Method for predicting stability of random vibration system in random vibration environment

Abstract

The invention discloses a stability prediction method of a random vibration system in a random vibration environment, belongs to the technical field of stability prediction of the random vibration system, and solves the problem that high-precision and rapid stability prediction of the random vibration system is lacked in the prior art. The method comprises the following steps: carrying out an experiment on a random vibration process of a random vibration system in a given vibration initial state, and obtaining a vibration state of each experiment time, a drift function and a spread function of the vibration state, and a failure threshold value of the vibration state; according to the fractional term expression of the effective working probability of the system, processing data obtained by an experiment by adopting a polynomial series expansion mode to obtain a corresponding relationship between each experiment time and the value of the effective working probability of the system so as to construct a sample set; training and testing the sample set to obtain a neural network model for solving the effective working probability of the system in real time; and predicting the stability of the random vibration system at the corresponding prediction time based on the neural network model passing the test.

Description

Technical Field

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

[0002] In the field of engineering technology, the evaluation of the working state of a system or equipment in a random vibration environment has always been a hot topic and a difficult point of research. With the advancement of science and technology and the development of industry, more and more equipment is applied to complex vibration environments, such as aerospace, high-speed railways, bridge engineering, etc. The equipment in these fields often needs to work under various random vibration conditions. Therefore, how to accurately evaluate the probability of the effective working state of a system or equipment in a random vibration environment is of great significance for predicting the stability of the equipment, ensuring the safe operation of the equipment, and improving the reliability of the system.

[0003] Traditional stability assessment methods are often based on static or simplified vibration models, which are difficult to accurately describe the complexity and dynamics of random vibration processes. With the development of mathematical theory and computer technology, random vibration theory has been deeply studied and applied, providing a more accurate theoretical basis and technical means for evaluating the performance of systems or equipment in random vibration environments. Among them, the time evolution random vibration equation model has become a research hotspot, which can more accurately describe the dynamic behavior of systems or equipment in random vibration environments.

[0004] In the field of engineering technology, random vibrations are widely present in various systems or equipment, such as the vibration of bridges under wind loads and vehicle loads, and the vibration of high-rise buildings under earthquakes. These random vibrations not only affect the normal operation of the system or equipment, but may also cause equipment failure and malfunction, posing a serious threat to people's lives and property. Therefore, accurately evaluating the probability of effective working state of a system or equipment under a random vibration environment is of great significance for guiding the stability evaluation, engineering design, and equipment maintenance of random vibrations.

[0005] Specifically, in the field of aerospace, aircrafts such as airplanes and rockets are affected by various random vibrations during flight, such as airflow disturbances, engine vibrations, etc. These vibrations not only affect the performance of the aircraft, but may also cause structural failure and control system failure. Therefore, evaluating the probability of an aircraft's effective working state in a random vibration environment and realizing stability evaluation based on this is of great significance to ensure flight safety.

[0006] In the field of high-speed railways, trains are affected by various factors such as track unevenness and bridge vibration during high-speed travel, which causes random vibrations in the vehicle. These vibrations not only affect the riding comfort of passengers, but may also threaten the vehicle structure and operational safety. Therefore, evaluating the probability of effective working state of the train under random vibration environment is of great significance to improving the safety and comfort of high-speed railways.

[0007] In summary, how to accurately and efficiently evaluate the probability of effective working state of a system or equipment in a random vibration environment while considering the complexity and randomness of the random vibration environment, and realize stability evaluation and prediction based on this, has become a problem to be solved urgently in the field of engineering technology. Summary of the invention

[0008] In view of the above analysis, an embodiment of the present invention aims to provide a method for predicting the stability of a random vibration system in a random vibration environment, so as to solve the problem of lack of high-precision and fast stability prediction of a random vibration system in the prior art.

[0009] The present invention discloses a method for predicting the stability of a random vibration system in a random vibration environment, the method comprising:

[0010] Conduct experiments on the random vibration process of the random vibration system under a given initial vibration state, and obtain the vibration state at each experimental time and its drift function, diffusion function, and failure threshold of the vibration state;

[0011] According to the fractional expression of the system effective working probability, the data obtained from the experiment are processed by a polynomial series expansion method to obtain the corresponding relationship between each experimental time and the value of the system effective working probability, so as to construct a sample set; the sample set is used to train and test a neural network model for real-time solution of the system effective working probability;

[0012] Based on the tested neural network model, the stability of the random vibration system at the corresponding prediction time is predicted.

[0013] On the basis of the above scheme, the present invention also makes the following improvements:

[0014] Furthermore, the fractional expression of the system effective working probability is:

[0015]

[0016] Where Q(t|S0) represents the probability of effective operation 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 (Sf ) 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.

[0017] Furthermore, the integral function α(S t ) is expressed as:

[0018]

[0019] 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 .

[0020] Furthermore, the corresponding relationship between each experimental time and the value of the system effective working probability is obtained by executing the following steps:

[0021] 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(S t ) takes the minimum value of the vibration state S min ;

[0022] Using polynomial series expansion, 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;

[0023] According to the relationship between the polynomial series expansion expression and formula (1) and formula (2), the value of the system effective working probability corresponding to the experimental time t is calculated;

[0024] Traverse all experimental times and obtain the corresponding relationship between each experimental time and the value of the system's effective working probability.

[0025] Furthermore, when α(S t ) in S min and S fWhen 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):

[0026] A=σ 2 (S f )·exp[-(α(S f )-α(S min ))]

[0027]

[0028] Furthermore, the value of the system effective working probability corresponding to the experimental time t is

[0029] Furthermore, the sample set is constructed in the following way:

[0030] A sample set is constructed by taking the experimental time t as input and the corresponding value of the system effective working probability Q(t|S0) as output as a set of sample data.

[0031] Furthermore, a neural network model for solving the effective working probability of the system in real time is obtained by the following method:

[0032] Divide the sample set into a training sample set and a test sample set;

[0033] The neural network model is trained using the training sample set, and the trained neural network model is tested using the test sample set until the test passes, thereby obtaining a neural network model for real-time solving the probability of effective operation of the system.

[0034] Furthermore, based on the tested neural network model, the stability of the random vibration system at the corresponding prediction time is predicted by executing:

[0035] In the actual operation process, when the random vibration system takes the vibration initial state as the vibration starting state, the predicted time is input into the neural network model that has passed the test, and the neural network model predicts the system effective working probability of the output predicted time;

[0036] The stability of the random vibration system at the corresponding prediction time is predicted according to the effective working probability of the system at the prediction time.

[0037] Furthermore, the stability of the random vibration system at the corresponding prediction time is predicted as follows:

[0038] Determine whether the system effective working probability at the predicted time is greater than the preset system effective working probability threshold,

[0039] If so, it indicates that the random vibration system has strong stability at the predicted time;

[0040] If not, it indicates that the random vibration system is not stable enough at the predicted time.

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

[0042] The stability prediction method of the random vibration system in the random vibration environment provided by the present invention firstly constructs a time-evolving random vibration equation model, including the determination of the probability of the effective working state and the solution of the fractional term. The model can more accurately describe the dynamic behavior of the random vibration system in the random vibration environment by considering the randomness of the vibration process and the time evolution characteristics. At the same time, through technical means such as polynomial series expansion, the calculation process is simplified, the calculation complexity is reduced, and the accurate calculation of the probability of the effective working state can be realized. This method not only improves the accuracy of the evaluation, but also has strong adaptability and robustness, and can adapt to random vibration environments of different complexities.

[0043] In addition, based on the neural network model, the present invention well fits the corresponding relationship between the experimental time and the value of the effective working probability of the system, thereby making the prediction process of the effective working state probability more efficient and convenient, and according to the predicted effective working probability of the system, it can accurately and quickly predict the stability of the random vibration system at the corresponding prediction time, which well solves the problem of lack of high-precision and fast stability prediction of random vibration systems in the prior art, and provides strong support for engineering design and equipment maintenance.

[0044] In the present invention, the above-mentioned technical solutions can also be combined with each other to achieve more preferred combination solutions. Other features and advantages of the present invention will be described in the subsequent description, and some advantages can become obvious from the description, or can be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The accompanying drawings are only used for the purpose of illustrating specific embodiments and are not to be considered as limiting the present invention. In the entire drawings, the same reference symbols represent the same components;

[0046] Figure 1 The present invention provides a flowchart of a method for predicting the stability of a random vibration system in a random vibration environment. DETAILED DESCRIPTION

[0047] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not used to limit the scope of the present invention.

[0048] A specific embodiment of the present invention discloses a method for predicting the stability of a random vibration system in a random vibration environment. The following first describes the relevant theoretical knowledge involved in this embodiment.

[0049] In the field of modern engineering technology, systems or equipment often need to work in various complex vibration environments, and such systems or equipment are collectively referred to as random vibration systems. The vibration environment of a random vibration system is often random, making it difficult to predict the operating state of the system or equipment. Therefore, how to accurately predict the probability of an effective working state of a system or equipment in a random vibration environment, and to achieve stability prediction based on this, has become a problem to be solved in this field. To solve this problem, the present embodiment proposes the following method suitable for evaluating and analyzing the effectiveness, reliability and stability of a random vibration system working in a random vibration environment. The method adopts an intelligent effective working state probability determination and fractional term solution method for a time-evolving random vibration equation, and constructs a model equation of the random vibration process, and uses a transfer probability density function to describe the time evolution of the system or equipment state, thereby solving the effective working state probability of the system or equipment under a given initial vibration state.

[0050] (1) Model setting

[0051] Assume the basic vibration function S t It is a random process used to characterize vibration characteristics, and its initial vibration state is S0. In practical applications, the vibration state corresponding to a system or device at the initial time t = 0 is S0. As time goes by, this vibration state will change and transfer to a new vibration state S t The process of this state transfer is random because it is affected by various uncertain factors, such as external environment, internal wear and tear, etc.

[0052] The system effective working probability Q(t|S0) 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. t Reach or exceed a certain failure threshold S f The random vibration system is considered to have failed when

[0053] In order to describe the process of random vibration state transfer, the vibration state transfer probability density function p(t,S t |S0). This function indicates that under the condition of a given initial vibration state S0, the system is in a vibration state S at time t. t Intuitively, it gives the probability density of the random vibration system from the initial vibration state S0 to the vibration state S t What is the possibility of .

[0054] Based on the random process theory and partial differential equations, the following model equation can be established to describe the transition probability density function p(t,S t |S0) dynamic changes:

[0055]

[0056] 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 t The average rate of change over time t, which describes the average rate of change of the random vibration process; σ 2 (S t ) is the 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 . This equation contains several key parts:

[0057] Time Variation Item: Represents the rate of change of the transition probability density function over time.

[0058] Drift term: Indicates that the system state is due to some average trend (such as m(S t )) due to changes.

[0059] Diffusion term: Indicates that due to the uncertainty of the system state (such as σ 2 (S t )) caused by the state change.

[0060] For a system or device, it is necessary to consider the probability that it remains in an effective working state within a given time t. This probability is called the effective working state probability Q(t|S0). In order to calculate this probability, it is necessary to calculate the transition probability density function p(t,S t |S0) in the failure range S f Specifically:

[0061]

[0062] This integral represents the t Therefore, by solving this integral, we can get the probability Q(t|S0) that the system will remain in an effective working state within a given time t.

[0063] (2) Setting the integral function and determining the expression of the effective working state probability solution

[0064] 1) Integration function setting

[0065] In the analysis of random vibration systems, in order to more accurately solve the effective working state probability Q(t|S0), a special integral function α(S t ), the function is defined as:

[0066]

[0067] Here, σ 2 (S t ) represents the system vibration state S t The variance under m(S t ) describes the average trend of system state changes.

[0068] In S t ∈(0,S f ), assuming that α(S t ) in S t =S min The minimum value is obtained at min is the interval such that α(S t ) takes the minimum value of S t In order to more accurately determine S min Nearby behavior, set [S min -ε,S min +ε] is S min An infinitesimal neighborhood of , where ε is a small positive number, defined as the width of the infinitesimal neighborhood. The integral function α(S t ) helps to better understand the sensitivity of system state changes to variance and average trend, thus providing a basis for the subsequent solution of the probability of effective working state.

[0069] 2) Determination of the expression of the probability solution of the effective working state

[0070] Based on the above integral function α(S t ), based on formulas (1)-(3), we can further derive the fractional expression of the effective working state probability Q(t|S0). Specifically:

[0071]

[0072] In this expression, σ 2 (S f ) represents the random vibration system at the failure threshold S f The two integral terms correspond to S min Nearby and Sf Nearby α(S t ). These two integral terms reflect the state of the random vibration system in S min and S f The sensitivity around 2 (S f ) together with time t determine the size of the effective working state probability Q(t|S0).

[0073] Through this expression, the probability of the system maintaining an effective working state under a given initial vibration state S0 and time t can be calculated more directly. This has important practical application value in evaluating the reliability and stability of systems or equipment and optimizing maintenance strategies.

[0074] (3) Method for solving the probability of effective working state based on fractional terms

[0075] In the process of solving the effective working state probability Q(t|S0), the choice of solution calculation method is the key. In order to simplify the calculation process and improve the solution accuracy, this embodiment proposes a method based on polynomial series expansion to process the integral function α(S t ).

[0076] 1) Polynomial series expansion

[0077] First, for α(S t ) at the minimum value S min and S f In order to simplify the calculation process, the higher-order terms are omitted and only the quadratic terms (i.e., the first-order derivative and the second-order derivative) are retained. min Expanded to:

[0078]

[0079] In S f Expanded to:

[0080]

[0081] 2) Conversion of fractional expressions

[0082] Next, substitute the above expansion into the fractional term and convert the numerator and denominator.

[0083] Molecular part A: Due to 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:

[0084] A=o2 (S f )·exp[-(α(S f )-α(S min ))] (7)

[0085] Denominator B: The denominator B contains two integral terms, corresponding to S min and S f Nearby α(S t ). Substituting the polynomial expansion into these two integrals, we obtain:

[0086] For S min Nearby points:

[0087]

[0088] For S f Nearby points:

[0089]

[0090] The product of the two integral terms is obtained and then multiplied by 2, the result of which is denoted as B.

[0091] 3) Solve Q(t|S0)

[0092] Finally, substituting the expressions of the numerator A and the denominator B into the original formula of Q(t|S0), we obtain:

[0093]

[0094] Explanation of each part of the above formula:

[0095] A: represents the variance σ 2 (S f ) and α(S f ) and α(S min ) is the product of the exponential difference of the failure threshold S f The variance at α(S f ) in S f and S min The sensitivity of the changes between .

[0096] B: It consists of two integral terms, reflecting the min and S f Nearby α(S t ) changes on the system state. These integral terms are expressed by α'(S t ) and α”(S t )(i.e. α(S t ) to capture α(S t ) local changes.

[0097] t: time variable, which represents the time interval from the initial vibration state S0 to the current time t. It reflects the evolution of the system state over time.

[0098] This method can be used to calculate Q(t|S0) more efficiently, and the calculation accuracy is also improved due to the use of polynomial series expansion. This has important application value in evaluating system reliability and predicting system life.

[0099] (4) Method for solving the probability of effective working state based on the fractional expression of series expansion

[0100] Based on the above description, this embodiment provides an algorithm implementation method for solving the probability of an effective working state based on a fractional expression of series expansion, which is particularly suitable for evaluating the performance of a system in the fields of reliability analysis, system life prediction, etc. The method efficiently calculates the fractional expression related to the probability of an effective working state by using Taylor series expansion and numerical integration technology.

[0101] This method mainly includes the following steps:

[0102] 1) Initialization parameters: initial vibration state S0, 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 )wait.

[0103] 2) Calculate the derivative: Use numerical differentiation method to calculate α(S t ) in S min and S f The first and second order derivatives at .

[0104] 3) Series expansion: Using Taylor series expansion, α(S t ) in S min and S f The polynomial form is approximated at , and the third-order and higher-order terms are neglected.

[0105] 4) Calculate the numerator A: Based on the result of the series expansion, calculate the numerator A of the fractional expression.

[0106] 5) Calculate the denominator B:

[0107] οDefine two integral functions, corresponding to S min and S f Nearby α(S t ) is the weighted integral of .

[0108] ο Compute these two integrals using numerical integration methods.

[0109] οMultiply the results of the two integrals to obtain the denominator B of the fractional expression.

[0110] 6) Calculate the probability of effective working state Q(t|S0): Substitute the numerator A and denominator B into the formula Calculate the probability of effective working state.

[0111] The above method can efficiently calculate the fractional expression through series expansion and numerical integration technology, so as to quickly evaluate the probability of effective working state of the system and meet the needs of reliability analysis and system life prediction. At the same time, this method is applicable to different types of α(S t ) functions and different system parameters, with strong flexibility and versatility.

[0112] According to the above process, by adjusting the time t, the Q(t|S0) corresponding to the corresponding time t can be obtained, or the relationship between the time t and the corresponding Q(t|S0) can be fitted through a neural network. After that, the probability of the effective working state at any time can be predicted using the fitted neural network.

[0113] This embodiment takes the above theoretical analysis as the core and forms the following stability prediction method of a random vibration system in a random vibration environment. The flowchart of the method is as follows: Figure 1 As shown, the following steps are included:

[0114] Step S1: Experiment on the random vibration process of the random vibration system under a given initial vibration state, and obtain the vibration state and its drift function, diffusion function, and failure threshold of the vibration state at each experimental time.

[0115] Step S2: According to the fractional expression of the system effective working probability, the data obtained from the experiment is processed by a polynomial series expansion method to obtain the corresponding relationship between each experimental time and the value of the system effective working probability, so as to construct a sample set; and the sample set is used to train and test to obtain a neural network model for real-time solution of the system effective working probability.

[0116] Step S3: Based on the tested neural network model, predict the stability of the random vibration system at the corresponding prediction time.

[0117] 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 vibrations, such as precision machine tool systems, aircraft engine systems, and automobile suspension systems. Under the influence of random vibrations, changes in vibration states can often reflect the health of the equipment, and the vibration state transfer probability density can monitor the vibration state of the equipment in real time, while the system effective working probability can evaluate the possibility of the system maintaining an effective working state within a period of time under a given initial vibration state condition, so as to achieve performance evaluation of the random vibration system. This method helps to evaluate the performance of the random vibration system within the predicted time and ensure the reliability 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 under 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.

[0118] When a random vibration system is subjected to random vibration, its initial vibration state will be affected by many factors, including but not limited to:

[0119] Initial conditions: the system's initial position, velocity, acceleration and other state quantities.

[0120] External excitation: Characteristics of the random vibration source, such as frequency, amplitude and duration of vibration.

[0121] System parameters: These include the mass and stiffness of the system, which affect the system's response to vibration.

[0122] Damping: Energy dissipation mechanisms in a system, such as friction and air resistance, which affect the rate at which vibrations decay.

[0123] 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.

[0124] 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.

[0125] Environmental factors: Environmental conditions such as temperature and humidity, which may change material properties and thus affect the vibration response.

[0126] Randomness: Since random vibrations are inherently uncertain, the vibration response of the system may vary due to randomness even under the same initial conditions.

[0127] Initial stress state: The initial stress or strain state that may exist in the system, which affects the system's response to vibration.

[0128] Boundary conditions: The support conditions and boundary constraints of the system, which determine how the vibration energy propagates.

[0129] 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.

[0130] 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:

[0131] Fluctuation amplitude: The difference between the maximum and minimum values ​​of the vibration state, reflecting the intensity of the vibration.

[0132] Fluctuation frequency: the speed of change of vibration state, that is, the number of times the vibration state changes per unit time.

[0133] Wave cycle: the time required to complete a complete wave.

[0134] Fluctuation phase: In periodic vibration, the phase of the vibration state at a specific point in time.

[0135] Randomness of fluctuations: Due to the influence of random vibrations, changes in vibration states may present unpredictable random fluctuations.

[0136] Nonlinearity of fluctuations: If the system response exhibits nonlinear characteristics, the changes in the vibration state may not follow a simple linear law.

[0137] Energy distribution of vibration: The distribution of energy in a vibration state at different frequencies can usually be described by the power spectral density.

[0138] Coherence of fluctuations: the consistency or stability of a vibrational state over time.

[0139] Autocorrelation of fluctuations: how similar the vibrational states are at different points in time.

[0140] Cross-correlation of fluctuations: correlation between vibration states in different degrees of freedom or in different directions.

[0141] To quantify the degree of fluctuation of the vibration state over time, the following methods can be used:

[0142] Time history analysis: Analyze the fluctuation characteristics by recording the changes of vibration state over time.

[0143] 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.

[0144] Power Spectrum Analysis: Calculate the power spectrum density of the vibration state to understand the energy distribution of different frequency components.

[0145] Autocorrelation and cross-correlation analysis: Analyze the similarity or correlation of vibration states at different time points or in different directions.

[0146] Statistical analysis: Use statistical methods, such as variance, standard deviation, mean, etc., to quantify the degree of fluctuation in vibration conditions.

[0147] 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.

[0148] Based on the above related descriptions, the fractional expression of the effective working state probability Q(t|S0) is shown in formula (4). 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 system effective working probability corresponding to the experimental time.

[0149] 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 the integral function α(S t ) takes the minimum value of the vibration state S min ; S f Indicates the failure threshold.

[0150] 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 (5) and (6), and the higher-order terms are omitted (the quadratic terms are retained as an example below), to obtain the corresponding polynomial series expansion expressions.

[0151] Step S23: Calculate the value of the system effective working probability corresponding to the experimental time t according to the correlation between the polynomial series expansion expression and formula (3) and formula (4).

[0152] Specifically, according to the relationship between the polynomial series expansion expression and formula (3) and formula (4), the following parameters are calculated:

[0153] A=σ 2 (S f )·exp[-(α(S f )-α(S min ))]

[0154]

[0155] Among them, ε represents the infinitesimal neighborhood width.

[0156] The value of the system effective working probability corresponding to the experimental time t

[0157] By traversing all experimental times, the corresponding relationship between each experimental time and the value of the system's effective working probability can be obtained. Afterwards, a sample set is constructed with the experimental time t as input and the corresponding value of the system's effective working probability Q(t|S0) as output as a set of sample data; and the sample set is divided into a training sample set and a test sample set. The neural network model is trained with the training sample set, and the trained neural network model is tested with the test sample set until the test passes, thereby obtaining a neural network model for real-time solution of the system's effective working probability.

[0158] After the test is passed, the neural network that has passed the test can be used to perform subsequent predictions. It should be noted that during the experiment of step S1, the number of experiments that can be performed is relatively limited, taking into account the experimental cost and difficulty. Therefore, this embodiment obtains the correlation between the experimental time t and the corresponding value Q(t|S0) of the system effective working probability by executing steps S1-S2, and simulates this correlation through a neural network. After that, the value of the system effective working probability of the random vibration system at any predicted time before failure can be predicted. Therefore, in step S3, the value of the corresponding system effective working probability can be predicted based on the predicted time, and the specific process is described as follows.

[0159] Step S31: During the actual operation, when the random vibration system takes the vibration initial state as the vibration starting state, the predicted time is input into the neural network model that has passed the test, and the neural network model predicts the system effective working probability of the output predicted time.

[0160] Step S32: Predict the stability of the random vibration system at the corresponding prediction time according to the system effective working probability at the prediction time.

[0161] In step S32, the following operations can be specifically performed to predict the stability of the random vibration system at the corresponding prediction time:

[0162] Judge whether the system effective working probability at the prediction time is greater than the preset system effective working probability threshold. If so, it indicates that the stability of the random vibration system at the prediction time is strong; if not, it indicates that the stability of the random vibration system at the prediction time is insufficient, and it is necessary to strengthen the monitoring of the random vibration process and prepare emergency measures.

[0163] The stability prediction method of the random vibration system provided in this embodiment is suitable for various different types of random vibration systems. Below, several random vibration systems and their application examples are given to help technicians better understand and implement the related technologies.

[0164] (1) High-speed railway train suspension system

[0165] Application background: The high-speed railway train suspension system is affected by various random vibrations such as track irregularities and bridge vibrations during operation, and its performance directly affects the running smoothness of the train and the comfort of passengers.

[0166] In the specific implementation process, collect vibration-related data of the train under different speeds and different track conditions, and implement the training and testing of the relevant neural network model by performing the above step S2. Then, according to the prediction results of the neural network model, the stability of the high-speed railway train suspension system can be predicted and necessary optimization and adjustment can be carried out. Exemplarily, the following quantitative judgment criteria can be formulated: Set the effective working state probability threshold (such as Q_threshold = 0.95). When the predicted Q(t|S_0) < Q_threshold, it is considered that the high-speed railway train suspension system needs maintenance or replacement.

[0167] (2) Offshore wind power equipment foundation structure

[0168] Application background: The foundation structure of offshore wind power equipment (such as wind turbines) is affected by various random loads such as wind, waves, and currents in the marine environment, and its stability is crucial for the safe operation of the equipment.

[0169] During the specific implementation process, the random load characteristics in the marine environment are analyzed, and the vibration state of the foundation structure is monitored in real time by installing sensors to realize the collection of vibration-related data. Based on the time-evolving random vibration equation, a dynamic model of the foundation structure of offshore wind power equipment is constructed. Subsequently, an intelligent method can be used to calculate the probability of an effective working state of the foundation structure within a given time. Subsequently, a stability assessment can be performed based on this, that is, the safety risk of the foundation structure is assessed based on the calculation results. Exemplarily, the following quantitative judgment criteria can be formulated: a failure probability threshold is set (such as P_fail=0.05). When the calculated failure probability is greater than the threshold, it is considered that the stability of the foundation structure is poor and there is a safety risk. Assuming that the failure probability of a certain offshore wind power equipment foundation structure during a specific storm is 0.03, which is lower than the threshold but close to the critical point, it is recommended to strengthen monitoring and prepare emergency measures.

[0170] (3) Industrial robot arm

[0171] Application background: When an industrial robot performs complex tasks, its arm will be affected by dynamic loads and mechanical vibrations. Accurately evaluating its working status is of great significance to ensuring production efficiency and product quality.

[0172] During the specific implementation process, the load characteristics of the industrial robot arm when performing different tasks are analyzed, and the vibration state of the arm is monitored by installing a vibration sensor. Subsequently, based on the time-evolved random vibration equation, a dynamic model of the arm is established, and the above fractional term solution method is used to calculate the probability of the arm's effective working state under a given task. After that, a maintenance plan can be formulated based on the evaluation results. Exemplarily, the following quantitative judgment criteria are formulated: a state stability threshold is set (such as Q_stable = 0.90). When the probability of an effective working state is lower than this threshold, the arm is considered to be insufficiently stable. Assuming that in a production task, the probability of the robot arm's effective working state is 0.88, which is lower than the stability threshold, it is recommended to inspect and adjust the arm to improve production stability and product quality.

[0173] 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.

[0174] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for predicting the stability of a random vibration system in a random vibration environment, characterized in that: The method comprises: Conduct experiments on the random vibration process of the random vibration system under a given initial vibration state, and obtain 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 system effective working probability, the data obtained from the experiment are processed by a polynomial series expansion method to obtain the corresponding relationship between each experimental time and the value of the system effective working probability, so as to construct a sample set; the sample set is used to train and test a neural network model for real-time solution of the system effective working probability; Based on the tested neural network model, the stability of the random vibration system at the corresponding prediction time is predicted.

2. The method for predicting the stability of a random vibration system in a random vibration environment according to claim 1, characterized in that: The fractional expression of the system effective working probability is: Where Q(t|S0) represents the probability of effective operation 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.

3. The method for predicting the stability of a random vibration system in a random vibration environment according to claim 2, 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 .

4. The method for predicting the stability of a random vibration system in a random vibration environment according to claim 3, characterized in that: The corresponding relationship between each experimental time and the value of the system effective working probability is obtained by executing the following steps: 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(S t ) takes the minimum value of the vibration state S min ; Using polynomial series expansion, 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 system effective working probability corresponding to the experimental time t is calculated; Traverse all experimental times and obtain the corresponding relationship between each experimental time and the value of the system's effective working probability.

5. The method for predicting the stability of a random vibration system in a random vibration environment according to claim 4, 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=σ 2 (S f )·exp[-(α(S f )-α(S min ))] 6. The method for predicting the stability of a random vibration system in a random vibration environment according to claim 5, characterized in that: The value of the system effective working probability corresponding to the experimental time t 7. The method for predicting the stability of a random vibration system in a random vibration environment according to claim 6, characterized in that: The sample set is constructed in the following way: A sample set is constructed by taking the experimental time t as input and the corresponding value of the system effective working probability Q(t|S0) as output as a set of sample data.

8. The method for predicting the stability of a random vibration system in a random vibration environment according to claim 7, characterized in that: The neural network model used to solve the effective working probability of the system in real time is obtained by the following method: Divide the sample set into a training sample set and a test sample set; The neural network model is trained using the training sample set, and the trained neural network model is tested using the test sample set until the test passes, thereby obtaining a neural network model for real-time solving the probability of effective operation of the system.

9. The method for predicting the stability of a random vibration system in a random vibration environment according to claim 7 or 8, characterized in that: Based on the tested neural network model, predict the stability of the random vibration system at the corresponding prediction time, and execute: In the actual operation process, when the random vibration system takes the vibration initial state as the vibration starting state, the predicted time is input into the neural network model that has passed the test, and the neural network model predicts the system effective working probability of the output predicted time; The stability of the random vibration system at the corresponding prediction time is predicted according to the effective working probability of the system at the prediction time.

10. The method for predicting the stability of a random vibration system in a random vibration environment according to claim 9, characterized in that: The stability of a random vibration system is predicted at the corresponding prediction time as follows: Determine whether the system effective working probability at the predicted time is greater than the preset system effective working probability threshold, If so, it indicates that the random vibration system has strong stability at the predicted time; If not, it indicates that the stability of the random vibration system is insufficient at the predicted time.

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