Mechanical system health monitoring method considering random vibration influence

Abstract

The invention relates to a mechanical system health monitoring method considering random vibration influence, belongs to the technical field of mechanical system operation prediction, and solves the problem of lack of an efficient and high-precision mechanical system health monitoring method in the prior art. The method comprises the following steps: experimenting the process of the mechanical system influenced by random vibration to obtain experimental data; solving an analytic solution of the transition probability density function of the vibration state according to the experimental data, and obtaining values of the transition probability density function corresponding to each experimental time and the vibration state thereof to construct a sample set; training and testing by using the sample set to obtain a neural network model for solving a transition probability density function of a vibration state in real time; in the actual operation process of the mechanical system, the prediction time and the vibration state are input into the neural network model, the prediction value of the transition probability density function corresponding to the vibration state of the prediction time is predicted and output, and accordingly the health condition of the mechanical system in the corresponding prediction time and the vibration state is monitored.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical system operation prediction, and in particular to a mechanical system health monitoring method considering the influence of random vibration. Background Art

[0002] In the field of random vibration analysis of mechanical systems, the probability density of vibration state transition can describe the conversion probability of mechanical systems under different vibration states, thereby helping to evaluate the long-term reliability of mechanical systems under the influence of random vibration environments. With the increasing complexity of mechanical systems and the increasing requirements for system reliability, traditional vibration analysis methods can no longer meet the needs of modern engineering. Therefore, the development of more accurate and intelligent vibration analysis methods has become an urgent need.

[0003] Random vibration is a ubiquitous phenomenon in the field of mechanical engineering and structural design. Random vibration not only affects the normal operation of the system, but also, in extreme cases, may cause system damage or failure, posing major hidden dangers to production and safety. In practical applications, the random vibration of mechanical systems is often affected by many factors, such as excitation from the external environment, material properties and structural characteristics within the system, etc. These factors make the vibration state of the mechanical system highly random and dynamic, which brings great difficulties to the vibration analysis and prediction of the system. Traditional vibration analysis methods are often based on simplified models or assumptions. Although these simplified models can describe the vibration characteristics of the system to a certain extent, they ignore the randomness and dynamic changes of the vibration state of the system and cannot accurately describe the randomness and dynamic changes of the vibration state of the system, resulting in insufficient prediction accuracy of the health monitoring results of the mechanical system based on the probability density of the vibration state transition. This inaccuracy of the prediction not only affects the maintenance strategy of the mechanical system, but also may lead to waste of resources and increase in costs.

[0004] Therefore, how to efficiently and accurately implement the health monitoring of mechanical systems taking into account the influence of random vibration has become the focus of current research. Summary of the invention

[0005] In view of the above analysis, an embodiment of the present invention aims to provide a mechanical system health monitoring method taking into account the influence of random vibration, so as to solve the problem of lack of efficient and high-precision mechanical system health monitoring method in the prior art.

[0006] The present invention discloses a mechanical system health monitoring method considering the influence of random vibration, the method comprising:

[0007] 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;

[0008] Obtain an analytical solution of the transition probability density function of the vibration state according to the experimental data, obtain the value of the transition probability density function corresponding to each experimental time and its vibration state, and use it 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 transition probability density function of the vibration state;

[0009] During the actual operation of the mechanical system, the predicted time and its vibration state are input into the tested neural network model, and the neural network model predicts and outputs the predicted value of the transfer probability density function corresponding to the vibration state at the predicted time; and based on the predicted value of the transfer probability density function, the health status of the mechanical system at the predicted time and its vibration state is monitored.

[0010] On the basis of the above scheme, the present invention also makes the following improvements:

[0011] Furthermore, the transition probability density function p(t,S t The analytical solution of |S0) is expressed as:

[0012]

[0013]

[0014] Among them, S0 represents the initial state of vibration, S t represents the transition from the initial vibration state S0 to 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.

[0015] Further, the values ​​of the transition probability density function corresponding to each experimental time and its vibration state are obtained by executing:

[0016] 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;

[0017] 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;

[0018] 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.

[0019] Furthermore, in formula (1), As an index term, As an integral term, d S t as a differential term.

[0020] 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:

[0021] 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 <S f , S f is the failure threshold of the vibration state; the initial value of the initialization cumulative item integral_sum is 0;

[0022] 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;

[0023] 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.

[0024] 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:

[0025] Parameter initialization: In [S t , Sf ] 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 assume that the initial value of the p_current vector is uniformly distributed; initialize the total number of iterations numiterations;

[0026] Perform iterative solution. In each round of iteration:

[0027] Create a p_new vector of the same size as S_vec and set the first element to 0;

[0028] 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

[0029] The value of integral2;

[0030] From S _t To S f The value of integrand2 is accumulated into the p_new vector S _t The corresponding position;

[0031] 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;

[0032] 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.

[0033] Furthermore, the vibration state S at the experimental time t tThe corresponding value of the transition probability density function is p = exp(-integral_sum)·p_approx·dS t .

[0034] Further, the sample set is constructed by executing:

[0035] The experimental time t, vibration state S t Taking as input and the value p of the corresponding transition probability density function 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.

[0036] Further, the sample set is used to train and test a neural network model for solving the transition probability density function of the vibration state in real time, and the following is performed:

[0037] 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 solution of the transfer probability density function of the vibration state.

[0038] Further, the monitoring of the health status of the mechanical system at the predicted time and under its vibration state comprises:

[0039] Determine whether the predicted value of the transfer probability density function corresponding to the vibration state at the predicted time is greater than the health monitoring threshold. If so, it indicates that the health status of the mechanical system at the predicted time and its vibration state is good; if not, it indicates that the health status of the mechanical system at the predicted time and its vibration state is poor, triggering a mechanical system health monitoring warning.

[0040] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0041] The method for monitoring the health of a mechanical system taking into account the influence of random vibration provided by the present invention uses the experimental data obtained by conducting experiments on the process of a mechanical system being affected by random vibration to obtain the analytical solution of the transfer probability density function of the vibration state, and based on this, constructs a sample set, trains and tests a neural network model for solving the transfer probability density function of the vibration state in real time, and fits the intrinsic correlation between each time and its vibration state and the transfer probability density function. Therefore, the neural network model that passes the test can quickly and accurately predict the value of the transfer probability density function of any time and its vibration state before the system fails. Finally, the health status of the mechanical system at the corresponding predicted time and its vibration state can be monitored according to the predicted value of the transfer probability density function. This method has the characteristics of high efficiency and high precision, and effectively solves the problem of the lack of efficient and high-precision methods for monitoring the health of mechanical systems in the prior art.

[0042] In the specific implementation process, the present invention adopts 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, the 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, which lays a data foundation for the subsequent data acquisition of the sample set. 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.

[0043] In addition, based on accurate prediction results, the present invention can provide scientific decision support for the health monitoring of mechanical systems, 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.

[0044] 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

[0045] 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;

[0046] Figure 1 A flow chart of a mechanical system health monitoring method considering the influence of random vibration provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0047] The preferred embodiments of the present invention are 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.

[0048] A specific embodiment of the present invention discloses a method for monitoring the health of a mechanical system taking into account the influence of random vibration. First, the theoretical analysis on which this embodiment is based is described as follows.

[0049] Random vibration is a common phenomenon in the operation of mechanical structures. When the random vibration exceeds the limit that the system structure can withstand, the system may be damaged or even fail. Before failure, the system is in an effective working state and can perform its functions normally.

[0050] In order to accurately describe the vibration state of the system, this embodiment introduces the basic vibration function S t To represent the random process of mechanical system vibration. Basic vibration function S t is a random variable that depends on time t, which reflects the characteristics of vibration changing with time t. Set the basic vibration function S t The initial vibration state is S0, which represents the vibration state when the system starts running. At the same time, in order to clarify the limit of system failure, the S that causes system failure is set t The value of S f , defined as the failure threshold. t More than S f When the mechanical system enters a failure state.

[0051] In order to quantitatively analyze the probability distribution of the effective working time of the mechanical system, this embodiment proposes to establish a vibration state probability density equation, which is used to describe the vibration state S of the mechanical system at different times t. t The probability of falling within a certain range. In this embodiment, by introducing probability theory and random process theory, the general form of the vibration state probability density equation is derived, which includes various influencing factors of system vibration and takes time t as a variable.

[0052] In describing the evolution of the random vibration state of a mechanical structure over time, the concept of the vibration state transition probability density function is introduced. This function describes the transition of the system from the initial vibration state S0 to the vibration state S at any time t. t In order to establish the mathematical model of this process, the transition probability density function of the vibration state is set to p(t, S t |S0). Based on the theory of random processes, the partial differential equation describing the change of the transition probability density of the vibration state can be derived as:

[0053]

[0054] 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 (S t ) is the variance function, that is, the vibration state S t The degree of fluctuation indicates the vibration state S of the mechanical system tThe degree of fluctuation over time t describes the variance of the random vibration state change. This partial differential equation describes the evolution of the transition probability density of the vibration state over time t, and also includes the vibration state S t spatial changes.

[0055] In order to solve the above partial differential equation, 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:

[0056] p(t,S f |S0)=0 (2)

[0057] 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.

[0058] By solving the above partial differential equation, we can obtain the analytical solution form of the transition probability density function, which is expressed as follows.

[0059]

[0060] By analyzing the analytical solution of the transition probability density function, it can be seen that the form of the analytical solution of the transition probability density function can be obtained by combining the following parts.

[0061] 1. Construct the index part

[0062] First, the analytical solution contains a single exponential term, which is in the form of:

[0063]

[0064] This exponential term is an exponential operation on the result of an integral. The integral contains the variance function σ 2 (S t ) and the drift function m(S t ), which describes the decay of the probability density due to diffusion and drift during the vibration state transition. To calculate this integral, numerical integration methods such as the trapezoidal method, Simpson's method or Gaussian integral method can be used. By choosing an appropriate integration step size and integration interval, the integral value in the exponential term can be approximately calculated. Once the integral value is obtained, the exponential term can be calculated.

[0065] 2. Processing internal features of the integral

[0066] In the exponential term and the subsequent integration process, there is a 2 (St ) and m(S t ) is processed. This part of the calculation is to obtain the dynamic characteristics of the vibration state change process. In particular, σ 2 (S t ) describes the rate of change of the variance of the vibration state with the vibration state, while m(S t ) directly represents the average rate of change of the vibration state.

[0067] These derivatives can be calculated analytically or numerically. For the analytical method, if σ 2 (S t ) and m(S t ) have clear analytical expressions, and we can directly differentiate them. For numerical methods, we can use difference methods or interpolation methods to approximate the derivatives.

[0068] 3. Calculate the definite integral limit and probability density

[0069] The next part of the analytical solution is a definite integral, whose integration limit is from S t To S f This integral includes the transition probability density function p(t, S t |S0) itself, and the processing of its derivative. This integral term is to calculate the current vibration state S t To the failure threshold S f The cumulative effect of probability density due to diffusion and drift.

[0070] The integral term is to solve the transition probability density function p(t, S t |S0) is the key part, which describes the transition from the current vibration state S t To the failure threshold S f The cumulative effect of the probability density of . This definite integral can be calculated by numerical integration. First, set the integration limit to t To S f , and select a suitable integration step. Then, select a series of discrete points in the integration interval and calculate the value of the integrand at each discrete point. Finally, according to the selected numerical integration method, these integrand values ​​are weighted and summed to obtain the approximate value of the definite integral. When calculating the integrand, it is necessary to consider the influence of weight factors, drift effects, diffusion effects, and cumulative effects. The weight factor is adjusted according to the variance of the current vibration state, reflecting the impact of the uncertainty of the change of the vibration state on the accumulation of probability density. The drift effect and diffusion effect describe the changes in probability density due to the average rate of change and uncertainty of the vibration state, respectively. The cumulative effect accumulates and amplifies or reduces the previous effects through exponential operations. The specific instructions are as follows:

[0071] (1) Setting weight factors

[0072] First, set a weight factor in front of the integral term This weight factor is based on the variance function σ of the current vibration state 2 (S t ) is adjusted to reflect the impact of the uncertainty of vibration state changes on the cumulative effect of probability density. The larger the variance, the higher the uncertainty, and the smaller the weight factor, and vice versa.

[0073] (2) Setting the drift and diffusion comprehensive effect model

[0074] The integral term contains two parts, representing the drift and diffusion effects of the vibration state change.

[0075] Drift effect: m(S t )·p(t,S t |S0) describes the average rate of change of the vibration state m(S t ) causes the probability density to change. When m(S t ) is positive, indicating that the vibration state tends to move to a higher value, which increases the probability density in the higher vibration state; conversely, when m(S t ) is negative, the probability density shifts toward lower vibrational states.

[0076] Diffusion effect: Describes the uncertainty due to the change of vibration state (i.e., variance σ 2 (S t )) caused by the probability density diffusion. This part takes into account the rate of change of the variance with the vibration state Impact on the state transition probability density. When the variance increases with the number of vibration states, the diffusion effect is enhanced, causing the state transition probability density to be distributed over a wider range of vibration states.

[0077] (3) Setting the exponential cumulative effect model

[0078] In the integral term, there is also an external exponential term, namely:

[0079]

[0080] It is an exponential operation on the internal integral result. This exponential term accumulates the weight factors and diffusion effects mentioned above, reflecting the transition from the initial state S0 to the current state S t The cumulative effect of the entire vibration process. This cumulative effect is amplified or reduced through exponential operations, further affecting the calculation of probability density.

[0081] (4) Setting the integration limit and the accumulation of probability density

[0082] Finally, set the entire integral term from S t Points to S f , indicating that from the current vibration state S t To the failure threshold S f The probability density accumulation. This accumulation process takes into account the influence of weight factors, drift effects, diffusion effects, and cumulative effects, and provides a method to accurately calculate the probability density from the current state to the failure state.

[0083] 4. Combined Probability Density

[0084] Finally, the exponential term, integral term and step length dS t Multiply them together to get the final transition probability density function p(t, S t |S0). This analytical solution comprehensively considers the influence of diffusion, drift and boundary conditions during the vibration state transfer process, and provides a method to accurately calculate the probability density of the system at any time and in any vibration state.

[0085] 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 calculation and insufficient precision. This embodiment proposes an intelligent improvement analysis method based on analytical solution. 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.

[0086] (1) Method for solving exponential terms

[0087] Assume that the random vibration variable S _t Transition from the initial vibration state S0 to the target vibration state S t , S t <S 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:

[0088] 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.

[0089] 2) Set the step size: Set the step size dSt , 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.

[0090] 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.

[0091] 4) Approximate integral:

[0092] 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 .

[0093] In each S _t At the point, calculate the variance function σ 2 (S _t ) and drift function m(S _t ) value.

[0094] 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).

[0095] Compute the integrand An approximate value of integrate1.

[0096] 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.

[0097] 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.

[0098] 6) Result output: The calculated exponential term return value, which 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.

[0099] (2) Method for solving the integral term

[0100] 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.

[0101] 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.

[0102] 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.

[0103] Next, perform an iterative solution. In each iteration, perform the following steps:

[0104] 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).

[0105] 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 .

[0106] 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.

[0107] 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.

[0108] 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.

[0109] 6) Repeat iteration: Repeat the above steps until the specified number of iterations num_iterations is reached.

[0110] 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.

[0111] At this time, the target vibration state S t The value of the transition probability density function p = exp(-integral_sum)·p_approx·dS t .

[0112] (3) Machine learning solution based on analytical solution

[0113] Combined with artificial intelligence technology, the analytical solution is intelligently processed to improve the accuracy and efficiency of the solution. This embodiment then achieves the intelligent improvement of the analytical solution in the following ways: First, the analytical solution is intelligently processed. The accuracy and efficiency of the solution are improved by training and optimizing the algorithm. Then, combined with experimental data and actual operation conditions, the analytical solution and the intelligent algorithm solution are verified to ensure their accuracy and reliability in practical applications.

[0114] After obtaining approximate solutions to the problem through analytical methods, these analytical solutions often contain complex integral terms that are difficult to calculate directly. This embodiment proposes a machine learning solution method based on analytical solutions, which aims to approximate these analytical solutions that are difficult to calculate directly through machine learning technology, and verify the accuracy of the machine learning model by comparing the machine learning solution with the analytical solution. The specific steps of this method are described as follows:

[0115] 1) Generate a dataset

[0116] In order to train the machine learning model, it is necessary to construct a dataset containing input features (such as time t, vibration state S corresponding to time t, etc.). t ) and the corresponding target vibration state S t The present embodiment uses the transition probability density function in the time range t_values ​​and the state range S t The dataset is generated by uniformly sampling the _values ​​and calculating the value of the analytical solution at each sample point. When generating the dataset, it is necessary to deal with boundary conditions and other factors that may affect the accuracy of the analytical solution.

[0117] 2) Training machine learning models

[0118] Next, the generated data set is used to train the machine learning model. This embodiment selects a neural network model with an appropriate hidden layer size and training parameters. By adjusting the parameters and training options of the model, the performance of the model is optimized and its ability to approximate the analytical solution is improved. During the training process, the training set is used to train the neural network, and the training effect of the model is evaluated by monitoring the performance indicators (such as mean square error) during the training process.

[0119] 3) Evaluate machine learning models

[0120] After training is completed, the performance of the machine learning model is evaluated. In the present invention, an independent test set is used to evaluate the accuracy of the model. By comparing the predicted value of the model with the approximate value of the analytical solution, performance indicators such as mean square error are calculated to evaluate the approximation ability and generalization ability of the model.

[0121] This embodiment takes the above theoretical analysis as the core and forms the following mechanical system health monitoring method considering the influence of random vibration. The flow chart of the method is as follows: Figure 1 As shown, the following steps are included:

[0122] 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.

[0123] In this embodiment, the mechanical system 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. Changes in vibration states can often reflect the health of the equipment. The probability density of vibration state transitions can monitor the vibration state of the equipment in real time, and by comparing the difference between the current state and the normal state, the fault diagnosis and health monitoring of the equipment can be achieved. This method helps to timely discover potential faults of equipment and avoid production accidents and losses caused by the expansion of faults. Among them, the failure threshold of the vibration state refers to the threshold of the vibration state that causes the failure of the mechanical system. 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 it is used as the failure threshold of the vibration state.

[0124] Step S2: Obtain an analytical solution of the transition probability density function of the vibration state based on the experimental data, and obtain the value of the transition probability density function corresponding to each experimental time and its vibration state, which is used 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 transition probability density function of the vibration state.

[0125] Step S3: During the actual operation of the mechanical system, the predicted time and its vibration state are input into the tested neural network model, and the neural network model predicts and outputs the predicted value of the transfer probability density function corresponding to the vibration state of the predicted time; and based on the predicted value of the transfer probability density function, the health status of the mechanical system at the predicted time and its vibration state is monitored.

[0126] During the experiment 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.

[0127] When a mechanical system is subjected to random vibration, its initial vibration state will be affected by many factors, including but not limited to:

[0128] Initial conditions: the system's initial position, velocity, acceleration and other state quantities.

[0129] External excitation: Characteristics of the random vibration source, such as frequency, amplitude and duration of vibration.

[0130] System parameters: These include the mass and stiffness of the system, which affect the system's response to vibration.

[0131] Damping: Energy dissipation mechanisms in a system, such as friction and air resistance, which affect the rate at which vibrations decay.

[0132] 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.

[0133] 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.

[0134] Environmental factors: Environmental conditions such as temperature and humidity, which may change material properties and thus affect the vibration response.

[0135] Randomness: Since random vibrations are inherently uncertain, the vibration response of the system may vary due to randomness even under the same initial conditions.

[0136] Initial stress state: The initial stress or strain state that may exist in the system, which affects the system's response to vibration.

[0137] Boundary conditions: The support conditions and boundary constraints of the system, which determine how the vibration energy propagates.

[0138] 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.

[0139] 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:

[0140] Fluctuation amplitude: The difference between the maximum and minimum values ​​of the vibration state, reflecting the intensity of the vibration.

[0141] Fluctuation frequency: the speed of change of vibration state, that is, the number of times the vibration state changes per unit time.

[0142] Wave cycle: the time required to complete a complete wave.

[0143] Fluctuation phase: In periodic vibration, the phase of the vibration state at a specific point in time.

[0144] Randomness of fluctuations: Due to the influence of random vibrations, changes in vibration states may present unpredictable random fluctuations.

[0145] Nonlinearity of fluctuations: If the system response exhibits nonlinear characteristics, the changes in the vibration state may not follow a simple linear law.

[0146] Energy distribution of vibration: The distribution of energy in a vibration state at different frequencies can usually be described by the power spectral density.

[0147] Coherence of fluctuations: the consistency or stability of a vibrational state over time.

[0148] Autocorrelation of fluctuations: how similar the vibrational states are at different points in time.

[0149] Cross-correlation of fluctuations: correlation between vibration states in different degrees of freedom or in different directions.

[0150] To quantify the degree of fluctuation of the vibration state over time, the following methods can be used:

[0151] Time history analysis: Analyze the fluctuation characteristics by recording the changes of vibration state over time.

[0152] 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.

[0153] Power Spectrum Analysis: Calculate the power spectrum density of the vibration state to understand the energy distribution of different frequency components.

[0154] Autocorrelation and cross-correlation analysis: Analyze the similarity or correlation of vibration states at different time points or in different directions.

[0155] Statistical analysis: Use statistical methods, such as variance, standard deviation, mean, etc., to quantify the degree of fluctuation in vibration conditions.

[0156] Based on the above related description, the analytical solution of the transition probability density function of the vibration state is composed of the product of the exponential term, the integral term and the differential term, see formula (2). Based on this, the specific execution process of step S2 is described in detail as follows.

[0157] 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.

[0158] 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 tDetermine the experimental time between 0 and t; start from the initial vibration state S0 and step 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 <S f , S f is the failure threshold of the vibration state; the initial value of the initialization cumulative item integral_sum is 0;

[0159] 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;

[0160] 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.

[0161] 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.

[0162] 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.

[0163] Step S222: Perform iterative solution. In each round of iteration:

[0164] Create a p_new vector of the same size as S_vec and set the first element to 0;

[0165] 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;

[0166] From S _t To S f The value of integrand2 is accumulated into the p_new vector S _t The corresponding position;

[0167] 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;

[0168] 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.

[0169] 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.

[0170] 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 .

[0171] By executing the operation in step S2, the values ​​of the transition probability density functions corresponding to multiple experimental times and their vibration states can be obtained. tAs input, the corresponding transfer probability density function value p is used as output as a set of sample data to construct a sample set; 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, and a neural network model for real-time solution of the transfer probability density function of the vibration state is obtained.

[0172] 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 in the experimental process of step S1, considering the experimental cost and experimental difficulty, the number of experiments that can be performed is relatively limited. Therefore, this embodiment obtains the experimental time t, vibration state S t The correlation between the input and the value p of the corresponding transfer probability density function is simulated by a neural network, and then the value of the transfer probability density function of any predicted time and its vibration state before the failure of the mechanical system can be predicted. Therefore, in step S3, the value of the corresponding transfer probability density function can be predicted based on the predicted time and its vibration state, that is, during the actual operation of the mechanical system, the predicted time and its vibration state are input into the neural network model that has passed the test, and the neural network model predicts the predicted value of the transfer probability density function corresponding to the vibration state of the output predicted time.

[0173] At the same time, since the predicted value of the transfer probability density function can characterize the conversion probability of the mechanical system under the vibration state at the corresponding prediction time, the health status of the mechanical system under the prediction time and its vibration state can be monitored accordingly. The specific process is described as follows:

[0174] Determine whether the predicted value of the transfer probability density function corresponding to the vibration state at the predicted time is greater than the health monitoring threshold. If so, it indicates that the health status of the mechanical system at the predicted time and its vibration state is good; if not, it indicates that the health status of the mechanical system at the predicted time and its vibration state is poor, triggering a mechanical system health monitoring warning.

[0175] In summary, the mechanical system health monitoring method considering the influence of 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 analytical solution of the transition probability density function of the vibration state, and constructs a sample set based on this, and trains and tests the neural network model for solving the transition probability density function of the vibration state in real time, and fits the intrinsic correlation between each time and its vibration state and the transition probability density function. Therefore, the neural network model that passes the test can quickly and accurately predict the value of the transition probability density function of any time and its vibration state before the system fails. Finally, the health status of the mechanical system at the corresponding predicted time and its vibration state can be monitored according to the predicted value of the transfer probability density function. 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 health monitoring methods in the prior art.

[0176] 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, which lays a data foundation for the subsequent data acquisition of the sample set. 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.

[0177] In addition, based on accurate prediction results, this embodiment can provide scientific decision support for the health monitoring 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.

[0178] 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.

[0179] 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 monitoring the health of a mechanical system considering the influence of random vibration, 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; Obtain an analytical solution of the transition probability density function of the vibration state according to the experimental data, obtain the value of the transition probability density function corresponding to each experimental time and its vibration state, and use it 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 transition probability density function of the vibration state; During the actual operation of the mechanical system, the predicted time and its vibration state are input into the tested neural network model, and the neural network model predicts and outputs the predicted value of the transfer probability density function corresponding to the vibration state at the predicted time; and based on the predicted value of the transfer probability density function, the health status of the mechanical system at the predicted time and its vibration state is monitored.

2. The method for monitoring the health of a mechanical system considering the influence of random vibration according to claim 1, characterized in that: The transition probability density function of the vibration state p(t,S t The analytical solution of |S0) is expressed as: Among them, S0 represents the initial state of vibration, S t represents the transition from the initial vibration state S0 to 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.

3. The method for monitoring the health of a mechanical system considering the influence of random vibration according to claim 2, characterized in that: The values ​​of the transfer probability density function corresponding to each experimental time and its vibration state are obtained by executing: 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.

4. The method for monitoring the health of a mechanical system considering the influence of random vibration according to claim 3, characterized in that: In formula (1), As an index term, As an integral term, d S t as a differential term.

5. The method for monitoring the health of a mechanical system considering the influence of random vibration according to claim 4, 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.

6. The method for monitoring the health of a mechanical system considering the influence of random vibration according to claim 5, 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.

7. The method for monitoring the health of a mechanical system considering the influence of random vibration according to claim 6, 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 .

8. The method for monitoring the health of a mechanical system considering the influence of random vibration according to claim 7, characterized in that: To construct the sample set, execute: The experimental time t, vibration state S t Taking as input and the value p of the corresponding transition probability density function 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.

9. The method for monitoring the health of a mechanical system considering the influence of random vibration according to claim 8, characterized in that: The sample set is used to train and test a neural network model for solving the transition probability density function of the vibration state in real time, and the following is performed: 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 solution of the transfer probability density function of the vibration state.

10. The method for monitoring the health of a mechanical system considering the influence of random vibration according to claim 9, characterized in that: The monitoring of the health status of the mechanical system at the predicted time and its vibration state is performed by: Determine whether the predicted value of the transfer probability density function corresponding to the vibration state at the predicted time is greater than the health monitoring threshold. If so, it indicates that the health status of the mechanical system at the predicted time and its vibration state is good; if not, it indicates that the health status of the mechanical system at the predicted time and its vibration state is poor, triggering a mechanical system health monitoring warning.

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