Failure early warning method of mechanical system under random vibration influence

Abstract

The invention discloses a failure early warning method for a mechanical system under the influence of random vibration, belongs to the technical field of mechanical system early warning and evaluation, and solves the problems of low speed and low precision of an existing failure early warning method for the mechanical system under the influence of random vibration. The method comprises the following steps: acquiring vibration state data according to a random vibration process of a mechanical system; solving a numerical solution of a transition probability density function of a vibration state based on the vibration state data to construct a sample set; training and testing by using the sample set to obtain a neural network model; obtaining the vibration state of the mechanical system uniformly sampled at each sampling time under the influence of random vibration, respectively inputting each sampling time and the vibration state thereof into the neural network model passing the test, and predicting and outputting the value of the transition probability density function corresponding to the vibration state of each sampling time, and drawing a distribution diagram of the transition probability density function, thereby realizing failure early warning under the influence of random vibration.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical system early warning assessment, and in particular to a failure early warning method for a mechanical system under the influence of random vibration. Background Art

[0002] In the fields of mechanical engineering, civil engineering, and transportation engineering, random vibration has always been a hot topic of research and application. In these fields, random vibration is a ubiquitous phenomenon, and when the random vibration of the mechanical structure exceeds the tolerance of the system itself, the system will face the risk of failure. Failure will not only lead to the loss of system function, but may also cause serious economic losses and safety hazards. Therefore, in practical applications, accurate prediction and evaluation of random vibration status is of great significance to ensure the "effective working" state of the system, achieve failure warning, and extend the service life of the system. How to accurately predict and evaluate the random vibration state to ensure that the system can operate in the "effective working" state and extend its service life has become an urgent problem to be solved.

[0003] With the continuous advancement of science and technology and the deepening of engineering practice, the demand for accurate prediction and evaluation of random vibration states is increasing. Early research mainly focused on describing random vibration phenomena by establishing simple mathematical models and empirical formulas. However, these methods often fail to accurately reflect the vibration characteristics of complex systems, and the prediction results are limited in accuracy, which limits their application in engineering practice.

[0004] Therefore, how to quickly and accurately predict and evaluate the vibration state and provide failure warning based on it is a technical problem that urgently needs to be solved. Summary of the invention

[0005] In view of the above analysis, an embodiment of the present invention aims to provide a failure warning method for a mechanical system under the influence of random vibration, so as to solve the problems of slow speed and low accuracy in the existing failure warning method for a mechanical system under the influence of random vibration.

[0006] The present invention discloses a failure warning method for a mechanical system under the influence of random vibration, the method comprising:

[0007] According to the random vibration process to which the mechanical system is subjected, vibration state data is obtained; the vibration state data includes an initial vibration state, a failure threshold of the vibration state, a drift function and a variance function of the vibration state;

[0008] Obtaining a numerical solution of a transition probability density function of a vibration state based on the vibration state data; and constructing a sample set for training a neural network model based on the numerical solution of the transition probability density function; and using the sample set to train and test a neural network model for real-time solution of the transition probability density function of the vibration state;

[0009] Obtaining the vibration state of each sampling time of the mechanical system uniformly sampled under the influence of random vibration, and inputting each sampling time and its vibration state into the neural network model that has passed the test, respectively, and the neural network model predicts and outputs the value of the transition probability density function corresponding to the vibration state at each sampling time, so as to draw a distribution diagram of the transition probability density function;

[0010] According to the distribution diagram of the transfer probability density function, failure warning under the influence of random vibration is achieved.

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

[0012] Further, the distribution diagram of the transition probability density function is drawn by executing:

[0013] The values ​​of the transfer probability density function corresponding to the vibration state at all sampling times are processed for non-negativity and normalization, so as to obtain the normalized value of the transfer probability density function corresponding to the vibration state at each sampling time;

[0014] A distribution diagram of the transition probability density function is drawn with the vibration state at each sampling time as the abscissa and the normalized value of the corresponding transition probability density function as the ordinate.

[0015] Further, according to the distribution diagram of the transfer probability density function, failure warning under the influence of random vibration is realized; executing:

[0016] Formulate a random vibration failure risk level according to a distribution diagram of the transfer probability density function;

[0017] Based on the random vibration failure risk level, failure warning under the influence of random vibration is achieved.

[0018] Further, according to the distribution diagram of the transfer probability density function, a random vibration failure risk level is formulated, and the following is performed:

[0019] The value of the vertical coordinate of the failure threshold of the vibration state in the distribution diagram of the transfer probability density function is represented as p f , and the maximum value of the ordinate in the distribution graph is represented by p max ; Set the high risk threshold margin th h , low risk threshold margin th l ;

[0020] The vertical coordinate range of the distribution diagram of the transition probability density function is [0, p f +th h ] indicates a high risk level of failure;

[0021] The vertical coordinate range of the distribution diagram of the transition probability density function is (p f +th h ,p max -th l The failure risk level of the vibration state range indicated by the horizontal axis between ] is medium risk;

[0022] The vertical coordinate range of the distribution diagram of the transition probability density function is (p max -th l ,p max ] The failure risk level of the vibration state range indicated by the horizontal axis is low risk.

[0023] Further, based on the random vibration failure risk level, failure warning under the influence of random vibration is realized by executing:

[0024] During the random vibration process of the mechanical system, the vibration state at the time to be predicted is compared with the vibration state range of each level of random vibration failure risk formulated by the failure risk level of the vibration state, and the failure risk level of the mechanical system at the warning time is determined;

[0025] If the failure risk level of the mechanical system at the warning time is high risk, a failure warning of the vibration state at the time to be predicted is performed in advance.

[0026] Further, a numerical solution of a transition probability density function of a vibration state is obtained based on the vibration state data, and the following is performed:

[0027] Parameter initialization: Get the initial vibration state S0 and the failure threshold S of the vibration state f ; Set the time step dt and vibration state step dS t , time steps Nt and state steps NS t ; Starting from the initial vibration state S0, with a state step length dS t As an increment, gradually increase the vibration state S _t until the failure threshold S of the vibration state is reached or exceeded. f , and obtain the vibration state S _t The corresponding drift function m(S _t ) and the variance function σ 2 (S _t ); create a size of (Nt+1)×(NS t+2) is used to store the numerical solution of the transition probability density function; and the relevant elements of the zero matrix p are initialized according to the boundary conditions;

[0028] The numerical method is used to discretize the partial differential equation of the change of the transition probability density of the vibration state, and the partial differential equation is transformed into a series of linear equations, each of which is a discretized difference equation.

[0029] On the basis of initializing the relevant elements of the zero matrix p according to the boundary conditions, for the other elements in the matrix p, at each time point t and vibration state point S_ t , calculate the transition probability density value of the vibration state at the next time point t+1 according to the discretized difference equation;

[0030] By continuously iteratively updating the element values ​​in the matrix p, the numerical solution of the transfer probability density function of all time points and vibration state points is finally obtained, and the iterative update is terminated.

[0031] Further, the partial differential equation for the change of the transition probability density of the vibration state is expressed as:

[0032]

[0033] 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, p(t, S t |S0) represents the transition probability density function of the vibration state; m(S t ) is the vibration state S t The drift function of the drift, σ 2 (S t ) represents the vibration state S t The variance function of .

[0034] Furthermore, in the calculation process according to the discretized difference equation, the time partial derivative is approximated by forward difference Approximating spatial partial derivatives using central differences and And update the corresponding element values ​​in the transfer probability density matrix p according to the difference equation.

[0035] Further, the related elements of the zero matrix p are initialized according to the boundary conditions, and the following is performed:

[0036] According to the boundary conditions p(t,S f |S0)=0, set the last column of matrix p to 0.

[0037] According to the initial condition p(t,S _t |S0)=delta(S _t-S0), set the element corresponding to position S0 in the first row of matrix p to 1.

[0038] Further, based on the numerical solution of the transition probability density function, a sample set for neural network model training is constructed, and the following steps are performed:

[0039] After the iterative update, the matrix p is processed non-negatively and normalized in turn to obtain the normalized matrix p1. The last column of the normalized matrix p1 is cut off to obtain the standardized matrix p2.

[0040] The time point t and vibration state point S corresponding to each element in the standardized matrix p2 _t A sample set for training the neural network model is constructed by taking the element values ​​of the corresponding elements in the standardized matrix p2 as input and the element values ​​of the corresponding elements in the standardized matrix p2 as output as a set of sample data.

[0041] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0042] The failure warning method of the mechanical system under the influence of random vibration proposed by the present invention uses the random vibration process to which the mechanical system is subjected to obtain vibration state data, and solves the numerical solution of the transfer probability density function of the vibration state based on this data, so as to construct a sample set, train and test the neural network model for solving the transfer probability density function of the vibration state in real time, and fit 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, and draw a distribution diagram of the transfer probability density function based on this, so as to indicate the corresponding relationship between different vibration states and their transfer probability density functions. At this point, different random vibration failure risk levels can be formulated according to the distribution diagram, and whether failure warning is needed can be judged according to the random vibration failure risk level of the vibration state at the time to be predicted. After the random vibration failure risk level is formulated, its failure risk can be directly determined according to the vibration state at the time to be predicted, thereby simplifying the judgment process of failure risk. Moreover, the present invention can effectively ensure the accuracy of the distribution map and the vibration failure risk level by executing the numerical solution and the fitting of the neural network model, thereby ensuring the accuracy of the failure risk prediction, and ultimately achieving fast and high-precision failure warning, effectively solving the problem of the lack of efficient and high-precision mechanical system health monitoring methods in the prior art.

[0043] In the specific implementation process, the present invention creatively proposes a solution method for the probability density equation of the time-evolving vibration state based on the intelligent numerical solution. The model describes the transition process of the vibration state from the initial state to any state over time by introducing the transition probability density function, thereby realizing efficient and accurate prediction and evaluation of the random vibration state. At the same time, when solving the probability density equation of the time-evolving vibration state, the present invention adopts an efficient numerical solution method, which combines specific boundary conditions and initial conditions on the basis of the traditional numerical solution method, and obtains the numerical solution of the probability density of the vibration state transition through iterative calculation. This method not only improves the accuracy of the solution, but also reduces the computational complexity, making large-scale calculations possible.

[0044] The present invention also combines the results of numerical solutions with artificial intelligence methods to further improve the accuracy of the solutions through intelligent analysis. This method combined with artificial intelligence can make full use of the advantages of machine learning to further optimize and correct the numerical solutions, thereby improving the accuracy of prediction and evaluation.

[0045] 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

[0046] 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;

[0047] Figure 1 The present invention provides a flowchart of a failure warning method for a mechanical system under the influence of random vibration. DETAILED DESCRIPTION

[0048] 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.

[0049] A specific embodiment of the present invention discloses a failure warning method for a mechanical system under the influence of random vibration. First, the theoretical analysis based on this embodiment is described as follows.

[0050] In the fields of mechanical engineering, civil engineering, and transportation engineering, random vibration has always been the focus of research and application. When the random vibration of the mechanical structure exceeds the tolerance of the system itself, the system will face the risk of failure. Therefore, accurate prediction and evaluation of random vibration state is of great significance to ensure the "effective working" state of the system and extend the service life of the system.

[0051] This embodiment aims to provide a failure warning method for a mechanical system under the influence of random vibration. The method establishes an accurate mathematical model and compares the numerical solution results with the artificial intelligence solution method to achieve efficient and accurate prediction and evaluation of the random vibration state, and performs subsequent warning operations based on the prediction results.

[0052] In order to solve the random vibration problem, this embodiment firstly establishes a transition probability density function model to describe the evolution of vibration state over time. t As a random process, the vibration characteristics are characterized, and its initial vibration state is set as S0. t Reaching or exceeding the threshold that causes system failure (i.e., the failure threshold of the vibration state) S f The system enters a failed state.

[0053] In order to describe the initial state of vibration from S0 to the vibration state S at time t t The transfer process, this embodiment introduces the transfer probability density function p(t,S t |S0), and establish the following partial differential equation for the change of the transition probability density of the vibration state:

[0054]

[0055] Among them, m(S t ) is the vibration state S t The drift term is expressed as a 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 ) represents the vibration state S t The diffusion term is expressed as a 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 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 The boundary condition of the equation in formula (1) is p(t,S f|S0)=0, indicating that when the vibration state reaches the failure threshold S f When , the transition probability density function is zero.

[0056] (1) Numerical solution method

[0057] When solving the partial differential equation of the change of the probability density of the transition of the vibration state that evolves over time, this embodiment uses an efficient numerical solution to process the equation. This method is mainly based on the finite difference method, and combined with specific boundary conditions and initial conditions, the numerical solution of the probability density of the transition of the vibration state is obtained through iterative calculation. The solution steps are as follows:

[0058] 1) Parameter setting and initialization

[0059] First, set the initial vibration state S0 and the failure threshold of the vibration state S f , time step dt and vibration state step dS t , time steps Nt and state steps NS t .

[0060] Starting from the initial vibration state S0, the state step length dS t As an increment, gradually increase the vibration state S _t until the failure threshold S of the vibration state is reached or exceeded. f , and gives the drift term m(S _t ) and the diffusion term σ 2 (S _t ) in functional form.

[0061] 2) Initialization of state transition probability density matrix

[0062] Create a (Nt+1)×(NS t +2) is used to store the numerical solution of the transition probability density function. One more column is added to accommodate S t =0.

[0063] According to the boundary conditions p(t,S f |S0)=0, set the last column of matrix p to 0.

[0064] According to the initial condition p(t,S _t |S0)=delta(S _t -S0), set the element corresponding to position S0 in the first row of matrix p to 1.

[0065] (2) Numerical solution

[0066] The numerical method is used to discretize the partial differential equation of the transition probability density change of the vibration state, and the partial differential equation is transformed into a series of linear equations, each of which is a discretized difference equation. Through two layers of loops traversing the time and state space, the element values ​​in the state transition probability density matrix p are updated according to the discretized difference equation.

[0067] For each time point t and vibration state point S_ t , according to the discretized difference equation, the transition probability density value of the vibration state at the next time point t+1 is calculated. In the calculation process, the state points near the boundary conditions and initial conditions need to be specially processed.

[0068] For the first vibration state point (S_ t =1), since there is no S_ t -1 state, special processing is required. For other vibration state points (S_ t >1), the standard finite difference scheme is used for the calculation.

[0069] By continuously iteratively updating the element values ​​in the matrix p, the numerical solution of the transfer probability density function of all time points and vibration state points is finally obtained.

[0070] (3) Specific forms of treatment for drift and diffusion terms

[0071] In the process of numerically solving the partial differential equation of the change of the transition probability density of the vibration state evolving over time, the calculation of the drift term and the diffusion term is involved. These terms may have various forms, and the difference in their forms is closely related to the calculation and processing method of the transition probability density. In view of the different forms that the drift term and the diffusion term may have, this embodiment proposes a strategy for handling different situations. This strategy can ensure the accuracy and stability of the calculation results, making the model more flexible and effective in handling various complex random vibration problems. Specifically, this embodiment adopts the following strategies according to different situations:

[0072] 1) Directly calculate the drift and diffusion terms

[0073] For the drift term m(S _t ) and the diffusion term σ 2 (S _t ), this embodiment performs direct calculation according to its specific function form. _t ) and σ 2 (S _t ) is a linear function, a polynomial function or other function that can be expressed analytically, and the corresponding mathematical formula is used to directly calculate its value at each vibration state point S _t This can avoid introducing additional numerical errors and ensure the accuracy of the calculation process.

[0074] 2) Basic mathematical operations to process exponential terms

[0075] In the iterative calculation of the difference equation, if the function involves the operation of the exponential term, it is converted into basic mathematical operations, such as multiplication, division, and addition and subtraction. Specifically, when processing expressions related to the exponential term, the present embodiment converts it into a form that is easier to calculate and process. For example, by Taylor series expansion or other mathematical approximation methods, the complex exponential function is simplified into a polynomial or other function form that is easy to calculate. This method not only improves the calculation efficiency, but also reduces the numerical errors that may be introduced by directly calculating the exponential term.

[0076] 3) Avoid numerical overflow or underflow

[0077] Exponential operations may cause numerical overflow (the calculation result exceeds the maximum range that the computer can represent) or underflow (the calculation result is close to zero, resulting in loss of precision) in some extreme cases. To avoid these problems, this embodiment performs appropriate scaling and translation processing on the exponential term during the calculation process. Specifically:

[0078] Scaling: When the value of the exponential term is too large, its absolute value is reduced by dividing it by an appropriate scaling factor to avoid overflow. At the same time, this scaling factor is recorded so that corresponding adjustments can be made in subsequent calculations to ensure the correctness of the final result.

[0079] Translation processing: To avoid underflow problems, when the value of the exponential term is too small (close to negative infinity), it can be translated as a whole to a more appropriate value range. This translation does not change the relative size relationship between the exponential terms, so it will not affect the final calculation result.

[0080] (4) Numerical solution methods for machine learning training data

[0081] Next, this embodiment provides a numerical solution method for machine learning training data, which includes the following steps:

[0082] 1) Initialization step: According to the actual situation of the problem (the process of the mechanical system being affected by random vibration), determine the time step dt and state step dS t , the number of time grid points N_t, the number of state grid points N_S, and initialize the transition probability density matrix p to a zero matrix with a size of (Nt+1)×(NS t +2).

[0083] 2) Initial condition setting: According to the initial conditions of the problem, set the probability distribution at the initial moment and set the initial vibration state S0.

[0084] 3) Discretization function: For the function m(S _t ) and σ 2 (S _t ) is discretized to obtain the drift function value m_S and diffusion function value sigma_sq_S corresponding to each time grid point and state grid point.

[0085] 4) Finite difference iteration: For each time step dt, the transition probability density matrix p is updated using the finite difference method. First, the transition probability density value of the boundary point is set to 0 according to the boundary conditions. Then, the time partial derivative is approximated using forward differences. Approximating spatial partial derivatives using central differences and And update each element in the transfer probability density matrix p according to the difference equation.

[0086] 5) Non-negativity and normalization processing (optional): In order to ensure the non-negativity and optional normalization requirements of the transition probability, the updated transition probability density matrix p is non-negative and normalized.

[0087] The numerical solution method in this embodiment can be applied as training data for solving partial differential equations using machine learning. The following is an analysis of the relevant features of the method:

[0088] 1) Data generation and representation: This method generates a series of numerical solutions at discrete points, which can be used as training data for machine learning models. Especially when it is necessary to approximate the solution of a partial differential equation or make a prediction, higher accuracy and resolution of the numerical solution (determined by N_t and N_S) will provide better results for the training of the machine learning model.

[0089] 2) Data integrity and quality: Appropriate treatment of boundary conditions ensures the integrity and accuracy of the numerical solution; in the iterative process, and The difference approximation of t+1 and the update of p(t+1,j) ensure the continuity and smoothness of the numerical solution. These features are helpful in generating high-quality training data and improving the performance of machine learning models.

[0090] 3) Iteration in combination with machine learning: This numerical solution can be used as the input and output data of the neural network to train the network to approximate the solution operator of the partial differential equation. The neural network can master the dynamic characteristics of the differential equation by learning these numerical solutions, thereby realizing the prediction and inference of unknown situations.

[0091] 4) Applicability and scalability: This method is applicable to various types of partial differential equations and boundary conditions, and has strong versatility and flexibility. When the parameters or initial conditions of the partial differential equations change, this method can generate new training data by simply adjusting N_t, N_S and other related parameters without rewriting or modifying the code. This scalability makes Method 2 a powerful tool for machine learning to solve differential equations.

[0092] (5) Machine learning solution method based on numerical solution

[0093] This embodiment provides a machine learning solution method based on numerical solutions. The method uses pre-generated numerical solutions as initial values ​​and training data, approximates the solution of the objective function or equation through a machine learning model, and evaluates and optimizes the machine learning model by comparing the numerical solution and the results of the machine learning solution.

[0094] Specifically, the machine learning solution method based on numerical solution in this embodiment includes the following steps:

[0095] 1) Prepare training data: First, the numerical solution calculated based on the above numerical solution method includes the numerical sequence t_span of independent variables (such as time, spatial coordinates, etc.) and the numerical sequence of corresponding dependent variables (such as physical quantities, function values, etc.). In order to avoid potential boundary effects, the last point in the numerical sequence is removed to obtain the independent variable sequence t_train and the corresponding dependent variable sequence in the training data set.

[0096] 2) Design the neural network structure: Next, design a suitable neural network model to approximate the numerical solution. Use a neural network with several hidden layers, and specify the size of the hidden layer through the parameter hidden_layer_size. The size of the hidden layer can be adjusted according to the complexity of the specific problem and the size of the training data.

[0097] 3) Configure neural network training parameters: Configure relevant training parameters before neural network training. In this method, the Levenberg-Marquardt algorithm is selected as the training function. This algorithm is an efficient optimization algorithm, which is particularly suitable for medium-sized neural network training. In addition, the ratios of training set, validation set and test set are set to 70%, 15% and 15% respectively to ensure that the neural network can fully learn the data features during the training process and has good generalization ability.

[0098] 4) Training the neural network: Use the configured training parameters and training data set to train the neural network. By continuously iteratively optimizing the weights and bias parameters of the neural network, the neural network can approach the numerical solution.

[0099] 5) Prediction and evaluation: After training is completed, the trained neural network model is used to predict the new input data to obtain the result of the machine learning solution. In the present invention, we use the independent variable sequence in t_span (removing the last point) as input data and obtain the corresponding predicted value through the neural network model. Then the predicted value is compared with the original numerical solution, and the prediction error or other evaluation indicators are calculated to evaluate the performance of the machine learning model.

[0100] 6) Model optimization and iteration: Based on the evaluation results, the neural network model can be optimized and adjusted. For example, you can try to change the structure of the neural network (such as increasing the number of hidden layers, changing the activation function, etc.), adjust the training parameters (such as learning rate, number of iterations, etc.), or use more advanced training algorithms and techniques to further improve the performance of the model. Through continuous iteration and optimization, a more accurate and efficient machine learning solution model can be obtained.

[0101] This embodiment takes the above theoretical analysis as the core and forms the following failure warning method of the mechanical system under the influence of random vibration. The flow chart of the method is as follows: Figure 1 As shown, the following steps are included:

[0102] Step S1: Acquire vibration state data according to the random vibration process to which the mechanical system is subjected; the vibration state data includes an initial vibration state, a failure threshold of the vibration state, a drift function and a variance function of the vibration state.

[0103] Step S2: based on the vibration state data, obtain a numerical solution of the transition probability density function of the vibration state; and based on the numerical solution of the transition probability density function, construct a sample set for training a neural network model; and use the sample set to train and test a neural network model for real-time solution of the transition probability density function of the vibration state.

[0104] Step S3: Obtain the vibration state of each sampling time of the mechanical system uniformly sampled under the influence of random vibration, and input each sampling time and its vibration state into the tested neural network model respectively, and use the neural network model to predict and output the value of the transfer probability density function corresponding to the vibration state of each sampling time, so as to draw a distribution diagram of the transfer probability density function.

[0105] Step S4: formulating a random vibration failure risk level according to the distribution diagram of the transfer probability density function; and implementing failure warning under the influence of random vibration based on the random vibration failure risk level.

[0106] 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.

[0107] In the above step S1, vibration state data can be obtained according to the random vibration process to which the mechanical system is subjected. It should be noted that the method for obtaining the vibration state data is not the focus of this embodiment. The focus of this embodiment is to use the vibration state data to solve the data value of the transfer probability density function, establish a correlation between the two, and fit this relationship through a neural network, and finally achieve a fast and high-precision solution of the transfer probability density function under different vibration states. Below, the method for obtaining the vibration state data is briefly introduced as follows.

[0108] When a mechanical system is subjected to random vibration, its initial vibration state will be affected by many factors, including but not limited to: initial conditions, external excitation, system parameters, damping, nonlinear factors, multi-degree-of-freedom effects, environmental factors, randomness, initial stress state, boundary conditions, etc.

[0109] The drift function of the vibration state, that is, the average rate at which the vibration state changes over time, usually refers to a measure of how the vibration state of the system (such as displacement, velocity or acceleration) changes 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.

[0110] The variance function of the vibration state, that is, 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: fluctuation amplitude, fluctuation frequency, fluctuation period, fluctuation phase, randomness of fluctuation, nonlinearity of fluctuation, energy distribution of fluctuation, coherence of fluctuation, autocorrelation of fluctuation and cross-correlation of fluctuation. To quantify the degree of fluctuation of the vibration state over time, the time history analysis method can be used to analyze its fluctuation characteristics by recording the changes of the vibration state over time.

[0111] Next, based on the above related descriptions, the specific execution process of step S2 is described in detail as follows.

[0112] Step S21: Parameter initialization: Obtain the initial vibration state S0 and the failure threshold value S of the vibration state f ; Set the time step dt and vibration state step dS t , time steps Nt and state steps NS t ; Starting from the initial vibration state S0, with a state step length dS t As an increment, gradually increase the vibration state S _t until the failure threshold S of the vibration state is reached or exceeded. f , and obtain the vibration state S _t The corresponding drift function m(S _t ) and the variance function σ 2 (S _t ); create a size of (Nt+1)×(NS t +2) is used to store the numerical solution of the transition probability density function; and the relevant elements of the zero matrix p are initialized according to the boundary conditions.

[0113] Specifically, in this embodiment, the relevant elements of the zero matrix p are initialized according to the boundary conditions, and the following is performed:

[0114] According to the boundary conditions p(t,S f |S0)=0, set the last column of matrix p to 0.

[0115] According to the initial condition p(t,S _t |S0)=delta(S _t -S0), set the element corresponding to position S0 in the first row of matrix p to 1.

[0116] Step S22: using a numerical method to discretize the partial differential equation of the change of the transition probability density of the vibration state, and converting the partial differential equation into a series of linear equations, each of which is a discretized difference equation.

[0117] Step S23: Based on the initialization of the relevant elements of the zero matrix p according to the boundary conditions, for other elements in the matrix p, at each time point t and vibration state point S_ t , the transition probability density value of the vibration state at the next time point t+1 is calculated according to the discretized difference equation. By continuously iteratively updating the element values ​​in the matrix p, the numerical solution of the transition probability density function of all time points and vibration state points is finally obtained, and the iterative update ends.

[0118] In the calculation process based on the discretized difference equation, the time partial derivative is approximated by forward difference Approximating spatial partial derivatives using central differences and And update the corresponding element values ​​in the transfer probability density matrix p according to the difference equation.

[0119] Step S24: After the iterative update, the matrix p is subjected to non-negativity and normalization processing in turn to obtain a normalized matrix p1, and the last column of the normalized matrix p1 is trimmed to obtain a standardized matrix p2.

[0120] Step S25: standardize the time point t and the vibration state point S corresponding to each element in the matrix p2 _t As input, the element value of the corresponding element in the standardized matrix p2 is used as output as a set of sample data to construct a sample set for training the neural network model; 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 transition probability density function of the vibration state is obtained.

[0121] After that, the neural network model can be used to predict the value of the transfer probability density function of any time and its vibration state before the failure of the mechanical system. It should be noted that, since the transfer probability density function is in the form of a function, and a single time and its vibration state can only predict a point at the corresponding position in the transfer probability density function. At the same time, the solution process of the numerical solution in step S2 is relatively cumbersome, and the selected time step and state step are relatively large. Therefore, in step S3, it is necessary to use the neural network model to predict the value of the transfer probability density function corresponding to the vibration state of each sampling time (dense sampling can be performed) of uniform sampling. At this time, the value of the transfer probability density function corresponding to the vibration state of all sampling times is non-negative and normalized, and the normalized value of the transfer probability density function corresponding to the vibration state of each sampling time is obtained, and a distribution diagram of the transfer probability density function is drawn with the vibration state of each sampling time as the horizontal coordinate and the normalized value of the corresponding transfer probability density function as the vertical coordinate.

[0122] In step S4 of this embodiment, a specific implementation method for formulating the random vibration failure risk level according to the distribution diagram of the transfer probability density function is given: the value of the vertical coordinate of the failure threshold of the vibration state in the distribution diagram of the transfer probability density function is represented as p f , and the maximum value of the ordinate in the distribution graph is represented by p max , set the high risk threshold margin th h , low risk threshold margin th l ; At this time, the random vibration failure risk level is formulated as follows:

[0123] The vertical coordinate range of the distribution diagram of the transition probability density function is [0, p f +th h ] indicates a high risk level of failure;

[0124] The vertical coordinate range of the distribution diagram of the transition probability density function is (p f +th h ,p max -th l The failure risk level of the vibration state range indicated by the horizontal axis between ] is medium risk;

[0125] The vertical coordinate range of the distribution diagram of the transition probability density function is (p max -th l ,p max ] The failure risk level of the vibration state range indicated by the horizontal axis is low risk.

[0126] Therefore, during the random vibration process, the mechanical system compares the vibration state at the time to be predicted with the vibration state range of each level of random vibration failure risk formulated by the failure risk level of the vibration state to determine the failure risk level of the mechanical system at the warning time. At the same time, if the failure risk level of the mechanical system at the warning time is high risk, the failure warning of the vibration state at the time to be predicted is carried out in advance.

[0127] In summary, the failure warning method of the mechanical system under the influence of random vibration proposed in this embodiment uses the random vibration process to obtain vibration state data, and solves the numerical solution of the transfer probability density function of the vibration state based on this, so as to construct a sample set, train and test the neural network model for real-time solution of the transfer probability density function of the vibration state, and fit 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, and draw a distribution diagram of the transfer probability density function based on this, so as to indicate the corresponding relationship between different vibration states and their transfer probability density functions. At this point, different random vibration failure risk levels can be formulated according to the distribution diagram, and whether failure warning is needed can be judged according to the random vibration failure risk level of the vibration state at the time to be predicted. After the random vibration failure risk level is formulated, its failure risk can be directly determined according to the vibration state at the time to be predicted, thereby simplifying the judgment process of failure risk. Moreover, this embodiment can effectively ensure the accuracy of the distribution map and the vibration failure risk level by executing the numerical solution and the fitting of the neural network model, thereby ensuring the accuracy of the failure risk prediction, and ultimately achieving fast and high-precision failure warning, effectively solving the problem of the lack of efficient and high-precision mechanical system health monitoring methods in the prior art.

[0128] In the specific implementation process, this embodiment creatively proposes a solution method for the probability density equation of the time-evolving vibration state based on the intelligent numerical solution. The model describes the transition process of the vibration state from the initial state to any state over time by introducing the transfer probability density function, thereby realizing efficient and accurate prediction and evaluation of the random vibration state. At the same time, when solving the probability density equation of the time-evolving vibration state, this embodiment adopts an efficient numerical solution method, which combines specific boundary conditions and initial conditions on the basis of the traditional numerical solution method, and obtains the numerical solution of the probability density of the vibration state transfer through iterative calculation. This method not only improves the accuracy of the solution, but also reduces the computational complexity, making large-scale calculations possible.

[0129] This embodiment also combines the results of the numerical solution with the artificial intelligence method to further improve the accuracy of the solution through intelligent analysis. This method combined with artificial intelligence can make full use of the advantages of machine learning to further optimize and correct the numerical solution, thereby improving the accuracy of prediction and evaluation.

[0130] 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.

[0131] 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 failure warning method for a mechanical system under the influence of random vibration, characterized in that: The method comprises: According to the random vibration process to which the mechanical system is subjected, vibration state data is obtained; the vibration state data includes an initial vibration state, a failure threshold of the vibration state, a drift function and a variance function of the vibration state; Obtaining a numerical solution of a transition probability density function of a vibration state based on the vibration state data; and constructing a sample set for training a neural network model based on the numerical solution of the transition probability density function; and using the sample set to train and test a neural network model for real-time solution of the transition probability density function of the vibration state; Obtaining the vibration state of each sampling time of the mechanical system uniformly sampled under the influence of random vibration, and inputting each sampling time and its vibration state into the neural network model that has passed the test, respectively, and the neural network model predicts and outputs the value of the transition probability density function corresponding to the vibration state at each sampling time, so as to draw a distribution diagram of the transition probability density function; According to the distribution diagram of the transfer probability density function, failure warning under the influence of random vibration is achieved.

2. The failure warning method of a mechanical system under the influence of random vibration according to claim 1 is characterized in that: The distribution diagram of the transfer probability density function is drawn by executing: The values ​​of the transfer probability density function corresponding to the vibration state at all sampling times are processed for non-negativity and normalization, so as to obtain the normalized value of the transfer probability density function corresponding to the vibration state at each sampling time; A distribution diagram of the transition probability density function is drawn with the vibration state at each sampling time as the abscissa and the normalized value of the corresponding transition probability density function as the ordinate.

3. The failure warning method of a mechanical system under the influence of random vibration according to claim 2 is characterized in that: According to the distribution diagram of the transfer probability density function, failure warning under the influence of random vibration is realized; implement: Formulate a random vibration failure risk level according to the distribution diagram of the transfer probability density function; Based on the random vibration failure risk level, failure warning under the influence of random vibration is achieved.

4. The failure warning method of a mechanical system under the influence of random vibration according to claim 3 is characterized in that: According to the distribution diagram of the transfer probability density function, the random vibration failure risk level is formulated and executed: The value of the vertical coordinate of the failure threshold of the vibration state in the distribution diagram of the transfer probability density function is represented as p f , and the maximum value of the ordinate in the distribution graph is represented by p max ; Set the high risk threshold margin th h , low risk threshold margin th l ; The vertical coordinate range of the distribution diagram of the transition probability density function is [0, p f +th h ] indicates a high risk level of failure; The vertical coordinate range of the distribution diagram of the transition probability density function is (p f +th h ,p max -th l The failure risk level of the vibration state range indicated by the horizontal axis between ] is medium risk; The vertical coordinate range of the distribution diagram of the transition probability density function is (p max -th l ,p max ] The failure risk level of the vibration state range indicated by the horizontal axis is low risk.

5. The failure warning method of a mechanical system under the influence of random vibration according to claim 4 is characterized in that: Based on the random vibration failure risk level, failure warning under the influence of random vibration is realized by executing: During the random vibration process of the mechanical system, the vibration state at the time to be predicted is compared with the vibration state range of each level of random vibration failure risk formulated by the failure risk level of the vibration state, and the failure risk level of the mechanical system at the warning time is determined; If the failure risk level of the mechanical system at the warning time is high risk, a failure warning of the vibration state at the time to be predicted is performed in advance.

6. The failure warning method of a mechanical system under the influence of random vibration according to any one of claims 1 to 5, characterized in that: The numerical solution of the transition probability density function of the vibration state is obtained based on the vibration state data, and the following is performed: Parameter initialization: Get the initial vibration state S0 and the failure threshold S of the vibration state f ; Set the time step dt and vibration state step dS t , time steps Nt and state steps NS t ; Starting from the initial vibration state S0, with a state step length dS t As an increment, gradually increase the vibration state S_ t until the failure threshold S of the vibration state is reached or exceeded. f , and obtain the vibration state S_ t The corresponding drift function m(S_ t ) and the variance function σ 2 (S_ t ); create a size of (Nt+1)×(NS t +2) is used to store the numerical solution of the transition probability density function; And initialize the relevant elements of the zero matrix p according to the boundary conditions; The numerical method is used to discretize the partial differential equation of the change of the transition probability density of the vibration state, and the partial differential equation is transformed into a series of linear equations, each of which is a discretized difference equation. On the basis of initializing the relevant elements of the zero matrix p according to the boundary conditions, for the other elements in the matrix p, at each time point t and vibration state point S_ t , calculate the transition probability density value of the vibration state at the next time point t+1 according to the discretized difference equation; By continuously iteratively updating the element values ​​in the matrix p, the numerical solution of the transfer probability density function of all time points and vibration state points is finally obtained, and the iterative update is terminated.

7. The failure warning method of a mechanical system under the influence of random vibration according to claim 6, characterized in that: The partial differential equation for the change in the transition probability density of the vibration state 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, p(t, S t |S0) represents the transition probability density function of the vibration state; m(S t ) is the vibration state S t The drift function of the drift, σ 2 (S t ) represents the vibration state S t The variance function of .

8. The failure warning method of a mechanical system under the influence of random vibration according to claim 7, characterized in that: In the calculation process based on the discretized difference equation, the time partial derivative is approximated by forward difference Approximating spatial partial derivatives using central differences and And update the corresponding element values ​​in the transfer probability density matrix p according to the difference equation.

9. The failure warning method of a mechanical system under the influence of random vibration according to claim 8, characterized in that: Initialize the relevant elements of the zero matrix p according to the boundary conditions and execute: According to the boundary conditions p(t,S f |S0)=0, set the last column of matrix p to 0. According to the initial condition p(t,S_ t |S0)=delta(S_ t -S0), set the element corresponding to position S0 in the first row of matrix p to 1.

10. The failure warning method of a mechanical system under the influence of random vibration according to claim 9, characterized in that: Based on the numerical solution of the transition probability density function, a sample set for neural network model training is constructed and executed: After the iterative update, the matrix p is processed non-negatively and normalized in turn to obtain the normalized matrix p1. The last column of the normalized matrix p1 is cut off to obtain the standardized matrix p2. The time point t and vibration state point S_ corresponding to each element in the standardized matrix p2 t A sample set for training the neural network model is constructed by taking the element values ​​of the corresponding elements in the standardized matrix p2 as input and the element values ​​of the corresponding elements in the standardized matrix p2 as output as a set of sample data.

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