Performance evaluation method of mechanical system under random vibration condition

Abstract

The invention relates to a method for evaluating the performance of a mechanical system under the condition of random vibration, belongs to the technical field of mechanical system performance evaluation, and solves the problems that a high-precision solving method for an effective working state probability solution is lacked in the prior art, and efficient performance evaluation of the mechanical system is realized according to the high-precision solving method. The method comprises the following steps: experimenting the process of the mechanical system influenced by random vibration to obtain experimental data; based on the experimental data, solving a corresponding relation between each experimental time and the value of the effective working probability of the system so as to construct a sample set; training and testing by using the sample set to obtain a neural network model for solving the effective working probability of the system in real time; in the actual operation process, when the vibration initial state of the mechanical system is the vibration initial state, the prediction time is input into the neural network model passing the test, and the neural network model predicts and outputs the effective working probability of the system of the prediction time; and evaluating the performance of the mechanical system according to the effective working probability of the system in the prediction time.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical system performance evaluation, and in particular to a performance evaluation method of a mechanical system under random vibration conditions. Background Art

[0002] In many fields such as reliability engineering, electronic engineering, materials science and mechanical engineering, random vibration or random load has an important impact on the reliability of equipment or devices. If the random vibration is too severe, it may cause material fatigue failure, electronic component failure or mechanical structure damage, which in turn affects the performance and life of the equipment or device. Therefore, the performance evaluation and life prediction of equipment or devices under random vibration or random load has always been a hot topic and difficulty in research. With the continuous development of science and technology, these fields have increasingly higher requirements for the performance and reliability of equipment or devices, making it particularly important to predict and evaluate the probability of effective working state of the system state evolving over time under random vibration.

[0003] Early studies mainly used empirical formulas and simplified models to predict system failures under random vibration, but these methods often have large errors due to the lack of in-depth and detailed description and consideration of the random vibration process. With the development and application of statistics, people began to try to use probability theory and mathematical statistics methods to model and analyze system failures under random vibration, which has improved the accuracy of prediction to a certain extent.

[0004] However, with the rapid development of modern technology, traditional prediction and evaluation methods have been unable to meet the needs of high precision and high efficiency. Especially in some high-precision and high-reliability application scenarios, such as aerospace, precision manufacturing and other fields, higher requirements are placed on the prediction and evaluation of the probability of effective working state of the system state evolving over time under random vibration. Therefore, accurately predicting and evaluating the effective working time before the system fails is crucial to ensure the reliability of equipment or devices.

[0005] In summary, how to accurately model and analyze the time evolution of the system state under random vibration, improve the accuracy of the probability solution of the system's effective working state, and conduct performance evaluation based on this has become an urgent problem to be solved. Summary of the invention

[0006] In view of the above analysis, an embodiment of the present invention aims to provide a performance evaluation method of a mechanical system under random vibration conditions, so as to solve the problem of lack of a high-precision solution method for an effective working state probability solution in the prior art, and thereby realize efficient performance evaluation of the mechanical system.

[0007] The present invention discloses a method for evaluating the performance of a mechanical system under random vibration conditions, the method comprising:

[0008] Conducting experiments on the process of a mechanical system being affected by random vibration to obtain experimental data; the experimental data includes: initial vibration state, vibration state at a certain experimental time, average rate and fluctuation degree of vibration state, and failure threshold of vibration state;

[0009] Based on the experimental data, the corresponding relationship between each experimental time and the value of the effective working probability of the system is obtained to construct a sample set; the sample set is used to train and test a neural network model for solving the effective working probability of the system in real time;

[0010] During actual operation, when the mechanical system takes the vibration initial state as the vibration starting state, the predicted time is input into the tested neural network model, and the neural network model predicts the system effective working probability of the output predicted time; and the performance of the mechanical system is evaluated based on the system effective working probability of the predicted time.

[0011] On the basis of the above scheme, the present invention also makes the following improvements:

[0012] Further, based on the system effective working probability at the predicted time, the performance of the mechanical system is evaluated, and the following is performed:

[0013] Determine whether the system effective working probability within the prediction time is greater than or equal to a first performance threshold, if so, the performance of the mechanical system within the prediction time is good;

[0014] determining whether the probability of effective operation of the system during the prediction time is between the second performance threshold and the first performance threshold, and if so, the performance of the mechanical system during the prediction time is average;

[0015] Otherwise, the performance of the mechanical system within the prediction time is poor.

[0016] Further, based on the experimental data, the corresponding relationship between each experimental time and the value of the system effective working probability is obtained, and the following is executed:

[0017] Obtaining the exponential term in the analytical solution of the transition probability density function of the vibration state according to the experimental data, and obtaining the value of the exponential term in the analytical solution of the transition probability density function corresponding to each experimental time and its vibration state;

[0018] Obtaining the integral term in the analytical solution of the transition probability density function of the vibration state according to the experimental data, and obtaining the value of the integral term in the analytical solution of the transition probability density function corresponding to each experimental time and its vibration state;

[0019] The values ​​of the exponential term, the integral term and the differential term of the vibration state in the analytical solution of the transfer probability density function corresponding to each experimental time and its vibration state are multiplied to obtain the values ​​of the transfer probability density function corresponding to the corresponding experimental time and its vibration state;

[0020] By integrating the value of the transfer probability density function from 0 to the failure threshold in each experimental time, the corresponding relationship between the corresponding experimental time and the value of the system effective working probability is obtained.

[0021] Furthermore, the transition probability density function of the vibration state satisfies:

[0022]

[0023] Among them, S0 represents the initial state of vibration, S t represents the vibration state at time t, m(S t ) is the vibration state S t The average rate, σ 2 (S t ) is the vibration state S t degree of volatility.

[0024] Furthermore, the effective working probability of the system Q(t|S0) is defined as: the probability that the mechanical system maintains an effective working state within time t under the condition of a given initial vibration state S0;

[0025]

[0026] Among them, S f is the failure threshold of the vibration state.

[0027] Furthermore, the transition probability density function p(t,S t The analytical solution of |S0) is expressed as:

[0028]

[0029] In formula (3), As an index term, As an integral term, dS t as a differential term.

[0030] Furthermore, the exponential term in the analytical solution of the transfer probability density function corresponding to each experimental time and its vibration state is obtained by executing:

[0031] Parameter initialization: Take the vibration state S at the experimental time t t As the target vibration state; starting from the initial vibration state S0, according to the step length dS tDetermine the experimental time between 0-t; start from the initial state of vibration s0, with a step size dS t As an increment, gradually increase the vibration state S _t until the target vibration state S is reached or exceeded. t , S t f , S f is the failure threshold of the vibration state; the initial value of the initialization cumulative item integral_sum is 0;

[0032] In each vibration state S _t , the average speed m(S) of the vibration state is obtained experimentally _t ) and the fluctuation degree of vibration state σ 2 (S _t ), calculate the integrand The value of integrand1; use dS t Multiply by integral1 and add the multiplication result to the cumulative term integral_sum;

[0033] Substitute the cumulative term integral_sum into the exponential function exp(-integral_sum) to obtain the vibration state S at the experimental time t. t The value of the exponential term in the analytical solution of the corresponding transition probability density function.

[0034] Furthermore, the value of the integral term in the analytical solution of the transfer probability density function corresponding to each experimental time and its vibration state is obtained by executing:

[0035] Parameter initialization: In [S t ,S f ] interval, according to the step size dS t Create equally spaced vibration states S _t Vector S_vec, and according to the step size dS t Determine tt f The experimental time between f Indicates S f Corresponding time; initialize a p_current vector of the same size as S_vec to store each vibration state S _t The approximate value of the transition probability density function and the assumption that the initial value of the p_current vector is uniformly distributed; initialize the total number of iterations num_iterations;

[0036] Perform iterative solution. In each round of iteration:

[0037] Create a p_new vector of the same size as S_vec and set the first element to 0;​

[0038] In each vibration state S _t According to the p_current vector of this round of iteration, the average rate m(S) of the vibration state is obtained experimentally _t ) and the fluctuation degree of vibration state σ 2 (S _t ), calculate the integrand

[0039] The value of integral2;

[0040] From S _t To S f The value of integrand2 is accumulated into the p_new vector S _t The corresponding position;

[0041] Assign the value of the p_new vector to the p_current vector and jump to the next iteration until the total number of iterations num_iterations is reached;

[0042] Use the interpolation algorithm to extract the vibration state S at the experimental time t from the p_current vector output from the last round of iteration t The corresponding approximate probability density value p_approx is used as the vibration state S at the experimental time t t The value of the integral term in the analytical solution of the corresponding transition probability density function.

[0043] Furthermore, the vibration state S at the experimental time t t The corresponding value of the transition probability density function is p = exp(-integral_sum)·p_approx·dS t .

[0044] Furthermore, the neural network model for solving the probability of effective operation of the system in real time is obtained by performing the following operations:

[0045] Taking the experimental time t as input and the corresponding value Q of the system effective working probability as output as a set of sample data, a sample set is constructed; and the sample set is divided into a training sample set and a test sample set;

[0046] The neural network model is trained using the training sample set, and the trained neural network model is tested using the test sample set until the test passes, thereby obtaining a neural network model for real-time solving the probability of effective operation of the system.

[0047] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0048] In summary, the performance evaluation method of the mechanical system under random vibration provided in this embodiment uses the experimental data obtained from the experiment on the process of the mechanical system being affected by random vibration to obtain the corresponding relationship between each experimental time and the value of the effective working probability of the system, and constructs a sample set based on this, and trains and tests the neural network model that solves the effective working probability of the system in real time, and fits the intrinsic correlation between each time and the effective working probability of the system. Therefore, the neural network model that passes the test can quickly and accurately predict the value of the effective working probability of the system at any time before the system fails. Finally, the performance of the mechanical system within the corresponding prediction time can be evaluated based on the predicted value of the effective working probability of the system. This method has the characteristics of high efficiency and high precision, and effectively solves the problem of the lack of efficient and high-precision mechanical system performance evaluation methods in the prior art.

[0049] In the specific implementation process, this embodiment uses the analytical solution method to accurately model and analyze the random vibration process of the mechanical structure. Through probability theory and random process theory methods, a partial differential equation of the transition probability density function of the vibration state is creatively established, and the expression form of the corresponding analytical solution is given. Based on this, the corresponding relationship between each experimental time and the value of the effective working probability of the system is obtained, laying a data foundation for the subsequent sample set data acquisition. This process fully considers the randomness and dynamic changes of the vibration state of the mechanical system, thereby effectively improving the accuracy of the analysis.

[0050] In addition, based on accurate prediction results, this embodiment can provide scientific decision support for the performance evaluation of the mechanical system, so that relevant technicians can take timely measures to avoid damage and failure of the mechanical system, thereby improving the reliability and stability of the system. By taking maintenance measures in a timely manner, the present invention can reduce the damage and failure of the mechanical system caused by vibration, thereby extending the service life of the system. This is of great significance for improving the economic benefits of equipment and reducing maintenance costs.

[0051] In the present invention, the above-mentioned technical solutions can also be combined with each other to achieve more preferred combination solutions. Other features and advantages of the present invention will be described in the subsequent description, and some advantages can become obvious from the description, or can be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The accompanying drawings are only used for the purpose of illustrating specific embodiments and are not to be considered as limiting the present invention. In the entire drawings, the same reference symbols represent the same components;

[0053] Figure 1A flow chart of a method for evaluating performance of a mechanical system under random vibration provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0054] The preferred embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not used to limit the scope of the present invention.

[0055] A specific embodiment of the present invention discloses a method for evaluating the performance of a mechanical system under random vibration conditions. First, the theoretical analysis on which this embodiment is based is described as follows.

[0056] The purpose of this embodiment is to provide an intelligent modeling and analysis method for improving the accuracy of the probability solution of the effective working state of the vibration equation of the state evolution over time, and to improve the accuracy of the probability solution of the effective working state of the system by accurately modeling and analyzing the evolution of the system state over time under random vibration.

[0057] 1. Model building method

[0058] In this embodiment, the basic vibration function S of random vibration is first set. t is a random process, the basic vibration function S t is a random variable that depends on time t, which reflects the characteristics of vibration changing with time t, and its initial state is S0. The system effective working probability Q(t|S0) is defined as: the probability that the system maintains an effective working state within time t under a given S0, and the S that causes the system to fail t For S f , defined as the failure threshold of the vibration state. t More than S f When the system enters the failure state, the state of random vibration evolves from S0 to S t Make the transfer.

[0059] In this embodiment, the transition probability density function of the vibration state is assumed to be p(t, S t |S0), and based on the transfer probability density function, the following model equation of the vibration state transfer process is established:

[0060]

[0061] This equation takes into account the diffusion and drift of the vibrational state, where m(S t ) is the drift function, that is, the vibration state S t The average rate represents the vibration state S of the mechanical system t The average rate of change over time t, which describes the average rate of change of the random vibration process; σ 2 (St ) is the variance function, that is, the vibration state S t The degree of fluctuation indicates the vibration state S of the mechanical system t The degree of fluctuation over time t, which describes the variance of the random vibration state change. This model equation describes the evolution of the transition probability density of the vibration state over time t, and also includes the vibration state S t In practical applications, m(S t ) and σ 2 (S t ) can be set and adjusted according to specific application scenarios.

[0062] 2. Model solution and analysis methods

[0063] Based on the above model equation, this embodiment further solves the key transition probability density function p(t,S t |S0). This function describes the transition of the system state from the initial state S0 to the state S over time t. t The probability density of .

[0064] In order to solve the above model equations, it is necessary to set appropriate boundary conditions. t Reach or exceed the failure threshold S of the vibration state of the mechanical system f When , the transition probability density function of the vibration state is 0, that is:

[0065] p(t,S f |S0)=0 (2)

[0066] This boundary condition reflects that when the mechanical system enters the failure state, its transfer probability density function no longer considers exceeding the failure threshold S f vibration state.

[0067] By solving the above model equation, we can get the expression of the analytical solution of the transition probability density function:

[0068]

[0069] By analyzing the analytical solution of the transition probability density function, it can be seen that the expression of the analytical solution of the transition probability density function can be divided into several key calculation steps for detailed explanation:

[0070] (1) Calculate the external exponential function

[0071]

[0072] This part involves the variance function σ 2 (S t) and the drift function m(S t ), which represent the "diffusion" coefficient and "drift" coefficient of the system state transition. This exponential function adjusts the amplitude of the entire probability density and reflects the dynamic characteristics of the system state transition process.

[0073] (2) Calculate the internal integral function

[0074] The internal integral part is to solve the transition probability density function p(t,S t |S0) is one of the key steps, which involves multiple mathematical concepts and operations. This part is further divided into several sub-steps for detailed explanation.

[0075] 1) Determine the integrand

[0076] The integrand is the core part of the inner integral function and is expressed as:

[0077]

[0078] It contains several mathematical elements:

[0079] a) Weighting Factor It is based on the "diffusion" coefficient σ 2 (S t ) to adjust the size of the integrand. When the "diffusion" is large, the weight factor is small, and vice versa.

[0080] b) Drift term m(S t )·p(t,S t |S0): describes the system state transferred to the oscillating state S due to "drift" t The probability of m(S t ) is the "drift" coefficient, which represents the average trend of system state changes over time.

[0081] c) Diffusion term Describes the change in state transition probability due to the "diffusion" effect. The partial derivative here represents the change in the transition probability density function with the vibration state S t The rate of change.

[0082] 2) Determine the adjusted exponential function of the internal integral function

[0083] In the integrand, an adjusted exponential function is also included:

[0084]

[0085] This adjustment index function is a function of the vibration state S tThe integral in the adjusted exponential function represents the relative rate of change of the "diffusion" coefficient and the "drift" coefficient. Through these parameters, the value of the entire integrand is adjusted.

[0086] 3) Determine the integral range

[0087] The integral range of the internal integral function is from the vibration state S t To the failure threshold S f , where S t is the current vibration state of the system, S f This integral range represents all possible state transition paths from the current vibration state to the failure state.

[0088] 4) Perform integral calculation

[0089] Finally, through the integration operation, the integrand is t To the failure threshold S f The value of the internal integral function is obtained by accumulating in the range of t To failure state S f The sum of the probabilities of all possible state transition paths.

[0090] (3) Calculate the external integral

[0091] After successfully deriving the transition probability density function p(t,S t |S0), the function is further used to calculate the probability of the effective working state of the system Q(t|S0), by transforming the transition probability density function from 0 to the failure threshold S in the effective working range. f Perform integration to achieve:

[0092]

[0093] The definition of the effective working probability of the system Q(t|S0) is: the probability that the mechanical system will maintain an effective working state within a time t given the initial vibration state S0. This probability value Q(t|S0) is crucial for system design and maintenance because it intuitively reflects the possibility that the system will maintain an effective working state within a certain time t. By monitoring and analyzing this probability, the reliability of the system can be predicted and necessary maintenance measures can be taken in a timely manner, thereby extending the service life of the system and ensuring its stable performance.

[0094] 3. Analytical solution method

[0095] This embodiment provides a method for solving the analytical solution of the model equation for the above model. The method can solve the analytical solution of the equation efficiently and accurately by combining the approximate calculation of the external integral function and the internal integral function.

[0096] Specifically, in this embodiment, the method for obtaining the analytical solution includes the following steps:

[0097] In order to solve the vibration state transfer probability density equation, traditional methods usually rely on numerical calculations or approximate solutions. However, these methods often have problems such as large amount of calculations and insufficient precision. This embodiment proposes an intelligent improvement analysis method based on analytical solutions. This method uses mathematical tools to derive and finally obtain the analytical solution of the equation by deeply studying the structure and properties of the vibration state probability density equation.

[0098] (1) Method for solving exponential terms

[0099] Assume that the random vibration variable S _t Transition from the initial vibration state S0 to the target vibration state S t , S t f , whose transition probability density function is given by the variance function σ 2 (S _t ) and drift function m(S _t ) is determined. In this embodiment, it is assumed that both functions are continuous and differentiable and can be represented in a computing environment. The exponential term solution is performed according to the following steps:

[0100] 1) Initialization parameters: set the initial vibration state S0 and the target vibration state S t , variance function σ 2 (S _t ) and drift function m(S _t These functional expressions should be determined based on the physical characteristics of the actual vibration system and the measured data to ensure that they can accurately describe the changes in the vibration state.

[0101] 2) Set the step size: Set the step size dS t , which is used to approximate the continuous changes in the integration process. The choice of step size should be based on the characteristics of the vibration system, the required calculation accuracy, and the limitation of computing resources. Generally, a smaller step size can improve the calculation accuracy, but it will also increase the calculation time and resource consumption.

[0102] 3) Initialize the cumulative term: Set the initial value of the cumulative term integral_sum to 0. This cumulative term will be used to store the sum of the approximate values ​​of the integrand in the exponential term during the integration process. In the subsequent approximate integration steps, new integrand values ​​will be continuously added to integral_sum. ​

[0103] 4) Approximate integral:

[0104] Starting from the initial vibration state S0, with a step size dS t As an increment, gradually increase S _t until the target vibration state S is reached or exceeded. t .

[0105] In each S _t At the point, calculate the variance function σ 2 (S _t ) and drift function m(S _t ) value.

[0106] And calculate the variance function with respect to S _t The derivative dσ 2 (S _ t) / dS t This can be done either by numerical differentiation methods (such as central differences) or analytical differentiation methods (if the variance function has an explicit analytical expression).

[0107] Compute the integrand An approximate value of integrate1.

[0108] Use dS t Multiply the integrand by the approximate value of the integrand1 and add the multiplication result to integral_sum. In this way, integral_sum gradually accumulates the values ​​from S0 to S t The sum of the approximate values ​​of the integrand over the entire integration interval.

[0109] 5) Calculate the exponential term: Substitute the cumulative term integral_sum into the exponential function exp(-integral_sum) to get the value of the exponential term. The exponential term is a key part of the transition probability density function, which describes the probability density attenuation caused by diffusion and drift during the vibration state change process.

[0110] 6) Result output: The return value of the calculated exponential term can be used to further calculate the transition probability density function p(t,S t |S0) and is used to analyze the evolution of the vibration state over time. By comparing and verifying with other analysis methods, the effectiveness and advantages of this method in improving the accuracy of the solution of the probability density equation of the time-evolving vibration state can be evaluated.

[0111] (2) Method for solving the integral term

[0112] In the integral term solving method proposed in this embodiment, the accuracy of the solution of the time-evolving vibration state probability density equation is implemented and improved through the following specific steps.

[0113] First, set the initial vibration state S0 and the target vibration state S t , Points Upper Limit S f (usually some absorbing edge or endpoint of interest), and the variance function σ 2 (S _t ) and drift function m(S _t ) function. At the same time, determine the number of iterations num_iterations.

[0114] In [S t ,S f ] Create an equally spaced interval (in dS t S _t vector S_vec, ensuring that each S _t Each point corresponds to an approximate value of the state transition probability density function. At the same time, initialize a p_current vector of the same size as S_vec to store each S _t The approximation of the transition probability density function at the point and assuming that the initial value of the p_current vector is uniformly distributed.

[0115] Next, perform an iterative solution. In each iteration, perform the following steps:

[0116] 1) Initialize a new probability density function vector: create a p_new vector of the same size as S_vec and set the first element to 0 (to meet the boundary conditions).

[0117] 2) Calculate the derivative: Each S_ in S_vec t Points (except boundary points), calculate the variance function σ 2 (S _t )About S _t The derivative dσ 2 (S _t ) / dS t .

[0118] 3) Calculate the integrand: At each S _t point, according to the p_current value of the current iteration, σ 2 (S _t )、m(S _t ) and dσ 2 (S _t ) / dS t , calculate the integrand The value of integrate2.

[0119] 4) Numerical integration: Use the trapezoidal rule or other numerical integration methods (such as Gauss-Legendre integration) to transform S _t To S f The value of integrand2 is accumulated into the p_new vector S _t The corresponding position. In the accumulation process, the boundary conditions need to be processed. For example, when S f When it is an absorbing boundary, the last element of p_new may need to be set to 0.

[0120] 5) Update the probability density function: assign the value of the p_new vector to the p_current vector for use in the next iteration.

[0121] 6) Repeat iteration: Repeat the above steps until the specified number of iterations num_iterations is reached.

[0122] Finally, the result is output and the interpolation method is used to extract the value in S from the p_current vector. t The approximate probability density value p_approx at is used as the return value of the integral term.

[0123] At this time, the target vibration state S t The value of the transition probability density function p(t,S t |S0)=exp(-integral_sum)·p_approx·dS t .

[0124] (3) Solution of effective work probability function

[0125] By calculating the transfer probability density function from 0 to the failure threshold S in the effective working range f By integrating, we can obtain the effective working probability of the system in the initial vibration state S0:

[0126]

[0127] 4. Machine learning solution based on analytical solution

[0128] This embodiment also provides a machine learning solution method based on the analytical solution. The method uses the analytical solution as the initial value and training data of the neural network, performs learning and prediction through a machine learning method, and finally compares the results of the analytical solution and the machine learning solution to evaluate the performance of the machine learning.

[0129] The machine learning solution based on analytical solution includes the following steps:

[0130] (1) Parameter definition: First, define the relevant parameters in the equation, including the time range t_span, initial state S0, failure state S f wait.

[0131] (2) Calculate the approximate analytical solution: Use the above analytical solution method to calculate the approximate analytical solution Q_analytical of the equation.

[0132] (3) Generate training data: The calculated approximate analytical solution Q_analytical is used as the training target, and the corresponding integral time range t_span (removing the last point to avoid boundary effects) is uniformly sampled to obtain each sampling time t_train and its corresponding Q_train (i.e., the corresponding Q(t|S0)), thereby forming a training data set. In practical applications, experimental data or simulation data can also be used as training data.

[0133] (4) Training the neural network: Create a neural network model whose number of hidden layer units can be adjusted as needed. Input the training data sets t_train and Q_train into the neural network, train it through the training algorithm, and obtain the trained neural network model net and training data trained_data. During the training process, the validation set and test set can be used to monitor the training effect.

[0134] (5) Prediction and comparison: Use the trained neural network model net to predict the time range t_span (remove the last point to avoid boundary effects) and obtain the predicted value Q_predicted. Compare the predicted value with the approximate analytical solution Q_analytical to evaluate the performance of the neural network. The comparison can be made by calculating error indicators (such as mean square error, relative error, etc.).

[0135] This embodiment takes the above theoretical analysis as the core and forms the following performance evaluation method of a mechanical system under random vibration. The flowchart of the method is as follows: Figure 1 As shown, the following steps are included:

[0136] Step S1: Experimenting on the process of a mechanical system being affected by random vibration to obtain experimental data; the experimental data includes: initial vibration state, vibration state at several experimental times, average rate and fluctuation degree of vibration state, and failure threshold of vibration state.

[0137] Step S2: Based on the experimental data, obtain the corresponding relationship between each experimental time and the value of the system effective working probability to construct a sample set; use the sample set to train and test to obtain a neural network model for real-time solution of the system effective working probability.

[0138] Step S3: During the actual operation, when the mechanical system takes the vibration initial state as the vibration starting state, the predicted time is input into the neural network model that has passed the test, and the neural network model predicts the system effective working probability of the output predicted time; and the performance of the mechanical system is evaluated based on the system effective working probability of the predicted time.

[0139] In this embodiment, the mechanical system of the present invention may involve multiple fields such as reliability engineering, electronic engineering, materials science, mechanical engineering, etc., and generally refers to related systems with mechanical structures and affected by random vibrations, such as precision machine tool systems, aircraft engine systems, and automobile suspension systems. Under the influence of random vibrations, changes in vibration states can often reflect the health of the equipment, and the vibration state transition probability density can monitor the vibration state of the equipment in real time, while the system effective working probability can evaluate the possibility of the system maintaining an effective working state within a period of time under a given initial vibration state condition, so as to achieve performance evaluation of the mechanical system. This method helps to evaluate the performance of the mechanical system within the predicted time and ensure the reliability of the operation of the mechanical system. In the experimental process in the above step S1, relevant technical personnel can obtain various experimental data in the experimental environment. The method of obtaining the experimental data is not the focus of this embodiment, and only the following relevant introduction is made.

[0140] When a mechanical system is subjected to random vibration, its initial vibration state will be affected by many factors, including but not limited to:

[0141] Initial conditions: the system's initial position, velocity, acceleration and other state quantities.

[0142] External excitation: Characteristics of the random vibration source, such as frequency, amplitude and duration of vibration.

[0143] System parameters: These include the mass and stiffness of the system, which affect the system's response to vibration.

[0144] Damping: Energy dissipation mechanisms in a system, such as friction and air resistance, which affect the rate at which vibrations decay.

[0145] Nonlinear factors: In some cases, the response of the system may not be linear, which may be caused by factors such as material properties, geometric nonlinearity, or contact nonlinearity.

[0146] Multiple degrees of freedom effects: If a system has multiple degrees of freedom, the vibration states of each degree of freedom may affect each other.

[0147] Environmental factors: Environmental conditions such as temperature and humidity, which may change material properties and thus affect the vibration response.

[0148] Randomness: Since random vibrations are inherently uncertain, the vibration response of the system may vary due to randomness even under the same initial conditions.

[0149] Initial stress state: The initial stress or strain state that may exist in the system, which affects the system's response to vibration.

[0150] Boundary conditions: The support conditions and boundary constraints of the system, which determine how the vibration energy propagates.

[0151] The average rate of change of the vibration state over time usually refers to a measure of the change of the vibration state of the system (such as displacement, velocity or acceleration) over time. In the case of random vibration, this average rate may be affected by a variety of factors, causing it to exhibit nonlinear and random characteristics. In the specific implementation process, the average rate of the system under random vibration can be obtained through experimental measurement or numerical simulation, and probability distribution, regression analysis or other statistical methods can also be considered to describe and predict the average rate of the vibration state at the corresponding experimental time. In practical applications, the average rate of change of the vibration state is an important parameter that can help design more effective vibration control strategies and predict the long-term behavior of the system.

[0152] The degree of fluctuation of the vibration state over time usually describes the fluctuation characteristics of the vibration state (such as displacement, velocity or acceleration) of the mechanical system under the influence of random vibration. This fluctuation characteristic can involve the following aspects:

[0153] Fluctuation amplitude: The difference between the maximum and minimum values ​​of the vibration state, reflecting the intensity of the vibration.

[0154] Fluctuation frequency: the speed of change of vibration state, that is, the number of times the vibration state changes per unit time.

[0155] Wave cycle: the time required to complete a complete wave.

[0156] Fluctuation phase: In periodic vibration, the phase of the vibration state at a specific point in time.

[0157] Randomness of fluctuations: Due to the influence of random vibrations, changes in vibration states may present unpredictable random fluctuations.

[0158] Nonlinearity of fluctuations: If the system response exhibits nonlinear characteristics, the changes in the vibration state may not follow a simple linear law.

[0159] Energy distribution of vibration: The distribution of energy in a vibration state at different frequencies can usually be described by the power spectral density.

[0160] Coherence of fluctuations: the consistency or stability of a vibrational state over time.

[0161] Autocorrelation of fluctuations: how similar the vibrational states are at different points in time.

[0162] Cross-correlation of fluctuations: correlation between vibration states in different degrees of freedom or in different directions.

[0163] To quantify the degree of fluctuation of the vibration state over time, the following methods can be used:

[0164] Time history analysis: Analyze the fluctuation characteristics by recording the changes of vibration state over time.

[0165] Frequency domain analysis: Use methods such as Fourier transform to convert the time history into the frequency domain and analyze the frequency components of the vibration state.

[0166] Power Spectrum Analysis: Calculate the power spectrum density of the vibration state to understand the energy distribution of different frequency components.

[0167] Autocorrelation and cross-correlation analysis: Analyze the similarity or correlation of vibration states at different time points or in different directions.

[0168] Statistical analysis: Use statistical methods, such as variance, standard deviation, mean, etc., to quantify the degree of fluctuation in vibration conditions.

[0169] In addition, it should be noted that the failure threshold of the vibration state refers to the threshold of the vibration state that causes the mechanical system to fail. In the specific implementation process, different vibration states can be adjusted, and whether the mechanical system fails can be determined based on the operation of the mechanical system; the minimum value of the vibration state that causes the mechanical system to fail is obtained and used as the failure threshold of the vibration state.

[0170] Based on the above related description, the analytical solution of the vibration state transition probability density function is composed of the product of the exponential term, the integral term and the differential term, see formula (2)-(6), and the calculation formula of the probability of the effective working state of the system is shown in formula (7). Based on this, the specific execution process of step S2 is described as follows.

[0171] Step S21: obtaining the exponential term in the analytical solution of the transition probability density function of the vibration state according to the experimental data, and obtaining the value of the exponential term in the analytical solution of the transition probability density function corresponding to each experimental time and its vibration state.

[0172] Step S211: Parameter initialization: Taking the vibration state S at the experimental time t as t As the target vibration state; starting from the initial vibration state S0, according to the step length dS t Determine the experimental time between 0-t; start from the initial state of vibration S0, with a step size dSt As an increment, gradually increase the vibration state S _t until the target vibration state S is reached or exceeded. t , S t f , S f is the failure threshold of the vibration state; the initial value of the initialization cumulative item integral_sum is 0;

[0173] Step S212: In each vibration state S _t , the average speed m(S) of the vibration state is obtained experimentally _t ) and the fluctuation degree of vibration state σ 2 (S _t ), calculate the integrand The value of integrand1; use dS t Multiply by integral1 and add the multiplication result to the cumulative term integral_sum;

[0174] Step S213: Substitute the cumulative term integral_sum into the exponential function exp(-integral_sum) as the vibration state S at the experimental time t t The value of the exponential term in the analytical solution of the corresponding transition probability density function.

[0175] Step S22: Calculate the integral term in the analytical solution of the transition probability density function of the vibration state according to the experimental data, and obtain the value of the integral term in the analytical solution of the transition probability density function corresponding to each experimental time and its vibration state.

[0176] Step S221: Parameter initialization: In [S t ,S f ] interval, according to the step size dS t Create equally spaced vibration states S _t Vector S_vec, and according to the step size dS t Determine tt f The experimental time between f Indicates S f Corresponding time; initialize a p_current vector of the same size as S_vec to store each vibration state S _t The approximate value of the transition probability density function and the assumption that the initial value of p_current is uniformly distributed; the total number of initialization iterations num_iterations.

[0177] Step S222: Perform iterative solution. In each round of iteration:

[0178] ​Create a p_new vector of the same size as S_vec and set the first element to 0;

[0179] In each vibration state S _t According to the p_current vector of this round of iteration, the average rate m(S) of the vibration state is obtained experimentally _t ) and the fluctuation degree of vibration state σ 2 (S _t ), calculate the integrand The value of integral2;

[0180] From S _t To S f The value of integrand2 is accumulated into the p_new vector S _t The corresponding position;

[0181] Assign the value of the p_new vector to the p_current vector and jump to the next iteration until the total number of iterations num_iterations is reached;

[0182] Step S213: Use the interpolation algorithm to extract the vibration state S at the experimental time t from the p_current vector output from the last round of iterations t The corresponding approximate probability density value p_approx is used as the vibration state S at the experimental time t t The value of the integral term in the analytical solution of the corresponding transition probability density function.

[0183] Step S23: Multiply the values ​​of the exponential term, the integral term and the differential term of the vibration state in the analytical solution of the transition probability density function corresponding to each experimental time and its vibration state to obtain the value of the transition probability density function corresponding to the corresponding experimental time and its vibration state.

[0184] According to formula (2), the differential term is dS t , therefore, the vibration state S at the experimental time t t The corresponding value of the transition probability density function is p = exp(-integral_sum)·p_approx·dS t .

[0185] Step S24: By changing the value of the transition probability density function from 0 to the failure threshold S in each experimental time t f By integrating, we can obtain the corresponding relationship between the experimental time and the value of the system effective working probability.

[0186] By executing the operation in step S2, the corresponding relationship between multiple experimental times and the values ​​of the effective working probability of the system can be obtained. Afterwards, a sample set is constructed with the experimental time t as input and the corresponding value Q of the effective working probability of the system as output as a set of sample data; and the sample set is divided into a training sample set and a test sample set. The neural network model is trained with the training sample set, and the trained neural network model is tested with the test sample set until the test passes, thereby obtaining a neural network model for solving the effective working probability of the system in real time.

[0187] After the test is passed, the neural network that has passed the test can be used to perform subsequent predictions. It should be noted that during the experiment of step S1, the number of experiments that can be performed is relatively limited, taking into account the experimental cost and difficulty. Therefore, this embodiment obtains the correlation between the experimental time t as input and the corresponding value Q of the system effective working probability by executing steps S1-S2, and simulates this correlation through a neural network. After that, the value of the system effective working probability at any predicted time before the failure of the mechanical system can be predicted. Therefore, in step S3, the value of the corresponding system effective working probability can be predicted based on the predicted time, that is, in the actual operation process, when the mechanical system takes the vibration initial state as the vibration starting state (that is, the vibration initial state remains unchanged), the predicted time is input into the neural network model that has passed the test, and the neural network model predicts the system effective working probability of the output predicted time.

[0188] At the same time, since the system effective working probability can characterize the possibility of the mechanical system maintaining an effective working state within time t under the condition of a given initial vibration state S0, this parameter directly reflects the performance of the mechanical system within the predicted time. Therefore, the performance evaluation of the mechanical system can be carried out based on this, and the specific process is described as follows:

[0189] Determine whether the system effective working probability within the prediction time is greater than or equal to a first performance threshold, if so, the performance of the mechanical system within the prediction time is good;

[0190] determining whether the probability of effective operation of the system during the prediction time is between the second performance threshold and the first performance threshold, and if so, the performance of the mechanical system during the prediction time is average;

[0191] Otherwise, the performance of the mechanical system within the predicted time is poor, and further analysis of the operation process of the mechanical system or improvement measures need to be taken.

[0192] In the above process, the first performance threshold is greater than the second performance threshold.

[0193] In summary, the performance evaluation method of the mechanical system under random vibration provided in this embodiment uses the experimental data obtained from the experiment on the process of the mechanical system being affected by random vibration to obtain the corresponding relationship between each experimental time and the value of the effective working probability of the system, and constructs a sample set based on this, and trains and tests the neural network model that solves the effective working probability of the system in real time, and fits the intrinsic correlation between each time and the effective working probability of the system. Therefore, the neural network model that passes the test can quickly and accurately predict the value of the effective working probability of the system at any time before the system fails. Finally, the performance of the mechanical system within the corresponding prediction time can be evaluated based on the predicted value of the effective working probability of the system. This method has the characteristics of high efficiency and high precision, and effectively solves the problem of the lack of efficient and high-precision mechanical system performance evaluation methods in the prior art.

[0194] In the specific implementation process, this embodiment uses the analytical solution method to accurately model and analyze the random vibration process of the mechanical structure. Through probability theory and random process theory methods, a partial differential equation of the transition probability density function of the vibration state is creatively established, and the expression form of the corresponding analytical solution is given. Based on this, the corresponding relationship between each experimental time and the value of the effective working probability of the system is obtained, laying a data foundation for the subsequent sample set data acquisition. This process fully considers the randomness and dynamic changes of the vibration state of the mechanical system, thereby effectively improving the accuracy of the analysis.

[0195] In addition, based on accurate prediction results, this embodiment can provide scientific decision support for the performance evaluation of the mechanical system, so that relevant technicians can take timely measures to avoid damage and failure of the mechanical system, thereby improving the reliability and stability of the system. By taking maintenance measures in a timely manner, the present invention can reduce the damage and failure of the mechanical system caused by vibration, thereby extending the service life of the system. This is of great significance for improving the economic benefits of equipment and reducing maintenance costs.

[0196] Those skilled in the art will appreciate that all or part of the processes of the above-mentioned embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, wherein the computer-readable storage medium is a disk, an optical disk, a read-only storage memory, or a random access memory, etc.

[0197] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for evaluating the performance of a mechanical system under random vibration conditions, characterized in that: The method comprises: Conducting experiments on the process of a mechanical system being affected by random vibration to obtain experimental data; the experimental data includes: initial vibration state, vibration state at a certain experimental time, average rate and fluctuation degree of vibration state, and failure threshold of vibration state; Based on the experimental data, the corresponding relationship between each experimental time and the value of the effective working probability of the system is obtained to construct a sample set; the sample set is used to train and test a neural network model for solving the effective working probability of the system in real time; During actual operation, when the mechanical system takes the vibration initial state as the vibration starting state, the predicted time is input into the tested neural network model, and the neural network model predicts the system effective working probability of the output predicted time; and the performance of the mechanical system is evaluated based on the system effective working probability of the predicted time.

2. The performance evaluation method of a mechanical system under random vibration according to claim 1, characterized in that: Based on the probability of effective operation of the system during the predicted time, the performance of the mechanical system is evaluated by performing: Determine whether the system effective working probability within the prediction time is greater than or equal to a first performance threshold, if so, the performance of the mechanical system within the prediction time is good; determining whether the probability of effective operation of the system during the prediction time is between the second performance threshold and the first performance threshold, and if so, the performance of the mechanical system during the prediction time is average; Otherwise, the performance of the mechanical system within the prediction time is poor.

3. The performance evaluation method of a mechanical system under random vibration according to claim 1 or 2, characterized in that: Based on the experimental data, the corresponding relationship between each experimental time and the value of the system effective working probability is obtained, and the following is executed: Obtaining the exponential term in the analytical solution of the transition probability density function of the vibration state according to the experimental data, and obtaining the value of the exponential term in the analytical solution of the transition probability density function corresponding to each experimental time and its vibration state; Obtaining the integral term in the analytical solution of the transition probability density function of the vibration state according to the experimental data, and obtaining the value of the integral term in the analytical solution of the transition probability density function corresponding to each experimental time and its vibration state; The values ​​of the exponential term, the integral term and the differential term of the vibration state in the analytical solution of the transfer probability density function corresponding to each experimental time and its vibration state are multiplied to obtain the values ​​of the transfer probability density function corresponding to the corresponding experimental time and its vibration state; By integrating the value of the transfer probability density function from 0 to the failure threshold in each experimental time, the corresponding relationship between the corresponding experimental time and the value of the system effective working probability is obtained.

4. The performance evaluation method of a mechanical system under random vibration according to claim 3, characterized in that: The transition probability density function of the vibration state satisfies: Among them, S0 represents the initial state of vibration, S t represents the vibration state at time t, m(S t ) is the vibration state S t The average rate, σ 2 (S t ) is the vibration state S t degree of volatility.

5. The performance evaluation method of a mechanical system under random vibration according to claim 4, characterized in that: The system effective working probability Q(t|S0) is defined as: the possibility that the mechanical system maintains an effective working state within time t under the condition of a given initial vibration state S0; Among them, S f is the failure threshold of the vibration state.

6. The performance evaluation method of a mechanical system under random vibration according to claim 5, characterized in that: The transition probability density function of the vibration state p(t,S t The analytical solution of |S0) is expressed as: In formula (3), As an index term, As an integral term, d S t as a differential term.

7. The performance evaluation method of a mechanical system under random vibration according to claim 6, characterized in that: The exponential term in the analytical solution of the transfer probability density function corresponding to each experimental time and its vibration state is obtained by executing: Parameter initialization: Take the vibration state S at the experimental time t t As the target vibration state; starting from the initial vibration state S0, according to the step length dS t Determine the experimental time between 0-t; start from the initial state of vibration S0, with a step size dS t As an increment, gradually increase the vibration state S_ t until the target vibration state S is reached or exceeded. t , S t f , S f is the failure threshold of the vibration state; the initial value of the initialization cumulative item integral_sum is 0;​ In each vibration state S_ t , the average speed m(S_) of the vibration state is obtained experimentally t ) and the fluctuation degree of vibration state σ 2 (S_ t ), calculate the integrand The value of integrand1; use dS t Multiply by integral1 and add the multiplication result to the cumulative term integral_sum; Substitute the cumulative term integral_sum into the exponential function exp(-integral_sum) to obtain the vibration state S at the experimental time t. t The value of the exponential term in the analytical solution of the corresponding transition probability density function.

8. The performance evaluation method of a mechanical system under random vibration according to claim 7, characterized in that: The value of the integral term in the analytical solution of the transfer probability density function corresponding to each experimental time and its vibration state is obtained by executing: Parameter initialization: In [S t ,S f ] interval, according to the step size dS t Create equally spaced vibration states s_ t Vector S_vec, and according to the step size dS t Determine tt f The experimental time between f Indicates S f corresponding time; initialize a p_current vector of the same size as S_vec to store each vibration state S_ t The approximate value of the transition probability density function and the assumption that the initial value of the p_current vector is uniformly distributed; initialize the total number of iterations num_iterations; Perform iterative solution. In each round of iteration: Create a p_new vector of the same size as S_vec and set the first element to 0; In each vibration state S_ t According to the p_current vector of this round of iteration, the average rate m(S_ t ) and the fluctuation degree of vibration state σ 2 (S_ t ), calculate the integrand The value of integral2; Will be from S_ t To S f The value of integrand2 is accumulated into the p_new vector S_ t The corresponding position; Assign the value of the p_new vector to the p_current vector and jump to the next iteration until the total number of iterations num_iterations is reached; Use the interpolation algorithm to extract the vibration state S at the experimental time t from the p_current vector output from the last round of iteration t The corresponding approximate probability density value p_approx is used as the vibration state S at the experimental time t t The value of the integral term in the analytical solution of the corresponding transition probability density function.

9. The performance evaluation method of a mechanical system under random vibration according to claim 8, characterized in that: The vibration state S at the experimental time t t The corresponding value of the transition probability density function is p = exp(-integral_sum)·p_approx·dS t .

10. The performance evaluation method of a mechanical system under random vibration according to claim 8, characterized in that: The neural network model for solving the probability of effective operation of the system in real time is obtained by performing the following operations: Taking the experimental time t as input and the corresponding value Q of the system effective working probability as output as a set of sample data, a sample set is constructed; and the sample set is divided into a training sample set and a test sample set; The neural network model is trained using the training sample set, and the trained neural network model is tested using the test sample set until the test passes, thereby obtaining a neural network model for real-time solving the probability of effective operation of the system.

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