A multi-source uncertain information structure reliability evaluation model and an accurate solving method

Abstract

The application discloses a multi-source uncertain information structure reliability evaluation model and an accurate solving method. A truncated random variable is used to describe sample sufficient uncertain parameters in the structure; a hyper-ellipsoid convex set non-probability variable is used to describe some sample insufficient uncertain parameters in the structure; a fuzzy random variable is used to describe uncertain parameters with both fuzziness and randomness; and an evidence variable is used to describe evidence information given by experts or experiments. A similar non-probability mixed reliability index is introduced to measure the absolute safety of the structure, and a hybrid optimization algorithm of outer genetic algorithm and inner point method is used for solving, so as to avoid solving errors caused by falling into local optimum. When the structure is not absolutely safe, a maximum possible failure point corresponding to the similar non-probability mixed reliability index is taken as an initial point, a first order second moment (AORM) method is used to solve a similar probability mixed reliability index, and a second order second moment (SORM) method is used to correct the similar probability mixed reliability index to obtain an accurate result.

Description

Technical Field

[0001] This invention belongs to the field of structural reliability analysis technology, specifically involving a multi-source uncertain information structural reliability assessment model and an accurate solution method. It defines a hybrid reliability model with four uncertain variables—probabilistic, non-probabilistic, fuzzy, and evidence—that coexist, and provides a high-precision solution method for its reliability indices. Background Technology

[0002] In engineering structures, uncertainties are prevalent in structural parameters such as material properties, manufacturing errors, and loads. When multiple uncertainties exist simultaneously in the same structural reliability assessment problem, hybrid reliability analysis is essential. When performing hybrid reliability analysis of structures with multiple sources of uncertainty, it is also necessary to consider that the structural function in engineering projects generally exhibits strong nonlinearity, thus requiring high-precision methods to solve for the hybrid reliability indices. Summary of the Invention

[0003] The purpose of this invention is to solve the problem of accurate reliability assessment of structures with strong nonlinearity of structural function functions and multiple sources of uncertain information in engineering. This invention provides a reliability assessment model and accurate solution method for structures with multiple sources of uncertain information, specifically a hybrid reliability model and high-precision solution method based on four types of uncertain information: truncated probability, non-probability, fuzzy, and evidence.

[0004] This invention provides a reliability assessment model and accurate solution method for multi-source uncertain information structures, comprising the following steps:

[0005] S1: Establish a mathematical model for structural reliability analysis, including the types of uncertain variables, boundary information of uncertain variables, and determination of structural function functions;

[0006] The roof structure used for assessment has top hangers and compression members reinforced with concrete, while tension members and bottom hangers are made of steel; the roof structure is subjected to a uniformly distributed load q, which can be equivalently converted into a nodal load P = ql / 4; at node C, the vertical deflection can be modeled using the following reliability analysis model:

[0007] Formula 20

[0008] In Formula 20, E C and E S These represent the Young's modulus of concrete and reinforcing steel, respectively; A C and A S They represent their cross-sectional areas respectively;

[0009] S2: When the number of data samples in an uncertain variable is greater than or equal to 30, the data sample is considered sufficient, and a truncated probability variable is used to describe it; when the number of data samples in an uncertain variable is less than 30, the data sample is considered insufficient, and a non-probability variable of a hyperellipsoidal convex set is used to describe it; when an uncertain variable has both randomness and fuzziness, a fuzzy random variable is used to describe it; when the variable information is given by experts or experiments, an evidence variable is used to describe it.

[0010] S3: When four types of uncertainty variables—probability, non-probability, fuzziness, and evidence—coexist in the structural function, establish a hybrid reliability model of probability-non-probability-fuzziness-evidence and give its comprehensive reliability index definition.

[0011] Formula 1

[0012] In Formula 1: For comprehensive reliability indicators; It is a hybrid reliability metric similar to nonprobabilistic ones; A hybrid reliability metric with similar probabilities; Represents the truncation probability variable; Represents a truncated fuzzy random variable; Represents the evidence variable; Represents non-probability variables; It is the most likely failure point in the standard normal space; It is the most likely failure point in the standard nonprobability space; It is the limit state surface in standard normal space at point No. Approximate principal curvature in each direction;

[0013] The expression is:

[0014] Formula 2

[0015] In Formula 2: It is a symbolic function; It is the first The equivalent interval variable after normalizing a truncated random variable; It is the first The equivalent interval variable after normalizing a fuzzy random variable; It is the equivalent interval variable after normalization of the h-th evidence variable; It is the first Known non-probability variables after normalization; It is a function;

[0016] The above It is a two-level optimization problem of minima and maxima. If the index can only exist at a certain intersection point of the hyperray passing through the origin and the vertices of the interval set with the standardized failure surface in infinite space, then the two-layer optimization problem can be transformed into a single-layer optimization problem, and the calculation formula is as follows:

[0017] Formula 3

[0018] In Formula 3: For the first One normalized non-probability variable; The number is for a non-probability variable. It is a truncated random variable. It is a fuzzy random variable. It is an evidentiary variable. It is a known non-probability variable;

[0019] The expression is:

[0020] Formula 4

[0021] In Formula 4: It is a truncated random vector in the standard normal space; It is a fuzzy random vector in the standard normal space; These are evidence variables in the standard normal space; It is unification A vector of sets of four variables. yes The lower and upper bounds; It is the first One normalized non-probability variable;

[0022] S4: Based on the boundary information of all uncertain variables, a hybrid optimization method using an outer genetic algorithm and an inner interior point method is used to solve for a hybrid reliability index that is similar to a non-probabilistic one.

[0023] S5: When the obtained similar non-probability hybrid reliability index is greater than 1, the structure is in an absolutely safe state and the solution is complete; when the obtained similar non-probability hybrid reliability index is less than 1, take the maximum possible failure point corresponding to the similar non-probability hybrid reliability index as the initial point, and use AFORM to solve for the similar probability hybrid reliability index.

[0024] S6: Based on the hybrid reliability index with similar probabilities obtained by AFORM, SORM is used for correction to obtain the corrected maximum probability of failure.

[0025] S7: The Monte Carlo method is used to solve for the maximum possible failure probability, and the accuracy of the maximum possible failure probability results obtained by AFORM and SORM is verified.

[0026] Preferably, the expressions for the truncated probability variable, the non-probability variable, the fuzzy random variable, and the evidence variable in S2 are as follows:

[0027] Assumption For in the interval The truncated probability variable on the above, and the corresponding probability density function With cumulative probability distribution function It is expressed as follows:

[0028] Formula 5

[0029] Formula 5: It is the first The probability density function of a truncated random variable. It is the first The cumulative distribution function of a truncated random variable;

[0030] The normalized representation of probability variables is as follows:

[0031] Formula Six

[0032] In Formula Six: It is the first Variables in a standard normal space; It is the first The cumulative distribution function of a random variable; It is the inverse function of the cumulative distribution of the standard normal distribution;

[0033] The expression for the non-probabilistic variables of the hyperellipsoidal convex set is as follows:

[0034] Formula 7

[0035] In Formula 7: It is a convex set of non-probability variables; It is the first Hyperellipsoidal variables The nominal value; It describes the first A known positive definite matrix of a hyperellipsoid shape; It describes the first The known positive real numbers representing the sizes of the hyperellipsoids; for ease of calculation, the hyperellipsoids are converted to units into hyperspheres, and the conversion formula is as follows:

[0036]

[0037] Formula 8

[0038] Formula 8: It is a diagonal matrix; It is an orthogonal matrix, by It is obtained through orthogonal decomposition. For a normalized hypersphere; obviously, when the positive definite matrix... At this point, the hyperellipsoidal variable degenerates into an interval variable; Described as the radius of an interval, the normalization formula for the interval variable is as follows:

[0039] Formula Nine

[0040] Formula 9: The midpoint of the interval variable; The radius of the interval; and These are the lower and upper bounds of the interval variable;

[0041] The fuzzy random variable: fuzzy random variable The fuzziness is determined by the membership function To describe; The randomness is determined by the probability density function. To describe; when the failure domain is not considered and security domain When the ambiguity is such that the generalized failure probability can be measured by the following formula:

[0042] Formula 10

[0043] Formula 10: As a regularization factor; For the space of all real numbers;

[0044] The product of the membership function and the probability density function is transformed into a function with probability density properties using the following formula:

[0045]

[0046] Formula Eleven

[0047] In Formula 11: The transformed probability density function; It is the cumulative distribution function;

[0048] Once the fuzzy random variable is transformed into a function with probability density properties, it can be converted into a truncated fuzzy random variable using the method of truncating random variables, as shown in the following formula:

[0049] Formula 12

[0050] In Formula 12: The transformed truncated probability density function; This is the truncated cumulative distribution function;

[0051] The evidence variable: using Represents the uncertainty parameters modeled by evidence theory and their contents. The sample space of all possible values, based on evidence theory, is referred to as the evidence variable, and the sample space is also called the identification frame; the identification frame contains only two mutually exclusive variables. ,but All possible subsets will form a power set. The basic probability assignment (BPA) represents the confidence level of a proposition, determined by a mapping function. However, the following conditions must be met:

[0052] Formula Thirteen

[0053] In Formula 13: Indicates an event The corresponding BPA;

[0054] Once BPA is allocated, it can be calculated using the following formula:

[0055]

[0056] Formula Fourteen

[0057] In Formula Fourteen: Indicates an event and events The sum of all BPAs of a subset of; Expressing a proposition All or part of the event Given a set of propositions with an intersection, calculate the sum of the BPAs of all propositions whose intersection is non-empty;

[0058] Evidence theory holds that events The true probability is between the intervals In engineering, uncertainties are typically categorized into... Each of the *n* mutually exclusive subintervals is assigned a corresponding Probability Distribution Allocation (BPA). Based on the Bayesian method and the maximum entropy principle, it is assumed that the probability distribution on the subintervals is piecewise uniform. In other words, the BPA of the evidence variable is uniformly distributed within the corresponding subintervals. According to the assumption of uniform distribution, the *n*th... probability density function on subinterval for:

[0059] Formula Fifteen

[0060] Formula 15: For the first BPA in each interval; For the first The upper limit of each interval, This is the lower limit of the interval;

[0061] Assumption For the first For a point within an interval, calculate Cumulative distribution function formula for points for:

[0062] Formula Sixteen

[0063] In Formula Sixteen: For the front The sum of BPA in each interval; for BPA of the interval where the point is located, and for The upper and lower limits of the interval containing the point.

[0064] Preferably, the specific steps of S3 are as follows:

[0065] S3-1: Process all variables into non-probability variables based on boundary information;

[0066] S3-2: Normalize all non-probability variables and substitute them into the structure function;

[0067] S3-3: A genetic algorithm is used to solve for a hybrid reliability index that is similar to a non-probabilistic one, with the initial population range set as follows: Set the relative error of the constraint conditions and objective function for a large number of evolutions. When the genetic algorithm reaches the convergence condition or meets the maximum number of evolutions, it switches to the interior point method for iterative convergence. The convergence condition of the interior point method is the same as that of the genetic algorithm.

[0068] S3-4: If the result is... ,but ;like Record this moment The corresponding maximum possible failure point is used as the solution. The initial point.

[0069] Preferably, the non-probabilistic hybrid reliability index in S4 The specific steps for solving the hybrid reliability index with similar probabilities when the probability is less than 1 are as follows:

[0070] S4-1: After normalizing all probability variables, we get After normalizing the non-probability variables, we get ,make ;

[0071] S4-2: Set the initial point of the iteration to the point that has already been obtained. , obtain the initial point ;

[0072] S4-3: First, iterate over the non-probability variables to obtain... Then, by iterating over the probability variables, we obtain... ,but ;

[0073] S4-4: Judgment If the convergence condition is met, then calculate If the condition is not met, return to S4-3 and continue the iteration.

[0074] S4-5: After iterative convergence, by calculate .

[0075] Preferably, in step S4-3, the non-probabilistic variables are first iterated to obtain... Then, by iterating over the probability variables, we obtain... The method is as follows:

[0076] Formula 17

[0077] In formula seventeen: It is the first The normalized nonprobabilistic vector of the next iteration; ;

[0078] After iterating over the non-probability variables, iterate over the probability variables:

[0079] Formula 18

[0080] Formula 18: For the first The standard normal space vector of the next iteration; .

[0081] Preferably, the specific method for obtaining the corrected maximum possible failure probability in S5 is as follows:

[0082] Formula 19

[0083] In Formula Nineteen: It is a hybrid reliability metric with similar probabilities; It is the most likely failure point in the standard normal space; It is the most likely failure point in the standard nonprobability space; It is the limit state surface in standard normal space at point No. Approximate principal curvature in each direction.

[0084] The present invention has the following advantages over the prior art:

[0085] This invention discloses a multi-source uncertain information structure reliability assessment model and accurate solution method. It employs truncated random variables to describe uncertain parameters with sufficient samples in the structure; hyperellipsoidal convex set non-probabilistic variables to describe uncertain parameters with insufficient sample numbers; fuzzy random variables to describe uncertain parameters exhibiting both fuzziness and randomness; and evidence variables to describe evidence information provided by experts or experiments. By introducing a hybrid reliability index similar to non-probabilistic metrics to measure the absolute safety of the structure, and using a hybrid optimization algorithm combining an outer layer genetic algorithm and an inner layer interior point method, it avoids solution errors caused by getting trapped in local optima. When the structure is not absolutely safe, the maximum probable failure point corresponding to the hybrid reliability index similar to non-probabilistic metrics is taken as the initial point. The first second-moment method (AORM) is used to solve the hybrid reliability index similar to probabilistic metrics, and then the second second-moment method (SORM) is used to correct it to obtain an accurate result. This paper addresses the technical challenge of lacking a unified reliability analysis model for engineering structures simultaneously exhibiting four types of uncertainties: non-probabilistic, fuzzy, and evidence-based. It fully utilizes boundary information and introduces a hybrid reliability index, similar to a non-probabilistic one, to measure the absolute safety of the structure. For cases where the structural function function has a high degree of nonlinearity, the second-order second-moment method (SORM) is used for accurate solution, avoiding the extensive computations required by the Monte Carlo method. A hybrid optimization algorithm is employed to solve the hybrid reliability index, similar to a non-probabilistic one, ensuring both global optimality and speed of the solution. Using the maximum probable failure point corresponding to the hybrid reliability index, similar to a non-probabilistic one, as the initial point for iteratively solving the hybrid reliability index, similar to a probabilistic one, guarantees the globality of the results, accelerates the convergence process, and reduces the number of iterations. Attached Figure Description

[0086] Figure 1 This is a flowchart of the overall technical solution and method of the present invention.

[0087] Figure 2 This is a diagram illustrating the calculation of the roof structure according to an embodiment of the present invention. Detailed Implementation

[0088] The invention will be further described below with reference to the accompanying drawings and a specific embodiment of a roof structure.

[0089] Please see the appendix Figure 1The overall technical solution and method flow of the present invention are as follows:

[0090] Step 1: Establish a mathematical model for structural reliability analysis, including uncertain variables, boundary information of uncertain variables, and determination of functional functions.

[0091] Please see the appendix Figure 2 The roof structure shown has its top hangers and compression members reinforced with concrete, while the tension bars and bottom hangers are made of steel. This roof structure bears a uniformly distributed load. This load can be equivalently converted into a nodal load. At node C, the vertical deflection can be used to establish the following reliability analysis model:

[0092] Formula 20

[0093] In Formula Twenty, and These represent the Young's modulus of concrete and steel reinforcement, respectively. and These represent their cross-sectional areas, respectively.

[0094] Step 2: When the number of data samples in the uncertain variable is greater than or equal to 30, the data sample is considered sufficient and can be described by a truncated probability variable; when the number of data samples in the uncertain variable is less than 30, the data sample is considered insufficient and can be described by a hyperellipsoidal convex set non-probability variable; when the uncertain variable has both randomness and fuzziness, it can be described by a fuzzy random variable; when the variable information is given by experts or experiments, it can be described by an evidence variable.

[0095] It exhibits fuzziness and randomness, and is treated as a random fuzzy variable. The information is provided by experts and processed as evidence variables. and If the sample size is greater than 30, it will be treated as a random variable. and Data points less than 30 and showing correlation are treated as hyperellipsoidal variables. The distribution parameters for all variables are shown in Table 1.

[0096] Table 1 Distribution parameters of all variables

[0097]

[0098] In Table 1, for random variables, parameter 1 is the mean and parameter 2 is the standard deviation; for evidential variables, parameter 1 is the uniformized segmented interval and parameter 2 is the BPA value; for non-probability variables, parameter 1 and parameter 2 are the upper and lower limits of the interval or the hyperellipsoidal constraint, respectively; the maximum value interval is the maximum range of the variable.

[0099] Membership function:

[0100] Formula 21

[0101] Step 3: Based on the boundary information of all uncertain variables, use a hybrid optimization method combining an outer genetic algorithm and an inner interior point method to solve for a hybrid reliability index similar to a nonprobabilistic one. .

[0102] Based on the boundary information of all variables obtained, an outer genetic algorithm is used, with 50 evolution iterations and a convergence condition of relative error less than 1 / 3. If the genetic algorithm fails to meet the convergence condition before the maximum number of evolutions, the interior point method is used to solve the problem. The initial point is taken from the result of the last generation of the genetic algorithm, and the convergence condition is set to a relative error of less than 1. .

[0103] Seeking 0.3967, [ 0.3967; 0.3967; -0.3967; -0.3967; -0.2727; -0.2881], transformed back to the original space as [ 2.1904*10 4 ; 12.2856; 1.1*10 11 2.7144*10 10 9.3727*10 -4 ; 0.0337]. Because It is necessary to consider mixed reliability metrics with similar probabilities. Solve the problem.

[0104] Step 4: Similar to non-probabilistic reliability indicators When the value is greater than 1, the structure is in an absolutely safe state, and the solution is complete. When less than 1, take Using the corresponding maximum possible failure point as the initial point, solve using AFORM. .

[0105] Pick The corresponding maximum probable failure point is used as the initial point for solving the AFORM problem, and a hybrid reliability index with similar probabilities is solved. .

[0106] Seeking The corresponding maximum possible failure point is [2.1860*10]. 4 ; 12.4847; 1.1268*10 11 2.9154*10 10 9.3301*10 -4 [0.0333]; The maximum possible failure probability of AFORM is .

[0107] Step 5: After obtaining Then, SORM is used to correct the results, and the maximum possible failure probability after correction is obtained.

[0108] Find curvature at the maximum possible failure point Substitute into Formula 22 to calculate the maximum failure probability after SORM correction.

[0109] Formula 22

[0110] The result of SORM is obtained.

[0111] Step 6: Use the Monte Carlo method to solve for the maximum possible failure probability and verify the accuracy of the results of SORM and AFORM.

[0112] Using the Monte Carlo method, the number of calculations is... The result was obtained. Using the Monte Carlo method as a benchmark, the relative errors of AFORM and SORM were compared, and the results are shown in Table 2:

[0113] Table 2 Relative Errors of AFORM and SORM

[0114]

[0115] In the example, the error between AFORM and MCS is 25.22%, which is relatively large. However, the error between SORM and MCS is only 2.94%, which is more accurate and acceptable in engineering.

[0116] If the mean point is taken as the initial iteration point, it will take 19 iterations to converge, while taking... Using the maximum possible failure point as the initial point, the method converges in just 15 iterations, indicating that it accelerates the convergence process and reduces the number of iterations.

[0117] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A reliability assessment model and accurate solution method for multi-source uncertain information structures, characterized in that, Includes the following steps: S1: Establish a mathematical model for structural reliability analysis, including the types of uncertain variables, boundary information of uncertain variables, and determination of structural function functions; For the evaluation of a roof structure, the top hangers and compression members of the roof structure are reinforced with concrete, while the tension members and bottom hangers are made of steel; the roof structure is subjected to a uniformly distributed load q, which can be equivalently converted into a nodal load P = ql / 4; at node C, the vertical deflection can be established using the following reliability analysis model: Formula 20 In Formula 20, E C and E S These represent the Young's modulus of concrete and reinforcing steel, respectively; A C and A S They represent their cross-sectional areas respectively; S2: When the number of data samples in an uncertain variable is greater than or equal to 30, the data sample is considered sufficient, and a truncated probability variable is used to describe it; when the number of data samples in an uncertain variable is less than 30, the data sample is considered insufficient, and a non-probability variable of a hyperellipsoidal convex set is used to describe it; when an uncertain variable has both randomness and fuzziness, a fuzzy random variable is used to describe it; when the variable information is given by experts or experiments, an evidence variable is used to describe it. S3: When four types of uncertainty variables—probability, non-probability, fuzziness, and evidence—coexist in the structural function, establish a hybrid reliability model of probability-non-probability-fuzziness-evidence and give its comprehensive reliability index definition. Formula 1 In Formula 1: For comprehensive reliability indicators; It is a hybrid reliability metric similar to nonprobabilistic ones; A hybrid reliability metric with similar probabilities; Represents the truncation probability variable; Represents a truncated fuzzy random variable; Represents the evidence variable; Represents non-probability variables; It is the most likely failure point in the standard normal space; It is the most likely failure point in the standard nonprobability space; It is the limit state surface in standard normal space at point No. Approximate principal curvature in each direction; The expression is: Formula 2 In Formula 2: It is a symbolic function; It is the first The equivalent interval variable after normalizing a truncated random variable; It is the first The equivalent interval variable after normalizing a fuzzy random variable; It is the equivalent interval variable after normalization of the h-th evidence variable; It is the first Known non-probability variables after normalization; For functional purposes; The It is a two-level optimization problem of minima and maxima. If the index can only exist at a certain intersection point of the hyperray passing through the origin and the vertices of the interval set in infinite space and the standardized failure surface, then the two-layer optimization problem can be transformed into a single-layer optimization problem: Formula 3 In Formula 3: For the first One normalized non-probability variable; The number is for a non-probability variable. It is a truncated random variable. It is a fuzzy random variable. It is an evidentiary variable. It is a known non-probability variable; The expression is: Formula 4 In Formula 4: It is a truncated random vector in the standard normal space; It is a fuzzy random vector in the standard normal space; These are evidence variables in the standard normal space; It is unification A vector of sets of four variables. yes The lower and upper bounds; It is the first One normalized non-probability variable; S4: Based on the boundary information of all uncertain variables, a hybrid optimization method using an outer genetic algorithm and an inner interior point method is used to solve for a hybrid reliability index that is similar to a non-probabilistic one. S5: When the obtained similar non-probability hybrid reliability index is greater than 1, the structure is in an absolutely safe state and the solution is complete; when the obtained similar non-probability hybrid reliability index is less than 1, take the maximum possible failure point corresponding to the similar non-probability hybrid reliability index as the initial point, and use AFORM to solve for the similar probability hybrid reliability index. S6: Based on the hybrid reliability index with similar probabilities obtained by AFORM, SORM is used for correction to obtain the corrected maximum probability of failure. S7: The Monte Carlo method is used to solve for the maximum possible failure probability, and the accuracy of the maximum possible failure probability results obtained by AFORM and SORM is verified.

2. The reliability assessment model and accurate solution method for multi-source uncertain information structures according to claim 1, characterized in that, The expressions for the truncated probability variable, the non-probability variable, the fuzzy random variable, and the evidence variable in S2 are as follows: For in the interval The truncated probability variable on the above, and the corresponding probability density function With cumulative probability distribution function It is expressed as follows: Formula 5 Formula 5: It is the first The probability density function of a truncated random variable. It is the first The cumulative distribution function of a truncated random variable; The normalized representation of probability variables is as follows: Formula Six In Formula Six: It is the first Variables in a standard normal space; It is the first The cumulative distribution function of a random variable; It is the inverse function of the cumulative distribution of the standard normal distribution; The expression for the non-probabilistic variables of the hyperellipsoidal convex set is as follows: Formula 7 In Formula 7: It is a convex set of non-probability variables; It is the first Hyperellipsoidal variables The nominal value; It describes the first A known positive definite matrix of a hyperellipsoid shape; It describes the first The known positive real numbers representing the sizes of the hyperellipsoids; for ease of calculation, the hyperellipsoids are converted to units into hyperspheres, and the conversion formula is as follows: Formula 8 Formula 8: It is a diagonal matrix; It is an orthogonal matrix, by Obtained by orthogonal decomposition; For a normalized hypersphere; obviously, when the positive definite matrix... At this point, the hyperellipsoidal variable degenerates into an interval variable; Described as the radius of an interval, the normalization formula for the interval variable is as follows: Formula Nine Formula 9: The midpoint of the interval variable; The radius of the interval; and These are the lower and upper bounds of the interval variable; The fuzzy random variable: fuzzy random variable The fuzziness is determined by the membership function To describe; The randomness is determined by the probability density function. To describe; when the failure domain is not considered and security domain When the ambiguity is such that the generalized failure probability can be measured by the following formula: Formula 10 Formula 10: As a regularization factor; For the space of all real numbers; The product of the membership function and the probability density function is transformed into a function with probability density properties using the following formula: Formula Eleven In Formula 11: The transformed probability density function; It is the cumulative distribution function; Once the fuzzy random variable is transformed into a function with probability density properties, it can be converted into a truncated fuzzy random variable using the method of truncated random variables: Official Twelve In Formula 12: The transformed truncated probability density function; This is the truncated cumulative distribution function; The evidence variable: using Represents the uncertainty parameters modeled by evidence theory and their contents. The sample space of all possible values, based on evidence theory, is referred to as the evidence variable, and the sample space is also called the identification frame; the identification frame contains only two mutually exclusive variables. ,but All possible subsets will form a power set. The basic probability assignment (BPA) represents the confidence level of a proposition, determined by a mapping function. However, the following conditions must be met: Formula Thirteen In Formula 13: Indicates an event The corresponding BPA; Once BPA is allocated, it can be calculated using the following formula: Formula Fourteen In Formula Fourteen: Indicates an event and events The sum of all BPAs of a subset of; Expressing a proposition All or part of the event Given a set of propositions with an intersection, calculate the sum of the BPAs of all propositions whose intersection is non-empty; Evidence theory holds that events The true probability is between the intervals The BPA of the evidence variable is evenly distributed within the corresponding sub-intervals. probability density function on subinterval for: Formula Fifteen Formula 15: For the first BPA in each interval; For the first The upper limit of each interval, This is the lower limit of the interval; For the first For a point within an interval, calculate Cumulative distribution function formula for points for: Formula Sixteen In Formula Sixteen: For the front The sum of BPA in each interval; for BPA of the interval where the point is located, and for The upper and lower limits of the interval containing the point.

3. The reliability assessment model and accurate solution method for multi-source uncertain information structures according to claim 1, characterized in that, The specific steps of S3 are as follows: S3-1: Process all variables into non-probability variables based on boundary information; S3-2: Normalize all non-probability variables and substitute them into the structure function; S3-3: A genetic algorithm is used to solve for a hybrid reliability index that is similar to a non-probabilistic one, with the initial population range set as follows: Set the relative error of the constraint conditions and objective function for a large number of evolutions. When the genetic algorithm reaches the convergence condition or meets the maximum number of evolutions, it switches to the interior point method for iterative convergence. The convergence condition of the interior point method is the same as that of the genetic algorithm. S3-4: If the result is... ,but ;like Record this moment The corresponding maximum possible failure point is used as the solution. The initial point.

4. The reliability assessment model and accurate solution method for multi-source uncertain information structures according to claim 1, characterized in that, The similar non-probabilistic hybrid reliability index in S4 The specific steps for solving the hybrid reliability index with similar probabilities when the probability is less than 1 are as follows: S4-1: After normalizing all probability variables, we get After normalizing the non-probability variables, we get ,make ; S4-2: Set the initial point of the iteration to the point that has already been obtained. , obtain the initial point ; S4-3: First, iterate over the non-probability variables to obtain... Then, by iterating over the probability variables, we obtain... ,but ; S4-4: Judgment If the convergence condition is met, then calculate If the condition is not met, return to S4-3 and continue the iteration. S4-5: After iterative convergence, by calculate .

5. The reliability assessment model and accurate solution method for multi-source uncertain information structures according to claim 4, characterized in that, In S4-3, the non-probability variables are first iterated to obtain... Then, by iterating over the probability variables, we obtain... The method is as follows: Formula 17 In formula seventeen: It is the first The normalized nonprobabilistic vector of the next iteration; ; After iterating over the non-probability variables, iterate over the probability variables: Formula 18 Formula 18: For the first The standard normal space vector of the next iteration; .

6. The reliability assessment model and accurate solution method for multi-source uncertain information structures according to claim 1, characterized in that, The specific method for obtaining the corrected maximum possible failure probability in S5 is as follows: Formula 19 In Formula Nineteen: It is a hybrid reliability metric with similar probabilities; It is the most likely failure point in the standard normal space; It is the most likely failure point in the standard nonprobability space; It is the limit state surface in standard normal space at point No. Approximate principal curvature in each direction.

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