Fault prediction method for random vibration system

Abstract

The invention discloses a fault prediction method for a random vibration system, belongs to the technical field of fault prediction, and solves the problem that the fault condition of the random vibration system cannot be accurately and quickly predicted in the prior art. The method comprises the following steps: acquiring experimental data of a random vibration system in a random vibration process, including a vibration state of each experimental time, a drift function and a spread function of the vibration state, and a failure threshold value of the vibration state; processing the experimental data to obtain a value of a probability density function of the system effective working time corresponding to each experimental time so as to construct a sample set; training and testing the sample set to obtain a machine learning model for solving the probability density of the effective working time of the system in real time; and based on the machine learning model passing the test, obtaining a prediction value of a probability density function of the system effective working time of each sampling time uniformly sampled in the random vibration process of the random vibration system, so as to realize fault prediction of the random vibration system.

Description

Technical Field

[0001] The present invention relates to the technical field of fault prediction, and in particular to a fault prediction method for a random vibration system. Background Art

[0002] Random vibration systems are widely used in aerospace, machinery manufacturing, transportation and other fields. In these fields, the effective working time of the random vibration system directly affects the performance and safety of the entire system. For example, in the aerospace field, the vibration state of the aircraft engine is directly related to its flight safety and performance stability; in the machinery manufacturing field, the vibration performance of the machine tool directly affects the processing accuracy and product quality; in the transportation field, the vibration performance of the vehicle is related to the comfort and driving safety of the passengers.

[0003] With the rapid development of engineering technology, random vibration systems play a vital role in various equipment and applications. The performance evaluation of random vibration systems, especially the prediction of the probability density function of their effective working time and the fault prediction derived from it, are of great significance to improving the reliability, safety and service life of the system. In the field of prediction of the effective working time of random vibration systems, traditional methods mainly rely on mathematical models and theoretical derivations. Although these methods can reflect the basic characteristics of random vibration systems to a certain extent, they often have great limitations when dealing with complex systems and nonlinear effects.

[0004] However, due to the complexity and randomness of random vibration systems, traditional prediction methods often fail to accurately reflect their actual performance and have the problem of insufficient accuracy. At the same time, these traditional methods may not fully consider the dynamic characteristics and nonlinear effects of the vibration system, resulting in prediction results that deviate from the actual situation.

[0005] Therefore, how to accurately and quickly predict the failure of random vibration systems is a technical problem that needs to be solved urgently. Summary of the invention

[0006] In view of the above analysis, an embodiment of the present invention aims to provide a fault prediction method for a random vibration system, so as to solve the problem in the prior art of lacking an accurate and rapid prediction method for the fault condition of a random vibration system.

[0007] The present invention discloses a fault prediction method for a random vibration system, the method comprising:

[0008] Acquire experimental data of the random vibration system during the random vibration process, including: the vibration state at each experimental time and its drift function, diffusion function, and failure threshold of the vibration state;

[0009] According to the fractional expression of the probability density function of the effective working time of the system, the experimental data are processed to obtain the value of the probability density function of the effective working time of the system corresponding to each experimental time, so as to construct a sample set;

[0010] The sample set is used to train and test a machine learning model for real-time solution of the probability density of the effective working time of the system; and based on the tested machine learning model, the predicted value of the probability density function of the effective working time of the random vibration system at each sampling time uniformly sampled during the random vibration process is obtained to realize fault prediction of the random vibration system.

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

[0012] Furthermore, the fault prediction of the random vibration system is achieved by performing the following operations:

[0013] According to the predicted value of the probability density function of the effective working time of the system at each sampling time uniformly sampled by the random vibration system during the random vibration process, a probability density function distribution curve of the effective working time of the system is formed; according to the peak position and distribution range of the probability density function distribution curve of the effective working time of the system, the effective working time period of the random vibration system is determined;

[0014] When the random vibration system operates in a time period outside the effective working time period, a fault warning is activated.

[0015] Further, the effective working time period of the random vibration system is determined by performing the following operations:

[0016] Determine the peak position according to the trend of the probability density function distribution curve of the effective working time of the system;

[0017] The distribution range of the abscissa of the probability density function distribution curve between the probability density threshold and the peak position is taken as the effective working time period of the random vibration system.

[0018] Furthermore, the peak position of the probability density function distribution curve of the effective working time of the system is one or more; wherein,

[0019] If a peak position is determined, the peak position is the global peak position of the distribution curve; at this time, the distribution range of the abscissa of the probability density function distribution curve between the probability density threshold and the global peak position is intercepted as the effective working time period of the random vibration system;

[0020] If multiple peak positions are determined, each peak position corresponds to a local peak position of the distribution curve; the local peak position is greater than the probability density threshold; at this time, the distribution range of the horizontal coordinate of the probability density function distribution curve between the probability density threshold and each local peak position is intercepted respectively, and the distribution range of the horizontal coordinate of the probability density function distribution curve between all local peak positions is summarized as the effective working time period of the random vibration system.

[0021] Furthermore, the fractional expression of the probability density function of the effective working time of the system is:

[0022]

[0023] Among them, p(T|S0) represents the probability density function of the effective working time T of the system; Q(t|S0) represents the effective working probability of the random vibration system starting from the initial vibration state S0 at time t; α(S t ) represents the integral function; S f represents the failure threshold, σ 2 (S f ) represents the diffusion function corresponding to the failure threshold; S t represents the vibration state at time t; S min Indicates that in S t ∈(0,S f ) within the range that makes the integral function α(S t ) takes the minimum value of the vibration state, and ε represents the infinitesimal neighborhood width.

[0024] Furthermore, the integral function α(S t ) is expressed as:

[0025]

[0026] Among them, m(S t ) is the vibration state S t The drift function, σ 2 (S t ) is the vibration state S t The diffusion function of .

[0027] Furthermore, the values ​​of the probability density function of the effective working time of the system corresponding to each experimental time are obtained by performing the following operations:

[0028] Get the vibration state S at the experimental time t t , drift function m(S t ), diffusion function σ 2 (S t ), and obtain S t ∈(0,S f ) within the range that makes the integral function α(St ) takes the minimum value of the vibration state S min ; S f represents the failure threshold;

[0029] For α(S t ) in S min and S f Perform polynomial series expansion at each of them and omit the high-order terms to obtain the corresponding polynomial series expansion expression;

[0030] According to the relationship between the polynomial series expansion expression and formula (1) and formula (2), the value of the probability density function of the effective working time of the system corresponding to the experimental time t is calculated;

[0031] All experimental times are traversed to obtain the value of the probability density function of the effective working time of the system corresponding to each experimental time.

[0032] Furthermore, when α(S t ) in S min and S f When the polynomial series expansion is performed at each position and only the first-order term and the second-order term are retained, the following parameters are calculated based on the relationship between the polynomial series expansion expression and formula (1) and formula (2):

[0033] A=σ 2 (S f )·exp[-(α(S f )-α(S min ))]

[0034]

[0035] Furthermore, the probability density function of the effective working time T of the system corresponding to the experimental time t is

[0036]

[0037] Furthermore, the sample set is constructed in the following way:

[0038] The sample set is constructed by taking the experimental time t as input and the probability density function p(T|S0) of the corresponding system effective working time T as output as a set of sample data;

[0039] The machine learning model for solving the probability density of the effective working time of the system in real time is obtained in the following way:

[0040] Divide the sample set into a training sample set and a test sample set;

[0041] The machine learning model is trained using the training sample set, and the trained machine learning model is tested using the test sample set until the test passes, thereby obtaining a machine learning model for real-time solving the probability of effective operation of the system.

[0042] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0043] The fault prediction method of the random vibration system provided by the embodiment of the present invention provides a new method for accurately predicting the probability density function of the effective working time of the system by introducing a machine learning algorithm and a method for determining the probability density function by fractional terms. This method can not only fully consider the complexity and nonlinear effects of the vibration system, but also can be adaptively adjusted and optimized according to actual data, so that the expression of the probability density function is more flexible and accurate, thereby achieving a more accurate prediction of the effective working time of the vibration system. At the same time, by introducing the machine learning algorithm into the prediction of the effective working time of the vibration equation, the complex characteristics and patterns of the vibration system can be automatically learned and identified, thereby more accurately predicting the probability density function of its effective working time. The introduction of the machine learning algorithm makes the prediction process no longer rely on fixed mathematical models and assumptions, but can be adaptively adjusted and optimized according to actual data. This method not only improves the accuracy of the prediction, but also improves the efficiency and stability of the solution.

[0044] In addition, after obtaining the prediction results based on the machine learning model, the probability density function distribution curve of the system's effective working time can be analyzed to determine its peak position and distribution range, thereby determining the effective working time period of the random vibration system; when the random vibration system operates outside the effective working time period, the fault warning is activated. In this way, rapid and accurate fault prediction of the random vibration system can be achieved.

[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 A fault prediction method for a random vibration system provided by an embodiment of the present invention. 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 fault prediction method for a random vibration system. First, the theory involved in this embodiment is explained as follows.

[0050] The fault prediction method of the random vibration system in this embodiment involves the intersection of random vibration analysis, machine learning and probability theory, and particularly a method for solving the probability density function of the effective working time of the vibration equation based on fractional terms of machine learning. By introducing a machine learning algorithm, combined with the vibration equation and probability theory, accurate prediction of the effective working time of the random vibration system can be achieved.

[0051] The model setting of this embodiment includes the following steps:

[0052] The first step is to establish the vibration equation

[0053] 1. Set the basic vibration function S t , this function characterizes the characteristics of vibration, and its initial vibration state is S0.

[0054] 2. Set the system effective working probability Q(t|S0), which is defined as the probability that the random vibration system maintains an effective working state within time t under a given initial vibration state S0.

[0055] 3. Assume that S, which causes the random vibration system to fail, t For S f , defined as the failure threshold, that is, when the vibration state S t Reach or exceed the failure threshold S f , the system fails.

[0056] The second step is to model the state transition probability density function

[0057] 1. Set the state transition probability density function p(t,S t |S0), which describes the vibration state from S0 to S t The transition probability.

[0058] 2. Based on the vibration equation and probability theory, the model equation of the state transition probability density function is established:

[0059]

[0060] Among them, m(S t ) is the drift function, that is, the vibration state S t The average rate represents the vibration state S of the random vibration system tThe 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 diffusion function, that is, the vibration state S t The degree of fluctuation indicates the vibration state S of the random vibration 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 spatial variation of m(S t ),σ 2 (S t ) respectively reflect the determinism and randomness of the system vibration state transition.

[0061] Step 3: Prediction of effective working time

[0062] 1. By solving the state transition probability density function p(t,S t |S0), and obtain the state distribution of the random vibration system at different times t.

[0063] 2. According to the definition of effective working state, use the state transition probability density function in the failure range S f The integral within , calculates the system effective working probability Q(t|S0):

[0064]

[0065] In order to solve the above equation more conveniently, the following transformation is performed on formula (1):

[0066] 1) Move the differential term with respect to time t to one side of the equation and t The differential term of is moved to the other side of the equation, and we get:

[0067]

[0068] 2) From 0 to S on both sides of the above equation f Integrate and set (S t =0, the right side of the equation is zero), we get:

[0069]

[0070] Starting from the above equations, after a series of mathematical transformations and derivations, especially at a specific position S min Nearby and S fBy integrating around, we can get the expression of the system effective working probability Q(t|S0). It should be noted that in a random vibration system, accurately predicting the probability density function of the system effective working time is crucial for system maintenance, fault warning, etc. This embodiment proposes a new method to determine the probability of the system effective working time.

[0071] Step 1: Integral function α(S t ) settings and interpretation

[0072] 1.α(S t )

[0073] First, set an integral function α(S t ), whose expression is:

[0074]

[0075] Here α(S t ) is a state related to the vibration S t The function involved integrates the diffusion function σ 2 (S t ), the reciprocal of 2 (S t ) t The derivative and drift function m(S t ). Through this integral function, the dynamic changes of the random vibration system related to the variance and mean during the random vibration process can be captured.

[0076] 2.α(S t )

[0077] Set α(S t ) in S t ∈(0,S f ), when S t =S min This means that at S min At a certain characteristic of the random vibration system (given by α(S t ) indicates that) reaches a local minimum point. In addition, a min An infinitesimal neighborhood centered on min -ε,S min +ε], this neighborhood is of great significance for subsequent calculations.

[0078] Step 2: Solution and interpretation of the system effective working probability Q(t|S0)

[0079] 1. Expression of Q(t|S0)

[0080] Based on the above α(S t) function, and the expression of the system effective working probability Q(t|S0) is obtained:

[0081]

[0082] This expression reveals that Q(t|S0) is related to σ 2 (S f ), α(S t ) over a specific interval and the relationship between time t.

[0083] 2. Explanation of each part of the expression

[0084] σ 2 (S f ): indicates the failure threshold S f The variance at , which reflects the fluctuation degree of the random vibration system vibration in the failure state.

[0085] This part is α(S t ) function in S min The integral over the infinitesimal neighborhood near S reflects the random vibration system min Some characteristic nearby (given by α(S t ) represents the cumulative effect of ).

[0086] This part is α(S t ) function in S f The integral over the infinitesimal neighborhood reflects the random vibration system close to the failure threshold S f A certain characteristic (given by α(S t ) represents the cumulative effect of ).

[0087] Time t: As the independent variable of the exponential function, it represents the length of time the random vibration system has been running.

[0088] The whole expression is expressed in the form of an exponential function, which converts the variance σ 2 (S f ), α(S t ) function and time t are combined to give the probability density function Q(t|S0) that the system will remain in an effective working state within time t under a given initial state S0.

[0089] Step 3: Solve the probability density function p(T|S0) of the system effective working time T

[0090] Based on the expression of Q(t|S0), we can further solve the fractional expression of the probability density function p(T|S0) of the effective working time T of the system:

[0091]

[0092] This expression is derived from Q(t|S0) with respect to time t, and t = T, to obtain the probability density function p(T|S0) of the random vibration system when the effective working time is T under a given initial vibration state S0. This probability density function provides detailed information about the distribution of the effective working time of the system, which helps to better understand and predict the performance of the system.

[0093] In the process of random vibration system analysis, determining the probability density function of the effective working time of the system is of great significance for predicting system performance and failures and guiding maintenance strategies. This embodiment also provides a solution method for the probability density function of the effective working time determined based on the fractional term, which simplifies the integral function through polynomial series expansion, thereby obtaining a probability density function expression that is easier to calculate.

[0094] The first step is to expand the polynomial series.

[0095] In order to solve the fractional term in the probability density function p(T|S0), we first calculate the integral function α(S t ) at the minimum value S min and the maximum value S f Here we assume that α(S t )’s behavior near these points can be approximated by its Taylor series.

[0096] In S min Nearby expansion:

[0097]

[0098] In order to simplify the calculation, the higher-order terms are omitted and only the quadratic terms are retained.

[0099] In S f Nearby expansion:

[0100]

[0101] Similarly, higher-order terms are omitted, leaving only the quadratic terms.

[0102] The second step is to determine the expressions of the numerator and denominator.

[0103] Based on the above polynomial series expansion, determine the numerator and denominator expressions of the fractional term. Since α(S f ) and α(S min ) is a constant, and the exp function satisfies exp(ab) = exp(a) / \exp(b), so the molecule A can be written as:

[0104] A=σ 2 (Sf )·exp[-(α(S f )-α(S min )) (10)

[0105] Here, α(S t ) in S f and S min The value at is used to calculate the numerator A.

[0106] Denominator B: The calculation of denominator B involves two integrals, one in S min and S f Substituting the polynomial expansion into these two integrals, we obtain:

[0107]

[0108] These two integrals capture the system in S min and S f Behavioral characteristics nearby.

[0109] The third step is to solve the probability density function p(T|S0)

[0110] Substitute the numerator A and denominator B obtained above into the expression of the probability density function p(T|S0):

[0111]

[0112] This expression gives the probability density of the system under a given initial vibration state S0 when the effective working time is T.

[0113] The method for solving the probability density function of the effective working time determined by the fractional term proposed in this embodiment simplifies the integral function through polynomial series expansion, making the solution process of the probability density function simpler and more intuitive. This not only improves the calculation efficiency, but also provides strong support for the performance prediction of the vibration system and the formulation of maintenance strategies.

[0114] Based on the above description, this embodiment provides a specific implementation process of the method for determining the probability density function of the effective working time based on the probability of the effective working state, that is, it provides how to determine the probability density function of the effective working time of the system, which provides an important basis for the performance prediction and maintenance strategy formulation of the random vibration system. The specific process is described as follows:

[0115] The first step is parameter initialization

[0116] First, the initial vibration state S0 and the failure threshold S f , infinitesimal neighborhood width ε; define time t, and the minimum value S directly related to time t min , variance function σ 2(S t ) and m(S t ) etc. These parameters will be used in subsequent calculations.

[0117] Step 2: Calculate Q(t|S0)

[0118] In order to calculate the effective working time probability Q(t|S0), a numerical integration method is used to calculate α(S t ) function in S min and S f Integrate in an infinitesimal neighborhood around . For each given time t, calculate the value of Q(t|S0).

[0119] Step 3: Determine p(T|S0)

[0120] Based on the expression of Q(t|S0), by taking the derivative and substituting the specific time T, the probability density p(T|S0) when the effective working time is T can be obtained.

[0121] According to the above process, by adjusting the time t, the p(T|S0) corresponding to the corresponding time t can be obtained, or the relationship between the time t and the corresponding p(T|S0) can be fitted through a neural network. After that, the probability density of the effective working time at any time when it is T can be predicted using the fitted neural network. By monitoring the state of the system in real time and inputting it into the machine learning model, the probability of the effective working state of the system in the future can be predicted in real time, providing decision support for the maintenance and management of the system. In addition, the method can also be extended to other application fields that require prediction of time-related probabilities. In the specific implementation process, the neural network type can be a feedforward neural network containing one or more hidden layers. Among them, the size of the hidden layer hiddenLayerSize can be adjusted as needed to optimize the performance of the model.

[0122] This embodiment takes the above theoretical analysis as the core and forms the following fault prediction method for random vibration system. The flowchart of the method is as follows: Figure 1 As shown, the following steps are included:

[0123] Step S1: Acquire experimental data of the random vibration system during the random vibration process, including: the vibration state at each experimental time and its drift function, diffusion function, and failure threshold of the vibration state.

[0124] Step S2: Process the experimental data according to the fractional expression of the probability density function of the effective working time of the system, obtain the value of the probability density function of the effective working time of the system corresponding to each experimental time, and construct a sample set.

[0125] Step S3: Use the sample set to train and test to obtain a machine learning model for real-time solution of the probability density of the effective working time of the system; and based on the tested machine learning model, obtain the predicted value of the probability density function of the effective working time of the random vibration system at each sampling time uniformly sampled during the random vibration process, so as to realize fault prediction of the random vibration system.

[0126] In this embodiment, the random vibration system of the present invention may involve multiple fields such as reliability engineering, electronic engineering, materials science, mechanical engineering, etc., and generally refers to related systems with mechanical structures and affected by random vibration, such as precision machine tool systems, aircraft engine systems, and automobile suspension systems. Under the influence of random vibration, the change in vibration state can often reflect the health of the equipment. The probability density function of the effective working time of the system can evaluate the possibility of the system maintaining an effective working state for a period of time under a given initial vibration state condition, so as to achieve fault warning when a fault occurs in the random vibration system, thereby effectively ensuring the reliability and stability of the operation of the random vibration system. In the experimental process in the above step S1, relevant technical personnel can obtain various experimental data in the experimental environment. The method of obtaining the experimental data is not the focus of this embodiment, and only the following relevant introduction is made.

[0127] Random Vibration When a system is subjected to random vibration, its 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 random vibration 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] In addition, it should be noted that the failure threshold of the vibration state refers to the threshold of the vibration state that causes the random vibration system to fail. In the specific implementation process, different vibration states can be adjusted, and according to the operation of the random vibration system, it can be judged whether the random vibration system fails; the minimum value of the vibration state that causes the random vibration system to fail is obtained and used as the failure threshold of the vibration state.

[0157] Based on the above related description, the fractional expression of the probability density function of the effective working time of the system is shown in formula (7). Based on this, the specific execution process of step S2 is described as follows. At each experimental time, the following operations are performed to obtain the value of the probability density function of the effective working time of the system.

[0158] Step S21: Obtain the vibration state S at the experimental time t t , drift function m(S t ), diffusion function σ 2 (S t ), and obtain S t ∈(0,S f ) within the range that makes the integral function α(S t ) takes the minimum value of the vibration state S min ; S f Indicates the failure threshold.

[0159] Step S22: Use polynomial series expansion to expand α(S t ) in S min and S f The polynomial series expansion is performed at each of the above formulas (8) and (9), and the higher-order terms are omitted (the quadratic terms are retained as an example below), to obtain the corresponding polynomial series expansion expressions.

[0160] Step S23: According to the correlation between the polynomial series expansion expression and formula (5) and formula (7), the value of the probability density function of the effective working time of the system corresponding to the experimental time t is calculated.

[0161] Specifically, according to the relationship between the polynomial series expansion expression and formula (5) and formula (7), the following parameters are calculated:

[0162] A=σ 2 (S f )·exp[-(α(S f )-α(S min ))]

[0163]

[0164] Among them, ε represents the infinitesimal neighborhood width.

[0165] Probability density function of the effective working time T of the system corresponding to the experimental time t

[0166] By traversing all experimental times, we can get the value of the probability density function of each experimental time and the corresponding system effective working time. Taking the experimental time t as input and the probability density function p(T|S0) of the corresponding system effective working time T as output as a set of sample data, a sample set is constructed.

[0167] In step S3, the sample set is used to train and test a machine learning model for real-time solution of the probability density of the effective working time of the system, and the following is performed:

[0168] (1) Divide the sample set into a training sample set and a test sample set;

[0169] (2) Using the training sample set to train the machine learning model, and using the test sample set to test the trained machine learning model until the test passes, a machine learning model for real-time solving of the probability density function of the effective working time of the system is obtained.

[0170] In the specific implementation process, after the test is passed, the machine learning model 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 correlation between the experimental time t and the corresponding probability density function p(T|S0) of the effective working time T of the system by executing the above steps, and simulates this correlation through the machine learning model. After that, the value of the probability density function of the effective working time of the random vibration system at any time before failure can be predicted. It should be emphasized that in this embodiment, the setting of the initial state of vibration directly determines the direction of the experimental data obtained, and the corresponding relationship fitted by the constructed machine learning model is also based on the set initial state of vibration. Therefore, in the subsequent prediction process based on the machine learning model that has passed the test, the sampling times uniformly sampled by the selected random vibration system during the random vibration process are also set to start with the same initial state of vibration.

[0171] The concept of effective working probability of the system refers to the probability that the random vibration system can maintain a normal working state under the influence of random vibration. This parameter directly reflects the reliability level of the random vibration system. The probability density function of the effective working time of the system describes the distribution of the effective working time of the system under a random vibration environment. By analyzing this function, we can understand the possibility of the random vibration system working effectively in different time periods. Accordingly, in step S3, after obtaining the predicted value of the probability density function of the effective working time of the random vibration system at each sampling time uniformly sampled during the random vibration process, the fault prediction of the random vibration system is realized by performing the following operations:

[0172] (1) Based on the predicted value of the probability density function of the effective working time of the random vibration system at each sampling time uniformly sampled during the random vibration process, a probability density function distribution curve of the effective working time of the system is formed; based on the peak position and distribution range of the probability density function distribution curve of the effective working time of the system, the effective working time period of the random vibration system is determined.

[0173] Exemplarily, the peak position is determined according to the trend of the probability density function distribution curve of the effective working time of the system; the distribution range of the horizontal axis of the probability density function distribution curve between the probability density threshold and the peak position is intercepted as the effective working time period of the random vibration system.

[0174] During the specific implementation, one or more peak positions may be determined according to the actual situation of the distribution curve.

[0175] 1) If a peak position is determined, the peak position is the global peak position of the distribution curve; at this time, the distribution range of the horizontal axis of the probability density function distribution curve between the probability density threshold and the global peak position is intercepted as the effective working time period of the random vibration system.

[0176] 2) If multiple peak positions are determined, each peak position corresponds to a local peak position of the distribution curve; the local peak position is greater than the probability density threshold; at this time, the distribution range of the horizontal coordinate of the probability density function distribution curve between the probability density threshold and each local peak position is intercepted respectively, and the distribution range of the horizontal coordinate of the probability density function distribution curve between all local peak positions is summarized as the effective working time period of the random vibration system.

[0177] In this process, the preset probability density threshold is used to limit the minimum probability of the random vibration system maintaining a normal working state under the influence of random vibration. This parameter can be set based on the accuracy of the early warning and combined with the probability density function distribution curve of the system's effective working time.

[0178] (2) When the random vibration system operates outside the effective working time period, the fault warning is activated. At this time, it is necessary to strengthen the early warning monitoring of the random vibration process and prepare corresponding emergency measures.

[0179] That is, the fault warning mechanism provided in this embodiment is: when the random vibration system operates in a time period outside the effective working time period, the fault warning is activated. This can be achieved by real-time monitoring of the effective working time of the random vibration system and comparing it with the defined effective working time period.

[0180] The fault prediction method for a random vibration system provided in this embodiment is applicable to a variety of different types of random vibration systems. Several random vibration systems and their application examples are given below to help technicians better understand and implement related technologies.

[0181] (1) High-rise building structure

[0182] Physical application background: During long-term use, high-rise buildings will be affected by wind loads, earthquakes and other factors. The changes in their structural vibration state directly affect the safety and service life of the building, which can be regarded as a random vibration system. By installing vibration sensors, vibration data of high-rise buildings under different working conditions can be collected.

[0183] Based on the above methods, the vibration equation and state transition probability density function model are established. The collected data is used to train the machine learning model to predict the probability density function of the effective working time of the vibration system. Based on the above prediction method, potential vibration anomalies of the structure can be discovered in advance, maintenance measures can be taken in time, and the safety of the building can be improved. In addition, historical data and prediction results can be combined to conduct long-term health assessment of the structure and optimize maintenance strategies.

[0184] (2) Precision instrument stability assessment

[0185] Physical application background: In the fields of scientific research and industry, the stability and accuracy of precision instruments (such as spectrometers, microscopes, etc.) directly affect the experimental results and product quality, and can be regarded as random vibration systems. In the specific implementation process, the main sources of instrument vibration can be analyzed, such as environmental vibration, internal mechanical movement, etc., and experimental data can be obtained on this basis, and the model training and testing can be completed. After that, prediction and early warning processing can be carried out. Regular maintenance and calibration can also be used to extend the service life of the instrument and improve the accuracy and reliability of the experimental results.

[0186] (3) Electric vehicle battery pack vibration analysis

[0187] Physical application background: The battery pack of an electric vehicle will be subjected to various vibration excitations during driving. Its vibration state has an important impact on the performance and life of the battery, and it can be regarded as a random vibration system. In the specific implementation process, the vibration environment of the electric vehicle under different road conditions is simulated by simulation or experiment, and a vibration equation is established based on the physical properties and vibration environment of the battery pack. Subsequently, a machine learning model is trained to predict the effective working time of the battery pack under different vibration conditions. Based on the prediction results, the probability density function of the effective working time of the battery pack is solved, and then an early warning can be issued in the above manner. The above method provides a reference for battery pack vibration analysis and life prediction for electric vehicle manufacturers. On this basis, it is also possible to consider optimizing the design and maintenance strategy of the battery pack to improve the overall performance and reliability of electric vehicles.

[0188] 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.

[0189] 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 fault prediction method for a random vibration system, characterized in that: The method comprises: Acquire experimental data of the random vibration system during the random vibration process, including: the vibration state at each experimental time and its drift function, diffusion function, and failure threshold of the vibration state; According to the fractional expression of the probability density function of the effective working time of the system, the experimental data are processed to obtain the value of the probability density function of the effective working time of the system corresponding to each experimental time, so as to construct a sample set; The sample set is used to train and test a machine learning model for real-time solution of the probability density of the effective working time of the system; and based on the tested machine learning model, the predicted value of the probability density function of the effective working time of the random vibration system at each sampling time uniformly sampled during the random vibration process is obtained to realize fault prediction of the random vibration system.

2. The fault prediction method of the random vibration system according to claim 1, characterized in that: Failure prediction of random vibration systems is achieved by performing the following: According to the predicted value of the probability density function of the effective working time of the system at each sampling time uniformly sampled by the random vibration system during the random vibration process, a probability density function distribution curve of the effective working time of the system is formed; according to the peak position and distribution range of the probability density function distribution curve of the effective working time of the system, the effective working time period of the random vibration system is determined; When the random vibration system operates in a time period outside the effective working time period, a fault warning is activated.

3. The fault prediction method of the random vibration system according to claim 2, characterized in that: Determine the effective operating time period of the random vibration system by doing the following: Determine the peak position according to the trend of the probability density function distribution curve of the effective working time of the system; The distribution range of the abscissa of the probability density function distribution curve between the probability density threshold and the peak position is taken as the effective working time period of the random vibration system.

4. The fault prediction method of the random vibration system according to claim 3, characterized in that: The peak position of the probability density function distribution curve of the effective working time of the system is one or more; wherein, If a peak position is determined, the peak position is the global peak position of the distribution curve; at this time, the distribution range of the abscissa of the probability density function distribution curve between the probability density threshold and the global peak position is intercepted as the effective working time period of the random vibration system; If multiple peak positions are determined, each peak position corresponds to a local peak position of the distribution curve; the local peak position is greater than the probability density threshold; at this time, the distribution range of the horizontal coordinate of the probability density function distribution curve between the probability density threshold and each local peak position is intercepted respectively, and the distribution range of the horizontal coordinate of the probability density function distribution curve between all local peak positions is summarized as the effective working time period of the random vibration system.

5. The fault prediction method for a random vibration system according to any one of claims 1 to 4, characterized in that: The fractional expression of the probability density function of the effective working time of the system is: Among them, p(T|S0) represents the probability density function of the effective working time T of the system; Q(t|S0) represents the effective working probability of the random vibration system starting from the initial vibration state S0 at time t; α(S t ) represents the integral function; S f represents the failure threshold, σ 2 (S f ) represents the diffusion function corresponding to the failure threshold; S t represents the vibration state at time t; S min Indicates that in S t ∈(0,S f ) within the range that the integral function α(S t ) takes the minimum value of the vibration state, and ε represents the infinitesimal neighborhood width.

6. The fault prediction method of random vibration system according to claim 5, characterized in that: The integral function α(S t ) is expressed as: Among them, m(S t ) is the vibration state S t The drift function, σ 2 (S t ) is the vibration state S t The diffusion function of .

7. The fault prediction method of the random vibration system according to claim 6, characterized in that: The values ​​of the probability density function of the effective working time of the system corresponding to each experimental time are obtained by performing the following operations: Get the vibration state S at the experimental time t t , drift function m(S t ), diffusion function σ 2 (S t ), and obtain S t ∈(0,S f ) within the range that the integral function α(S t ) takes the minimum value of the vibration state S min ; S f represents the failure threshold; For α(S t ) in S min and S f Perform polynomial series expansion at each of them and omit the high-order terms to obtain the corresponding polynomial series expansion expression; According to the relationship between the polynomial series expansion expression and formula (1) and formula (2), the value of the probability density function of the effective working time of the system corresponding to the experimental time t is calculated; All experimental times are traversed to obtain the value of the probability density function of the effective working time of the system corresponding to each experimental time.

8. The fault prediction method of random vibration system according to claim 7, characterized in that: When α(S t ) in S min and S f When the polynomial series expansion is performed at each position and only the first-order term and the second-order term are retained, the following parameters are calculated based on the relationship between the polynomial series expansion expression and formula (1) and formula (2): A=s 2 (S f )·exp[-(α(S f )-α(S min ))] 9. The fault prediction method of random vibration system according to claim 8, characterized in that: Probability density function of the effective working time T of the system corresponding to the experimental time t 10. The fault prediction method of random vibration system according to claim 9, characterized in that: The sample set is constructed in the following way: The sample set is constructed by taking the experimental time t as input and the probability density function p(T|S0) of the corresponding system effective working time T as output as a set of sample data; The machine learning model for solving the probability density of the effective working time of the system in real time is obtained in the following way: Divide the sample set into a training sample set and a test sample set; The machine learning model is trained using the training sample set, and the trained machine learning model is tested using the test sample set until the test passes, thereby obtaining a machine learning model for real-time solving the probability of effective operation of the system.

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