A reliability assessment method for mechanical systems under the influence of random vibration

Abstract

The present invention relates to a reliability assessment method for a mechanical system under the influence of random vibration, belongs to the field of reliability assessment technology, and solves the problem of the lack of accurate and fast reliability assessment methods for mechanical systems under the influence of random vibration in the prior art. The method comprises: analyzing the process of the mechanical system being affected by random vibration, obtaining historical data of the random vibration state of the mechanical system under the influence of different random vibrations and constructing a sample set, obtaining a first neural network model for real-time solution of the probability of effective working of the system, a second neural network model for real-time solution of the probability density function of the effective working time of the system, and a third neural network model for real-time solution of the average effective working time of the system; processing real-time data to obtain model input, using three neural network models to respectively solve the probability of effective working of the system, the probability density function of the effective working time of the system, and the average effective working time of the system to achieve reliability assessment.

Description

Technical Field

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

[0002] In the field of mechanical engineering, the prediction and evaluation of the dynamic response of mechanical systems under the influence of random vibration has always been a hot topic and a difficult topic. With the rapid development of modern industrial technology, the random vibration environment faced by mechanical systems has become increasingly complex and diverse, such as earthquakes, wind loads, traffic vibrations, etc. These random vibrations have a significant impact on the performance, life and safety of mechanical systems. Therefore, how to accurately predict and evaluate the dynamic response of mechanical systems under the influence of random vibration has become the key to ensuring the safe and stable operation of mechanical systems.

[0003] Traditional mechanical vibration analysis methods are mainly based on linear vibration theory and deterministic analysis methods. These methods are effective in dealing with simple vibration problems. However, these methods often fail to meet the needs of complex random vibration environments. On the one hand, they cannot accurately describe the time-varying characteristics and uncertainty of random vibrations; on the other hand, they ignore the structural characteristics and nonlinear effects of the system itself, resulting in a large deviation between the predicted results and the actual situation.

[0004] In order to overcome the limitations of traditional methods, researchers began to explore mechanical vibration analysis methods based on random vibration theory. Random vibration theory regards vibration as a random process and introduces probability statistics to describe the time-varying characteristics and uncertainty of vibration. This method can more accurately reflect the dynamic response of mechanical systems in random vibration environments, and provides new ideas for the optimization design and reliability evaluation of mechanical systems.

[0005] However, the mechanical vibration analysis method based on random vibration theory also has certain challenges. On the one hand, the modeling and solution of the random vibration process requires the use of complex mathematical tools, which is computationally intensive and difficult to solve; on the other hand, how to combine random vibration theory with the actual working conditions of the mechanical system to establish an accurate and reliable model is also a problem that needs to be solved urgently.

[0006] In summary, how to achieve accurate and rapid reliability assessment of mechanical systems under the influence of random vibration has become a problem that needs to be solved urgently. Summary of the invention

[0007] In view of the above analysis, an embodiment of the present invention aims to provide a reliability assessment method for a mechanical system under the influence of random vibration, so as to solve the problem of lack of an accurate and fast reliability assessment method for a mechanical system under the influence of random vibration in the prior art.

[0008] The present invention discloses a reliability evaluation method for a mechanical system under the influence of random vibration, the method comprising:

[0009] Analyze the process of the mechanical system being affected by random vibration, and obtain historical data of the random vibration state of the mechanical system under the influence of different random vibrations; the random vibration state includes: the initial vibration state, and the average rate and fluctuation degree of the initial vibration state changing over time;

[0010] Based on the historical data, sample sets of each neural network model are respectively constructed to train and test a first neural network model for solving the probability of effective working of the system in real time, a second neural network model for solving the probability density function of the effective working time of the system in real time, and a third neural network model for solving the average effective working time of the system in real time;

[0011] Acquire real-time data of the initial vibration state of the mechanical system under the influence of the current random vibration, and generate inputs of each neural network model based on the real-time data, and use the first neural network model, the second neural network model and the third neural network model that have passed the test to solve the system effective working probability corresponding to the real-time data, the probability density function of the system effective working time, and the average effective working time of the system;

[0012] Based on the system effective working probability, the probability density function of the system effective working time, and the system average effective working time corresponding to the real-time data, the reliability evaluation of the mechanical system under the influence of the current random vibration is achieved.

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

[0014] Furthermore, the first neural network model for solving the effective working probability of the system in real time is trained and tested in the following way:

[0015] At each initial state of vibration Next, based on the initial state of vibration Average rate of change over time and volatility Based on the system effective working probability equation, the corresponding initial vibration state is derived The probability of effective operation of the system under The approximate analytical solution of the system effective working probability is the approximate analytical solution containing the initial state of vibration and time The analytical expression of is used to describe the probability of effective operation of the system With the initial state of vibration and time changes;

[0016] According to each initial state of vibration The approximate analytical solution of the system effective working probability under the condition of Next time The corresponding analytical solution ;

[0017] The initial state of vibration ,time And the corresponding analytical solution As a set of sample data, construct a sample set of a first neural network model; and divide the sample set of the first neural network model into a first training sample set and a first test sample set;

[0018] Obtain each group of sample data in the first training sample set, and use the initial state of vibration in each group of sample data ,time As input, the corresponding analytical solution As an output, training the first neural network model, and adjusting the parameters and structure of the first neural network model through a back propagation algorithm;

[0019] Obtain each group of sample data in the first test sample set, and use the initial state of vibration in each group of sample data ,time As input, the corresponding analytical solution As an output, the trained first neural network model is tested until the test passes, thereby obtaining a first neural network model for solving the probability of effective operation of the system in real time.

[0020] Furthermore, a second neural network model for solving the probability density function of the effective working time of the system in real time is obtained by training and testing in the following manner:

[0021] Get different time Discrete value, set time The upper limit is ; In different initial vibration states and time The grid composed of discrete points is initialized to store the numerical solution A matrix of values;

[0022] Based on the system effective working probability equation, according to the initial state of vibration , initial state of vibration Average rate of change over time and volatility , using explicit finite difference method, gradually updating the storage of numerical solutions The values ​​in the matrix of values ​​until the time limit is obtained Corresponding ;

[0023] The initial state of vibration And the corresponding numerical solution , As a set of sample data, construct a sample set of the second neural network model; and divide the sample set of the second neural network model into a second training sample set and a second test sample set;

[0024] Obtain each group of sample data in the second training sample set, and use the initial state of vibration in each group of sample data As input, the corresponding numerical solution , As an output, training a second neural network model, and adjusting the parameters and structure of the second neural network model through a back-propagation algorithm;

[0025] Obtain each group of sample data in the second test sample set, and use the initial state of vibration in each group of sample data As input, the corresponding numerical solution , As an output, the trained second neural network model is tested until the test passes, thereby obtaining a second neural network model for solving the probability density function of the effective working time of the system in real time.

[0026] Furthermore, the third neural network model for real-time solution of the average effective working time of the system is obtained by training and testing in the following way:

[0027] According to different initial vibration states , construct a memory for storing numerical solutions A matrix of values;

[0028] Based on the average effective working time equation, according to the initial state of vibration , initial state of vibration Average rate of change over time and volatility , using explicit finite difference method, gradually updating the storage of numerical solutions A matrix of values;

[0029] The initial state of vibration And the corresponding numerical solution As a set of sample data, construct a sample set of a third neural network model; and divide the sample set of the third neural network model into a third training sample set and a third test sample set;

[0030] Obtain each group of sample data in the third training sample set, and use the initial state of vibration in each group of sample data As input, the corresponding numerical solution As an output, training a third neural network model, and adjusting parameters and structure of the third neural network model through a back propagation algorithm;

[0031] Obtain each group of sample data in the third test sample set, and use the initial state of vibration in each group of sample data As input, the corresponding numerical solution As an output, the trained third neural network model is tested until the test passes, thereby obtaining a third neural network model for solving the average effective working time of the system in real time.

[0032] Furthermore, the system effective working probability equation is in the form of:

[0033] (1).

[0034] Furthermore, the average effective working time equation is in the form of:

[0035] (2)

[0036] when hour, is the average effective working time. is a preset value.

[0037] Further, the probability density function of the effective working time of the system corresponding to the real-time data is obtained by solving the following method:

[0038] The real-time data of the initial state of vibration is used as the input of the second neural network model that has passed the test, and the second neural network model predicts and outputs the system effective working probability corresponding to the real-time data , ;right , Perform differentiation to obtain the probability density function of the effective working time of the system .

[0039] Furthermore, the average effective working time of the system corresponding to the real-time data is obtained by solving the following method:

[0040] The real-time data of the initial state of vibration is used as the input of the third neural network model that has passed the test, and the third neural network model predicts and outputs the average effective working time of the system corresponding to the real-time data .

[0041] Furthermore, the system effective working probability corresponding to the real-time data is obtained by solving the following method:

[0042] The real-time data of the initial state of vibration is converted into time As the input of the first neural network model that has passed the test, the first neural network model predicts and outputs the real-time data and time The corresponding system effective working probability .

[0043] Furthermore, the reliability assessment of the mechanical system under the influence of the current random vibration is achieved by:

[0044] analyze The peak position and distribution range of the mechanical system are used to determine the effective working time period of the mechanical system; and Cumulative probability during the effective working period;

[0045] like Within the effective working time period, at this time, if The cumulative probability during the effective working time period is greater than the cumulative probability threshold, and If it is greater than the system effective working probability threshold, the evaluation result of the mechanical system is high reliability;

[0046] like Within the effective working time period, at this time, if The cumulative probability during the effective working period is not greater than the cumulative probability threshold, or, If it is not greater than the system effective working probability threshold, the evaluation result of the mechanical system is medium reliability;

[0047] Otherwise, the mechanical system is evaluated as having low reliability.

[0048] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0049] The reliability assessment method of a mechanical system under the influence of random vibration provided by the present invention obtains historical data of the random vibration state of the mechanical system under the influence of different random vibrations by analyzing the process in which the mechanical system is affected by random vibration; and based on the historical data, respectively constructs a high-precision sample set of each neural network model, which is used for training and testing to obtain a first neural network model for real-time solution of the effective working probability of the system, a second neural network model for real-time solution of the probability density function of the effective working time of the system, and a third neural network model for real-time solution of the average effective working time of the system; then, the model after the test can be used to quickly solve the effective working probability of the system corresponding to the real-time data, the probability density function of the effective working time of the system, and the average effective working time of the system; and by formulating a reliability assessment criterion matching therewith, the reliability assessment of the mechanical system under the influence of the current random vibration can be realized.

[0050] In this invention, by introducing the basic vibration function and random process theory, the dynamic response of the mechanical structure in the random vibration process can be accurately described. The model not only takes into account the time-varying characteristics and uncertainty of the vibration, but also combines the structural characteristics of the system itself, thereby improving the accuracy and reliability of the model.

[0051] The present invention also establishes an intelligent model and provides an efficient solution method. By solving the system effective working probability equation, the effective working time probability density function and the average effective working time equation, the effective working time of the system under a random vibration environment can be accurately predicted and evaluated. This method not only has high calculation efficiency, but also has accurate and reliable results, which provides strong support for the optimization design and reliability evaluation of mechanical structures. And by innovatively introducing the concept of effective working probability of the system, the working state of the system under random vibration is quantified. By setting thresholds and probability density functions, the reliability of the system can be intuitively evaluated, providing a scientific basis for system maintenance and fault prevention. It also intuitively reflects the performance of the system by defining and solving the average effective working time of the system, providing an important reference for system design and optimization.

[0052] In summary, the present invention uses intelligent means to accurately model and efficiently solve the mechanical vibration equations under the influence of random vibration, which solves the problem that traditional methods cannot accurately predict and evaluate the effective working time of the system, and provides strong support for the optimal design and reliability evaluation of mechanical structures.

[0053] 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

[0054] 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;

[0055] Figure 1 A flow chart of a reliability assessment method for a mechanical system under the influence of random vibration provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0056] 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.

[0057] A specific embodiment of the present invention discloses a reliability assessment method for a mechanical system under the influence of random vibration. First, the theoretical analysis based on this embodiment is described as follows.

[0058] In a random vibration environment, the vibration process of a mechanical system can be regarded as a complex random process. This embodiment first defines a basic vibration function , which describes the time-varying characteristics of the vibration of the mechanical system, where Represents time, Represents the initial state of vibration of the mechanical system.

[0059] Under the influence of random vibration, the performance of the mechanical system will change over time. When the vibration is too large and exceeds the structural bearing capacity of the mechanical system itself, the mechanical system will fail. Before failure, the mechanical system is in an "effective working" state. In order to quantify this effective working state, this embodiment introduces the system effective working probability The probability is defined as: given the initial vibration state Under the condition of time The possibility of maintaining effective working status within.

[0060] Furthermore, this embodiment sets a threshold , when the basic vibration function When the threshold is exceeded, the mechanical system is considered to be in failure. In order to describe the distribution of the effective working time of the system, this embodiment introduces the effective working time of the system. The probability density function of This function describes the initial vibration state. The effective working time of the mechanical system The probability distribution of .

[0061] In addition, in order to more intuitively evaluate the reliability of the system, this embodiment also defines the average effective working time of the system This indicator indicates that at a given initial vibration state The average length of time a mechanical system can remain effective under load.

[0062] (1) Model establishment

[0063] 1) System effective working probability equation

[0064] In order to describe the effective working probability of the mechanical system under random vibration, this embodiment introduces the system effective working probability equation, which describes the probability density function Over time and the initial vibration state The system effective working probability equation is as follows:

[0065] (1)

[0066] in, is the drift term, which represents the initial vibration state of the mechanical system The average rate of change over time, which describes the average motion trend of a random vibration process. is the wave term, representing the initial vibration state of the mechanical system The degree of fluctuation over time, which represents the uncertainty of the random vibration process.

[0067] 2) Probability density function of effective working time

[0068] In solving Afterwards, in order to get effective working time The probability density function of , need to About time Find the derivative and Value at:

[0069] (2)

[0070] 3) Average effective working time equation

[0071] In order to solve the average effective working time of the mechanical system , this implementation introduces a time The power function of and compare it with After multiplication, perform time integration. In this way, we can get The equation of Is effective work of The average effective working time equation is in the form of:

[0072] (3)

[0073] In particular, when hour, is the average effective working time. is a preset value.

[0074] (2) Parameter solution

[0075] 1) Solution

[0076] This embodiment proposes a method for solving the effective working probability of a mechanical system under the influence of random vibration. This method combines the approximate analytical solution and the neural network model to achieve different initial vibration states. and time Accurate estimation of the probability of effective operation of the system under .

[0077] Solve with approximate analytical solution: Under certain conditions, it can be derived that An approximate analytical solution of . Based on the given drift term function and the fluctuation function , using a specific function to approximate Changes with time and initial state. It should be noted that in this process, the approximate analytical solution is used to simplify With initial vibration state and time Although the expression of the relationship between will lose some accuracy, it can speed up the related solution process.

[0078] Solving with neural network model: In order to further improve the accuracy and efficiency of the solution, a neural network model is introduced to approximate The real solution of the problem. First, the approximate analytical solution is used to train the neural network. By adjusting the parameters and structure of the neural network, the neural network can accurately fit the training data. Then, the performance of the neural network is evaluated using test data, and the neural network is further optimized based on the evaluation results. Finally, the trained neural network can be used to quickly predict the probability of effective operation of the system under different initial states and times.

[0079] 2) Solution

[0080] This embodiment proposes a method for solving a given initial state of vibration The time when a certain event or threshold is reached The probability density function of Method. Probability density function Describes the initial state of vibration Starting from , the time distribution of the system reaching a certain state or threshold for the first time. This embodiment uses a method combining numerical solution and neural network model to estimate .

[0081] Solve with numerical solution: To estimate more accurately , using the finite difference method as a numerical method. First, a grid is constructed to store The associated stochastic process equations are then solved using an explicit finite difference method to update When the specified time is reached After that, by calculating the time and The two adjacent time steps The difference of the values ​​is approximated This difference approximation provides It should be noted that in this process, the initial state of vibration can be obtained by using the numerical solution method. and time More precise in certain situations To ensure that the difference accuracy.

[0082] Solving with a neural network model: A neural network model is further introduced to approximate First, the approximate analytical solution is used as training data to build and train the neural network model. By adjusting the parameters and structure of the neural network, the neural network can accurately fit the training data. Then the trained neural network model is used to predict the initial states of different vibrations. Next value.

[0083] However, since neural networks are usually used to approximate the function itself rather than its derivative, it is not possible to directly use neural networks to predict In contrast, this embodiment trains a neural network to approximate , and then through the output of the neural network Differences are used to approximate This embodiment assumes a fictitious "time increment" for performing the differencing.

[0084] 3) Solution

[0085] This embodiment also proposes a method for solving a given initial state of vibration Next moment The first moment It is usually related to the expectation or average value of a random process and is used to describe the evolution trend of the system state over time. The following describes in detail the solution method of the numerical solution and the neural network solution. The solution method.

[0086] Solve with numerical solution: In order to solve more accurately , build a grid to store different Under value Then, an explicit finite difference method is used to solve the first-order moment differential equation associated with the stochastic process. At each iteration, the current Under value and Update value Finally, extract all Under value value as a numerical solution.

[0087] Solving with a neural network model: To further improve the solution To improve the efficiency and accuracy of the problem, a neural network model is used to solve the problem. First, an approximate analytical solution or numerical solution is used as training data to build and train the neural network model. The value is taken as the input feature, and the corresponding The trained neural network model is then used to predict different Under value It should be noted that the performance and generalization ability of the neural network model depends on the quantity and quality of training data, the choice of network structure, and the setting of training parameters. Therefore, in practical applications, these parameters need to be carefully adjusted to optimize the performance of the neural network model.

[0088] This embodiment takes the above theoretical analysis as the core and forms the following reliability assessment method of a mechanical system under the influence of random vibration. The flow chart of the method is as follows: Figure 1 As shown, the following steps are included:

[0089] Step S1: Analyze the process of a mechanical system being affected by random vibration, and obtain historical data of random vibration states of the mechanical system under the influence of different random vibrations; the random vibration states include: an initial vibration state, and an average rate and fluctuation degree of the initial vibration state changing over time;

[0090] Step S2: constructing sample sets of each neural network model based on the historical data, respectively, for training and testing to obtain a first neural network model for real-time solution of the probability of effective working of the system, a second neural network model for real-time solution of the probability density function of the effective working time of the system, and a third neural network model for real-time solution of the average effective working time of the system;

[0091] Step S3: acquiring real-time data of the initial vibration state of the mechanical system under the influence of the current random vibration, and generating inputs of each neural network model based on the real-time data, and using the first neural network model, the second neural network model and the third neural network model that have passed the test to obtain the system effective working probability corresponding to the real-time data, the probability density function of the system effective working time, and the system average effective working time;

[0092] Step S4: Based on the system effective working probability, the probability density function of the system effective working time, and the system average effective working time corresponding to the real-time data, the reliability evaluation of the mechanical system under the influence of the current random vibration is realized.

[0093] Based on the above content, it can be known that in the specific implementation process, the random vibration state of the mechanical system under the influence of different random vibrations mentioned in step S1 includes: the initial vibration state , and the average rate at which the initial state of vibration changes over time and volatility . By obtaining the historical data of the random vibration state of the mechanical system under the influence of different random vibrations, it can be used as the basis for the subsequent neural network model training. It should be noted that the research focus of this embodiment is on how to obtain the effective working probability of the system, the probability density function of the effective working time of the system, and the average effective working time of the system on the basis of the known random vibration state, so as to realize the reliability assessment of the mechanical system under the current random vibration. Therefore, the method of obtaining the random vibration state is not the research focus of this embodiment. Relevant technical personnel can use existing methods or actual conditions to obtain the historical data and real-time data of the random vibration state, and implement the reliability assessment in this embodiment accordingly. Therefore, the following is only a brief analysis of the method of obtaining the random vibration state.

[0094] When a mechanical system is subjected to random vibration, its initial vibration state will be affected by many factors, including but not limited to:

[0095] Initial conditions: the system's initial position, velocity, acceleration and other state quantities.

[0096] External excitation: Characteristics of the random vibration source, such as frequency, amplitude and duration of vibration.

[0097] System parameters: These include the mass and stiffness of the system, which affect the system's response to vibration.

[0098] Damping: Energy dissipation mechanisms in a system, such as friction and air resistance, which affect the rate at which vibrations decay.

[0099] 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.

[0100] 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.

[0101] Environmental factors: Environmental conditions such as temperature and humidity, which may change material properties and thus affect the vibration response.

[0102] Randomness: Since random vibrations are inherently uncertain, the vibration response of the system may vary due to randomness even under the same initial conditions.

[0103] Initial stress state: The initial stress or strain state that may exist in the system, which affects the system's response to vibration.

[0104] Boundary conditions: The support conditions and boundary constraints of the system, which determine how the vibration energy propagates.

[0105] Therefore, in practical applications, if you want to accurately predict and analyze the initial vibration state of a mechanical system under the influence of random vibration, you usually need to use a combination of numerical simulation and experimental testing. Through these methods, you can better understand the behavior of the system and get a more accurate initial vibration state.

[0106] The average rate of change of the initial state of vibration over time usually refers to a measure of the change of the system's vibration state (such as displacement, velocity or acceleration) over time. In the case of random vibration, this rate may be affected by a variety of factors, causing it to exhibit nonlinear and random characteristics. In the specific implementation process, the response data 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 change of the vibration state. 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.

[0107] The degree of fluctuation of the initial state of vibration over time usually describes the fluctuation characteristics of the vibration state (such as displacement, velocity or acceleration) of the mechanical system under the influence of random vibration over time. This fluctuation characteristic can involve the following aspects:

[0108] Fluctuation amplitude: The difference between the maximum and minimum values ​​of the vibration state, reflecting the intensity of the vibration.

[0109] Fluctuation frequency: the speed of change of vibration state, that is, the number of times the vibration state changes per unit time.

[0110] Wave cycle: the time required to complete a complete wave.

[0111] Fluctuation phase: In periodic vibration, the phase of the vibration state at a specific point in time.

[0112] Randomness of fluctuations: Due to the influence of random vibrations, changes in vibration states may present unpredictable random fluctuations.

[0113] Nonlinearity of fluctuations: If the system response exhibits nonlinear characteristics, the changes in the vibration state may not follow a simple linear law.

[0114] Energy distribution of vibration: The distribution of energy in a vibration state at different frequencies can usually be described by the power spectral density.

[0115] Coherence of fluctuations: the consistency or stability of a vibrational state over time.

[0116] Autocorrelation of fluctuations: how similar the vibrational states are at different points in time.

[0117] Cross-correlation of fluctuations: correlation between vibration states in different degrees of freedom or in different directions.

[0118] To quantify the degree of fluctuation of the initial state of vibration over time, the following methods can be used:

[0119] Time history analysis: Analyze the fluctuation characteristics by recording the changes of vibration state over time.

[0120] 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.

[0121] Power Spectrum Analysis: Calculate the power spectrum density of the vibration state to understand the energy distribution of different frequency components.

[0122] Autocorrelation and cross-correlation analysis: Analyze the similarity or correlation of vibration states at different time points or in different directions.

[0123] Statistical analysis: Use statistical methods, such as variance, standard deviation, mean, etc., to quantify the degree of fluctuation in vibration conditions.

[0124] In practical applications, understanding the degree of fluctuation of the initial vibration state over time is crucial for designing vibration control strategies, predicting system life, and evaluating system performance. Through these analyses, we can better understand the behavior of the system in a random vibration environment and take appropriate measures to mitigate the impact of vibration.

[0125] Below, the training process of the three neural network models in step S2 is highlighted as follows:

[0126] (1) The first neural network model for real-time calculation of the system's effective working probability

[0127] At each initial state of vibration Next, based on the initial state of vibration Average rate of change over time and volatility Based on the system effective working probability equation, the corresponding initial vibration state is derived The probability of effective operation of the system under The approximate analytical solution of (for example, the partial differential equation method can be used); the approximate analytical solution of the system effective working probability is the initial state of vibration and time The analytical expression of is used to describe the probability of effective operation of the system With the initial state of vibration and time changes.

[0128] According to each initial state of vibration The approximate analytical solution of the system effective working probability under the condition of Next time The corresponding analytical solution .

[0129] The initial state of vibration ,time And the corresponding analytical solution As a set of sample data, construct a sample set of a first neural network model; and divide the sample set of the first neural network model into a first training sample set and a first test sample set;

[0130] Obtain each group of sample data in the first training sample set, and use the initial state of vibration in each group of sample data ,time As input, the corresponding analytical solution As an output, training the first neural network model, and adjusting the parameters and structure of the first neural network model through a back propagation algorithm;

[0131] Obtain each group of sample data in the first test sample set, and use the initial state of vibration in each group of sample data ,time As input, the corresponding analytical solution As an output, the trained first neural network model is tested until the test passes, thereby obtaining a first neural network model for solving the probability of effective operation of the system in real time.

[0132] (2) The second neural network model for real-time solution of the probability density function of the effective working time of the system

[0133] Get different time Discrete value, set time The upper limit is ; In different initial vibration states and time The grid composed of discrete points is initialized to store the numerical solution A matrix of values;

[0134] Based on the system effective working probability equation, according to the initial state of vibration , initial state of vibration Average rate of change over time and volatility , using explicit finite difference method, gradually updating the storage of numerical solutions The values ​​in the matrix of values ​​until the time limit is obtained Corresponding .

[0135] The initial state of vibration And the corresponding numerical solution , As a set of sample data, construct a sample set of the second neural network model; and divide the sample set of the second neural network model into a second training sample set and a second test sample set;

[0136] Obtain each group of sample data in the second training sample set, and use the initial state of vibration in each group of sample data As input, the corresponding numerical solution , As an output, training a second neural network model, and adjusting the parameters and structure of the second neural network model through a back-propagation algorithm;

[0137] Obtain each group of sample data in the second test sample set, and use the initial state of vibration in each group of sample data As input, the corresponding numerical solution , As an output, the trained second neural network model is tested until the test passes, thereby obtaining a second neural network model for solving the probability density function of the effective working time of the system in real time.

[0138] (3) The third neural network model for real-time solution of the average effective working time of the system

[0139] According to different initial vibration states , construct a memory for storing numerical solutions A matrix of values;

[0140] Based on the average effective working time equation, according to the initial state of vibration , initial state of vibration Average rate of change over time and volatility , using explicit finite difference method, gradually updating the storage of numerical solutions A matrix of values.

[0141] The initial state of vibration And the corresponding numerical solution As a set of sample data, construct a sample set of a third neural network model; and divide the sample set of the third neural network model into a third training sample set and a third test sample set;

[0142] Obtain each group of sample data in the third training sample set, and use the initial state of vibration in each group of sample data As input, the corresponding numerical solution As an output, training a third neural network model, and adjusting parameters and structure of the third neural network model through a back propagation algorithm;

[0143] Obtain each group of sample data in the third test sample set, and use the initial state of vibration in each group of sample data As input, the corresponding numerical solution As an output, the trained third neural network model is tested until the test passes, thereby obtaining a third neural network model for solving the average effective working time of the system in real time.

[0144] The specific implementation process of step S3 is described below:

[0145] (1) Solution of the probability density function of the system's effective working time

[0146] The real-time data of the initial state of vibration is used as the input of the second neural network model that has passed the test, and the second neural network model predicts and outputs the system effective working probability corresponding to the real-time data , ;right , Perform differentiation to obtain the probability density function of the effective working time of the system .

[0147] (2) Solution for the system's average effective working time

[0148] The real-time data of the initial state of vibration is used as the input of the third neural network model that has passed the test, and the third neural network model predicts and outputs the average effective working time of the system corresponding to the real-time data .

[0149] (3) Solution for the system effective working probability corresponding to real-time data

[0150] The real-time data of the initial state of vibration is converted into time As the input of the first neural network model that has passed the test, the first neural network model predicts and outputs the real-time data and time The corresponding system effective working probability .

[0151] In step S4, the system effective working probability, the probability density function of the system effective working time, and the system average effective working time corresponding to the real-time data of the initial vibration state are solved, and the reliability assessment of the mechanical system under the influence of the current random vibration can be realized based on the above data. The specific process is described as follows.

[0152] According to the concept of the effective working probability of the system, it refers to the probability that the mechanical system can maintain a normal working state under the influence of random vibration. This parameter directly reflects the reliability level of the mechanical system. According to the concept of the probability density function of the effective working time of the system, this function describes the distribution of the effective working time of the system under a random vibration environment. By analyzing this function, we can understand the possibility of the mechanical system working effectively in different time periods. That is, the peak position and distribution range of the probability density function of the effective working time of the system are analyzed to determine the effective working time period of the mechanical system. Using this function, the cumulative probability of the system maintaining effective work in a specific time period can be calculated, thereby evaluating the reliability of the system in this time period. According to the concept of the average effective working time of the system, it describes the average length of time that the mechanical system can maintain normal work under a random vibration environment. This indicator reflects the overall performance stability and durability of the system. Based on the above analysis, considering the correlation between the three indicators, the following evaluation method is set:

[0153] Step S41: Analysis The peak position and distribution range of the mechanical system are used to determine the effective working time period of the mechanical system; and The cumulative probability during the effective working period.

[0154] Step S42: If Within the effective working time period, at this time, if The cumulative probability during the effective working time period is greater than the cumulative probability threshold, and If it is greater than the system effective working probability threshold, the evaluation result of the mechanical system is high reliability.

[0155] Step S43: If Within the effective working time period, at this time, if The cumulative probability during the effective working period is not greater than the cumulative probability threshold, or, If the reliability is not greater than the probability threshold of effective operation of the system, the evaluation result of the mechanical system is medium reliability. At this time, it is necessary to pay attention to potential risks and consider optimization measures.

[0156] Step S44: Otherwise, the evaluation result of the mechanical system is low reliability; immediate measures need to be taken, such as improving the design, strengthening maintenance or replacing parts.

[0157] In the specific implementation process, parameters such as the cumulative probability threshold and the system effective working probability threshold can be adaptively set according to the accuracy requirements of the mechanical system for reliability in the engineering practice process, and this example does not impose any restrictions on this.

[0158] In step S4, by combining the three parameters of the system effective working probability, the probability density function of the system effective working time and the system average effective working time solved by the neural network model, a comprehensive reliability evaluation system can be constructed. This reliability evaluation system not only takes into account the overall reliability level of the system, but also reveals the dynamic reliability changes of the system under random vibration environment through the analysis of the time dimension. This provides strong data support and scientific basis for the optimization design and reliability evaluation of mechanical structures.

[0159] 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.

[0160] 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 reliability assessment method for a mechanical system under the influence of random vibration, characterized in that: The method comprises: Analyze the process of the mechanical system being affected by random vibration, and obtain historical data of the random vibration state of the mechanical system under the influence of different random vibrations; the random vibration state includes: the initial vibration state, and the average rate and fluctuation degree of the initial vibration state changing over time; Based on the historical data, sample sets of each neural network model are respectively constructed to train and test a first neural network model for solving the probability of effective working of the system in real time, a second neural network model for solving the probability density function of the effective working time of the system in real time, and a third neural network model for solving the average effective working time of the system in real time; Acquire real-time data of the initial vibration state of the mechanical system under the influence of the current random vibration, and generate inputs of each neural network model based on the real-time data, and use the first neural network model, the second neural network model and the third neural network model that have passed the test to solve the system effective working probability corresponding to the real-time data, the probability density function of the system effective working time, and the system average effective working time; Based on the system effective working probability, the probability density function of the system effective working time, and the system average effective working time corresponding to the real-time data, the reliability evaluation of the mechanical system under the influence of the current random vibration is realized; The first neural network model for real-time solution of the system's effective working probability was obtained by training and testing in the following way: At each initial state of vibration Next, based on the initial state of vibration Average rate of change over time and volatility Based on the system effective working probability equation, the corresponding initial vibration state is derived The probability of effective operation of the system under The approximate analytical solution of the system effective working probability is the approximate analytical solution containing the initial state of vibration and time The analytical expression of is used to describe the probability of effective operation of the system With the initial state of vibration and time changes; According to each initial state of vibration The approximate analytical solution of the system effective working probability under the condition of Next time The corresponding analytical solution ; The initial state of vibration ,time And the corresponding analytical solution As a set of sample data, construct a sample set of a first neural network model; and divide the sample set of the first neural network model into a first training sample set and a first test sample set; Obtain each group of sample data in the first training sample set, and use the initial state of vibration in each group of sample data ,time As input, the corresponding analytical solution As an output, training the first neural network model, and adjusting the parameters and structure of the first neural network model through a back propagation algorithm; Obtain each group of sample data in the first test sample set, and use the initial state of vibration in each group of sample data ,time As input, the corresponding analytical solution As an output, the trained first neural network model is tested until the test passes, thereby obtaining a first neural network model for solving the probability of effective operation of the system in real time; The second neural network model for real-time solution of the probability density function of the effective working time of the system is obtained by training and testing in the following way: Get different time Discrete value, set time The upper limit is ; In different initial vibration states and time The grid composed of discrete points is initialized to store the numerical solution A matrix of values; Based on the system effective working probability equation, according to the initial state of vibration , initial state of vibration Average rate of change over time and volatility , using explicit finite difference method, gradually updating the storage of numerical solutions The values ​​in the matrix of values ​​until the time limit is obtained Corresponding ; The initial state of vibration And the corresponding numerical solution , As a set of sample data, construct a sample set of the second neural network model; and divide the sample set of the second neural network model into a second training sample set and a second test sample set; Obtain each group of sample data in the second training sample set, and use the initial state of vibration in each group of sample data As input, the corresponding numerical solution , As an output, a second neural network model is trained, and parameters and structure of the second neural network model are adjusted through a back-propagation algorithm; Obtain each group of sample data in the second test sample set, and use the initial state of vibration in each group of sample data As input, the corresponding numerical solution , As an output, the trained second neural network model is tested until the test passes, thereby obtaining a second neural network model for solving the probability density function of the effective working time of the system in real time; The third neural network model for real-time solution of the average effective working time of the system is obtained by training and testing in the following way: According to different initial vibration states , construct a memory for storing numerical solutions A matrix of values; Based on the average effective working time equation, according to the initial state of vibration , initial state of vibration Average rate of change over time and volatility , using explicit finite difference method, gradually updating the storage of numerical solutions A matrix of values; The initial state of vibration And the corresponding numerical solution As a set of sample data, construct a sample set of a third neural network model; and divide the sample set of the third neural network model into a third training sample set and a third test sample set; Obtain each group of sample data in the third training sample set, and use the initial state of vibration in each group of sample data As input, the corresponding numerical solution As an output, training a third neural network model, and adjusting parameters and structure of the third neural network model through a back propagation algorithm; Obtain each group of sample data in the third test sample set, and use the initial state of vibration in each group of sample data As input, the corresponding numerical solution As an output, the trained third neural network model is tested until the test passes, thereby obtaining a third neural network model for solving the average effective working time of the system in real time; The system effective working probability equation is in the form of: （1）； The average effective working time equation is in the form of: （2） when hour, is the average effective working time. is a preset value; The reliability assessment of the mechanical system under the influence of current random vibration is achieved by: Analyze the probability density function of the system effective working time corresponding to real-time data The peak position and distribution range of the mechanical system are used to determine the effective working time period of the mechanical system; and Cumulative probability during the effective working period; If the system average effective working time corresponding to the real-time data Within the effective working time period, at this time, if The cumulative probability during the effective working time period is greater than the cumulative probability threshold, and The corresponding system effective working probability If it is greater than the system effective working probability threshold, the evaluation result of the mechanical system is high reliability; like Within the effective working time period, at this time, if The cumulative probability during the effective working period is not greater than the cumulative probability threshold, or, If it is not greater than the system effective working probability threshold, the evaluation result of the mechanical system is medium reliability; Otherwise, the mechanical system is evaluated as having low reliability.

2. The reliability assessment method of a mechanical system under the influence of random vibration according to claim 1, characterized in that: The probability density function of the effective working time of the system corresponding to the real-time data is obtained by solving the following method: The real-time data of the initial state of vibration is used as the input of the second neural network model that has passed the test, and the second neural network model predicts and outputs the system effective working probability corresponding to the real-time data , ;right , Perform the difference to obtain the probability density function of the effective working time of the system .

3. The reliability assessment method of a mechanical system under the influence of random vibration according to claim 2, characterized in that: The average effective working time of the system corresponding to the real-time data is obtained by solving the following method: The real-time data of the initial state of vibration is used as the input of the third neural network model that has passed the test, and the third neural network model predicts and outputs the average effective working time of the system corresponding to the real-time data .

4. The reliability assessment method of a mechanical system under the influence of random vibration according to claim 3, characterized in that: The effective working probability of the system corresponding to the real-time data is obtained by solving the following method: The real-time data of the initial state of vibration is converted into time As the input of the first neural network model that has passed the test, the first neural network model predicts and outputs the real-time data and time The corresponding system effective working probability .

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