Amusement facility reduction gear reliability analysis method based on agent model

Abstract

The application provides a method for analyzing reliability of amusement facility reduction gear based on a proxy model, comprising: analyzing working characteristics of a reduction gear planetary gear of high-flying amusement facility; performing finite element analysis on the reduction gear planetary gear; qualitatively evaluating and quantitatively processing influences of uncertain factors on the reduction gear planetary gear of the amusement facility; deriving response surface data and constructing a performance function, having two variables, respectively representing torque of the high-flying amusement facility reduction gear and elastic modulus of material, and setting a type of fitting function as a second-order function; constructing a reliability model of the reduction gear planetary gear of the amusement facility, and running a corresponding algorithm program in matlab, so that the corresponding reliability can be calculated. The application uses a Kriging proxy model to approximate a real model, reduces a number of calls to the real model, and significantly improves calculation efficiency.

Description

TECHNICAL FIELD

[0001] The application provides a kind of amusement facility decelerator gear reliability analysis method based on agent model belongs to reliability analysis technical field. BACKGROUND

[0002] The decelerator used in the amusement facility "high flight" is its key equipment, and once it is damaged, the consequences are unpredictable, so it is necessary to study the reliability of its key equipment. There are many common reliability analysis methods, mainly divided into analytical method, random sampling method and agent model method. The first-order second-moment method is an analytical method, which linearizes the function function near the mean point, i.e. using the first-order approximation of Taylor expansion to represent the function function, but since only the first-order and second-order moments are considered, this method may not accurately capture the influence of high-order moments, such as skewness and kurtosis. For nonlinear or highly complex systems, analytical solution may be very difficult or infeasible. Monte Carlo simulation (MCS) is a mathematical simulation method based on random numbers, which is a random sampling method that approximates mathematical problems by simulating a large number of samples of random variables, and is particularly suitable for complex problems that are difficult to solve analytically. In static reliability analysis, MCS can be used to estimate the failure probability or reliability of the system under certain conditions.

[0003] The basic steps of MCS static reliability analysis are as follows:

[0004] Define the problem: Clearly define the reliability requirements of the system and determine the failure criteria.

[0005] Establish a model: Build a reliability model of the system, including all relevant random variables and their probability distributions.

[0006] Generate samples: Use a pseudo-random number generator to generate a large number of samples of random variables.

[0007] Simulate the operation: For each sample, run the simulation to determine whether the system fails.

[0008] Result analysis: Count the number of failures and the total number of simulations, and calculate the failure probability or reliability.

[0009] Precision evaluation: Evaluate the precision of the simulation results, and if necessary, increase the sample size to improve the precision.

[0010] The advantage of MCS method lies in its flexibility and applicability, which can handle various types of random variables and complex probability models. However, MCS also has its limitations, such as high computational cost, especially when a large number of samples are needed to obtain high-precision results. In addition, MCS usually needs enough samples to obtain stable and reliable results.

[0011] Kriging surrogate model is a widely used method in the field of engineering design and optimization, which is based on statistical principles to predict the response value of unknown points through known data points. Kriging model was first proposed by D.G. Krige, a South African mining engineer, in 1951, and further developed by French mathematician G. Matheron. This model was popularized in the field of experimental design by Sacks et al. in the 1980s, forming a method of experimental design and analysis based on computer simulation and Kriging model. Echard et al. proposed an iterative method based on Monte Carlo simulation and Kriging model to more effectively evaluate the reliability of structures. This method is called AK-MCS active learning reliability method, which is a combination of Kriging and Monte Carlo simulation. The application of Kriging model in reliability analysis mainly lies in the construction of surrogate model, which is used to approximate the limit state function of complex systems for structural reliability analysis. The core idea of Kriging surrogate model is to use Gaussian process to model the unknown relationship and infer the model through observed data points. Bayesian inference is used to analyze input and output samples to extract potential relationships, and error terms are described by probability distribution to represent prediction results and their uncertainties. The two main components of Kriging surrogate model are mean function and covariance function. Mean function provides a global prediction to capture the general trend of the system, while covariance function describes the local properties of the system by setting the relationship between each observation point. Kriging model has become one of the most popular surrogate models due to its ability to predict the error of unknown points, good prediction of non-linear and multi-peak values, and its application to high-order and highly nonlinear problems. Compared with other types of surrogate models, Kriging model can ensure that the response surface passes through all sample points and smoothly simulates the original model with less data.

[0012] The MCS (Monte Carlo Simulation) method in the technical scheme of analyzing the reliability of amusement facility reducer planetary gear can be divided into the following five steps:

[0013] Step 1: Define the problem and objectives, first clarify the reliability requirements of the amusement facility reducer planetary gear to be analyzed, determine the failure criteria and analysis objectives.

[0014] Step 2: Establish the reliability model, build a system reliability model containing all relevant random variables and their probability distributions, such as input torque, material properties, geometric dimensions, etc.

[0015] Step 3: Generate random samples, use a pseudo-random number generator to generate a large number of samples of random variables. The generation of samples needs to be based on the probability distribution of random variables.

[0016] Step four: simulation run, for each set of samples, run the simulation to determine whether the system fails. This usually involves substituting the sample points into the function function and checking whether its output leads to failure.

[0017] Step five: result analysis, count the number of failures and the total number of simulations, calculate the failure probability or reliability. Usually expressed as the ratio of the number of failures to the total number of simulations, that is, the failure probability, the reliability and the sum of the failure probability is 1.

[0018] However, MCS usually requires a large number of samples to simulate, in order to obtain a sufficiently accurate failure probability estimate, which is computationally expensive and time-consuming. In terms of calculation accuracy, the accuracy of MCS method is limited by the number of samples, increasing the number of samples can improve the accuracy, but this will increase the calculation cost. In terms of computational efficiency, MCS usually requires a large number of samples to simulate, in order to obtain a sufficiently accurate failure probability estimate, which may be very expensive and time-consuming in calculation. In terms of applicability, MCS method is suitable for various types of probability models, especially when the model is complex or the analytical solution is difficult to obtain. In terms of active learning ability, MCS method has no active learning ability, the selection of sample points is random. In terms of application range, due to its simplicity, MCS can be applied to a wide range of engineering problems. SUMMARY

[0019] In view of the above technical problems, the amusement facility speed reducer gear reliability analysis method based on the proxy model is provided to achieve the following purposes:

[0020] 1. The reliability of the amusement facility speed reducer gear is analyzed and calculated.

[0021] 2. The AK-MCS (Active Learning Kriging combined with Monte Carlo Simulation) method is used in the present application, which reduces the number of calls to the original simulation model through the adaptive Kriging proxy model, thereby reducing the calculation cost. The AK-MCS method can obtain a more accurate estimate of the failure probability with fewer calls to the structure function.

[0022] 3. AK-MCS uses an active learning strategy to locally search for the best sample point near the limit state surface, and globally searches for the best sample point according to the size of the model prediction variance, which can more effectively improve the accuracy of the Kriging model.

[0023] 4. The AK-MCS method is improved in global and local search ability, and can estimate the accurate failure probability value with fewer calls to the limit state function.

[0024] The specific technical solutions are as follows:

[0025] The amusement facility reducer gear reliability analysis method based on the agent model comprises the following steps:

[0026] Step one: first, according to the actual service condition of the amusement facility high-flying, analyze the working characteristics of the reducer planetary gear;

[0027] Step two: finite element analysis is performed on the reducer planetary gear, which includes meshing of the planetary gear and adding boundary conditions according to its service characteristics, to provide simulation response values for subsequent construction of Kriging agent model;

[0028] Step three: the random variables of the amusement facility reducer planetary gear include uncertain factors in the actual service process, the working environment is complex, the temperature, humidity, material characteristics, and the applied torque;

[0029] In the reliability analysis, the influence of these uncertain factors on the amusement facility reducer planetary gear is qualitatively evaluated and quantitatively processed; the elastic modulus of the material of the amusement facility reducer planetary gear and the input torque of the sun gear are taken as variables, and the response surface between the input torque, the material elastic modulus and the maximum equivalent stress is established by using the test analysis function (Design of Experiments) in the Response Surface Optimization module of Ansys Workbench software, so that the random variables are subject to normal distribution and are independent of each other;

[0030] Step four: export the response surface data and construct the performance function, there are two variables, respectively representing the high-flying amusement facility reducer gear torque and the elastic modulus of the material, and the type of fitting function is set to second-order function;

[0031] Step five: construct the reliability model of the amusement facility reducer planetary gear, and take whether the stress of the amusement facility reducer planetary gear exceeds the yield strength of the material as the reliability index, that is, , R is the structural resistance; S is the comprehensive effect of the structure. According to the strength theory, if the maximum equivalent stress of the amusement facility reducer planetary gear exceeds the yield strength of the material during the working process, it can be considered as failure, and the failure criterion is: , is the maximum equivalent stress of the amusement facility reducer planetary gear; is the yield strength of the material. Therefore, the limit state function is: ; the reliability of the amusement facility reducer planetary gear is the probability of calculating .

[0032] Through the above analysis, the reliability model of the amusement facility deceleration planetary gear is established:

[0033] ;

[0034] where is the elastic modulus of the material; is the input torque.

[0035] Two learning functions are selected: U function and EFF function.

[0036] (1) U function

[0037] Learning function is based on the concept of error classification probability, the prediction value of the Kriging model obeys the Gaussian distribution, and the mean and variance of the prediction value are expressed as:

[0038]

[0039] The U function is expressed as:

[0040] For the Kriging surrogate model, the new test point is obtained by solving the following function:

[0041]

[0042] The convergence criterion of the adaptive Kriging model is:

[0043] The threshold is:

[0044] (2) EFF function

[0045] Based on the mean and variation of the Kriging model, the optimal solution that can be obtained at each sampling point in the design space is obtained. It is used to judge the degree to which the true value of the function function satisfies the equality constraint based on a given threshold.

[0046] The expected feasible function EFF is expressed as:

[0047]

[0048] The EFF function aims to measure the probability that the true model response is zero, and the determination of the new test point is achieved by solving a specific function:

[0049] The convergence criterion of the EFF function is: ;

[0050] Step six: According to the two learning functions, run the corresponding algorithm program in matlab, that is, the corresponding reliability can be calculated.

[0051] The present application has the technical effects of:

[0052] (1) By using Kriging surrogate model to approximate the real model, the number of calls to the real model is reduced, thereby significantly improving the calculation efficiency.

[0053] (2) Through the active learning strategy, sample points can be increased in key areas to more effectively improve model accuracy while controlling computational cost.

[0054] (3) The Kriging model can be continuously updated according to new data to reflect the latest information and improve the accuracy of prediction.

[0055] (4) It is suitable for problems that can build effective surrogate models, especially for high-dimensional and nonlinear problems.

[0056] (5) Parallel computing can also be realized, especially in the construction and updating stage of the Kriging model.

[0057] (6) It has active learning ability and can select the most informative sample points for simulation according to the performance of the current model.

[0058] (7) It is suitable for complex engineering problems that require high efficiency and high accuracy, especially when the surrogate model can effectively approximate the real model. BRIEF DESCRIPTION OF DRAWINGS

[0059] Figure 1 Boundary conditions are set for the present application;

[0060] Figure 2 Experimental design is set for the present application;

[0061] Figure 3 Response surface is set for the present application;

[0062] Figure 4 Fitting function is set for the present application. DETAILED DESCRIPTION

[0063] The main steps of the present application in analyzing the reliability of the amusement facility reduction gear are as follows:

[0064] Step one: First, according to the actual service condition of the amusement facility high-flying, analyze the working characteristics of the reduction gear planetary gear; The working environment of the amusement facility reduction gear planetary gear in the present application is that the inner gear ring is fixed and the sun wheel obtains a torque.

[0065] Step two: then the reducer planetary gear finite element analysis, finite element analysis needs to be meshed and according to its service characteristics to add certain boundary conditions as follows Figure 1 As shown in Fig. 1, the simulation response value with high precision can be provided for subsequent construction of Kriging surrogate model, and necessary conditions for construction of high-precision surrogate model are provided.

[0066] Step three: considering the random variables that may affect it, in the actual service process, the working environment is complex, temperature, humidity, material characteristics, applied torque are all objective existence of uncertainty. In reliability analysis, the influence of these uncertain factors on the amusement facilities reducer planetary gear must be qualitatively evaluated and quantitatively processed, so as to facilitate the follow-up reliability analysis work. The present application takes the elastic modulus of the material of the amusement facilities reducer planetary gear and the input torque of the sun gear as variables, and uses the test analysis function (Design of Experiments) in the Response Surface Optimization module of Ansys Workbench software to establish the response surface between the input torque, material elastic modulus and maximum equivalent stress, as shown in Fig. 2. Figure 2 As shown in Fig. 2, the workbench experimental design interface, Figure 3 The response surface, assuming that the random variables are subject to normal distribution and are independent of each other, the present application selects three design points for study, and the variable distribution of the three design points is as follows:

[0067] For design point 1, there are ;

[0068] For design point 2, there are ;

[0069] For design point 3, there are ;

[0070] Step four: export the response surface data and construct the performance function, the present application only considers the two factors of high-altitude flying amusement facilities reducer gear torque and material elastic modulus, so there are only two variables in the construction of performance function, which represent the two factors of high-altitude flying amusement facilities reducer gear torque and material elastic modulus, and the type of fitting function is set to second-order function, as shown in Fig. 3. Figure 4 ;

[0071] Step five: then the reliability model of the amusement park reducer planetary gear is built, because the performance function of the structure of the amusement park reducer planetary gear is relatively complex, it is very difficult to calculate the reliability by using direct integration method, generally needs to calculate by using relatively simple approximate method, first the reliability index of the structure is solved, then the corresponding failure probability is solved. , R is the structural resistance; S is the comprehensive effect of the structure. According to the strength theory, if the maximum equivalent stress of the amusement park reducer planetary gear exceeds the yield strength of the material during the working process, it can be considered as failure, then the failure criterion is: , is the maximum equivalent stress of the amusement park reducer planetary gear; is the yield strength of the material. Therefore, the limit state function is: In the application, the reliability of the amusement park reducer planetary gear is to calculate the probability of .

[0072] Through the above analysis, the reliability model of the amusement park reducer planetary gear can be established as: In the formula, is the elastic modulus of the material; is the input torque.

[0073] The function of AK-MCS method has many, the application selects two learning functions: U function and EFF function.

[0074] (1) U function

[0075] Learning function is proposed based on the concept of error classification probability, the prediction value of the Kriging model obeys Gaussian distribution, the mean and variance of the prediction value can be expressed as:

[0076]

[0077] The U function can be expressed as:

[0078] For the Kriging surrogate model, the new test point can be obtained by solving the following function:

[0079]

[0080] Generally, the convergence criterion of the adaptive Kriging model is:

[0081] Generally, the threshold is:

[0082] (2) EFF function

[0083] The expected feasibility function is proposed under the guidance of the expected improvement function. Based on the mean and variation of Kriging model, the optimal solution of each sampling point in the design space is obtained. The degree to which the true value of the function function satisfies the equality constraint is judged on the basis of a given threshold.

[0084] The expected feasibility function (EFF) is also an adaptive learning function, which can be expressed as:

[0085]

[0086] The EFF function aims to measure the probability that the true model response is zero. The determination of the new test point can be achieved by solving a specific function:

[0087] Generally, the convergence criterion of the EFF function is:

[0088] Step six: According to the two functions, run the corresponding algorithm program in matlab, and the corresponding reliability can be calculated. Compared with the results calculated by the MCS method, it can be found that the error is within 5%.

[0089] Table 1. Solution results of different adaptive learning methods under design point 1

[0090]

[0091] Table 2. Solution results of different adaptive learning methods under design point 2

[0092]

[0093] Table 3. Solution results of different adaptive learning methods under design point 3

[0094]

[0095] As shown in Tables 1, 2 and 3, the running results of three design points prove that the proposed method is effective in calculation accuracy.​​

Claims

1. A reliability analysis method for gears in amusement park ride reducers based on a proxy model, characterized in that, Includes the following steps: Step 1: First, based on the actual service conditions of the amusement ride flying high in the air, analyze the working characteristics of its reducer planetary gears; Step 2: Perform finite element analysis on the planetary gears of the reducer. The finite element analysis includes meshing the planetary gears and adding boundary conditions according to their service characteristics, so as to provide simulation response values ​​for the subsequent construction of the Kriging proxy model. Step 3: In the reliability analysis, the impact of uncertainties on the planetary gears of the amusement ride reducer is qualitatively assessed and quantified; using the elastic modulus of the planetary gear material and the input torque of the sun gear as variables, a response surface is established between the input torque, the elastic modulus of the material, and the maximum equivalent stress, ensuring that the random variables all follow a normal distribution and are independent of each other; Step 4: Export the response surface data and construct the performance function. There are two variables, representing the gear torque of the high-altitude flying amusement ride reducer and the elastic modulus of the material, respectively. At the same time, set the fitting function type to a second-order function. Step 5: Construct a reliability model for the planetary gears of the amusement ride reducer. The reliability model is established based on whether the stress on the planetary gears of the amusement ride reducer exceeds the yield strength of the material. Choose one of two learning functions: the U function and the EFF function; Step Six: Based on these two learning functions, run the corresponding algorithm program in MATLAB to calculate the corresponding reliability.

2. The reliability analysis method for amusement ride reducer gears based on a proxy model according to claim 1, characterized in that, In step three, the experimental analysis function in the Response Surface Optimization module of Ansys Workbench software is used to establish the response surface between the input torque, the material elastic modulus, and the maximum equivalent stress.

3. The reliability analysis method for amusement ride reducer gears based on a proxy model according to claim 1, characterized in that, In step five, whether the stress on the planetary gears of the amusement park ride reducer exceeds the yield strength of the material is used as a reliable indicator. R represents structural resistance; S represents the overall effect of the structure. According to strength theory, if the maximum equivalent stress of the planetary gear in the amusement ride reducer exceeds the yield strength of the material during operation, it can be considered to have failed. Therefore, its failure criterion is: , The maximum equivalent stress of the planetary gears in the amusement park ride reducer; Let be the yield strength of the material; the limit state function is: The reliability of planetary gears in amusement park ride reducers is calculated. The probability of.

4. The reliability analysis method for amusement ride reducer gears based on a proxy model according to claim 3, characterized in that, The reliability model for the planetary gears of the amusement park ride reducer, established in step five, is as follows: ； In the formula The elastic modulus of the material; This is the input torque.

5. The reliability analysis method for amusement ride reducer gears based on a proxy model according to claim 4, characterized in that, Step 5 involves selecting two learning functions: the U function and the EFF function; specifically: (1) U function Learning function Based on the concept of misclassification probability, the Kriging model's predicted values ​​follow a Gaussian distribution, and the mean and variance of the predicted values ​​are expressed as: ， The U-function is represented as: , For the Kriging surrogate model, new test points are obtained by solving the following function: ， The criteria for determining whether an adaptive Kriging model converges are as follows: , (2) EFF function Based on the averaging and variation of the Kriging pattern, the optimal solution obtainable at each sampling point in the design space is derived. This solution is then used to determine whether the true value of the function satisfies the equality constraint given a threshold. The degree; The expected feasibility function EFF is expressed as: ， The EFF function is designed to measure the probability that the real model response is zero. New test points are determined by solving a specific function: , The convergence criterion for the EFF function is: .

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