An active learning method for fast stochastic model updating of offshore platform structures

Abstract

The present invention provides an active learning type fast random model correction method for marine platform structures. The present invention first considers sensitivity to select correction parameters, then designs an experimental scheme, and establishes an initial Kriging model; finds new correction parameter training samples, calculates the corresponding frequency of the new samples, uses a new training set to reconstruct the Kriging model, performs random model correction based on the reconstructed Kriging model, uses measured frequency data and initial finite element model frequency data to construct an objective function, takes the correction parameter mean and standard deviation as the solution target, uses an optimization algorithm to solve, obtains the mean and standard deviation of the correction parameters of the finite element model to be corrected, repeats iterations, and realizes random correction of marine platform structures. The present invention realizes fast, efficient, and accurate model correction under small samples and noise errors, and can use fewer training samples to obtain higher correction accuracy.

Description

Technical Field

[0001] The invention belongs to the technical field of finite element model correction based on computer data processing, and in particular relates to an active learning type fast random model correction method for an offshore platform structure. Background Art

[0002] Offshore platforms are key infrastructure for the development of marine resources (such as oil and natural gas extraction). They work in complex and changeable marine environments. At the same time, their structures are complex and consist of multiple parts such as pile legs, decks, and support structures. The mechanical properties and dynamic responses of these structures are affected by the interaction of multiple factors. Theoretical models such as the initially established offshore platform finite element model often deviate from the actual structure, mainly from modeling assumptions (such as material property assumptions, boundary condition assumptions, etc.), manufacturing errors, installation errors, and other aspects. For example, when modeling, it is assumed that the elastic modulus of the material is a fixed value, but the elastic modulus of the actual material may vary due to factors such as production batches and environmental corrosion. Model correction can improve the accuracy of the model, thereby more accurately predicting the response of the platform under various working conditions.

[0003] During the service process, offshore platforms are often subjected to erosion from severe marine environmental loads such as super typhoons, huge waves and drifting ice. Various damages such as seawater corrosion, fatigue cracks, and component dents and deformations occur from time to time. These damages are extremely hidden and difficult to detect, resulting in a high degree of uncertainty in the structure of offshore platforms. Considering the limitations of factors such as the need for underwater operations to install sensors during the service period, offshore platform structures can only be equipped with relatively few sensors to obtain structural vibration responses. At the same time, due to the limitations of modal information extraction technology, only low-order modal parameters of the structure can be obtained, which usually contain noise. These factors will affect the model correction results. Therefore, it is necessary to improve the effectiveness of the random model correction method of the structure under the influence of noise.

[0004] In the prior art, invention patent CN201710154817.8 discloses a finite element model establishment method based on the kriging function, which includes the following steps: step 1, establishing an initial finite element model based on design data; step 2, using Latin hypercube for sampling, and calculating the static and dynamic responses of the model based on the sampling results; step 3, constructing a kriging model based on parameter sampling samples and static and dynamic responses; step 4, dividing the feasible domain of parameters into multiple regions; step 5, using an improved particle swarm algorithm to solve multiple possible more accurate finite element models. Invention patent CN201710375215.5 discloses a structural finite element model correction method based on the inverse kriging function. First, an initial finite element model of the structure is established based on the design data and a sensitivity analysis is performed. In combination with engineering experience, the design parameters to be corrected are reasonably selected from the parameters with high sensitivity; the Halton sequence sampling method is used to sample the design parameters, and the static and dynamic responses of the model are calculated based on the sampling results; an inverse kriging function model that meets the accuracy requirements is constructed based on the design parameter sampling samples and the static and dynamic responses; finally, the static and dynamic responses of the actual structure are measured and substituted as input into the constructed inverse kriging function to solve the design parameter values ​​to be corrected, thereby completing the structural finite element model correction.

[0005] The above two correction schemes, if applied to random model correction of offshore platform structures, do not consider the influence of small samples and variances of design parameters on the correction results, and thus cannot solve the problem of large random correction errors and low efficiency of offshore platform structures under small samples and noise pollution conditions. Summary of the invention

[0006] In view of the above problems, the present invention provides an active learning method for fast random model correction of marine platform structure, which includes the following process:

[0007] S1, select the correction parameters of the random correction of the marine platform structure through sensitivity analysis; transform the random correction process of the marine platform structure into the correction process of the mean and standard deviation of the correction parameters;

[0008] S2, Latin hypercube sampling based on modified parameter mean and standard deviation times, and obtain the modified parameter matrix;

[0009] S3, obtain the structural frequency matrix through finite element analysis, and construct the initial training set based on the modified parameter matrix and the structural frequency matrix , and establish the initial Kriging model;

[0010] S4, establish a new learning function expression considering the uncertainty of the measured frequency, calculate the learning function value, and make the optimal structural correction parameter vector corresponding to the maximum learning function value ;

[0011] S5, the optimal correction parameter vector Substitute into the finite element model for finite element model analysis and obtain the corresponding structural frequency vector ;

[0012] S6, the optimal correction parameter vector and the structural frequency vector Add to the initial training set and create a new training set ,use Construct a new Kriging model;

[0013] S7, constructing an objective function using the measured frequency data and the initial finite element model frequency data, taking the mean and standard deviation of the correction parameters as the solution target, solving using an optimization algorithm, and obtaining the mean and standard deviation of the correction parameters of the finite element model to be corrected;

[0014] Repeat the above steps S4 to S7 until the model converges to achieve random correction of the offshore platform structure.

[0015] Preferably, the specific process of S1 is:

[0016] Select parameters with certain sensitivity in offshore platform structures through sensitivity analysis As correction parameters, Representative Correction parameters; transform the random correction process of the offshore platform structure into a correction process for the mean and standard deviation of the correction parameters, and determine the initial mean and standard deviation of each parameter ,in and Represents the correction parameters The mean and standard deviation of .

[0017] The random correction process of the marine platform structure is transformed into the mean and standard deviation of the correction parameters. The correction process of the random model of the marine platform structure can be regarded as a correction process in which the correction parameters obey the normal distribution. Therefore, it can be summarized as the correction of the mean and standard deviation of the correction parameters.

[0018] Preferably, the specific process of S3 is:

[0019] For each correction parameter vector in the correction parameter matrix Substitute the modified parameters into the finite element model, wherein the finite element model refers to the finite element model of the offshore platform structure established by using finite element analysis software;

[0020] Obtaining the structural frequency matrix vector through eigenvalue analysis , and get The corresponding parameter combination structural frequency vectors, thus forming a structural frequency matrix , each set of structural parameters and corresponding structural frequencies are recorded as a set of sample data, and a total of Group sample data;

[0021] Obtaining the structural frequency matrix vector through eigenvalue analysis The specific process is: by correcting the parameter vector Update the finite element model with the physical parameters and dimensional parameters of the structure, and perform eigenvalue analysis to obtain the structural natural frequency ;

[0022] Determine the correlation function as a Gaussian model, the basis function as a quadratic polynomial model, and the value of the correlation function coefficient, select the first 80% of the sample data as the training sample pool, and the remaining sample data as the test set, and then select the first 20% of the sample data from the sample pool as the initial training set Establish the initial Kriging model.

[0023] Preferably, the specific process of S4 is:

[0024] Based on the established new learning function expression XEFF that takes into account the uncertainty of the measured frequency, the measured frequency and a training sample remaining in the sample pool are calculated in turn. The learning function value is used to find the structural correction parameter vector corresponding to the maximum learning function value. , the new learning function XEFF is expressed as follows:

[0025] ;

[0026] Where: , Represents a training sample The corresponding structural frequency vector Quantity, and , , represents the standard normal distribution density function, is the Gaussian distribution function, and express the standard deviation and mean of the corresponding structural frequency vector; is the order of the measured frequency; is the first frequency vector of the structure measured A quantity.

[0027] Preferably, in S6, the XEFF learning function values ​​of the remaining sample points in the training sample pool are calculated, the sample points corresponding to the maximum value of the XEFF learning function are selected to be added to the training sample set, the corresponding first five-order frequencies are added to the response set, and the active learning Kriging model is reconstructed.

[0028] Preferably, the specific process of S7 is: using the constructed active learning Kriging model to perform random model correction, the objective function is the Euclidean norm and KL divergence between frequency distributions, the initial value of the correction parameter refers to the benchmark model, the optimization function is the NSGA-Ⅱ multi-objective genetic algorithm, the population size and the number of iterations are set, the fitness deviation value is set, and the mean and variance of the correction parameters after the model is corrected using the active learning Kriging model are obtained.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] An active learning algorithm is introduced to improve the point adding criterion of the Kriging model. The constructed Kriging model can reduce the number of required training samples through the improved point adding method. At the same time, the uncertainty factors in the measured data are considered when constructing the learning function. A new learning function considering the uncertainty of the measured data is constructed, thereby realizing fast, efficient and accurate model correction under small samples and noise errors. The present invention can obtain higher correction accuracy with fewer training samples and has high noise robustness, making it more suitable for practical engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a schematic diagram of the overall process flow of the present invention.

[0032] Figure 2 A comparison diagram of the finite element model and the active learning Kriging model in an embodiment of the present invention;

[0033] Figure 2 (a) represents the comparison of the first-order frequencies of the finite element model and the active learning Kriging model, and (b) represents the first-order frequencies of the finite element model and the active learning Kriging model.

[0034] Figure 3 The mean and standard deviation errors of the first five order frequencies before and after correction in the embodiment of the present invention;

[0035] Figure 3 (a) represents the mean error before and after the correction of the first five frequencies, and (b) represents the standard deviation error before and after the correction of the first five frequencies.

[0036] Figure 4 It is the confidence ellipses before and after the first three order frequency correction of the active learning Kriging model in the embodiment of the present invention.

[0037] Figure 5 It is the confidence ellipses before and after the first three-order frequency correction of the traditional Kriging model in the embodiment of the present invention.

[0038] Figure 6 Schematic diagram of parameter mean and standard deviation error before and after correction in an embodiment of the present invention;

[0039] Figure 6 (a) represents the mean error of parameters before and after correction under different noise levels, and (b) represents the standard deviation error of parameters before and after correction under different noise levels.

[0040] Figure 7 Schematic diagram of the mean and standard deviation correction errors of the structure frequency of the active learning Kriging model of the present invention at different noise levels in an embodiment of the present invention;

[0041] Figure 7 (a) represents the mean error of the structural frequency under different noise levels, and (b) represents the standard deviation correction of the structural frequency under different noise levels.

[0042] Figure 8 Schematic diagram of the mean and standard deviation correction errors of the structure frequency of the traditional Kriging model with different noise levels in an embodiment of the present invention;

[0043] Figure 8 (a) represents the mean error of the structural frequency obtained before and after correction using the Kriging model method under different noise levels, and (b) represents the standard deviation correction of the structural frequency obtained before and after correction using the Kriging model method under different noise levels.

[0044] Fig. 9 Schematic diagram of the fitness function value after correction for different numbers of measured frequencies. DETAILED DESCRIPTION

[0045] The present invention is further described below in conjunction with the embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0046] In this embodiment, an active learning method for fast random model correction of an offshore platform structure is provided. The overall process is as follows: Figure 1 shown.

[0047] The initial finite element model correction parameters, i.e., the mean and standard deviation of elastic modulus and density, and measured data are used as input, and the mean and standard deviation of the corrected finite element model correction parameters are used as output. The elastic modulus and density ranges of each unit are proposed to be [150, 220] GPa and [7000, 7900] kg / m 3 , and Latin hypercube sampling is used to generate 100 groups of structural parameter samples, and the structural parameter samples are substituted into the finite element model of the jacket structure to obtain the first five frequencies of the structure corresponding to each parameter sample. The first 80 groups are selected as the training sample pool, and the rest are the test sets.

[0048] Firstly, the first 16 groups of parameter samples and the corresponding first five-order frequency data were extracted from the training sample pool to establish the initial Kriging model, in which the quadratic polynomial model was selected as the regression model to fit the regression relationship between the correction parameters and the frequency response, and the Gaussian function was used as the correlation function to describe the correlation between the correction parameters, and the correlation parameter was 10.

[0049] Subsequently, the XEFF learning function values ​​of the remaining sample points in the training sample pool are calculated, and the sample points corresponding to the maximum value of the XEFF learning function and their first five-order frequencies are selected and added to the training sample set to reconstruct the active learning Kriging model.

[0050] Secondly, the constructed active learning Kriging model is used to correct the random model. The objective function is the Euclidean norm and KL divergence between the two frequency distributions. The initial values ​​of the correction parameters refer to the benchmark model. The optimization function is the NSGA-Ⅱ multi-objective genetic algorithm. The population size is set to 200, the number of iterations is set to 100, and the fitness deviation value is set to 1×10 -6 , and obtain the mean and variance of the corrected parameters after the model is corrected using the active learning Kriging model.

[0051] Finally, the XEFF learning function value of the candidate sample points in the training sample pool is calculated to determine whether it meets the learning stopping criterion, that is, it is less than 0.001. If not, continue to select sample points corresponding to the maximum value of the XEFF learning function and their first five-order frequencies to add to the training sample set to reconstruct the active learning Kriging model until the learning stopping criterion is met. At this time, the mean and standard deviation of the corrected finite element model parameters are obtained.

[0052] In order to verify the fitting accuracy of the active learning Kriging model, the relative mean square error RMSE and the determination coefficient R 2 The effectiveness of the established active learning Kriging model was evaluated, and the finite element model value of the test set and the active learning Kriging model value were calculated: R 2 The minimum value is 0.9998, which is close to 1; the maximum RMSE is 8.4×10 -4, close to 0; indicating that the active learning Kriging model has a high accuracy. At the same time, 50 sets of frequency data were generated using the finite element model and the active learning Kriging model. Figure 2 It can be seen that the active learning Kriging model has a good fit with the prediction data of the first two frequencies and the frequency data of the finite element model. In general, the active learning Kriging model can replace the finite element simulation to quickly and efficiently calculate the output response such as the modal frequency of the model to be corrected.

[0053] Table 1 shows the mean and standard deviation of the correction parameters obtained by using the active learning Kriging model to perform random model correction, where the mean of the elastic modulus parameter is and standard deviation corrected error is 0.016% and 8.654%, the mean value of density parameter and standard deviation corrected error The relative errors of the traditional Kriging model in Table 2 are 0.154% and 14.678% and 0.166% and 14.368% respectively; from the mean, the maximum correction error of the traditional Kriging model is 0.166%, and the maximum correction error of the active learning Kriging model is 0.016%, and the relative error is reduced by 90.36%; from the standard deviation, the maximum correction error of the traditional Kriging model is 14.678%, and the maximum correction error of the active learning Kriging model is 8.654%, and the relative error is reduced by 41.04%. The results show that the active learning Kriging model method can effectively improve the correction accuracy of the standard deviation of structural parameters.

[0054] Table 1 Correction parameter errors of active learning Kriging model before and after correction

[0055]

[0056] Table 2 Parameter errors of the traditional Kriging model before and after correction

[0057]

[0058] Depend on Figure 3It can be seen that the maximum value of the frequency mean error after correction by the active learning Kriging model is 0.014% at the fifth-order frequency, which is 93.33% lower than the maximum frequency error of 0.21% after correction by the traditional Kriging model; the frequency standard deviation correction error decreases to varying degrees after correction, and the error stabilizes at around 7%, with the maximum error being 7.09%, which is 52.7% lower than the maximum frequency standard deviation error of 14.99% of the traditional Kriging model, indicating that the active learning Kriging model method has significantly improved the correction effect of the structural frequency.

[0059] Depend on Figure 4 and Figure 5 It can be seen that the first three-order frequency confidence ellipses of the corrected finite element model are highly similar to the measured frequency confidence ellipses in shape, and the overlapping area between the two is significantly increased compared with the traditional Kriging model. The above also proves that the correction effect of the random model correction method based on the active learning Kriging model proposed in the present invention is better than that of the random model correction method based on the Kriging model.

[0060] Considering the influence of noise, 0.15% small noise and 1%, 3%, and 5% large noise are added to the first five frequencies of the structure as measured data. Finally, the NSGA-Ⅱ multi-objective genetic algorithm is used to iteratively solve the mean and standard deviation of the finite element model correction parameters, and the Euclidean norm and KL divergence between the two frequency distributions are used to construct the multi-objective function. The initial value of the correction parameter refers to the benchmark model.

[0061] The mean and standard deviation correction errors of structural parameters under different noise levels are given. When the noise level is 0-1%, there is no significant increase in the mean and standard deviation correction errors of the parameters, the mean correction error is about 0.015%, and the standard deviation correction error is about 10%. When the noise level is 3%-5%, the parameter correction error increases significantly, but the mean correction error is still less than 0.1%, and the standard deviation correction error is less than 20%.

[0062] In order to more clearly show the changes before and after the correction of the first five frequencies of the finite element model, 1000 sample points were obtained through Monte Carlo sampling according to the mean and standard deviation of the parameters of the corrected structural finite element model, and the sample points were substituted into the active learning Kriging model to obtain 1000 sets of frequency response data. The frequency response data were statistically analyzed to obtain the mean and standard deviation of the first five frequencies of the corrected finite element model, and the error comparison diagram of the mean and standard deviation of the first five frequencies of the structure after correction was drawn as shown in the figure. Figure 6 shown.

[0063] Depend on Figure 6It can be seen that the method proposed in the present invention has a better correction effect on the measured frequency with a noise level of 0-1%, and the correction errors of the frequency mean and standard deviation are about 0.02% and 10%. When the noise level is 3%-5%, the frequency correction error shows an upward trend, and its increase is significantly reduced. At the same time, the frequency correction error of the method proposed in the present invention under the condition of 5% high noise is smaller than the correction error of the traditional Kriging model method under the condition of 1% noise level. The correction results show that the method proposed in the present invention can effectively improve the correction effect on the first five frequencies of the structure.

[0064] like Figure 7 and Figure 8 , a schematic diagram of the structural frequency mean and standard deviation correction error of the active learning Kriging model with different noise levels and a schematic diagram of the structural frequency mean and standard deviation correction error of the traditional Kriging model with different noise levels are given respectively. The random model correction method based on the active learning Kriging model has good noise robustness. When the noise level is 5%, it still has an excellent correction effect. The corrected finite element model can reflect the true state of the structure.

[0065] In order to explore the influence of different numbers of measured frequencies on the correction results, the KL divergence of the frequency distribution of the finite element model before and after correction is used as the fitness function to quantify the correction effect, and 12 groups of different numbers of measured frequencies are generated by Monte Carlo simulation and active learning Kriging model. The optimization algorithm is set as above. During the optimization process, the smaller the fitness function value, the better the correction effect. When the fitness function value is 0, it means that the finite element model frequency is completely consistent with the measured frequency distribution. Fig. 9 The values ​​of the fitness function after correction for different numbers of measured frequencies are given.

[0066] When the measured frequency is only 10 groups, the fitness function value after random model correction is the largest, around 1.8; when it increases to 20 groups of data, the fitness function value decreases significantly; when it exceeds 20, the increase in the number of measured frequencies has little effect on the correction effect. At this time, the calculation cost of the structural random model correction increases, but the correction accuracy remains basically unchanged. Therefore, the number of samples can be selected as 20, indicating that the patent of this invention can be applied to the efficient, accurate and rapid model correction of marine platform structures under small samples and noise pollution.

[0067] In general, the method proposed in the present invention is suitable for efficient, accurate and rapid random correction of marine platform structures with a small amount of measured data.

[0068] The above description is only the preferred embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

[0069] Although the above describes the specific implementation methods of the present invention, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. An active learning method for fast stochastic model correction of offshore platform structures, characterized in that: The process includes: S1, select the correction parameters of the random correction of the marine platform structure through sensitivity analysis; transform the random correction process of the marine platform structure into the correction process of the mean and standard deviation of the correction parameters; S2, Latin hypercube sampling based on modified parameter mean and standard deviation times, and obtain the modified parameter matrix; S3, obtain the structural frequency matrix through finite element analysis, and construct the initial training set based on the modified parameter matrix and the structural frequency matrix , and establish the initial Kriging model; S4, establish a new learning function expression considering the uncertainty of the measured frequency, calculate the learning function value, and make the optimal structural correction parameter vector corresponding to the maximum learning function value ; The details are as follows: Based on the established new learning function expression XEFF that takes into account the uncertainty of the measured frequency, the measured frequency and a training sample remaining in the sample pool are calculated in turn. The learning function value is used to find the structural correction parameter vector corresponding to the maximum learning function value. , the new learning function XEFF is expressed as follows: ; Where: , Represents a training sample The corresponding structural frequency vector Quantity, and , , represents the standard normal distribution density function, is the Gaussian distribution function, and express the standard deviation and mean of the corresponding structural frequency vector; is the order of the measured frequency; is the first frequency vector of the structure measured Quantity; S5, the optimal correction parameter vector Substitute into the finite element model for finite element model analysis and obtain the corresponding structural frequency vector ; S6, the optimal correction parameter vector and the structural frequency vector Add to the initial training set and create a new training set ,use Construct a new Kriging model; S7, constructing an objective function using the measured frequency data and the initial finite element model frequency data, taking the mean and standard deviation of the correction parameters as the solution target, solving using an optimization algorithm, and obtaining the mean and standard deviation of the correction parameters of the finite element model to be corrected; Repeat the above steps S4 to S7 until the model converges to achieve random correction of the offshore platform structure.

2. The active learning type fast random model correction method for offshore platform structure according to claim 1, characterized in that: The specific process of S1 is as follows: Select parameters with certain sensitivity in offshore platform structures through sensitivity analysis As correction parameters, Representative Correction parameters; The random correction process of the offshore platform structure is transformed into a correction process for the mean and standard deviation of the correction parameters, and the initial mean and standard deviation of each parameter are determined. ,in and Represents the correction parameters The mean and standard deviation of .

3. The active learning fast stochastic model correction method for marine platform structure according to claim 1, characterized in that: The specific process of S3 is as follows: For each correction parameter vector in the correction parameter matrix Substitute the modified parameters into the finite element model, wherein the finite element model refers to the finite element model of the offshore platform structure established by using finite element analysis software; Obtaining the structural frequency matrix vector through eigenvalue analysis , and get The corresponding parameter combination structural frequency vectors, thus forming a structural frequency matrix , each set of structural parameters and corresponding structural frequencies are recorded as a set of sample data, and a total of Group sample data; Obtaining the structural frequency matrix vector through eigenvalue analysis The specific process is: by correcting the parameter vector Update the finite element model with the physical parameters and dimensional parameters of the structure, and perform eigenvalue analysis to obtain the structural natural frequency ; Determine the correlation function as a Gaussian model, the basis function as a quadratic polynomial model, and the value of the correlation function coefficient, select the first 80% of the sample data as the training sample pool, and the remaining sample data as the test set, and then select the first 20% of the sample data from the sample pool as the initial training set Establish the initial Kriging model.

4. The active learning type fast random model correction method for offshore platform structure according to claim 1, characterized in that: In S6, the XEFF learning function values ​​of the remaining sample points in the training sample pool are calculated, the sample points corresponding to the maximum value of the XEFF learning function are selected to be added to the training sample set, the corresponding first five-order frequencies are added to the response set, and the active learning Kriging model is reconstructed.

5. The active learning fast stochastic model correction method for offshore platform structure according to claim 1, characterized in that: The specific process of S7 is: using the constructed active learning Kriging model to perform random model correction, the objective function is the Euclidean norm and KL divergence between frequency distributions, the initial value of the correction parameter refers to the benchmark model, the optimization function is the NSGA-Ⅱ multi-objective genetic algorithm, the population size and the number of iterations are set, the fitness deviation value is set, and the mean and variance of the correction parameters after the model is corrected using the active learning Kriging model are obtained.

Images