Method for calculating mechanism reliability based on multi-fidelity active learning surrogate model

Abstract

The present invention relates to the technical field of mechanism reliability analysis, and specifically discloses a method for calculating the reliability of a mechanism based on a multi-fidelity active learning surrogate model, including steps such as determining a sample space, initial experimental design, constructing a multi-fidelity model, adding sample points based on an active learning function, updating the model, calculating the failure probability and coefficient of variation, obtaining the mechanism performance function and reliability analysis results, etc. Compared with the prior art, by constructing a multi-fidelity surrogate model, the computational cost of constructing the model is reduced on the premise of ensuring the fitting accuracy of the model; an active learning function is applied to screen and add the optimal sample points, and the multi-fidelity Kriging model is updated, improving the accuracy of the constructed surrogate model; by setting the TAEA convergence criterion, the computational accuracy and computational efficiency of the model are balanced, improving the computational efficiency of the surrogate model.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanism reliability analysis, and particularly to a method for calculating the reliability of a mechanism based on a multi-fidelity active learning surrogate model. Background Art

[0002] The reliability analysis of mechanical structures is to measure the reliable state of each performance index of mechanical structures under uncertain factors such as random fluctuations in dimensions, loads, vibrations, and accelerations. Mechanical structures are usually composed of multiple component devices and key components, and the component devices and their components affect each other. Under the interaction of complex environments and random loads, their internal relationships are complex and full of uncertainties, resulting in complex and diverse failure mechanisms and coexistence of multiple failure modes, which increases the difficulty of accurately evaluating their reliability. In addition, in actual engineering, it is difficult to explicitly express the mapping relationship between uncertain variables and performance indexes by an analytical physical equation, that is, the so-called "black box function". For the problem of calculating the reliability of mechanical structures with black box functions, the method of calling finite element models and Monte Carlo simulations is usually used for calculation. Although this method can obtain relatively satisfactory analysis results, the calculation time is long and the efficiency is low, making it difficult to be widely applied. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for calculating the reliability of a mechanism based on a multi-fidelity active learning surrogate model to solve the problems of large calculation difficulty and low calculation efficiency caused by multiple uncertain variables in the calculation of the reliability of mechanical structures in the prior art.

[0004] To solve the above technical problems, the present invention provides a method for calculating the reliability of a mechanism based on a multi-fidelity active learning surrogate model, including the following steps:

[0005] S1. Based on an existing multi-physical field coupling simulation system, set the dimensions and working conditions of the mechanism to be analyzed in the multi-physical field coupling simulation system to obtain a two-dimensional thermodynamic model, a three-dimensional multi-body dynamics model of the mechanism to be analyzed, and a sample space of uncertainty variable parameters;

[0006] S2. Use the Latin hypercube method to perform an initial experimental design based on the two-dimensional thermodynamic model, the three-dimensional multi-body dynamics model of the mechanism to be analyzed, and the set sample space of uncertainty variable parameters, obtain initial low-fidelity sample points of the mechanism to be analyzed from the sample space of uncertainty variable parameters, and randomly select a certain proportion from the initial low-fidelity sample points as initial high-fidelity sample points. The initial low-fidelity sample points and the initial high-fidelity sample points jointly form the current sample space;

[0007] S3. Using the multi - physical - field coupling simulation system, the two - dimensional thermodynamic model of the mechanism to be analyzed, the three - dimensional multi - body dynamics model, and the sample space of the uncertainty variable parameters, calculate the low - fidelity sample response values and high - fidelity sample response values of the mechanism to be analyzed respectively. Based on the low - fidelity sample points, high - fidelity sample points, low - fidelity sample response values, and high - fidelity sample response values, construct a multi - fidelity Kriging model. The multi - fidelity Kriging model includes a low - fidelity Kriging model and a high - fidelity Kriging model. Obtain the performance function of the mechanism to be analyzed according to the constructed multi - fidelity Kriging model. Calculate the failure probability and coefficient of variation of the mechanism to be analyzed according to the performance function. If the coefficient of variation meets the accuracy requirements, execute step S5; otherwise, execute step S4;

[0008] S4. Use the improved MRU active learning function to screen the optimal sample points from the sample space of the uncertainty variable parameters, and add the optimal sample points to the current sample space. Use the TAEA convergence criterion as the stop condition for the active learning process of the MRU active learning function. When the TAEA convergence criterion is met, update the multi - fidelity Kriging model and execute step S3. When the TAEA convergence criterion is not met, repeat this step until the TAEA convergence criterion is met;

[0009] S5. Output the performance function, failure probability, and coefficient of variation of the mechanism to be analyzed to obtain the reliability result of the mechanism.

[0010] Preferably, in step S3, the performance function of the mechanism to be analyzed is:

[0011] ;

[0012] Wherein, is the performance function of the mechanism to be analyzed, is the performance threshold of the mechanism to be analyzed, is the prediction value of the multi - fidelity Kriging model.

[0013] Preferably, in step S3, the failure probability of the mechanism to be analyzed is:

[0014] ;

[0015] Wherein, is the failure probability of the mechanism to be analyzed, is an n - dimensional random vector, is the probability density function of the random variable.

[0016] Preferably, in step S3, the coefficient of variation of the mechanism to be analyzed is:

[0017] ;

[0018] Among them, is the coefficient of variation of the mechanism to be analyzed, is the failure probability predicted by the multi-fidelity Kriging model, is the total number of samples in the sample space.

[0019] Preferably, in step S4, the MRU active learning function is:

[0020] ;

[0021] Among them, is the MRU active learning function, is the predicted mean of the high-fidelity Kriging model, is the standard deviation of the high-fidelity Kriging model, is the model fidelity, is the constructed low-fidelity Kriging model, is the constructed high-fidelity Kriging model. is the multi-fidelity correlation function, is the cost ratio function, is the probability density function.

[0022] Preferably, in step S4, the multi-fidelity correlation function is:

[0023] ;

[0024] Among them, is the predicted mean of the low-fidelity Kriging model, is the standard deviation of the low-fidelity Kriging model.

[0025] Preferably, in step S4, the cost ratio function is:

[0026] ;

[0027] Among them, .

[0028] Preferably, in step S4, the TAEA convergence criterion includes convergence criterion A and convergence criterion B, and the TAEA convergence criterion expression is:

[0029] ;

[0030] Among them, is the failure probability predicted by the multi-fidelity Kriging model, is the number of samples generated by the Monte Carlo method, is the cumulative distribution function.

[0031] Preferably, in step S5, the mechanism performance function of the mechanism to be analyzed is:

[0032] ;

[0033] where is the mechanism performance function of the mechanism to be analyzed, is the threshold of the mechanism performance, is the predicted value of the current active learning Kriging model.

[0034] The failure probability of the mechanism to be analyzed is:

[0035] ;

[0036] where is the failure probability of the mechanism to be analyzed, is an n-dimensional random vector, is the probability density function of the random variable.

[0037] The coefficient of variation of the mechanism to be analyzed is:

[0038] ;

[0039] where is the failure probability predicted by the multi-fidelity Kriging model, is the total number of samples in the sample space.

[0040] Compared with the prior art, the beneficial effects of the present invention are as follows: By constructing a multi-fidelity surrogate model, the computational cost of model construction is reduced on the premise of ensuring the model fitting accuracy; the active learning MRU function is applied to screen and add the optimal sample points, and the multi-fidelity Kriging model is updated, improving the accuracy of the constructed surrogate model; by setting the TAEA convergence criterion, the computational accuracy and computational efficiency of the model are balanced, improving the computational efficiency of the surrogate model. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 is the flowchart of the embodiment of the present invention;

[0042] Figure 2 The curve of the fitting accuracy change of the multi-fidelity Kriging model in the first embodiment of the present invention;

[0043] Figure 3 is the schematic diagram of the dynamic model of the piston cylinder group of the aero-engine in the second embodiment of the present invention;

[0044] Figure 4 is the thermodynamic prediction result in the second embodiment of the present invention;

[0045] Figure 5 It is the multi-body dynamics prediction result of the second embodiment of the present invention;

[0046] Figure 6 The failure probability curve of the second embodiment of the present invention. Specific implementation manners

[0047] The following further describes in detail the implementation manners of the present invention with reference to the drawings and embodiments. The following embodiments are used to illustrate the present invention, but cannot be used to limit the scope of the present invention.

[0048] Embodiment 1: As Figure 1 shown, this embodiment provides a method for calculating the reliability of a mechanism based on a multi-fidelity active learning surrogate model, including the following steps:

[0049] S1. Based on the existing multi-physics field coupling simulation system, set the dimensions and working conditions of the mechanism to be analyzed in the multi-physics field coupling simulation system, and construct the two-dimensional and three-dimensional digital models of the mechanism to be analyzed and the sample space of the uncertainty variable parameters. In this embodiment, the two-dimensional and three-dimensional digital models are the two-dimensional thermodynamics model and the three-dimensional multi-body dynamics model of the mechanism to be analyzed;

[0050] S2. Use the Latin hypercube method. Based on the two-dimensional thermodynamics model and the three-dimensional multi-body dynamics model of the mechanism to be analyzed constructed in step S1, and the sample space of the set uncertainty variable parameters, perform an initial experimental design, obtain the initial low-fidelity sample points of the mechanism to be analyzed from the sample space of the uncertainty variable parameters, and randomly select a certain proportion from the initial low-fidelity sample points as the initial high-fidelity sample points. In this embodiment, the extraction ratio is 25%. The initial low-fidelity sample points and the initial high-fidelity sample points together form the current sample space;

[0051] S3. Use the multi-physics field coupling simulation system, the two-dimensional thermodynamics model and the three-dimensional multi-body dynamics model of the mechanism to be analyzed, and the sample space of the uncertainty variable parameters to calculate the low-fidelity sample response values and high-fidelity sample response values of the mechanism to be analyzed respectively. Construct a multi-fidelity Kriging model based on the low-fidelity sample points, high-fidelity sample points, low-fidelity sample response values and high-fidelity sample response values. The multi-fidelity Kriging model includes a low-fidelity Kriging model and a high-fidelity Kriging model. Obtain the performance function of the mechanism to be analyzed according to the constructed multi-fidelity Kriging model, and calculate the failure probability and coefficient of variation of the mechanism to be analyzed according to the performance function. If the coefficient of variation meets the accuracy requirements, execute step S5; otherwise, execute step S4;

[0052] The performance function of the mechanism to be analyzed is:

[0053] ;

[0054] Among them, is the performance function of the mechanism to be analyzed, is the performance threshold of the mechanism to be analyzed, is the predicted value of the multi-fidelity Kriging model;

[0055] The failure probability of the mechanism to be analyzed is:

[0056] ;

[0057] Among them, is the failure probability of the mechanism to be analyzed, is an n-dimensional random vector, is the probability density function of the random variable;

[0058] The coefficient of variation of the mechanism to be analyzed is:

[0059] ;

[0060] Among them, is the coefficient of variation of the mechanism to be analyzed, is the failure probability predicted by the multi-fidelity Kriging model, is the total number of sample points in the sample space.

[0061] S4. Use the improved MRU active learning function to screen the optimal sample points from the sample space of the uncertainty variable parameters, and add the optimal sample points to the current sample space. Use the TAEA convergence criterion as the stopping condition for the active learning process of the MRU active learning function. When the TAEA convergence criterion is satisfied, update the multi-fidelity Kriging model. As Figure 2 shown is the fitting accuracy change curve of the multi-fidelity Kriging model in Embodiment 1 of the present invention. Execute step S3. When the TAEA convergence criterion is not satisfied, repeat this step until the TAEA convergence criterion is satisfied;

[0062] The MRU active learning function is:

[0063] ;

[0064] Among them, is the MRU active learning function, is the predicted mean of the high-fidelity Kriging model, is the standard deviation of the high-fidelity Kriging model, is the model fidelity, is the constructed low-fidelity Kriging model, is the constructed high-fidelity Kriging model. is the multi-fidelity correlation function, is the cost ratio function, is the probability density function;

[0065] The multi-fidelity correlation function is:

[0066] ;

[0067] where, is the predicted mean of the low-fidelity Kriging model, is the standard deviation of the low-fidelity Kriging model;

[0068] The cost ratio function is:

[0069] ;

[0070] where, .

[0071] The TAEA convergence criterion includes convergence criterion A and convergence criterion B, and the expression of the TAEA convergence criterion is:

[0072] ;

[0073] where, is the failure probability predicted by the multi-fidelity Kriging model, is the number of samples generated by the Monte Carlo method, is the cumulative distribution function.

[0074] S5. Output the performance function, failure probability, and coefficient of variation of the mechanism to be analyzed to obtain the reliability result of the mechanism;

[0075] The performance function of the mechanism to be analyzed is:

[0076] ;

[0077] where, is the performance function of the mechanism to be analyzed, is the performance threshold of the mechanism to be analyzed, is the predicted value of the multi-fidelity Kriging model.

[0078] The calculation expression of the failure probability of the mechanism to be analyzed is:

[0079] ;

[0080] where, is the failure probability of the mechanism to be analyzed, is an n-dimensional random vector, is the probability density function of the random variable.

[0081] The coefficient of variation of the mechanism to be analyzed is:

[0082] ;

[0083] wherein, is the failure probability predicted by the multi-fidelity Kriging model, is the total number of samples in the sample space.

[0084] Embodiment 2: This embodiment provides a method for calculating the reliability of a mechanism based on a multi-fidelity active learning surrogate model, including the following steps:

[0085] S1. Based on the existing multi-physics field coupling simulation system, by setting parameters such as mechanism dimensions and working conditions in the multi-physics field coupling simulation system, the thermodynamic model of the piston cylinder group of the aero-engine and the multi-body dynamics model of the crankshaft connecting rod mechanism are obtained in sequence, and the sample space of the uncertainty variable parameters of the mechanism to be analyzed is obtained through the multi-physics field coupling simulation system.

[0086] The principle of its thermodynamic analysis is that the purpose of establishing a two-dimensional cylinder piston group model for thermodynamic analysis is to obtain the cylinder pressure change required for multi-body analysis. The rigid adiabatic cylinder piston group established in this analysis is based on the following assumptions and simplification methods: in the cylinder, only air is considered as a fluid; the heat generated by combustion is evenly distributed in space; the convection effect inside the cylinder is ignored; all equations are solved in the original domain, and the influence of the change in the volume of the cylinder is analyzed in the equations.

[0087] This heat transfer equation is used to simulate the temperature distribution of the air in the cylinder. When the piston does work, the temperature rises and the pressure work increases. The pressure distribution in the air is simulated with the ideal gas equation. Its expression is:

[0088] ;

[0089] wherein, respectively represent the cylinder pressure, air quality, in-cylinder current volume, specific gas constant, and in-cylinder temperature.

[0090] The expression for the piston displacement changing with the crank rotation angle is:

[0091] ;

[0092] In the formula, is the piston displacement, is the crank radius, the connecting rod length is the crank angle.

[0093] The dynamic model of the cylinder piston group is as Figure 3 shown. The dynamic expression of the piston cylinder group is:

[0094] ;

[0095] In the formula, is the explosion pressure, is the connecting rod force, is the oil film pressure, is the friction force of the bushing wall on the piston sleeve, is the torque around the piston pin, caused by the oil film pressure, and are the normal force and tangential force acting on the piston by the equivalent ring respectively, is the piston mass, is the moment of inertia of the piston about the pin, is the nominal diameter of the piston, are respectively Figure 3 the distances shown, is the reciprocating inertia force.

[0096] S2. Use the Latin hypercube method for initial experimental design to obtain the initial low-fidelity sample points of the mechanism to be analyzed from the sample space of the uncertainty variable parameters, and randomly select 25% of the samples from the low-fidelity samples as the initial high-fidelity sample points.

[0097] In this embodiment, the variable parameters are: piston radius, connecting rod length, crankshaft length, and combustion heat.

[0098] S3. Use the multi-physics field coupling simulation system to calculate the response values of the low-fidelity samples and the high-fidelity samples respectively. Construct an initial multi-fidelity Kriging model based on the initial sample points and the corresponding response values. Obtain the performance function of the mechanism according to the constructed multi-fidelity Kriging model, and calculate the failure probability and coefficient of variation of the mechanism according to the performance function. If the coefficient of variation meets the accuracy requirements, execute step S6, otherwise execute step S4.

[0099] The calculation expression of the multi-fidelity active learning function MRU is:

[0100] ;

[0101] Wherein, is the MRU active learning function, is the predicted mean value of the high-fidelity Kriging model, is the standard deviation of the high-fidelity Kriging model, is the model fidelity, is the constructed low-fidelity Kriging model, is the constructed high-fidelity Kriging model. is the multi-fidelity correlation function, is the cost ratio function, is the probability density function.

[0102] The multi-fidelity correlation function is:

[0103] ;

[0104] where, is the predicted mean of the low-fidelity Kriging model, is the standard deviation of the low-fidelity Kriging model;

[0105] The cost ratio function is:

[0106] ;

[0107] where, .

[0108] The TAEA convergence criterion includes convergence criterion A and convergence criterion B, and the expression of the TAEA convergence criterion is:

[0109] ;

[0110] where, is the failure probability predicted by the multi-fidelity Kriging model, is the number of samples generated by the Monte Carlo method, is the cumulative distribution function.

[0111] S4. Use the improved MRU learning function to screen the optimal sample points from the sample space and add them to the current sample space. Use the TAEA convergence criterion as the stopping condition for the active learning process. When the convergence criterion is met, update the multi-fidelity Kriging model and execute step S3. Otherwise, execute step S5.

[0112] S5. Repeat step S4 until the TAEA convergence criterion is met.

[0113] S6. According to the current multi-fidelity Kriging model, obtain the current mechanism performance function and output the failure probability and coefficient of variation of the current mechanism performance function calculated by the current mechanism performance function.

[0114] The calculation expression of the mechanism performance function is:

[0115] ;

[0116] where, is the mechanism performance function, is the threshold of the mechanism performance, is the predicted value of the current active learning Kriging model.

[0117] The expression for calculating the failure probability is as follows:

[0118] ;

[0119] Wherein, is the failure probability, is an n-dimensional random vector, is the probability density function of the random variable.

[0120] The expression for calculating the coefficient of variation is as follows:

[0121] ;

[0122] Wherein, is the failure probability predicted by the multi-fidelity Kriging model, is the total number of samples in the sample space.

[0123] The dynamic model of the piston cylinder group of this aero-engine is as shown in Figure 3 The thermodynamic prediction results and multi-body dynamic prediction results of this aero-engine are as shown in Figure 4 , 5 The failure probability curve of its multi-fidelity active learning Kriging model is as shown in Figure 6 It can be seen from the following table that the failure probability prediction results of the method of the present invention have high accuracy under different cost ratios. And the proposed method reduces the waste of computational cost on the basis of ensuring the prediction accuracy.

[0124] ;

[0125] The embodiments of the present invention are given for purposes of illustration and description, and are not intended to be exhaustive or to limit the invention to the disclosed form. Many modifications and variations are obvious to those of ordinary skill in the art. The embodiments are chosen and described in order to best explain the principles of the invention and its practical application, and to enable those of ordinary skill in the art to understand the invention and design various embodiments with various modifications suitable for a particular purpose.

Claims

1. A method for calculating the reliability of a mechanism based on a multi-fidelity active learning surrogate model, characterized in that The steps include: S1. Based on the existing multi-physics field coupling simulation system, set the dimensions and working conditions of the mechanism to be analyzed in the multi-physics field coupling simulation system to obtain the two-dimensional thermodynamic model, three-dimensional multi-body dynamics model of the mechanism to be analyzed, and the sample space of uncertainty variable parameters. S2. Use the Latin hypercube method. Based on the two-dimensional thermodynamic model, three-dimensional multi-body dynamics model of the mechanism to be analyzed, and the set sample space of uncertainty variable parameters, conduct an initial experimental design. Obtain the initial low-fidelity sample points of the mechanism to be analyzed from the sample space of uncertainty variable parameters, and randomly select a certain proportion from the initial low-fidelity sample points as the initial high-fidelity sample points. The initial low-fidelity sample points and the initial high-fidelity sample points jointly form the current sample space. S3. Use the multi-physics field coupling simulation system, the two-dimensional thermodynamic model, three-dimensional multi-body dynamics model of the mechanism to be analyzed, and the sample space of uncertainty variable parameters to calculate the low-fidelity sample response values and high-fidelity sample response values of the mechanism to be analyzed respectively. Construct a multi-fidelity Kriging model based on the low-fidelity sample points, high-fidelity sample points, low-fidelity sample response values, and high-fidelity sample response values. The multi-fidelity Kriging model includes a low-fidelity Kriging model and a high-fidelity Kriging model. Obtain the performance function of the mechanism to be analyzed according to the constructed multi-fidelity Kriging model, and calculate the failure probability and coefficient of variation of the mechanism to be analyzed according to the performance function. If the coefficient of variation meets the accuracy requirements, execute step S5; otherwise, execute step S4. S4. Use the improved MRU active learning function to screen the optimal sample points from the sample space of uncertainty variable parameters, and add the optimal sample points to the current sample space. Use the TAEA convergence criterion as the stopping condition for the active learning process of the MRU active learning function. When the TAEA convergence criterion is met, update the multi-fidelity Kriging model and execute step S3. When the TAEA convergence criterion is not met, repeat this step until the TAEA convergence criterion is met. The MRU active learning function is: ； Among them, is the MRU active learning function, is the predicted mean of the high-fidelity Kriging model, is the standard deviation of the high-fidelity Kriging model, is the model fidelity, is the constructed low-fidelity Kriging model, is the constructed high-fidelity Kriging model, is the multi-fidelity correlation function, is the cost ratio function, is the probability density function; The TAEA convergence criterion includes convergence criterion A and convergence criterion B, and the expression of the TAEA convergence criterion is: ； wherein, is the failure probability predicted by the multi-fidelity Kriging model, is the number of samples generated by the Monte Carlo method, is the cumulative distribution function; S5. Output the performance function, failure probability, and coefficient of variation of the mechanism to be analyzed to obtain the mechanism reliability result.

2. The method for calculating the reliability of a mechanism based on a multi-fidelity active learning surrogate model according to claim 1, characterized in that In step S3, the performance function of the mechanism to be analyzed is: ； Among them, is the performance function of the mechanism to be analyzed, is the performance threshold of the mechanism to be analyzed, is the predicted value of the multi-fidelity Kriging model.

3. The method for calculating the reliability of a mechanism based on a multi-fidelity active learning surrogate model according to claim 1, characterized in that, In step S3, the failure probability of the mechanism to be analyzed is: ； Among them, is the failure probability of the mechanism to be analyzed, is an n-dimensional random vector, is the probability density function of the random variable.

4. The method for calculating the reliability of a mechanism based on a multi-fidelity active learning surrogate model according to claim 1, characterized in that In step S3, the coefficient of variation of the mechanism to be analyzed is: ； Among them, is the coefficient of variation of the mechanism to be analyzed, is the failure probability predicted by the multi-fidelity Kriging model, is the total number of samples in the sample space.

5. The method for calculating the reliability of a mechanism based on a multi-fidelity active learning surrogate model according to claim 1, characterized in that, In step S4, the multi-fidelity correlation function is: ； wherein, is the predicted mean of the low-fidelity Kriging model, is the standard deviation of the low-fidelity Kriging model.

6. The method for calculating the reliability of a mechanism based on a multi-fidelity active learning surrogate model according to claim 1, characterized in that In step S4, the cost ratio function is: ； Among them, .

7. The method for calculating the reliability of a mechanism based on a multi-fidelity active learning surrogate model according to claim 1, characterized in that In step S5, the performance function of the mechanism to be analyzed is: ； Among them, is the performance function of the mechanism to be analyzed, is the threshold of the mechanism to be analyzed, is the predicted value of the multi-fidelity Kriging model; The failure probability of the mechanism to be analyzed is: ； Among them, is the failure probability of the mechanism to be analyzed, is an n-dimensional random vector, is the probability density function of the random variable; The coefficient of variation of the mechanism to be analyzed is: ； Among them, is the failure probability predicted by the multi-fidelity Kriging model, is the total number of samples in the sample space.

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