Vibration process control method of random vibration system

Abstract

The invention discloses a vibration process control method of a random vibration system, belongs to the technical field of vibration control of the random vibration system, and solves the problems that in the prior art, a system effective working probability solving mode comprehensively considering randomness and uncertain influences in a random vibration environment is lacked, and vibration process control is achieved based on a solving result. The method comprises the following steps: respectively experimenting random vibration processes of a random vibration system under different working conditions, respectively processing experiment data under each working condition, and obtaining a corresponding relation among a vibration initial state under each working condition, each experiment time and a value of an effective working probability of the system to construct a sample set; training and testing the sample set to obtain a neural network model; when the actual vibration process of the random vibration system is controlled, the neural network model is utilized to predict a curve that the system effective working probability of the random vibration system changes along with the sampling time under different working conditions, and the actual vibration process of the random vibration system is controlled according to the curve.

Description

Technical Field

[0001] The invention relates to the technical field of random vibration system vibration control, and in particular to a random vibration system vibration process control method. Background Art

[0002] In the field of evaluating and analyzing the probability of effective operation of systems under random vibration environments, the development of technology has experienced an evolution from simple to complex, from qualitative to quantitative. In the early days, due to the limitations of technology and computing power, the evaluation of system stability and reliability mainly relied on experience and simple physical models, which made it difficult to accurately capture the impact of random vibration processes on the probability of effective operation of the system.

[0003] With the advancement of science and technology and the development of computer technology, especially the continuous improvement of numerical calculation methods and probability statistics theory, people have begun to try to use reliability block diagram method, fault tree analysis method and other methods to describe and analyze the vibration behavior of the system. These methods have improved the accuracy and reliability of the evaluation to a certain extent.

[0004] However, with the increasing complexity of application scenarios and the diversification of vibration environments, traditional evaluation methods have gradually exposed their limitations. On the one hand, these methods often have difficulty in accurately describing the dynamic characteristics and uncertainties of random vibration processes, resulting in large errors in the evaluation results; on the other hand, there is also a lack of effective methods for neighborhood analysis of the probability of effective operation of the system, which cannot provide detailed probability distribution information and is difficult to meet the needs of system design and optimization.

[0005] In summary, how to evaluate and analyze the probability of effective operation of the system in a random vibration environment and thereby realize vibration process control of the random vibration system is a 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 vibration process control method for a random vibration system, so as to solve the problem in the prior art of lacking a solution method for the effective operation probability of the system in a random vibration environment that comprehensively considers the influence of randomness and uncertainty, and realizing vibration process control based on the solution results.

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

[0008] Experiments are conducted on the random vibration process of the random vibration system under different working conditions to obtain experimental data under each working condition; the experimental data include: the initial state of vibration, the vibration state at each experimental time and its drift function, diffusion function and transition probability density function, and the failure threshold of the vibration state;

[0009] The experimental data under each working condition are processed respectively to obtain the corresponding relationship between the initial state of vibration under each working condition, each experimental time and the value of the effective working probability of the system, so as to construct a sample set; the sample set is used to train and test a neural network model for solving the effective working probability of the system in real time;

[0010] In the actual vibration process control of the random vibration system, the tested neural network model is used to predict the curve of the effective working probability of the random vibration system under different working conditions as a inverse of the sampling time, and the actual vibration process control of the random vibration system is performed according to the curve.

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

[0012] Furthermore, the actual vibration process control of the random vibration system is carried out in the following manner:

[0013] According to the curve of the effective working probability of the system under each working condition changing with the sampling time, the effective working time period of the random vibration system under the corresponding working condition is obtained;

[0014] The working condition with the longest effective working time period is selected, and the actual vibration process of the random vibration system is controlled by using the initial vibration state, the vibration state at each time, the drift function and the diffusion function under this working condition.

[0015] Furthermore, the effective working time period of the random vibration system under the corresponding working condition is obtained by performing the following operations:

[0016] According to the peak position and distribution range of the curve of the effective working probability of the random vibration system under the corresponding working conditions versus the sampling time, the effective working time period of the random vibration system under the corresponding working conditions is determined.

[0017] Furthermore, according to the peak position and distribution range of the curve of the system effective working probability varying with the sampling time, the effective working time period of the random vibration system under the corresponding working condition is determined, and the following is executed:

[0018] Determine the peak position according to the trend of the probability density function distribution curve of the effective working time of the random vibration system under the corresponding working conditions;

[0019] 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 under the corresponding working conditions.

[0020] Furthermore, the experimental data under each working condition are processed separately to obtain the corresponding relationship between the initial state of vibration under each working condition, each experimental time and the value of the effective working probability of the system, and execute:

[0021] Get the vibration state S at the experimental time t under the current working condition t , drift function m(S t ), diffusion function σ 2 (S t ), the transition probability density function P(t,S t |S0), 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 represents the failure threshold;

[0022] According to the expression of the system effective working probability Q(t|S0), the system effective working probability corresponding to the experimental time t under the current working condition is obtained;

[0023] By traversing all the experimental times under the current working condition, the corresponding relationship between the values ​​of the system effective working probability corresponding to each experimental time under the current working condition can be obtained.

[0024] Furthermore, the expression of the system effective working probability Q(t|S0) is:

[0025]

[0026] 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 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 size of the infinitesimal neighborhood.

[0027] Furthermore, the integral function α(S t ) is expressed as:

[0028]

[0029] Further, when the neural network model is an independent neural network model,

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

[0031] And divide the sample set into a training sample set and a test sample set;

[0032] 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.

[0033] Furthermore, when multiple neural network sub-models are combined as a neural network model,

[0034] Configure a neural network sub-model for each working condition;

[0035] Only the initial vibration state S0 and experimental time t under the current working condition are used as input, and the corresponding value of the system effective working probability Q(t|S0) is used as output as a set of sample data to construct a neural network sub-model sample set of the current working condition configuration, and divide it into a training sample set and a test sample set.

[0036] Furthermore, the neural network sub-model is trained using the training sample set, and the trained neural network sub-model is tested using the test sample set until the test passes, thereby obtaining a neural network sub-model for real-time solving the probability of effective operation of the system under the current working conditions.

[0037] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0038] The present invention discloses a vibration process control method for a random vibration system. Experiments are conducted on the random vibration process of the random vibration system under different working conditions to obtain experimental data under each working condition. According to the theoretical analysis in this embodiment, the corresponding relationship between the initial state of vibration under each working condition, each experimental time and the value of the effective working probability of the system is obtained, and the training, testing and prediction of the relevant model are realized accordingly. After that, the tested neural network model can be used to predict the curve of the effective working probability of the random vibration system under different working conditions as the sampling time changes, and the vibration process of the random vibration system is controlled according to the curve. The process comprehensively considers the influence of randomness and uncertainty in the random vibration environment, and the solution process is simple, efficient and accurate, which provides good technical guidance for technical personnel in this field to solve related problems. The method is applicable to various types of complex vibration environments. By adjusting the parameters and equations of the model, the present invention can flexibly cope with various types of vibration conditions and has wide applicability.

[0039] 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

[0040] 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;

[0041] Figure 1 The present invention provides a flowchart of a random vibration system vibration process control method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0042] 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.

[0043] A specific embodiment of the present invention discloses a vibration process control method for a random vibration system. First, the theory on which this embodiment is based is analyzed as follows.

[0044] The present invention relates to a neighborhood analysis method for the probability of effective working state based on intelligent integral function solution, which is particularly suitable for evaluating and analyzing the probability of effective working of a system under a random vibration environment. The method realizes accurate calculation and neighborhood analysis of the probability of effective working of the system by constructing a probability density transfer function of a random vibration process and combining intelligent integral solution technology.

[0045] (1) Model setting and equation transformation

[0046] Basic vibration function: Set the basic vibration function S t It is a random process that characterizes vibration characteristics, and its initial vibration state is S0. This function reflects the dynamic changes of the vibration state of the system.

[0047] System effective working probability: Define the system effective working probability as Q(t|S0), which represents the probability that the system maintains an effective working state within time t under a given initial vibration state S0. t The failure threshold S is defined as the vibration state f .

[0048] State transition probability density function: Establish the vibration state S from the initial vibration state S0 to any time t t The transition probability density function p(t,S t |S0), which describes the dynamic transition law of the system's vibration state over time.

[0049] Based on the above model settings, this embodiment constructs the following equation to describe the probability density transfer process of the system vibration state:

[0050]

[0051] 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 m(S t ),σ 2 (S t ) respectively reflect the determinism and randomness of the system vibration state transition.

[0052] The probability of effective working state Q(t|S0) is given by the state transition probability density function p(t,S t |S0) in the failure range S f The integral inside is obtained, that is:

[0053]

[0054] In order to solve the above equation more conveniently, the following transformation is performed:

[0055] 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:

[0056]

[0057] 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:

[0058]

[0059] On this basis, we can combine the intelligent integral solving technology to solve the above transformed equations and obtain the expression of the system effective working probability Q(t|S0).

[0060] (2) Q value solution

[0061] Based on the above description, it can be seen that this embodiment establishes a probability density function model to describe the system vibration state transition, and introduces the definition of the system effective working probability Q(t|S0). In order to calculate this probability more accurately, the model equation needs to be further analyzed and transformed.

[0062] 1) Set the integral function α(S t )

[0063] First, define an integral function α(S t ), the integral function reflects the vibration state variable S during the vibration process t With the diffusion function σ 2 (S t ) and drift function m(S t ). Specifically, α(S t ) is given by the following formula:

[0064]

[0065] This function plays a key role in subsequent calculations because it contains important information about the dynamic characteristics of the system's vibration process.

[0066] 2) Analysis of α(S t ) in S t ∈(0,S f )

[0067] Next, focus on α(S t ) in S t The value is (0,S f ) interval. In particular, assuming that in S t =S min At α(S t ) takes the minimum value. This usually means: when the system vibration state is S min When it is near, the probability density function of its state transition has a higher value, that is, the system state is more stable or easier to change in this area.

[0068] In order to more precisely describe S min The properties of the neighborhood, set an infinitesimal neighborhood [S min -ε,S min +ε], where ε is a small positive number. This neighborhood will be used for subsequent integral calculations.

[0069] 3) Solve the expression of Q(t|S0)

[0070] Based on the above settings, the specific expression of Q(t|S0) can be derived. First, starting from the previously obtained equations (1)-(5), after a series of mathematical transformations and derivations, the following expression of Q(t|S0) is obtained:

[0071]

[0072] This expression contains several key components:

[0073] a) Probability density function p(t,S f |S0) and its derivative: This part reflects that the random vibration system reaches the failure threshold S after time t in the initial vibration state S0. f The probability of S f The rate of change.

[0074] b) Diffusion function σ 2 (S f ): This coefficient describes the randomness of the system's vibration state, and its size determines the uncertainty of the system's state transition.

[0075] c) Integral term: It contains two integral parts, corresponding to α(S t ) in S min and S f The two integral terms reflect the stability or transition trend of the system state near these key points and play a decisive role in the calculation of Q(t|S0).

[0076] Through the above expression, the probability Q(t|S0) that the system remains in an effective working state can be calculated more accurately, and the reliability and stability of the system under different working environments can be evaluated by analyzing the changes in this probability under different parameters and conditions. This method provides a powerful tool and support for system design and optimization.

[0077] (4) Direct calculation method of Q value

[0078] Based on the above description, this embodiment also proposes a method for determining the probability α(t|S0) that the system remains in an effective working state by direct calculation. The method is based on integration and numerical approximation technology. The following is a detailed description of the steps of this solution method.

[0079] 1) Define related functions

[0080] First, define the functions related to the calculation of Q(t|S0), including σ 2 (S t )(diffusion function), m(S t )(drift function) and p(t,S f|S0)(probability density function). These functions can be set according to specific application scenarios and physical models.

[0081] 2) Set parameters

[0082] Set the system's initial vibration state S0, time parameter t, and system failure state S f , α(S t ) The point S where the minimum value is obtained min and the size of the infinitesimal neighborhood ε. These parameters can be adjusted according to the actual operation of the system.

[0083] 3) Calculate α(S t ) Function value

[0084] In order to calculate α(S t ), we need to first calculate σ 2 (S t )About S t By setting a difference step size h, S can be calculated t The function values ​​on the left and right sides are used to obtain the approximate value of the derivative. Then, according to α(S t ) and calculate its value in S t The value at .

[0085] 4) Calculate the value of Q(t|S0)

[0086] When calculating Q(t|S0), first calculate S min Nearby and S f The integral values ​​in two infinitesimal neighborhoods near . For these two integrals, by setting the integral step size h, the integral interval is divided into several subintervals, and the area approximation is used in each subinterval. Then, according to the definition of Q(t|S0), Q_factor (including m(S f ) and σ 2 (S f ), that is, the partial derivative of and compare it with the two

[0087] The integrated values ​​are multiplied to obtain the final result of Q(t|S0).

[0088] (5) Q value conversion calculation method

[0089] In addition, this embodiment also provides a method for evaluating the probability Q(t|S0) that the system remains in an effective working state by transforming calculations. Compared with the direct calculation method, a new method is used for processing the integral. Based on the use of polynomials to approximate the function curve. The integral interval is divided into several small intervals, and then the function curve in each small interval is interpolated to calculate the integral value of each small interval, and these integral values ​​are added to obtain the final approximate value. This method can further handle complex integral problems related to the state transition of the vibration system. Compared with the previous method, this method is better in the approximate calculation of smooth functions. In actual use, you can choose to use direct calculation or transformation calculation method according to the specific situation of the function.

[0090] 1) Define related functions

[0091] First, we define functions closely related to the calculation of Q(t|S0), including σ 2 (S t )(diffusion function), m(S t )(drift function) and p(t,S f |S0)(probability density function). These functions describe the dynamic characteristics of the system state.

[0092] 2) Set parameters

[0093] Set the system's initial vibration state S0, time parameter t, and system failure state S f , α(S t ) The point S where the minimum value is obtained min and the size of the infinitesimal neighborhood ε. At the same time, the difference step size h is also set for derivative and integral calculations in numerical approximation.

[0094] 3) Calculate α(S t ) Function value

[0095] α(S t ) function is the key part in the calculation of Q(t|S0). By using the central difference method, using the set difference step size h, we can calculate σ 2 (S t )About S t The derivative of Then, combined with m(S t ) value, calculate α(S t ) in a specific S t The function value at the point.

[0096] 4) Calculate the value of Q(t|S0)

[0097] In the calculation of Q(t|S0), S is first calculated. min Nearby and S fThe integral values ​​in two infinitesimal neighborhoods nearby (integral1 and integral2). By setting an appropriate step size h, the integral interval is divided into several subintervals, and the Simpson rule is applied to perform integral calculations in each subinterval. Then, according to the definition of Q(t|S0), the integral value containing m(S f ) and σ 2 (S f ) The Q_factor of the partial derivative. Finally, multiply the Q_factor with the two integral values ​​to get the final result of Q(t|S0).

[0098] (6) Neural network calculation method of Q value

[0099] This embodiment also provides a Q value calculation method based on a neural network. The method trains a neural network model to approximate the complex functions in the model, and calculates the precise Q value accordingly.

[0100] First, a specific implementation method of the direct calculation method of the Q value

[0101] The specific implementation method of the direct calculation method of the system effective working probability Q value is as follows:

[0102] First, define the system state variance function σ 2 (i.e. σ 2 (S t )), mean function m(i.e. m(S t )) and the probability density function p(i.e., p(t,S f |S0)). Among them, σ 2 The function receives the state variable S_t as input and returns the variance value under this state; the m function also receives S_t as input and returns the corresponding mean; the p function calculates the probability density of transition from the S_0 state to the S_f state based on the given time t, failure state S_f and initial vibration state S0. Set the parameters required for calculation according to the actual situation.

[0103] Next, in the process of calculating the Q value, firstly, each value of the time parameter t is traversed by looping. For each value of t, the Q_t_given_S0 function (designed according to formula (6)) is called to calculate the corresponding Q value.

[0104] In the Q_t_given_S0 function, first set the difference step size h. Then calculate the integral value near S_min and S_f. Specifically, by passing in different functions and integral ranges, calculate the integral value integral1 of exp(-alpha(S_t,sigma2,m,h)) in the range [S_min-epsilon,S_min+epsilon] and the integral value integral2 of exp(alpha(S_t,sigma2,m,h)) in the range [S_f-epsilon,S_f]. Therefore, integral1 corresponds to the integral value in formula (6) Integral2 corresponds to the formula (6)

[0105] In calculating the remainder of Q_t_given_S0 (i.e. When , the Q_factor is obtained by calculating the partial_derivative of the differential approximate derivative of the sigma2 function near S_f (in this case, the p function is regarded as a function of t, not a function of S_f), and combining the values ​​of the m function and the p function at S_f. If the p function is a function of S_f, the partial_derivative of the differential approximate derivative of the sigma2 function and the p function near S_f is calculated instead, and the Q_factor is obtained by combining the values ​​of the m function and the p function at S_f.

[0106] Finally, Q_factor is multiplied by integral1 and integral2 to obtain the system effective working probability Q value.

[0107] Through the above steps, the effective working probability Q value of the system at different times t can be efficiently calculated.

[0108] Second: Specific implementation method of Q value transformation calculation method

[0109] This process provides a specific implementation method for the transformation calculation of the system effective working probability Q value, and calculates the effective working probability of the system state at different times.

[0110] First, set the system initial state S0, the range of the time parameter t, the system failure state S_f, the point S_min where alpha takes the minimum value, and the size of the infinitesimal neighborhood epsilon. These parameters can be defined according to the actual system situation. And define a difference step size h, which is used to approximate the derivative calculation, and the size of the step size can be adjusted as needed.

[0111] Then, call the Q_t_given_S0 function to calculate the Q value at different times t. In the Q_t_given_S0 function, calculate the integral value near S_min and S_f. Specifically, by passing in different functions and integral ranges, calculate the integral value integral1 of exp(-alpha(S_t,sigma2,m,h)) in the range [S_min-epsilon,S_min+epsilon], and the integral value integral2 of exp(alpha(S_t,sigma2,m,h)) in the range [S_f-epsilon,S_f].

[0112] Before calculating the integral value, the value of the alpha function is calculated first. Specifically, for a given S_t value, the function values ​​S_left and S_right on the left and right sides of S_t are calculated, and then the derivative of sigma2, d_sigma2, is calculated. Next, the value of alpha_integrand is calculated according to the definition of the alpha function and returned as the value of the alpha function.

[0113] When calculating the rest of Q_t_given_S0, the Q_factor is obtained by calculating the partial_derivative of the differential approximate derivative of the sigma2 function near S_f and combining the values ​​of the m function and the p function at S_f. Finally, Q_factor is multiplied by integral1 and integral2 to obtain the effective working probability Q value of the system.

[0114] In the implementation of the integral method, we first check whether the number of intervals is an even number, then generate a sequence of equally spaced x values ​​and calculate the corresponding sequence of y values. Then we calculate the integral value integral.

[0115] Through the above steps, the effective working probability Q value of the system at different times t can be calculated.

[0116] The specific implementation of the Q value calculation method based on the neural network is described as follows:

[0117] First, set the necessary parameters, including S_min, S_f, epsilon, etc. These parameters are determined according to the specific model input.

[0118] Next, generate data for training the neural network. Use thousands of equally spaced training data points S_t_train generated in the interval [S_min-epsilon, S_f+epsilon] as the input of the neural network. At the same time, due to the known d_sigma2 and m(S_t) functions, set the target function targets to the corresponding function form and calculate the corresponding target value target_values.

[0119] Then, create a neural network model. Set the appropriate hidden layer size, create a neural network, and assign the neural network object to the variable net.

[0120] Next, prepare the neural network training data. Arrange the input data S_t_train and target value target_values, and use the train function to train the neural network. Pass the input data S_t_train and target value target_values ​​as parameters to the train function, train the neural network and return the trained network net and training record tr.

[0121] After training is completed, the Q_t_given_S0_nn function is called to calculate the Q value. For a given time series t, each time point is traversed and the Q_t_given_S0_nn function is called to calculate the corresponding Q value. The function first calls the approx_alpha_part_nn function to use the trained neural network net to approximate the value of d_sigma2-2.*m(S_t). Then, alpha_integrand is calculated based on the approximation result, and the Q value is finally obtained.

[0122] In the approx_alpha_part_nn function, the dimension of the input S_t is first checked. If S_t is a column vector, it is transformed into a two-dimensional matrix (size [numSamples, 1]) by transposing it to ensure that the input requirements of the neural network are met. Then, S_t is passed as input to the neural network net to obtain the approximated d_sigma2-2.*m(S_t) value and return it as output.

[0123] In the alpha function, alpha_integrand is calculated using the approximation obtained by the approx_alpha_part_nn function.

[0124] Finally, in the Q_t_given_S0_nn function, the alpha function is integrated to get integral1 and integral2. Then the Q_factor is calculated. Finally, the Q_factor, integral1 and integral2 are multiplied to get the Q value.

[0125] Through the above implementation steps, the Q value calculation method based on neural network is realized, which improves the accuracy and efficiency of numerical calculation. More directly, since the above process can establish the corresponding relationship between time t and its corresponding system effective working probability, the neural network can be used to fit this relationship to obtain the corresponding prediction method of the system effective working probability.

[0126] This embodiment is based on the above theoretical analysis to form the following random vibration system vibration process control method, the flow chart of which is as follows: Figure 1 As shown, the following steps are included:

[0127] Step S1: Experiments are performed on the random vibration process of the random vibration system under different working conditions to obtain experimental data under each working condition; the experimental data include: the initial state of vibration, the vibration state at each experimental time and its drift function, diffusion function and transition probability density function, and the failure threshold of the vibration state.

[0128] Step S2: respectively process the experimental data under each working condition to obtain the corresponding relationship between the initial state of vibration under each working condition, each experimental time and the value of the effective working probability of the system, so as to construct a sample set; and use the sample set to train and test to obtain a neural network model for real-time solution of the effective working probability of the system.

[0129] Step S3: During the actual vibration process control of the random vibration system, the tested neural network model is used to predict the curve of the effective working probability of the random vibration system under different working conditions as a function of sampling time, and the actual vibration process control of the random vibration system is performed according to the curve.

[0130] 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, aerospace vibration systems, and automobile suspension systems. Under the influence of random vibration, the change of vibration state 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, and 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 the performance evaluation of the random vibration system. This method is helpful 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.

[0131] 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:

[0132] Initial conditions: the system's initial position, velocity, acceleration and other state quantities.

[0133] External excitation: Characteristics of the random vibration source, such as frequency, amplitude and duration of vibration.

[0134] System parameters: These include the mass and stiffness of the system, which affect the system's response to vibration.

[0135] Damping: Energy dissipation mechanisms in a system, such as friction and air resistance, which affect the rate at which vibrations decay.

[0136] 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.

[0137] 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.

[0138] Environmental factors: Environmental conditions such as temperature and humidity, which may change material properties and thus affect the vibration response.

[0139] Randomness: Since random vibrations are inherently uncertain, the vibration response of the system may vary due to randomness even under the same initial conditions.

[0140] Initial stress state: The initial stress or strain state that may exist in the system, which affects the system's response to vibration.

[0141] Boundary conditions: The support conditions and boundary constraints of the system, which determine how the vibration energy propagates.

[0142] 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.

[0143] 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:

[0144] Fluctuation amplitude: The difference between the maximum and minimum values ​​of the vibration state, reflecting the intensity of the vibration.

[0145] Fluctuation frequency: the speed of change of vibration state, that is, the number of times the vibration state changes per unit time.

[0146] Wave cycle: the time required to complete a complete wave.

[0147] Fluctuation phase: In periodic vibration, the phase of the vibration state at a specific point in time.

[0148] Randomness of fluctuations: Due to the influence of random vibrations, changes in vibration states may present unpredictable random fluctuations.

[0149] Nonlinearity of fluctuations: If the system response exhibits nonlinear characteristics, the changes in the vibration state may not follow a simple linear law.

[0150] Energy distribution of vibration: The distribution of energy in a vibration state at different frequencies can usually be described by the power spectral density.

[0151] Coherence of fluctuations: the consistency or stability of a vibrational state over time.

[0152] Autocorrelation of fluctuations: how similar the vibrational states are at different points in time.

[0153] Cross-correlation of fluctuations: correlation between vibration states in different degrees of freedom or in different directions.

[0154] To quantify the degree of fluctuation of the vibration state over time, the following methods can be used:

[0155] Time history analysis: Analyze the fluctuation characteristics by recording the changes of vibration state over time.

[0156] 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.

[0157] Power Spectrum Analysis: Calculate the power spectrum density of the vibration state to understand the energy distribution of different frequency components.

[0158] Autocorrelation and cross-correlation analysis: Analyze the similarity or correlation of vibration states at different time points or in different directions.

[0159] Statistical analysis: Use statistical methods, such as variance, standard deviation, mean, etc., to quantify the degree of fluctuation in vibration conditions.

[0160] 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.

[0161] Based on the above related descriptions, the fractional expression of the effective working state probability Q(t|S0) is shown in formula (6). According to formulas (5) and (6), and the above related descriptions, the specific execution process of step S2 is described as follows.

[0162] In this embodiment, the initial vibration state under the same working condition is the same, and the vibration state at different times and its drift function, diffusion function and transfer probability density function are affected by the same or similar vibration excitation. The vibration excitations of the experimental data between different working conditions are different, and the corresponding vibration laws are also different.

[0163] In step S2, for each operating condition, at each experimental time of the operating condition, the following operations are performed to obtain the value of the system effective working probability corresponding to the experimental time.

[0164] Step S21: Obtain the vibration state S at the experimental time t under the current working condition t , drift function m(S t ), diffusion function σ 2 (S t ), the transition probability density function p(t,S t |S0), 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.

[0165] Step S22: According to the expression of the system effective working probability Q(t|S0), the data obtained in step S21 are operated (for operation details, see the above theoretical description) to obtain the system effective working probability corresponding to the experimental time t under the current working condition.

[0166] Step S23: traverse all experimental times under the current working condition to obtain the corresponding relationship between the values ​​of the system effective working probability corresponding to each experimental time under the current working condition.

[0167] The experimental data of each working condition executes the process of step S2, and the corresponding relationship between the initial state of vibration under each working condition, each experimental time and the value of the effective working probability of the system can be obtained to construct a sample set.

[0168] After that, the neural network model can be trained in two ways:

[0169] (1) Independent neural network model

[0170] The initial vibration state S0 and experimental time t under a working condition are used as input, and the corresponding value of the system effective working probability Q(t|S0) is used as output as a set of sample data to construct a sample set. The sample set is divided into a training sample set and a test sample set. The neural network model is trained with the training sample set, and the trained neural network model is tested with the test sample set until the test passes, and a neural network model for real-time solution of the system effective working probability is obtained.

[0171] (2) Combining multiple neural network sub-models as a neural network model

[0172] During the specific implementation process, if the results of the effective working probability of the system corresponding to different working conditions have large deviations, in order to improve the fitting accuracy and subsequent prediction accuracy, it is also possible to consider configuring a neural network sub-model for each working condition; and perform the following operations to train and test each neural network sub-model:

[0173] Only the initial vibration state S0 and experimental time t under the current working condition are used as input, and the corresponding value of the system effective working probability Q(t|S0) is used as output as a set of sample data to construct a neural network sub-model sample set of the current working condition configuration, and divide it into a training sample set and a test sample set.

[0174] The neural network sub-model is trained using the training sample set, and the trained neural network sub-model is tested using the test sample set until the test passes, thereby obtaining a neural network sub-model for real-time solving the probability of effective operation of the system under the current working conditions.

[0175] It should be noted that, in this embodiment, each neural network sub-model is independent of each other and combined in parallel to form a neural network model.

[0176] In the specific implementation process, if there is only one independent neural network model, the initial vibration state of different working conditions and the sampling times of uniform sampling are directly input into the neural network model, and the neural network model predicts and outputs the curves of the probability of effective operation of the random vibration system under different working conditions as the sampling time changes. If multiple neural network sub-models are combined as a neural network model, the initial vibration state of each working condition and the sampling times of uniform sampling are respectively input into the neural network sub-model configured for the corresponding working condition, and the neural network sub-model configured for the corresponding working condition predicts and outputs the curve of the probability of effective operation of the random vibration system under the corresponding working condition as the sampling time changes.

[0177] It should be noted that in the actual vibration process control process of the random vibration system, the effective working time length of the random vibration system is required to be relatively high, and it is hoped that the random vibration system can be kept in an effective working state for a long time to ensure the safe, stable and long-term operation of the random vibration system. Therefore, in this embodiment, after obtaining the curve of the effective working probability of the random vibration system under various working conditions as a function of the sampling time, the actual vibration process control of the random vibration system can be performed in the following manner:

[0178] (1) According to the curve of the effective working probability of the system under each working condition changing with the sampling time, the effective working time period of the corresponding working condition is obtained.

[0179] In the specific implementation process, the effective working time period of the random vibration system under the corresponding working condition is determined according to the peak position and distribution range of the curve of the effective working probability of the random vibration system under the corresponding working condition versus the sampling time. For example, the peak position is determined according to the trend of the probability density function distribution curve of the effective working time of the random vibration system under the corresponding working condition; the distribution range of the abscissa 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 under the corresponding working condition.

[0180] (2) Select the working condition with the longest effective working time period, and use the initial vibration state, vibration state at each time, drift function and diffusion function under the working condition to control the actual vibration process of the random vibration system. That is, select the vibration parameters corresponding to the working condition with the longest effective working time period to guide the actual vibration process of the random vibration system, so as to ensure that the random vibration system maintains an effective working state for a relatively long time and effectively improve the performance of the random vibration system. Exemplarily, the above process can be applied to the vibration control of precision mechanical equipment. By comparing the Q value comparison chart under different working conditions (i.e. control strategies), analyze the effect of each strategy on improving system performance. And adjust the actual control vibration working condition of the random vibration system through the comparison results to reduce the impact of vibration on the equipment.

[0181] 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.

[0182] 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 vibration process control method for a random vibration system, It is characterized in that The method comprises: Experiments are conducted on the random vibration process of the random vibration system under different working conditions to obtain experimental data under each working condition; the experimental data include: the initial state of vibration, the vibration state at each experimental time and its drift function, diffusion function and transition probability density function, and the failure threshold of the vibration state; The experimental data under each working condition are processed respectively to obtain the corresponding relationship between the initial state of vibration under each working condition, each experimental time and the value of the effective working probability of the system, so as to construct a sample set; the sample set is used to train and test a neural network model for solving the effective working probability of the system in real time; In the actual vibration process control of the random vibration system, the tested neural network model is used to predict the curve of the effective working probability of the random vibration system under different working conditions as a inverse of the sampling time, and the actual vibration process control of the random vibration system is performed according to the curve.

2. The random vibration system vibration process control method according to claim 1, It is characterized in that The actual vibration process control of the random vibration system is carried out in the following ways: According to the curve of the effective working probability of the system under each working condition changing with the sampling time, the effective working time period of the random vibration system under the corresponding working condition is obtained; The working condition with the longest effective working time period is selected, and the actual vibration process of the random vibration system is controlled by using the initial vibration state, the vibration state at each time, the drift function and the diffusion function under this working condition.

3. The random vibration system vibration process control method according to claim 2, It is characterized in that Obtain the effective working time period of the random vibration system under the corresponding working conditions by performing the following operations: According to the peak position and distribution range of the curve of the effective working probability of the random vibration system under the corresponding working conditions versus the sampling time, the effective working time period of the random vibration system under the corresponding working conditions is determined.

4. The random vibration system vibration process control method according to claim 3, It is characterized in that According to the peak position and distribution range of the curve of the system's effective working probability changing with the sampling time, determine the effective working time period of the random vibration system under the corresponding working conditions and execute: Determine the peak position according to the trend of the probability density function distribution curve of the effective working time of the random vibration system under the corresponding working conditions; 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 under the corresponding working conditions.

5. The random vibration system vibration process control method according to any one of claims 1 to 4, It is characterized in that Process the experimental data under each working condition separately, obtain the corresponding relationship between the initial state of vibration under each working condition, each experimental time and the value of the effective working probability of the system, and execute: Get the vibration state S at the experimental time t under the current working condition t , drift function m(S t ), diffusion function σ 2 (S t ), the transition probability density function P(t,S t |S 0 ), 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 represents the failure threshold; According to the system effective working probability Q(t|S 0 ) to obtain the effective working probability of the system corresponding to the experimental time t under the current working condition; By traversing all the experimental times under the current working condition, the corresponding relationship between the values ​​of the system effective working probability corresponding to each experimental time under the current working condition can be obtained.

6. The random vibration system vibration process control method according to claim 5, It is characterized in that The system effective working probability Q(t|S 0 ) is: Among them, Q(t|S 0 ) represents the random vibration system with the initial vibration state S 0 is the probability of effective operation of the system at the start and time t; α(S t ) represents the integral function; 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 size of the infinitesimal neighborhood.

7. The random vibration system vibration process control method according to claim 6, It is characterized in that The integral function α(S t ) is expressed as:

8. The random vibration system vibration process control method according to claim 7, It is characterized in that When the neural network model is an independent neural network model, Take the initial vibration state S under one working condition 0 and experimental time t as input, with the corresponding value of the system effective working probability Q(t|S 0 ) is output as a set of sample data to construct a sample set; And 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 random vibration system vibration process control method according to claim 7, It is characterized in that When multiple neural network sub-models are combined as a neural network model, Configure a neural network sub-model for each working condition; Only the initial vibration state S under the current working condition 0 and experimental time t as input, with the corresponding value of the system effective working probability Q(t|S 0 ) is output as a set of sample data to construct a neural network sub-model sample set of the current working condition configuration and divide it into a training sample set and a test sample set.

10. The random vibration system vibration process control method according to claim 9, It is characterized in that The neural network sub-model is trained using the training sample set, and the trained neural network sub-model is tested using the test sample set until the test passes, thereby obtaining a neural network sub-model for real-time solving the probability of effective operation of the system under the current working conditions.

Images