Vibration isolation system uncertainty quantification method based on multilevel Bayesian network

Abstract

The invention discloses a vibration isolation system uncertainty quantification method based on a multilevel Bayesian network. Comprising the following steps: dividing a vibration isolation system into different layers; combining prior distribution of model parameters and a calculation model to obtain a model error, and giving measurement error distribution; establishing a Bayesian network, establishing a relationship between test data and model parameters among layers, and completing establishment of a likelihood function; samples of model parameters are extracted through a Markov chain Monte Carlo method, and posterior distribution is constructed based on a kernel density method; calculating the model reliability of each data point and constructing unconditional distribution of the model reliability; quantifying similar weights of different levels and system levels; dividing regions according to the weight values to complete sample extraction of system-level model parameters and construct comprehensive distribution, and completing system-level output prediction calculation through iterative convergence. Through a complete process of model calibration, physical correlation calculation and uncertainty integration, quantification of system-level output uncertainty is realized, and dispersibility of output response of the vibration isolation system is obtained.

Description

Technical Field

[0001] The present invention belongs to the field of anti-shock reliability assessment of ship equipment, and particularly relates to a method for quantifying the uncertainty of a vibration isolation system based on a multi-level Bayesian network. Background Art

[0002] The ship power system and its equipment, as the "heart" of the ship, provide the power and electricity required for the whole ship, ensuring the ship's navigation and daily life needs, and occupying a very important position among ship equipment. During the mission execution, it may face shock loads that cause serious damage to the ship's power equipment, leading to the collapse of the whole ship's power equipment or even the power system, and further affecting the ship's navigation requirements. To improve the anti-shock performance of the ship's power equipment, light, medium shock machines or floating shock platforms are used to conduct shock tests on the power equipment.

[0003] For the anti-shock ability test assessment of ship equipment, corresponding standard specifications have been formed for the assessment methods of ship equipment. These standards stipulate corresponding shock test methods such as lightweight shock, medium-weight shock, explosion shock, double-wave shock, etc. The results of a large number of full-scale ship explosion experiments show that the shock input environment generated by the underwater explosion energy transmitted to the equipment foundation shows a displacement / velocity / acceleration shock spectrum in the frequency domain, which can be equivalent to the positive and negative shock pulse waves in the time domain. The previous shock machines mainly simulated shock energy and could only simulate simple waveforms such as half-sine waves. However, the double-wave shock test bench for marine equipment can generate a positive wave pulse by the impact of the shock machine hammer on the elastic waveform generator directly below the center of the test bench body. During the upward movement of the bench body under the action of the impact force, it acts on the buffer (negative wave waveform generator) installed on the bench body to generate a negative wave shock pulse. By adjusting the different impact air pressures of the shock test machine hammer, the energy required for the positive and negative waves required by the test conditions can be generated. There is very little shock test data such as full-scale ship explosions, and it is difficult to statistically analyze the dispersion of the response output of the vibration isolation system. In the existing uncertainty quantification methods, due to the complexity of the vibration isolation system and the lack of system-level double-wave shock test data, it is difficult to quantify the model parameters of the vibration isolation system. Summary of the Invention

[0004] To quantify the uncertainty of the vibration isolation system under double-wave shock tests, the present invention provides a method for quantifying the uncertainty of a vibration isolation system based on a multi-level Bayesian network, and the vibration isolation system is installed in the fixture of a double-wave shock test bench.

[0005] To achieve the above object, the technical solution adopted by the present invention is: a method for quantifying the uncertainty of a vibration isolation system based on a multi-level Bayesian network, including the following steps:

[0006] Step S1: Divide the vibration isolation system into multiple levels, establish a calculation model for each level, and obtain test data at different levels;

[0007] Step S2: Given the prior distribution of the calculation model parameters, given the calculation model error and the measurement error, and construct the likelihood function;

[0008] Step S3: Define the calculation model of the vibration isolation system, considering the correlation between model parameters, calculate its covariance matrix to provide a basis for posterior distribution sampling;

[0009] Step S4: Generate posterior distribution samples of the model parameters through MCMC, and use the kernel density estimation method to construct the posterior distribution of the calculation model parameters at each level;

[0010] Step S5: Define the model reliability metric of the multi-output system, update the calculation model to a multi-output model group, and convert the original data of different quantities into a comparable scale through the Mahalanobis distance;

[0011] Step S6: Given the tolerance value of the response data and calculate the reliability of each data point, and then obtain the unconditional distribution of the model reliability of the calculation model at each level ;

[0012] Step S7: Define the impact energy input metric as the product of the first positive wave peak and the pulse time of the acceleration response curve;

[0013] Step S8: Select the total effect index S value to quantify the similarity weights at different levels and the system level, and initially set the S value to 1;

[0014] Step S9: Establish the comprehensive distribution of the model parameters, and extract samples according to the weights to construct the probability density function;

[0015] Step S10: Iteratively calculate until the S value converges and predict the output of the vibration isolation system.

[0016] The present invention has the following beneficial effects:

[0017] By considering the correlation between the model parameters and the multi-output quantities, it provides a reference for model verification and uncertainty integration, and uses global sensitivity to assign physical correlation weights to each level and the system level, ensuring that the uncertainties in each link are fully considered, and improving the accuracy of the model. It establishes a method flow for multi-level quantification of output uncertainty for the double-wave impact test of the isolation system, and can provide a reference for the subsequent quantification of uncertainty of the same type of system. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a schematic flow chart of the method for quantifying the uncertainty of the vibration isolation system based on the multi-level Bayesian network of the present invention.

[0019] Figure 2 is a schematic Bayesian network diagram of the method for quantifying the uncertainty of the vibration isolation system based on the multi-level Bayesian network of the present invention.

[0020] Figure 3 Schematic diagram of the shock test of the vibration isolation system for the method of quantifying the uncertainty of the vibration isolation system based on the multi-level Bayesian network according to the present invention.

[0021] Figure 4 Comparison between the predicted distribution and the prior distribution of the system response of the method for quantifying the uncertainty of the vibration isolation system based on the multi-level Bayesian network according to the present invention and verification diagram of test data. Detailed implementation manners

[0022] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above objectives, the present invention adopts the following technical solutions.

[0023] The following will describe in detail a method for quantifying the uncertainty of a vibration isolation system based on a multi-level Bayesian network according to the present invention with reference to the accompanying drawings.

[0024] In the embodiment of the present invention, the test piece is a vibration isolation system of a certain type of ship gas turbine. The adapter plate of the test bench in the fixture is made of 45 steel, and the counterweight is made of ordinary carbon steel.

[0025] As Figure 1 shown, the specific steps of the present invention include:

[0026] Step S1: Divide the vibration isolation system into multiple levels, establish calculation models for each level and obtain test data at different levels;

[0027] Step S2: Given the prior distribution of the calculation model parameters, given the calculation model error and measurement error, and construct the likelihood function;

[0028] Step S3: Define the calculation model of the vibration isolation system, and considering the correlation between the model parameters, calculate its covariance matrix to provide a basis for posterior distribution sampling;

[0029] Step S4: Generate posterior distribution samples of the model parameters through MCMC, and use the kernel density estimation method to construct the posterior distribution of the calculation model parameters at each level;

[0030] Step S5: Define the model reliability measure of the multi-output system, update the calculation model to a multi-output model group, and convert the original data of different quantities into a comparable scale through the Mahalanobis distance;

[0031] Step S6: Given the tolerance value of the response data and calculate the reliability of each data point, and then obtain the model reliability of the calculation models at each level Unconditional distribution;

[0032] Step S7: Define the shock energy input metric as the product of the first positive wave peak and the pulse time of the acceleration response curve;

[0033] Step S8: Select the total effect index S value to quantify the similarity weights at different levels and system levels, and initially set the S value to 1;

[0034] Step S9: Establish the comprehensive distribution of model parameters, and extract samples according to the weights to construct the probability density function;

[0035] Step S10: Iteratively calculate until the S value converges and predict the output of the vibration isolation system.

[0036] Preferably, in the said step S1:

[0037] Furthermore, the vibration isolation system consists of three shock absorbers and a limiter, with a complex structure. Considering the maximum acceleration response and the maximum relative displacement response, it is extended to a multi-level problem: the first level is the drop hammer impact of the shock absorber, the second level is the double-wave impact of the shock absorber, and the third level is the system-level double-wave impact. The three-level problems can provide model parameter data and test data to calibrate the model parameters of the isolation system three times: use the first-level calibration; use the second-level calibration; use the first-level and the second-level for calibration.

[0038] Preferably, in the said step S2:

[0039] Furthermore, make the prediction of the calculation model match the test data through model parameters. As Figure 2 shown, establish the relationship between the low-level test data, model parameters, and model inputs through the calculation model, and introduce model error and measurement error to ensure the accuracy of the calculation model. Represent all the parameters to be calibrated as , assuming there are data points D, then the likelihood function can be defined as the product of the posterior probabilities of all data points :

[0040] (1)

[0041] Preferably, in the said step S3:

[0042] Furthermore, the calculation models of the vibration isolation system are respectively expressed in the low-level system and the isolation system as:

[0043] (2)

[0044] (3)

[0045] In the formula, M is the weight of the mass block, g is the acceleration due to gravity, is the parallel damping of three shock absorbers, v is the velocity at the maximum impact displacement of the mass block, and x is the relative displacement of the mass block. is the compression amount at rest. is the equivalent impact stiffness of the shock absorber. The compression amount at rest in the system-level test.

[0046] Furthermore, the KOH framework is used to calibrate the model parameters, and the model error is also modeled as a GP model. The calculated model output is not exactly the same as the true value, and the difference is the model error, which is defined as In the low-level test, there is a measurement error in the measured test data, which is defined as Given that the distribution of the measurement error is a normal distribution Define the test data as z, and the calculation model is expressed as where are the model parameters, and x0 is the model input, then there is:

[0047] (4)

[0048] The measured value of the test output is the sum of the output of the calculation model, the model error, and the measurement error. Under this framework, Bayesian inference is applied to estimate the posterior distribution of the model parameters. Since the input of the calculation model is fixed, the model error is simplified to a single unknown quantity Express all the parameters to be calibrated as .

[0049] Furthermore, the parameters to be calibrated are the equivalent impact stiffness and the damping c, the measurement error of the test data and its standard deviation By building a Bayesian network, establish the probability dependence relationship between the model parameters and the test data at each level, and match the multi-level data with the system-level model parameters.

[0050] Preferably, in the step S4:

[0051] Furthermore, define the conditional probability as the probability of the output given the parameters, which is in direct proportion to the likelihood function Define the prior marginal distribution of each calibration parameter. By constructing and Use the Markov chain Monte Carlo method (MCMC) to generate samples of the posterior distribution Finally, use the kernel density estimation method to construct the posterior distribution of the model parameters.

[0052] Preferably, in the step S5:

[0053] Furthermore, the vibration isolation system has two low-level multi-level problems. By using first-level calibration, second-level calibration, or a combination of the two-level calibration, and through quantitative probabilistic measurement of the effectiveness of the computational model, the degree to which the test data at each level supports the system-level prediction model can be provided.

[0054] Furthermore, in the reliability degree of the computational model, if the correct availability of the computational model is defined as G and the random variable is d, then the reliability degree of the computational model is denoted as the probability that the model is correct:

[0055] (5)

[0056] where, is the predefined tolerance.

[0057] Furthermore, when each level in the multi-level problem provides multivariate output quantities, the data obtained in the i-th test is defined as , then the K-dimensional vector of the difference between the computational model prediction and the measured data is obtained. Then, the model reliability degree can be defined as the norm less than the tolerance vector , and the model reliability degree can be expressed as:

[0058] , (6)

[0059] Furthermore, the Mahalanobis distance can establish a data matrix for two physical outputs of the vibration isolation system and convert it into a comparable scale. Based on the covariance matrix, the correlation between multivariate outputs is fully considered. When the Mahalanobis distance between z and is less than , then the model is correct, which can be defined as:

[0060] (7)

[0061] where, is the covariance matrix of z, is the predefined tolerance vector.

[0062] Preferably, in the step S6:

[0063] Furthermore, the model reliability value is calculated for each data point, and the model reliability is obtained. The epistemic uncertainty represented by the probability distribution can also be considered as the contribution representing the epistemic uncertainty.

[0064] Preferably, in the step S8:

[0065] Furthermore, there are two failure criteria for the vibration isolation system. In order to more accurately predict the maximum acceleration and the maximum relative displacement output, it is also necessary to consider the possible correlation between the two. At the same time, the lower level is physically closer to the system level and can be given more weight. Therefore, it is necessary to objectively quantify the correlation. The Sobol global sensitivity analysis method based on variance decomposition not only considers the contribution of variables themselves to uncertainty, but also includes the influence of the interaction between variables on uncertainty. The total effect index is selected as the sensitivity quantification index S, and the sensitivity vectors of the lower level and the system level are respectively and , and the physical correlation index is defined as the square of the cosine similarity of the two index vectors, denoted as:

[0066] (8)

[0067] Preferably, in the step S9:

[0068] Furthermore, based on the comprehensive distribution of the parameters for model calibration and model verification is:

[0069] (9)

[0070] In the formula is the model calibration data, is the model verification data, means that the calculation model is incorrect, is defined as Assuming are independent of each other, a sample is generated from each of the distributions of and . The interval [0, 1] is divided into four regions, and the length of each region is equal to , , and weights. A random number is generated from the uniform distribution . If the random number corresponds to a certain region, a sample is generated from its distribution. The establishment of the probability density function is completed through a large number of samples obtained by repeating the above steps.

[0071] Preferably, in the step S10:

[0072] Furthermore, when performing global sensitivity analysis, it is considered that the overall distribution of variables is unknown, and this problem needs to be solved through an iterative algorithm. The initial value of S can be set to 1 first, and the unconditional distribution of model parameters is obtained using the cumulative formula and sensitivity analysis is performed to calculate the new S value. The above process is iterated until the S value converges.

[0073] The input forms of the shock tests at each level of the vibration isolation system are not exactly the same. The product of the peak value of the first positive wave of the acceleration output response curve and the pulse time is used as a measure of the shock test energy input. The present invention is designed based on the double-wave shock test of a certain ship vibration isolation system. The vibration isolation system and the shock absorber are fixed on the test bench through a double-wave shock test fixture.

[0074] As Figure 2 shown, in the embodiment of the present invention, the drop hammer shock is the input of the first-level model, and the double-wave shock is the input of the second-level and two-level models. The equivalent shock stiffness and damping data, measurement errors, and their standard deviation distributions are obtained through the shock test for the first level and the second level, and a calculation model for each level is established. The data at the lower level is matched with the output data of the calculation model through model calibration to complete the establishment of the posterior distribution of the model parameters.

[0075] As Figure 3 shown, in the embodiment of the present invention, the shock absorber and the limiter are connected to the load and the test bench through bolts, and the fixture is fixed to the test shock bench through bolt connections. The double half-sine shock wave is provided for the fixture and the shock absorber by the hammer impact and the buffer. The shock test bench and the fixture move vertically under the impact of large energy, and no relative displacement occurs at the connection position during the whole shock process. The relative displacement response is measured by a high-speed camera measurement system, and the system acceleration response is measured by an acceleration sensor measurement system.

[0076] As Figure 4 shown, in the embodiment of the present invention, the predicted result of the acceleration output response obtained by calibrating and validating the model parameters of the vibration isolation system through a multi-level Bayesian network, compared with the prior distribution, proves the high precision of this method. At the same time, the high accuracy of this method is verified through the system-level test data.

[0077] In the present invention, unless otherwise clearly specified and defined, terms such as "installation", "connection", "connection", "fixation", etc. should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or integrated; it can be a mechanical connection, an electrical connection, or communication with each other; it can be directly connected, or indirectly connected through an intermediate medium, and it can be the internal connection of two components or the interaction relationship between two components, unless otherwise clearly defined. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0078] Obviously, the embodiments described above are only a part of the embodiments of the present invention, rather than all of them. The preferred embodiments of the present invention are shown in the drawings, but do not limit the scope of the present invention. The present invention can be implemented in many different forms. On the contrary, the purpose of providing these embodiments is to make the understanding of the disclosed content of the present invention more thorough and comprehensive. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing specific embodiments, or perform equivalent replacements for some of the technical features. Any equivalent structure made by using the content of the specification and drawings of the present invention, directly or indirectly applied in other related technical fields, is equally within the protection scope of the present invention.

Claims

1. A vibration isolation system uncertainty quantification method based on a multi-level Bayesian network, characterized in that: include: Step S1, dividing the vibration isolation system into multiple levels, establishing a calculation model for each level and obtaining test data for different levels; Step S2: Given the prior distribution of the calculation model parameters, given the calculation model error and the measurement error, and constructing a likelihood function; Step S3, defining a vibration isolation system calculation model, taking into account the correlation between model parameters, calculating its covariance matrix to provide a basis for posterior distribution sampling; Step S4, generating the posterior distribution samples of the model parameters through MCMC, and constructing the posterior distribution of the calculation model parameters at each level using the kernel density estimation method; Step S5, defining a model reliability metric for a multi-output system, updating the calculation model to a multi-output model group, and converting different amounts of raw data into comparable scales through Mahalanobis distance; Step S6: Given the tolerance value of the response data and calculating the reliability of each data point, the model reliability of the calculation model at each level is obtained. The unconditional distribution of Step S7, defining the impact energy input measurement as the product of the first positive wave peak of the acceleration response curve and the pulse time; Step S8, selecting the total effect index S value to quantify the similarity weights of different levels and system levels, and the initial setting S value is 1; Step S9, establish a comprehensive distribution of model parameters, extract samples according to the weights to construct a probability density function; Step S10, iterative calculation until the S value converges and the output of the vibration isolation system is predicted.

2. The method according to claim 1, characterized in that: In the step S1: considering the maximum acceleration response and the maximum relative displacement response, the vibration isolation system is expanded into a multi-level problem: the first level is the drop hammer impact of the shock absorber, the second level is the double-wave impact of the shock absorber, and the third level is the system-level double-wave impact; the three levels of problems provide model parameter data and test data to calibrate the model parameters of the isolation system three times: use the first level for calibration; use the second level for calibration; use the first and second levels for calibration.

3. The method according to claim 2, characterized in that In step S2, the prediction of the computational model is matched with the test data through the model parameters, and the relationship between the low-level test data and the model parameters and the model input is established through the computational model. According to Bayesian reasoning, conditional probability is defined The probability of outputting D under given parameters is directly proportional to the likelihood function. By constructing and And generate samples of the posterior distribution, while introducing model errors and measurement errors, and express all parameters to be calibrated as , assuming that there are data points D, then the likelihood function is defined as the posterior probability of all data points The product of: （1）。 4. The method according to claim 3, characterized in that In step S3: the calculation model of the vibration isolation system is respectively expressed in the low-level system and the isolation system as: （2） （3） Where M is the mass of the mass block, g is the acceleration due to gravity, is the parallel damping of the three shock absorbers, v is the velocity of the mass block at the maximum impact displacement, x is the relative displacement of the mass block, is the compression at rest; is the equivalent impact stiffness of the shock absorber, Compression amount when the system level test is stationary; The model parameters are calibrated and the difference between the model output and the true value is calculated as the model error, which is defined as , the test data obtained in the low-level test have measurement errors when measuring, which is defined as , given that the distribution of measurement error is normal , the test data is defined as z, and the calculation model is expressed as ,in is the model parameter and x0 is the model input, then there exists: （4） The measured value of the test output is the sum of the output of the computational model, the model error, and the measurement error. In this framework, Bayesian inference is applied to estimate the posterior distribution of the model parameters; the model error is simplified to a single unknown quantity , all parameters to be calibrated are expressed as .

5. The method according to claim 4, characterized in that The parameters that need to be calibrated are equivalent impact stiffness and damping c, test data measurement error and its standard deviation , by building a Bayesian network, the probabilistic dependency relationship between model parameters and experimental data at each level is established, and the multi-level data is matched with the system-level model parameters to complete the construction of the likelihood function.

6. The method according to claim 4, characterized in that In step S4, the conditional probability is defined as the probability of output under given parameters, which is consistent with the likelihood function In direct proportion, define the prior marginal distribution of each calibration parameter , by constructing and Generate posterior distribution using Markov Chain Monte Carlo (MCMC) Finally, the kernel density estimation method is used to construct the posterior distribution of the model parameters.

7. The method according to claim 6, characterized in that In step S5, the reliability of the calculated model is defined as G, and the random variable is d. The reliability of the calculated model is the probability that the model is correct, which is expressed as: （5） in, is a predefined tolerance; When each level in the multi-level problem provides a multivariate output, the data obtained in the i-th experiment is defined as , then we get a K-dimensional vector that calculates the difference between the model prediction and the measured data , then the model reliability is defined as the norm less than the tolerance vector The norm of the model is expressed as: ， （6） When z and The Mahalanobis distance between , then the model is correct and is defined as: （7） in, is the covariance matrix of z, is the predefined tolerance vector.

8. The method according to claim 7, characterized in that In step S6, the model reliability value is calculated for each data point. , and obtain the model reliability Epistemic uncertainty represented by a probability distribution.

9. The method according to claim 8, characterized in that In step S8, the total effect index is selected as the sensitivity quantification index S, and the sensitivity vectors at the lower level and system level are and , the physical correlation index is defined as the square of the cosine similarity of the two indicator vectors: （8）。 10. The method according to claim 9, characterized in that In step S9, based on the parameters of model calibration and model validation The comprehensive distribution of is: （9） In the formula Calibrate the data for the model, To validate the model, The calculation model is incorrect. Defined as , assuming Independent of each other, and Generate a sample from each distribution, divide the interval [0,1] into four regions, and the length of each domain is equal to , , and The weights are uniformly distributed A random number is generated in the distribution, and a sample is generated from the distribution of the random number in a certain area. The above steps are repeated to obtain a large number of samples. Establishment of probability density function.

11. The method according to claim 10, characterized in that In step S10, the initial value of S is first set to 1, the unconditional distribution of the model parameters is obtained using the cumulative formula, and a sensitivity analysis is performed to calculate a new S value, and the above process is iterated until the S value converges.

12. The method according to claim 1, characterized in that: In the step S2 of constructing the likelihood function, the Bayesian network establishes a probability dependency relationship between the test data at different levels and the model parameters that need to be calibrated, and constructs the likelihood function based on this.

13. The method according to claim 11, characterized in that: The total effect index S value quantifies the correlation between low-level and system-level using the global sensitivity analysis method and is a value on the interval [0,1].

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