e L The fusion order of (t) is 1, 2, …, L. Based on this, the correlation matrix C is expressed as:

[0128]

[0129] According to the correlation matrix C, calculate e i The overall correlation coefficient Tdd of (t) i (t):

[0130]

[0131] e i The correlation coefficient between (t) and all evidence is d i (t), i.e., the RTDC value, can be obtained by the following formula:

[0132]

[0133]

[0134] According to the above formula, d i (t)∈[0,1], and d i The larger the value of (t), the greater the i (t) is less relevant than all the evidence.

[0135] 5. Risk assessment model based on ERR-DE

[0136] Based on the above method, the present invention proposes a new ERR-DE (Related Evidence Reasoning Rule) model. For an evidence e represented by formula (5) i (t), weight and reliability are w i and r i (t), FoD is Θ={H1,H2,…,H n}. Its mixed probability mass can be expressed as:

[0137]

[0138] in, Represents an empty set; is the mixing weight, and P(Θ) is the power set of Θ, including 2 n Subsets are used to describe the local and global ignorance in the evaluation, P(Θ) is expressed as:

[0139]

[0140] For the evidence e under Θ i (t) and e j (t), after combining the two, the evidence combination based on ERR-DE can be expressed as:

[0141]

[0142]

[0143] Among them, β e(2),θ (t) is e i (t) and e j (t) The confidence level relative to the risk level θ after combination, m e(2),θ (t) represents the unnormalized combined probability mass assigned to θ; m i,φ (t) and m j,ψ (t) respectively represent e i (t) and e j (t) the mixed probability mass assigned to risk levels φ and ψ;

[0144] For L pieces of evidence e1(t),e2(t),…,e L (t), iterate formula (17) and formula (18) L-1 times to obtain the final risk assessment result, which is in the following confidence distribution form:

[0145]

[0146] Among them, β e(L),θ (t) is the confidence level of risk level θ,

[0147] Obviously, since θ is not just a single subset, S e(L) There is local and global ignorance in (t). Therefore, S e(L) (t) is mapped to H p The actual probability For subsequent evaluation and decision making:

[0148]

[0149] in, The system is at risk level H at time t p probability.

[0150] Assumption Level H p The utility is u(H p ), then the expected utility (i.e., risk) of the system is calculated as:

[0151]

[0152] Among them, RD(t)∈[0,1] can quantitatively characterize the risk of the system. p In comparison, RD(t) is a continuous variable that can more effectively describe the degree of risk. The closer the value of RD(t) is to 1, the higher the risk; and the closer RD(t) is to 0, the lower the risk.

[0153] 6. Parameter optimization model constructed by the present invention

[0154] In the ERR-DE model, experts provide many evidence parameters, including evidence weights, reference values ​​of risk levels in different FoDs, and conversion matrices, which will lead to strong subjective uncertainty in the risk assessment results. As mentioned above, the evidence weight belongs to the interval [w i,2 ,w 1,M-1 ], which will make RD(t) fluctuate within a certain range. Assuming that the expected risk is RD, the observed result is RD(t). In order to reduce the subjective uncertainty of the evidence parameters, the present invention establishes a parameter optimization model. By solving the parameter optimization model, the optimized parameters can be obtained, including the optimal conversion matrix, evidence weight, and reference values ​​of risk levels in different FoDs. The parameter optimization model is:

[0155]

[0156] st

[0157]

[0158] Where, Γ represents the objective function; and Represent the weight of evidence w i The upper and lower bounds of and Respectively represent h i,k Reference upper and lower bounds at initial FoD.

[0159] Example

[0160] The present invention uses the above-established model to conduct risk assessment on the laser gyroscope. According to the mechanism analysis, the risk of the laser gyroscope is mainly related to the drift coefficient and the light intensity. Therefore, a risk assessment index system for the laser gyroscope is constructed, such as Figure 2 shown.

[0161] exist Figure 2 In the example, K0 and K1 represent the zero-order and first-order drift coefficients of the laser gyroscope, respectively. LT is the light intensity. In this embodiment, the gravity acceleration at the sampling location is 9.8015 m / s 2 A total of 100 sets of data were collected, such as Figure 3 shown.

[0162] 1. Obtaining evidence and determining initialization parameters

[0163] Based on factory parameters and expert knowledge, the reference levels and reference values ​​of risk indicators are obtained as shown in Tables 1 and 2.

[0164] Table 1 Reference levels and reference values ​​of drift coefficient

[0165]

[0166] Table 2 Reference levels and values ​​of light intensity

[0167]

[0168] According to Table 1, the FoD of drift coefficient can be expressed as Θ1 = {small, medium, large}. In Table 2, the unit of light intensity is V, which is the output of the A / D conversion circuit. Therefore, the FoD of light intensity can be expressed as Θ2 = {very weak, weak, medium, strong, very strong}. By using the rule / utility-based input information conversion technique, all observation data are converted into evidence. For example, in Figure 3 The value of K0 on the first day is 0.0023° / h. 1,1 =-0.02° / h and h 1,2 =0° / h, based on equations (1)-(3), the following evidence is obtained:

[0169]

[0170] Therefore, the evidence generated by K0 on the first day can be expressed as:

[0171] e1(1)={(small, 0.1150),(medium, 0.8850),(large, 0)} (25)

[0172] In order to obtain the weight of evidence, five experts were invited to participate in the empowerment. In addition, the FoD of the risk assessment results was set to Θ = {low, medium, high}. Obviously, there is inconsistency between Θ1, Θ2 and Θ. Therefore, the evidence in Θ1 and Θ2 needs to be converted to Θ. The evidence parameters under Θ1 and Θ2 are shown in Table 3.

[0173] Table 3 Initial parameters of risk indicators

[0174]

[0175] Table 4 Reference values ​​for risk levels in Θ

[0176]

[0177]

[0178] Therefore, according to the transformation matrices A1, A2, and A3 given by the experts, all evidence under Θ1 and Θ2 can be unified to the same FoD, i.e., Θ, through formula (7). By using the distance-based method, the dynamic reliability of each risk indicator is calculated, and then according to formula (8), the reliability of the evidence can be obtained, as follows: Figure 4 shown.

[0179] According to formula (9)-formula (14) and Figure 3-Figure 4 , setting the significance level to 5%, we can obtain the RTDC values ​​of each risk indicator: d1=1, d2=0.3496, d3=0.5106.

[0180] 2. Parameter Optimization

[0181] Based on formula (22), the objective function can be established, and the constraints are the values ​​in Tables 1 to 4.

[0182]

[0183] In this embodiment, the initial values ​​of all evidence parameters are set to the average values ​​of the corresponding intervals. The Fmincon function in the Matlab optimization tool is used to solve equation (27) to obtain the optimal transformation matrix shown in equation (28). Other optimal evidence parameters are shown in Tables 5 to 8.

[0184]

[0185] Table 5 Reference values ​​of optimal drift coefficients

[0186]

[0187] Table 6 Optimal light intensity reference values

[0188]

[0189] Table 7 Optimal risk indicator weights

[0190]

[0191] Table 8 Optimal reference values ​​for reference levels in Θ

[0192]

[0193] Based on the optimized parameters, the ERR-DE model is used to obtain the risk probability P of the laser gyroscope relative to different risk levels. Hp (t), such as Figure 5 shown.

[0194] from Figure 5 It can be seen that as the number of test days increases, the risk probability of the "low" level drops sharply, from about 0.88 to about 0.06. For the "medium" level, the risk probability fluctuates around 0.10, and the fluctuation range is relatively slow. In contrast, the risk probability of the "high" level increases rapidly, from about 0.04 to 0.82. This also means that the possibility of risk of laser gyroscopes is increasing.

[0195] In order to further reveal the overall change of the risk level of laser gyroscopes, the risk assessment results of the optimized ERR-DE model were compared with the expected results, such as Figure 6 As shown. Figure 6 It can be seen that the mean square error (MSE) value between the evaluation results and the expected results of the optimized ERR-DE model is 0.0079. This shows that the optimized ERR-DE model can well describe the changes in the risk level of the laser gyroscope. Overall, the risk level increases from about 0.10 to 0.87. The increase in RD(t) means the increase in the risk level, which is also consistent with Figure 5 Therefore, the effectiveness of the proposed ERR-DE model is verified.

[0196] 3. Comparison with the traditional ERR model

[0197] In this example, the ERR-DE model proposed in the present invention is compared with the traditional ERR model to verify the effectiveness of the ERR-DE model. In the ERR model, the inconsistency of FoD is not considered, and the dependency index of evidence is ignored. In order to unify the FoD of evidence, we set Θ2 = {weak, medium, strong}, and the reference value of LT is shown in Table 9. Other parameters are consistent with the ERR-DE model.

[0198] Table 9 Reference levels and values ​​of light intensity under the ERR framework

[0199]

[0200] Use the Fmincon function in Matlab optimization tool to optimize the ERR model. Figure 7 The risk assessment results generated by different ER models were compared in .

[0201] from Figure 7 It can be seen that the MSE value between the evaluation results of the optimized ERR model and the expected results is 0.0172. Compared with the ERR model, the evaluation accuracy of the ERR-DE model is improved by about 54.7%. Since the ERR model does not fully consider uncertainty, its risk assessment accuracy is relatively low. This also proves the effectiveness of the proposed ERR-DE model.

[0202] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A complex system risk assessment method based on relevant evidence reasoning rules, characterized by: The following steps are involved: Step 1: Construct a risk assessment indicator system for complex systems and determine risk indicators; Step 2: Determine the reference level and reference value of each risk indicator; Step 3: Use rule / utility-based input information conversion technology to convert the observed data of risk indicators at each moment into evidence; Step 4: Introduce the conversion matrix to convert the evidence obtained in step 3 into evidence under the evaluation result FoD; Step 5: Use intervals to describe the weights assigned by experts to risk indicators and calculate the reliability of the evidence obtained in step 4; Step 6: According to the reliability of evidence obtained in step 5, determine the fusion order of risk indicators and calculate the correlation coefficient of all evidence; Step 7: Establish a parameter optimization model, determine the optimization parameters, and obtain the optimal parameter set; Step 8: Based on the optimal parameters, a risk assessment model based on relevant evidence reasoning rules is constructed to calculate the system risk level; The specific steps of step 4 include: Step 41: Define the identification framework of risk assessment results as Θ = {H1, H2, …, H n }, the evidence under Θ is obtained according to the following formula: e(t)={(H p ,β p (t));p∈[1,n]} (5) Among them, β p (t) represents the evidence relative to the risk level H p Confidence level; Step 42: Establish Θ and Θ i The transformation matrix A between i : Among them, A i All elements in are obtained based on expert knowledge; Step 43: According to formula (7), Θ i All evidence under θ is transformed into evidence under θ: B=β i A i (7) Among them, β i Indicates e i (t) in Θ i The confidence matrix under , and β i =[β i,1 ,β i,2 ,…,β i,n(i) ]; B represents e i (t) The confidence matrix under Θ, and Β = [β1,β2,…,β n ].

2. The complex system risk assessment method based on relevant evidence reasoning rules according to claim 1 is characterized in that: Step 3: The specific steps for obtaining evidence include: Step 31: Set the risk indicator x i The FoD is defined as Θ i ={H i,1 ,H i,2 ,…,H i,n(i) }, where H i,k is x i The k-th risk level of , and i∈[1,L], k∈[1,n(i)]; Step 32: Obtain the observed data x according to formula (1)-formula (3) i (t) are H respectively corresponding to the risk level. i,k and H i,k+1 Confidence of: b i,k+1 (t)=1-β i,k (t) (2) β i,j (t) = 0; j ≠ k, k + 1 and j ∈ [1, n(i)] (3) Among them, x i (t) represents the i-th risk indicator x i Observation data at time t; h i,k Indicates risk level H i,k Reference value of β i,k (t), β i,k+1 (t) and β i,j (t) represents x i (t)Assessed as risk level H i,k , H i,k+1 and H i,j Confidence level when Step 34: According to the following formula, we can get i The risk indicator x i The confidence distribution of the evidence provided at time t takes the form: e i (t)={(H i,j ,β i,j (t));j∈[1,n(i)]} (4) Among them, e i (t) represents the evidence provided at time t.

3. The complex system risk assessment method based on relevant evidence reasoning rules according to claim 2 is characterized in that: The specific steps of step 5 include: Step 51: M experts give risk indicator x i Assign different weights of evidence w i,1 ,w i,2 ,…,w i,M , and sort all weights in ascending order to get w i,1 <w i,2 <… <w 1,M-1 <w i,M , determine x i The weight of evidence interval is [w i,2 ,w 1,M-1 ]; Step 52: Calculate the reliability of evidence according to formula (8): r i (t)=αr i s +(1-α)r i d (t) (8) Among them, r i s Represents the static reliability, r i d (t) represents dynamic reliability, and α∈[0,1] represents the discount factor.

4. The complex system risk assessment method based on relevant evidence reasoning rules according to claim 3 is characterized in that: The specific steps of step 6 include: Step 61: Determine the two pieces of evidence e at time t according to equation (9): i (t) and e j The relative order Seq of (t) i,j (t): Among them, Seq i (t) and Seq. j (t) respectively represent e i (t) and e j (t) the fusion order; Step 62: For the observation data matrix Z i (t) and Z j (t), calculate e according to the following formula i (t) and e j (t) distance correlation coefficient: Among them, v 2 (Z i (t),Z j (t)) represents Z i (t) and Z j (t) empirical distance covariance; v 2 (Z i (t)) and v 2 (Z j (t)) respectively represent Z i (t) and Z j The autocovariance of (t); Step 63: Based on Seq i,j (t) determine the evidence e1(t), e2(t),…,e L The fusion order of (t) is as follows: Step 64: Calculate e based on the correlation matrix C i The overall correlation coefficient Tdd of (t) i (t): Step 65: According to Tdd i (t) Calculate e i The correlation coefficient d between (t) and all evidence i (t): Among them, d i (t)∈[0,1], and d i The larger the value of (t), the greater the i (t) is less relevant than all the evidence.

5. The complex system risk assessment method based on relevant evidence reasoning rules according to claim 4 is characterized in that: The specific steps of step 7 include: Step 71: Construct parameter optimization objective function: st Where, Γ represents the objective function; and Represent the weight of evidence w i The upper and lower bounds of and Respectively represent h i,k The upper and lower bounds of the reference value at the initial FoD; Step 72: Solve equation (22) to obtain the optimal evidence weight, reference value of risk level and conversion matrix.

6. The complex system risk assessment method based on relevant evidence reasoning rules according to claim 5 is characterized in that: Step 8 The steps to construct the ERR-DE based risk assessment model include: Step 81: Obtain the evidence e under Θ according to the optimized evidence weight and evidence reliability i The mixing probability mass of (t) is: in, Represents an empty set; is the mixing weight, and P(Θ) is the power set of Θ, and Step 82: For evidence e under Θ i (t) and e j (t), the confidence β of the combination of the two relative to the risk level θ e(2),θ (t) and the unnormalized combined probability mass m assigned to θ e(2),θ (t) are: Among them, m i,φ (t) and m j,ψ (t) respectively represent e i (t) and e j (t) the mixed probability mass assigned to risk levels φ and ψ; Step 83: For L pieces of evidence e1(t), e2(t),…,e L (t), iterate equations (17)-(18) L-1 times to obtain the final risk assessment result S e(L) (t), its confidence distribution is: Among them, β e(L),θ (t) is the confidence level of risk level θ, Step 84: Substitute S by equation (20) e(L) (t) is mapped to risk level H p The actual probability of in, The system is at risk level H at time t p The probability of Step 85: Calculate the expected utility of the system using equation (21): Among them, RD(t)∈[0,1] represents the expected utility of the system, that is, the risk of the system. The closer the value of RD(t) is to 1, the higher the risk; and the closer RD(t) is to 0, the lower the risk.

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