Degradation and different strategies based on the resilience of the engineering structure design optimization method

Abstract

The application belongs to the field of engineering structure design, and discloses a kind of engineering structure design optimization methods based on toughness under degradation and different maintenance strategies. The application sets sample particles for variables in the domain of engineering structure design, establishes an engineering structure performance function surrogate model through the sample set, calculates the reliability of the toughness design optimization, and calculates the toughness constraint value of the engineering structure toughness design optimization by combining the performance loss and the performance recovery. Then, the application designs an engineering structure toughness design optimization mathematical model according to the maintenance cost and obtains the optimal design result. Compared with the prior art, the application has the beneficial effects that it can obtain the optimal result for engineering structure design under different maintenance strategies, avoid the technical problem that the operation elements change unevenly due to different maintenance modes, and improve the accuracy of the surrogate model by using active learning U function to ensure that the final optimization design model can obtain the optimal value.

Description

Technical Field

[0001] This invention relates to the field of engineering structures, specifically to a method for optimizing the design of engineering structures based on resilience under degradation and different strategies. Background Technology

[0002] Complex engineering structures often endure extreme environments such as sandstorms, extreme cold, high temperatures, and corrosion during service, making them prone to various faults or failures, and in severe cases, even catastrophic consequences. Therefore, quantifying the service performance of complex engineering structures requires considering not only their own condition but also the impact of uncertainties such as load conditions and service environment. Furthermore, during service-ready maintenance, the economics of maintenance must be considered to achieve a balance between maintaining service condition / capability and maintenance efficiency. Although a comprehensive R&D system integrating design, manufacturing, and operation and maintenance has been established for complex engineering structures, the lack of connection and coordination between the design, development, and operation / maintenance stages limits the improvement of overall design capabilities. Considering the different operating modes of design and maintenance, the uneven changes in various operating elements, and the differences in components and influencing factors, improving their service performance throughout their entire lifespan becomes increasingly difficult. Therefore, based on a comprehensive consideration of the reliability, safety, and economy of complex engineering structures, a resilience-based optimization method for engineering structure design under degradation and different maintenance strategies is proposed. Summary of the Invention

[0003] To comprehensively consider the reliability, safety, and economy of complex engineering structures, this invention proposes a resilience-based engineering structure design optimization method under degradation and different strategies.

[0004] The technical solution adopted by this invention to achieve the above objectives is: a method for optimizing engineering structure design based on resilience under degradation and different strategies, characterized by comprising the following steps:

[0005] S1: Set sample particles n for variables within the engineering structure design domain. p Let the set be S, and the velocity of the samples be v. i ;

[0006] S2: Set the iteration count i = 1, and update the sample to the current sample set S(i);

[0007] S3: Using the sample set S(i), establish a proxy model for the performance function of the engineering structure and calculate the reliability R of the toughness design optimization;

[0008] S4: Calculate the performance loss Q of the structure loss ;

[0009] S5: Calculate the performance recovery Q of the structure recover ;

[0010] S6: Based on the reliability R described in S3 and the performance loss Q described in S4 loss The performance recovery amount Q described in S5 recover The toughness constraint Ψ for the toughness design optimization of engineering structures is calculated, and the particles are divided into S1(i) and S2(i). If the toughness value Ψ of the sample is... S(i) If the value is greater than or equal to [Ψ], where [Ψ] is the target toughness value, then S(i) is merged into S1(i); otherwise, S(i) is merged into S2(i).

[0011] S7: Calculate the total cost of preventive maintenance of engineering structures.

[0012] S8: Calculate the total cost of subsequent repairs to the engineering structure.

[0013] S9: Total cost of preventive maintenance based on the reliability R described in S3, the toughness constraint Ψ described in S6, and the preventive maintenance described in S7. The total cost of post-repair as described in S8 Establish a mathematical model for optimizing the toughness design of engineering structures;

[0014] S10: Obtain the local optimum position based on the mathematical model for optimizing the toughness design of the engineering structure. and the global optimal position

[0015] S11: Obtain the optimal solution in the current iteration.

[0016] S12: Determine the optimal solution Does it meet the toughness requirements? Execute step S14; otherwise, proceed based on the optimal solution. Update S1(i) and S2(i);

[0017] S13: Update the iteration count and set i = i + 1;

[0018] S14: Determine if the maximum number of iterations n has been reached. max , if i<n max If so, execute S3; otherwise, proceed to the next step.

[0019] S15: Output the optimal value

[0020] Preferably, step S3 specifically includes the following steps:

[0021] S3.1: Set a random variable X, a random process Y(t), and time t, and let their set be M;

[0022] S3.2: Estimate the performance function g of the samples in set M;

[0023] S3.3: Constructing an initial Kriging proxy model based on the performance function g and the set M Where d represents the design variable. Represents an estimate of the performance function;

[0024] S3.4: Generating N based on Monte Carlo simulation method mcs N samples are used to update the initial Kriging surrogate model using the actively learned U function. Specifically, based on the actively learned U function, N samples are updated. mcs The samples were divided into two groups, GP1 and GP2, and a new sample was selected based on the minimum value.

[0025] S3.5: Utilize the selected new sample p new Update the Kriging proxy model until the model meets the accuracy requirements;

[0026] S3.6: Calculate the reliability of the engineering structure.

[0027] Preferably, in step S3.1, X = [X1, X2, ..., X...]. n [] represents a vector of n random variables; Y(t) = [Y1(t), Y2(t), ..., Y... m [t] represents a vector of m random processes;

[0028] In step S3.2 Let represent the performance function estimation vector of n0 random samples. In step S3.4, the surrogate model samples are updated using the active learning U function, where the expression of the active learning U function is:

[0029]

[0030] Among them, (X) k ,Y k (t),t k () represents the input variable. This represents the mean of the input variable. This represents the variance of the input variable, where k represents the index of X, Y, and t.

[0031] In step S3.4, the active learning U function, N is utilized. mcs The samples can be divided into two groups: GP1 (U≥2) and GP2 (U<2). A new sample will be selected based on the minimum value, and its function expression is:

[0032]

[0033] Among them, U min This represents the minimum value of the active learning function, where r is considered a constant greater than 2, and v kLet m represent the k-th sample at velocity v, m represent the range of values ​​for j, and j represent the index of t.

[0034] Preferably, in step S3.5, a new sample p is added. new The function expression is:

[0035]

[0036] in,

[0037] Where i represents the index of X, Y, and d, j represents the index of t, and n represents the range of values ​​for i.

[0038] In step S3.5, the expression for the accuracy requirement condition is:

[0039]

[0040] Where cov represents covariance, R is reliability, and n is the total number of samples;

[0041] In step S3.6, the expression for the reliability constraint is:

[0042]

[0043] Where Pr represents the probability of g ≤ 0, and R represents the given time interval [t0, t... e The reliability of the internal system, t0, t e These refer to the reliable service time of the engineering structure.

[0044] Preferably, in step S4, the performance loss is the sum of the losses caused by natural degradation and foreign object impact, and its functional expression is:

[0045]

[0046] Where d = [d1, d2, ..., d n ] represents the design variable, Y i N1(t1,t2) represents the performance loss after the i-th impact, and N1(t1,t2) represents the number of impacts within the time interval (t1,t2).

[0047] Preferably, in step S5, preventive maintenance and reactive maintenance strategies are used to restore the performance of the engineering structure, and the performance restoration amount can be expressed as:

[0048]

[0049] Where v(t) represents the performance improvement ratio, t represents the maintenance cycle, Q0 represents the initial performance of the structure before maintenance, a represents the maintenance rate, and v ti Indicates ti Previous performance ratio, t i This indicates the start time of the i-th maintenance.

[0050] Preferably, in step S6, the functional expression of the toughness constraint Ψ for the toughness design optimization of the engineering structure is:

[0051]

[0052] Where 0 and t are the start time of the entire service life of the engineering structure, respectively, R represents the reliability, and P re Q represents the probability of successful performance recovery. recover Q represents the performance quantity of the structure after repair. loss This indicates the amount of performance loss in the engineering structure.

[0053] Preferably, in step S7, the total cost of preventive maintenance of the engineering structure is:

[0054]

[0055] in, This refers to the cost of lost work time due to maintenance downtime. This indicates the cost paid to the maintenance staff. Indicates the repair time. This indicates the cost of replacing parts. This indicates the cost of preventative maintenance operations, s c p represents the cost of lost work time per unit of time. c The unit of time for maintenance labor costs, m c This refers to the repair cost incurred in restoring unit performance.

[0056] Preferably, in step S8, the expression for the total cost of post-repair maintenance is:

[0057]

[0058] Among them, C s C represents the cost of lost wages. P Indicates repair cost, C r Indicates the cost of replacing parts, C m Let n represent the repair cost of repairable parts, K represent the types of non-repairable parts, and n represent the repair cost of repairable parts. i Let c be the number of the i-th type of non-repairable parts. i v represents the cost of replacing a single non-repairable part of type i. e This indicates the residual performance ratio of the system before maintenance begins.

[0059] Preferably, in step S9,

[0060] The expression for the optimization design model when there is no maintenance strategy is:

[0061]

[0062] stΨ(d,X,Y(t),t)≥[Ψ]

[0063] Pr{g i (d,X,Y(t),t=0)≤0}≥[R i ]

[0064]

[0065] When only post-repair maintenance is considered, the expression for the mathematical model of structural toughness design optimization is:

[0066]

[0067] stΨ(d,X,Y(t),t)≥[Ψ]

[0068] Pr{g i (d,X,Y(t),t=0)≤0}≥[R i ]

[0069]

[0070] Taking both preventative and reactive maintenance into account, the mathematical model for optimizing the engineering structure based on resilience design is expressed as follows:

[0071]

[0072] stΨ(d,X,Y(t),t)≥[Ψ]

[0073] Pr{g i (d,X,Y(t),t=0)≤0}≥[R i ]

[0074]

[0075] Among them, C design [Ψ] represents the total cost of the preliminary design of the engineering structure, and [Ψ] represents the target toughness value. X Let Pr{g} represent the mean of X. i (d,X,Y(t),t=0)≤0} represents the current reliability of the structure, which is greater than the target reliability of the i-th performance [R]. i ], g represents the performance function of the structure, d L and d U Let be the lower and upper bounds of d, respectively. and μX The lower and upper bounds

[0076] Compared with the prior art, the beneficial effects of this invention are that it can obtain the optimal results for engineering structure design under different maintenance strategies, avoiding the technical problem of uneven changes in operating elements due to different maintenance modes. At the same time, it uses active learning of the U function to improve the accuracy of the surrogate model, improve the stability of the model, and ensure that the final optimized design model can obtain the optimal value. Attached Figure Description

[0077] Figure 1 This is a flowchart of a resilience-based engineering structure design optimization method under degradation and different strategies according to the present invention.

[0078] Figure 2 This is the design optimization result of the lower limb exoskeleton dynamic harmonic reducer in the embodiment of the present invention under a maintenance-free strategy.

[0079] Figure 3 This is the design optimization result of the lower limb exoskeleton dynamic harmonic reducer in the embodiment of the present invention, considering only post-maintenance.

[0080] Figure 4 The design optimization results of the lower limb exoskeleton dynamic harmonic reducer in this embodiment of the invention take into account both preventive maintenance and reactive maintenance. Detailed Implementation

[0081] The specific embodiments of the present invention are as follows:

[0082] A method for optimizing the design of engineering structures based on resilience under degradation and different strategies, characterized by comprising the following steps:

[0083] S1: Set sample particles n for variables within the engineering structure design domain. p Let the set be S, and the velocity of the samples be v. i ;

[0084] S2: Set the iteration count i = 1, and update the sample to the current sample set S(i);

[0085] S3: Using the sample set S(i), establish a proxy model for the performance function of the engineering structure and calculate the reliability R of the toughness design optimization;

[0086] S3.1: Let there be a random variable X, a random process Y(t), and time t, and let their set be M, where X = [X1, X2, ..., Xt]. n [] represents a vector of n random variables; Y(t) = [Y1(t), Y2(t), ..., Y... m [(t)] represents a vector of m random processes;

[0087] S3.2: Estimate the performance function g of the samples in set M, where Let T represent the performance function estimation vector for n0 random samples, and let T denote the sign of the transpose of the matrix.

[0088] S3.3: Constructing an initial Kriging proxy model based on the performance function g and the set M Where d represents the design variable. Represents an estimate of the performance function;

[0089] S3.4: Generating N based on Monte Carlo simulation method mcs N samples are used to update the initial Kriging surrogate model using the actively learned U function. Specifically, based on the actively learned U function, N samples are updated. mcs The samples were divided into two groups, GP1 and GP2, and a new sample was selected based on the minimum value.

[0090] The expression for the active learning U function is:

[0091]

[0092] Among them, (X) k ,Y k (t),t k () represents the input variable. This represents the mean of the input variable. This represents the variance of the input variable, where k represents the index of X, Y, and t.

[0093] Using active learning of the U function, N mcs The samples can be divided into two groups: GP1 (U≥2) and GP2 (U<2). A new sample will be selected based on the minimum value, and its function expression is:

[0094]

[0095] Among them, U min This represents the minimum value of the active learning function, where r is considered a constant greater than 2, and v k Let m represent the k-th sample at velocity v, m represent the range of values ​​for j, and j represent the index of t.

[0096] S3.5: Utilize the selected new sample p new Update the Kriging proxy model until the model meets the accuracy requirements;

[0097] New sample p new The function expression is:

[0098]

[0099] in,

[0100] Where i represents the index of X, Y, and d, j represents the index of t, and n represents the range of values ​​for i.

[0101] The expression for the precision requirement is:

[0102]

[0103] Where cov represents covariance, R is reliability, and n is the total number of samples;

[0104] S3.6: Calculate the reliability of the engineering structure. The expression for the reliability constraint is:

[0105]

[0106] Where Pr represents the probability of g ≤ 0, and R represents the given time interval [t0, t... e The reliability of the internal system, t0, t e These refer to the reliable service time of the engineering structure;

[0107] S4: Considering the natural degradation of the engineering structure and the impact of foreign objects, calculate the performance loss Q of the structure. loss ;

[0108] The performance loss is the sum of the losses caused by natural degradation and foreign object impact, and its functional expression is:

[0109]

[0110] Where d = [d1, d2, ..., d n ] represents the design variable, Y i N1(t1,t2) represents the performance loss after the i-th impact, and N1(t1,t2) represents the number of impacts within the time interval (t1,t2).

[0111] S5: Considering preventive and reactive maintenance, calculate the structural performance recovery Q. recover ;

[0112] The performance of an engineering structure is restored by employing preventative and reactive maintenance strategies. The amount of performance restoration can be expressed as:

[0113]

[0114] Where v(t) represents the performance improvement ratio, t represents the maintenance cycle, Q0 represents the initial performance of the structure before maintenance, a represents the maintenance rate, and v ti Indicates t i Previous performance ratio, t i Indicates the start time of the i-th repair;

[0115] S6: Based on the reliability R described in S3 and the performance loss Q described in S4 loss The performance recovery amount Q described in S5 recover The toughness constraint Ψ for the toughness design optimization of engineering structures is calculated, and the particles are divided into S1(i) and S2(i). If the toughness value Ψ of the sample is... S(i) If the value is greater than or equal to [Ψ], where [Ψ] is the target toughness value, then S(i) is merged into S1(i); otherwise, S(i) is merged into S2(i).

[0116] The functional expression for the toughness constraint Ψ in the toughness design optimization of engineering structures is:

[0117]

[0118] Where 0 and t are the start time of the entire service life of the engineering structure, respectively, R represents the reliability, and P re Q represents the probability of successful performance recovery. recover Q represents the performance quantity of the structure after repair. loss Indicates the amount of performance loss in the engineering structure;

[0119] S7: Calculate the total cost of preventive maintenance of engineering structures.

[0120] The total cost of preventive maintenance of the engineering structure is:

[0121]

[0122] in, This refers to the cost of lost work time due to maintenance downtime. This indicates the cost paid to the maintenance staff. Indicates the repair time. This indicates the cost of replacing parts. This indicates the cost of preventative maintenance operations, s c p represents the cost of lost work time per unit of time. c The unit of time for maintenance labor costs, m c This represents the repair cost incurred for restoring unit performance;

[0123] S8: Calculate the total cost of subsequent repairs to the engineering structure.

[0124] The total cost of post-repair repairs is expressed as follows:

[0125]

[0126] Among them, C s C represents the cost of lost wages. P Indicates repair cost, C r Indicates the cost of replacing parts, Cm Let n represent the repair cost of repairable parts, K represent the types of non-repairable parts, and n represent the repair cost of repairable parts. i Let c be the number of the i-th type of non-repairable parts. i v represents the cost of replacing a single non-repairable part of type i. e This indicates the residual performance ratio of the system before maintenance began;

[0127] S9: Total cost of preventive maintenance based on the reliability R described in S3, the toughness constraint Ψ described in S6, and the preventive maintenance described in S7. The total cost of post-repair as described in S8 Establish a mathematical model for optimizing the toughness design of engineering structures;

[0128] The expression for the optimization design model when there is no maintenance strategy is:

[0129]

[0130] stΨ(d,X,Y(t),t)≥[Ψ]

[0131] Pr{g i (d,X,Y(t),t=0)≤0}≥[R i ]

[0132]

[0133] When only post-repair maintenance is considered, the expression for the mathematical model of structural toughness design optimization is:

[0134]

[0135] stΨ(d,X,Y(t),t)≥[Ψ]

[0136] Pr{g i (d,X,Y(t),t=0)≤0}≥[R i ]

[0137]

[0138] Taking both preventative and reactive maintenance into account, the mathematical model for optimizing the engineering structure based on resilience design is expressed as follows:

[0139]

[0140] stΨ(d,X,Y(t),t)≥[Ψ]

[0141] Pr{g i (d,X,Y(t),t=0)≤0}≥[R i ]

[0142]

[0143] Among them, C design [Ψ] represents the total cost of the preliminary design of the engineering structure, and [Ψ] represents the target toughness value. X Let Pr{g} represent the mean of X. i (d,X,Y(t),t=0)≤0} represents the current reliability of the structure, which is greater than the target reliability of the i-th performance [R]. i ], g represents the performance function of the structure, d L and d U Let be the lower and upper bounds of d, respectively. and μ X The lower and upper bounds

[0144] S10: Obtain the local optimum position based on the mathematical model for optimizing the toughness design of the engineering structure. and the global optimal position

[0145] S11: Obtain the optimal solution in the current iteration.

[0146] S12: Determine the optimal solution Does it meet the toughness requirements? Execute step S14; otherwise, proceed based on the optimal solution. Update S1(i) and S2(i);

[0147] S13: Update the iteration count and set i = i + 1;

[0148] S14: Determine if the maximum number of iterations n has been reached. max , if i<n max If so, execute S3; otherwise, proceed to the next step.

[0149] S15: Output the optimal value

[0150] The specific application process of this embodiment is as follows:

[0151] A flowchart illustrating the design optimization method for a resilience-based lower limb exoskeleton dynamic harmonic reducer under degradation and different maintenance strategies, including the following steps:

[0152] S1: Variables within the design domain for the lower limb exoskeleton dynamic harmonic reducer, setting particle n. p Let the set be S, and the velocity of the samples be v. i ;

[0153] S2: Set the iteration count i = 1, and update the sample to the current sample set S(i);

[0154] S3: Using the sample set S(i), establish the performance function of the lower limb exoskeleton dynamic harmonic reducer: The expression of the performance function is:

[0155]

[0156] Where g σ X represents the threshold of the performance function. R Let X represent a random variable. I d represents an interval variable. m Indicates the diameter of the middle circle of the flexure;

[0157] The expression for calculating reliability constraints is:

[0158] Where Pr represents the probability of g ≤ 0, and R represents the given time interval [t0, t... e The reliability of the internal system, t0, t e Reliable service time of engineering structures

[0159] S4: Calculate the performance loss of the lower limb exoskeleton dynamic harmonic reducer:

[0160]

[0161] Among them W t (t) represents the random degradation amount, Y i N1(t1,t2) represents the performance loss after the i-th impact, and N1(t1,t2) represents the number of impacts within the time interval (t1,t2).

[0162] S5: Calculate the performance recovery Q of the lower limb exoskeleton dynamic harmonic reducer. recover :

[0163]

[0164] Where v(t) represents the performance improvement ratio, t represents the maintenance cycle, Q0 represents the initial structural performance before maintenance, and a represents the maintenance rate. Indicates t i Previous performance ratio, t i Indicates the start time of the i-th maintenance.

[0165] S6: Based on S3, S4, and S5, calculate the toughness constraint Ψ of the lower limb exoskeleton dynamic harmonic reducer.

[0166]

[0167] Where 0 and t are the start time of the entire service life of the engineering structure, respectively, R represents the reliability, and P re Q represents the probability of successful performance recovery. recoverQ represents the performance quantity of the structure after repair. loss Indicates the amount of performance loss in engineering structures

[0168] The particles are divided into S1(i) and S2(i). If the toughness value Ψ of the sample... S(i) If the value is greater than or equal to [Ψ], where [Ψ] is the target toughness value, then S(i) is merged into S1(i); otherwise, S(i) is merged into S2(i).

[0169] S7: Calculate the total cost of preventative maintenance for the lower limb exoskeleton's dynamic harmonic reducer.

[0170]

[0171] in, This refers to the cost of lost work time due to maintenance downtime. This indicates the cost paid to the maintenance staff. Indicates the repair time. This indicates the cost of replacing parts. This indicates the cost of preventative maintenance operations, s c p represents the cost of lost work time per unit of time. c The unit of time for maintenance labor costs, m c This represents the repair cost incurred for restoring unit performance;

[0172] S8: Calculate the total cost of post-repair maintenance for the lower limb exoskeleton's dynamic harmonic reducer.

[0173]

[0174] Where C s C represents the cost of lost wages. P Indicates repair cost, C r Indicates the cost of replacing parts, C m Let n represent the repair cost of repairable parts, K represent the types of non-repairable parts, and n represent the repair cost of repairable parts. i Let c be the number of the i-th type of non-repairable parts. i v represents the cost of replacing a single non-repairable part of type i. e This indicates the residual performance ratio of the system before maintenance began;

[0175] S9: Based on S3, S6, S7, and S8, establish a mathematical model for the toughness design optimization of the lower limb exoskeleton dynamic harmonic reducer.

[0176] The expression for the optimization design model when there is no maintenance strategy is:

[0177]

[0178] stΨ(d,X,Y(t),t)≥0.94

[0179] Pr{g1(d,X,Y(t),t)≤0}≥0.9

[0180] g j (d,X)≤0,j∈[2,6]

[0181] 0.013mZ r ≤δ≤0.026mZ r

[0182] 0.05mZ r ≤b≤0.3mZ r

[0183] When only post-repair maintenance is considered, the toughness design optimization model is as follows:

[0184]

[0185] stΨ(d,X,Y(t),t)≥0.94

[0186] Pr{g1(d,X,Y(t),t)≤0}≥0.9

[0187] g j (d,X)≤0,j∈[2,6]

[0188] 0.013mZ r ≤δ≤0.026mZ r

[0189] 0.05mZ r ≤b≤0.3mZ r

[0190] When both preventative and reactive maintenance are considered, the model for resilience design optimization is as follows:

[0191]

[0192] stΨ(d,X,Y(t),t)≥0.94

[0193] Pr{g1(d,X,Y(t),t)≤0}≥0.9

[0194] g j (d,X)≤0,j∈[2,6]

[0195] 0.013mZ r ≤δ≤0.026mZ r

[0196] 0.05mZ r≤b≤0.3mZ r

[0197] Among them, C design Let X represent the total cost of the preliminary design of the engineering structure, Y(t) represent the random process, t represent time, d represent the design variable, [Ψ] represent the target toughness value, g represent the performance function of the structure, j represent the sequence number, δ represent the wall thickness of the flexure gear ring, b represent the tooth width of the flexure gear, Pr{g1(d,X,Y(t),t)≤0} represent the current reliability of the structure, m represent the module, and Zr represent the number of teeth of the flexure gear.

[0198] S10: Obtain the local optimum position and the global optimal position

[0199] S11: Obtain the optimal solution in the current iteration.

[0200] S12: Determine the optimal solution Does it meet the toughness requirements? Execute step S14; otherwise, proceed based on the optimal solution. Update S1(i) and S2(i);

[0201] S13: Update the iteration count and set i = i + 1;

[0202] S14: Determine if the maximum number of iterations n has been reached. max , if i<n max If so, execute S3; otherwise, proceed to the next step.

[0203] S15: Output the optimal value

[0204] Table 1 Results of toughness optimization design

[0205] design 3.0449 13.0000 - 0.9332 - 427.9210 427.9210 Design + Post-Construction Maintenance 3.0610 15.0000 20.0000 0.9390 0.9889 679.0484 681.1484 Design + Regular Maintenance + Post-Incident Maintenance 3.0786 15.0000 20.0000 0.9636 0.9897 441.6326 443.8326

[0206] Compared with the prior art, the beneficial effects of this invention are that it can obtain the optimal results for engineering structure design under different maintenance strategies, avoiding the technical problem of uneven changes in operating elements due to different maintenance modes. At the same time, it uses active learning of the U function to improve the accuracy of the surrogate model, improve the stability of the model, and ensure that the final optimized design model can obtain the optimal value.

[0207] This invention has been described through embodiments. Those skilled in the art will understand that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of this invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, this invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of this invention.

Claims

1. A method for optimizing the design of engineering structures based on resilience under degradation and different strategies, characterized in that, Includes the following steps: S1: Set sample particles n for variables within the engineering structure design domain. p Let the set be S, and the velocity of the samples be v. i ; S2: Set the iteration count i = 1, and update the sample to the current sample set S(i); S3: Using the sample set S(i), establish a proxy model for the performance function of the engineering structure and calculate the reliability R of the toughness design optimization; S4: Calculate the performance loss Q of the structure loss ; S5: Calculate the performance recovery Q of the structure recover ; S6: Based on the reliability R described in S3 and the performance loss Q described in S4 loss The performance recovery amount Q described in S5 recover The toughness constraint Ψ for the toughness design optimization of engineering structures is calculated, and the particles are divided into S1(i) and S2(i). If the toughness value Ψ of the sample is... S(i) If the value is greater than or equal to [Ψ], where [Ψ] is the target toughness value, then S(i) is merged into S1(i); otherwise, S(i) is merged into S2(i). S7: Calculate the total cost of preventive maintenance of engineering structures. S8: Calculate the total cost of subsequent repairs to the engineering structure. S9: Total cost of preventive maintenance based on the reliability R described in S3, the toughness constraint Ψ described in S6, and the preventive maintenance described in S7. The total cost of post-repair as described in S8 Establish a mathematical model for optimizing the toughness design of engineering structures; S10: Obtain the local optimum position based on the mathematical model for optimizing the toughness design of the engineering structure. and the global optimal position S11: Obtain the optimal solution in the current iteration. S12: Determine the optimal solution Does it meet the toughness requirements? Execute step S14; otherwise, proceed based on the optimal solution. Update S1(i) and S2(i); S13: Update the iteration count and set i = i + 1; S14: Determine if the maximum number of iterations n has been reached. max , if i<n max If so, execute S3; otherwise, proceed to the next step. S15: Output the optimal value 2. The method for optimizing engineering structure design based on resilience under degradation and different strategies according to claim 1, characterized in that, Step S3 specifically includes the following steps: S3.1: Set a random variable X, a random process Y(t), and time t, and let their set be M; S3.2: Estimate the performance function g of the samples in set M; S3.3: Constructing an initial Kriging proxy model based on the performance function g and the set M Where d represents the design variable. Represents an estimate of the performance function; S3.4: Generating N based on Monte Carlo simulation method mcs N samples are used to update the initial Kriging surrogate model using the actively learned U function. Specifically, based on the actively learned U function, N samples are updated. mcs The samples were divided into two groups, GP1 and GP2, and a new sample was selected based on the minimum value. S3.5: Utilize the selected new sample p new Update the Kriging proxy model until the model meets the accuracy requirements; S3.6: Calculate the reliability of the engineering structure.

3. The method for optimizing engineering structure design based on resilience under degradation and different strategies according to claim 2, characterized in that, In step S3.1, X = [X1, X2, ..., X...] n [] represents a vector of n random variables; Y(t) = [Y1(t), Y2(t), ..., Y... m [t] represents a vector of m random processes; In step S3.2 Let represent the performance function estimation vector of n0 random samples. In step S3.4, the surrogate model samples are updated using the active learning U function, where the expression of the active learning U function is: Among them, (X) k ,Y k (t),t k () represents the input variable. This represents the mean of the input variable. This represents the variance of the input variable, where k represents the index of X, Y, and t. In step S3.4, the active learning U function, N is utilized. mcs The samples can be divided into two groups: GP1 (U≥2) and GP2 (U<2). A new sample will be selected based on the minimum value, and its function expression is: Among them, U min This represents the minimum value of the active learning function, where r is considered a constant greater than 2, and v k Let m represent the k-th sample at velocity v, m represent the range of values ​​for j, and j represent the index of t.

4. The method for optimizing engineering structure design based on resilience under degradation and different strategies according to claim 3, characterized in that, In step S3.5, a new sample p is added. new The function expression is: in, Where i represents the index of X, Y, and d, j represents the index of t, and n represents the range of values ​​for i. In step S3.5, the expression for the accuracy requirement condition is: Where cov represents covariance, R is reliability, and n is the total number of samples; In step S3.6, the expression for the reliability constraint is: Where Pr represents the probability of g ≤ 0, and R represents the given time interval [t0, t...]. e The reliability of the internal system, t0, t e These refer to the reliable service time of the engineering structure.

5. The method for optimizing engineering structure design based on resilience under degradation and different strategies according to claim 4, characterized in that, In step S4, the performance loss is the sum of the losses caused by natural degradation and foreign object impact, and its functional expression is: Where d = [d1, d2, ..., d n ] represents the design variable, Y i N1(t1,t2) represents the performance loss after the i-th impact, and N1(t1,t2) represents the number of impacts within the time interval (t1,t2).

6. The method for optimizing engineering structure design based on resilience under degradation and different strategies according to claim 5, characterized in that, In step S5, preventive and reactive maintenance strategies are used to restore the performance of the engineering structure. The amount of performance restoration can be expressed as: Where v(t) represents the performance improvement ratio, t represents the maintenance cycle, Q0 represents the initial structural performance before maintenance, and a represents the maintenance rate. Indicates t i Previous performance ratio, t i This indicates the start time of the i-th maintenance.

7. The method for optimizing engineering structure design based on resilience under degradation and different strategies according to claim 6, characterized in that, In step S6, the functional expression for the toughness constraint Ψ in the toughness design optimization of the engineering structure is: Where 0 and t are the start time of the entire service life of the engineering structure, respectively, R represents the reliability, and P re Q represents the probability of successful performance recovery. recover Q represents the performance quantity of the structure after repair. loss This indicates the amount of performance loss in the engineering structure.

8. The method for optimizing engineering structure design based on resilience under degradation and different strategies according to claim 7, characterized in that, In step S7, the total cost of preventive maintenance of the engineering structure is: in, This refers to the cost of lost work time due to maintenance downtime. This indicates the cost paid to the maintenance staff. Indicates the repair time. This indicates the cost of replacing parts. This indicates the cost of preventative maintenance operations, s c p represents the cost of lost work time per unit of time. c The unit of time for maintenance labor costs, m c This refers to the repair cost incurred in restoring unit performance.

9. The method for optimizing engineering structure design based on resilience under degradation and different strategies according to claim 8, characterized in that, In step S8, the total cost of post-repair maintenance is expressed as follows: Among them, C s C represents the cost of lost wages. P Indicates repair costs, C r Indicates the cost of replacing parts, C m Let n represent the repair cost of repairable parts, K represent the types of non-repairable parts, and n represent the repair cost of repairable parts. i Let c be the number of the i-th type of non-repairable parts. i v represents the cost of replacing a single non-repairable part of type i. e This indicates the residual performance ratio of the system before maintenance begins.

10. The method for optimizing engineering structure design based on resilience under degradation and different strategies according to claim 9, characterized in that, In step S9 The expression for the optimization design model when there is no maintenance strategy is: stΨ(d,X,Y(t),t)≥[Ψ] Pr{g i (d,X,Y(t),t=0)≤0}≥[R i ] d L ≤d≤d U , When only post-repair maintenance is considered, the expression for the mathematical model of structural toughness design optimization is: stΨ(d,X,Y(t),t)≥[Ψ] Pr{g i (d,X,Y(t),t=0)≤0}≥[R i ] d L ≤d≤d U , Taking both preventative and reactive maintenance into account, the mathematical model for optimizing the engineering structure based on resilience design is expressed as follows: stΨ(d,X,Y(t),t)≥[Ψ] Pr{g i (d,X,Y(t),t=0)≤0}≥[R i ] d L ≤d≤d U , Among them, C design [Ψ] represents the total cost of the preliminary design of the engineering structure, and [Ψ] represents the target toughness value. X Let Pr{g} represent the mean of X. i (d,X,Y(t),t=0)≤0} represents the current reliability of the structure, which is greater than the target reliability of the i-th performance [R]. i ], g represents the performance function of the structure, d L and d U Let be the lower and upper bounds of d, respectively. and μ X The lower and upper bounds.

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