Step-by-step Fast Random Model Updating Method for Offshore Platform Structures

Abstract

The present invention relates to the field of ocean engineering technology, and provides a method for rapidly and randomly correcting the model of a step-type ocean platform structure. According to the design parameters of the ocean platform, an initial finite element model of the ocean platform is established; among the design parameters, the parameters to be corrected are selected, and the maximum and minimum values of each parameter to be corrected are determined; sub-sampling is performed on the maximum and minimum values of each parameter to be corrected to obtain a matrix of corrected parameters; the matrix of corrected parameters is substituted into the initial finite element model to obtain an updated finite element model, and the structural frequency vector corresponding to the vector of corrected parameters is obtained, and a Kriging model is established; based on the vector of corrected parameters and the Kriging model, the frequency of the initial finite element model is calculated; a distance objective function and a distribution objective function are constructed to perform two corrections on the mean and standard deviation of the corrected parameters; based on the frequency of the finite element model after the second correction, the corrected finite element model of the ocean platform is obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of ocean engineering, and particularly relates to a method for rapidly and randomly correcting the model of a step-type ocean platform structure. Background Art

[0002] Ocean platforms are key infrastructure for ocean resource development (such as oil and gas extraction). They are long-term in complex and harsh ocean environments and are mainly composed of various components such as pile legs, decks, and support structures. The assessment of the dynamic response and health monitoring technology of ocean platform structures under complex ocean environment loads are current research hotspots and difficulties, and obtaining a finite element model that can replace the actual ocean platform structure for monitoring and assessment is the key core.

[0003] Theoretical models such as the initially established finite element model of an ocean platform often deviate from the actual structure. The influencing factors of the deviation mainly come from multiple aspects such as modeling assumptions (such as material property assumptions, boundary condition assumptions, etc.), manufacturing errors, and installation errors. 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. By model correction, the accuracy of the model can be improved, so as to more accurately predict the response of the platform under various working conditions.

[0004] Traditional model correction methods considering the uncertainty of ocean structure parameters require a large number of iterations and multiple calls to the finite element model for optimization and solution. Due to the complex composition and numerous degrees of freedom of ocean structure elements, the model correction process often has problems such as large computational amount and low efficiency. Simplifying the finite element model or finding a surrogate model has become an important measure to improve the operation efficiency of model correction. The stochastic model correction based on the surrogate model is proposed and widely used based on this idea. Its main idea is to use an explicit surrogate model to fit the complex implicit relationship between the structural frequency response and the selected parameters to be corrected, so as to achieve the purpose of replacing the finite element model for numerical operations and simplifying the iteration process. Compared with other surrogate models such as polynomial regression and neural networks, the Kriging model has excellent performance in dealing with non-linear data. For the optimization and solution link in stochastic model correction, the selection of the objective function and correction strategy is crucial for the correction accuracy. The stochastic model correction method based on the traditional or active learning type Kriging model uses the Euclidean norm and KL divergence between the measured frequency and the finite element model frequency to construct a multi-objective function. The correction results show that there is a large difference in the variance between the frequency of the corrected finite element model and the measured frequency. The interference of different objective functions in selecting the optimal solution of the distribution index on the Pareto front is the main reason for this problem.

[0005] Before the random model updating of the structure, the means and variances of the updating parameters are unknown. The direct structural random model updating method takes the means and variances of the updating parameters as unknowns and inputs them into the optimization algorithm for direct iterative solution. Research shows that for indicators measuring the differences between the probability distributions of the measured frequencies and the finite element model frequencies, such as the Bhattacharyya distance and the KL divergence, when there is no overlap between the measured frequencies and the finite element model frequencies, these indicators are meaningless. Therefore, the direct structural random model updating method combines the distribution difference indicators with objective functions such as the Euclidean norm between the two frequencies to construct a multi-objective function for optimization solution, so as to obtain the optimal solutions of the mean and standard deviation of the structural updating parameters at one time. However, for multi-objective optimization, the selection of the optimal solution is restricted by all objective functions, thus forming the Pareto front. The Pareto front refers to the state where, under the given constraints, it is impossible to improve one objective without damaging another objective. In multi-objective optimization problems, the solutions on the Pareto front are very important, as they represent a trade-off where no single objective can be improved without affecting other objectives. Therefore, when using the KL divergence to construct the objective function, the selection of its optimal solution is affected by the Euclidean norm, and the optimization effect of the KL divergence cannot be fully exerted, inevitably interfering with the correction of the variance between the frequencies of the finite element model and the measured frequencies.

[0006] For the above reasons, it is necessary to study a random updating method for the offshore platform structure model that can reduce the variance difference between the actual frequency and the finite element frequency after updating. Summary of the Invention

[0007] The purpose of the present invention is to solve the above technical problems and provide a step-by-step fast random model updating method for offshore platform structures.

[0008] To achieve the above purpose, in some embodiments of the present invention, the following technical solutions are provided:

[0009] A step-by-step fast random model updating method for offshore platform structures, characterized by comprising the following steps:

[0010] According to the design parameters of the offshore platform, establish an initial finite element model of the offshore platform;

[0011] Among the design parameters of the offshore platform, select parameters to be updated, and determine the maximum and minimum values of each parameter to be updated;

[0012] Perform samplings on the maximum and minimum values of each parameter to be updated to obtain a correction parameter matrix , where is the correction parameter vector obtained from the rd sampling, and each correction parameter vector contains a correction parameter; wherein, is an integer greater than 1;

[0013] Substitute the correction parameter matrix into the initial finite element model, update the structural parameters or dimensional parameters corresponding to the correction parameters in the correction parameter matrix to obtain an updated finite element model, perform modal analysis or finite element analysis on the updated finite element model to obtain the structural frequency vector corresponding to the correction parameter vector; establish a Kriging model based on the correction parameter vector and its corresponding structural frequency vector;

[0014] Calculate the frequency of the initial finite element model based on the correction parameter and the Kriging model;

[0015] Construct a distance objective function based on the frequency and standard deviation of the initial finite element model, as well as the measured frequency and standard deviation of the offshore platform, and perform the first optimization correction on the mean and standard deviation of the correction parameter based on the optimization objective;

[0016] Substitute the mean and standard deviation after the first optimization correction into the Kriging model, calculate the frequency of the finite element model after the first correction, construct a distribution objective function using the KL divergence based on the measured frequency of the offshore platform and the frequency of the corrected finite element model, and perform the second optimization correction on the mean and standard deviation of the correction parameter based on the optimization objective;

[0017] Substitute the mean and standard deviation of the correction parameter after the second optimization correction into the Kriging model to obtain the frequency of the finite element model after the second correction, calculate the error between the frequency of the finite element model after the second correction and the measured frequency of the offshore platform, and if the error meets the accuracy requirement, obtain the corrected finite element model of the offshore platform based on the frequency of the finite element model after the second correction.

[0018] In some embodiments of the present invention, the step of selecting the parameters to be corrected includes:

[0019] Perform a sensitivity analysis on the design parameters, and select the parameters with high sensitivity as the parameters to be corrected.

[0020] In some embodiments of the present invention, the design parameters of the offshore platform include structural parameters and material parameters.

[0021] In some embodiments of the present invention, the steps of establishing a Kriging model include:

[0022] Record each group of correction parameter vectors and the corresponding structural frequencies as a group of sample data, and a total of groups of sample data are obtained; select the first 80% of the sample data as the training set, and the remaining sample data as the test set to establish a Kriging model.

[0023] In some embodiments of the present invention, after establishing the Kriging model, the following steps are further included:

[0024] The established Kriging model is verified by using the effectiveness evaluation indexes determination coefficient R2 and relative root mean square error RMSE, and the model verification accuracy is set.

[0025] If the accuracy of the Kriging model meets the model verification accuracy requirement, the established Kriging model is used to continue calculating the frequency of the initial finite element model. If the accuracy of the Kriging model does not meet the model verification accuracy requirement, the Latin hypercube sampling step is repeated, and the modified parameter matrix obtained by Latin hypercube sampling is re-substituted into the initial finite element model, and the Kriging model is re-established until the accuracy of the Kriging model meets the model verification accuracy requirement.

[0026] In some embodiments of the present invention, the steps of calculating the initial finite element frequency include:

[0027] Calculate the initial mean and standard deviation of each modified parameter, and perform times of Monte Carlo sampling on the initial mean and standard deviation of each modified parameter to obtain the finite element model parameter samples , where is the vector of the initial mean and standard deviation of the modified parameter obtained by the th Monte Carlo sampling; substitute the parameter samples into the Kriging model to obtain the initial finite element model frequency .

[0028] In some embodiments of the present invention, the distance objective function includes a mean objective function and a standard deviation objective function, and the steps of constructing the distance objective function include:

[0029] ;

[0030] ;

[0031] Where: represents the mean objective function, represents the standard deviation objective function, represents the frequency order, represents the th order mean of the finite element model frequency, represents the th order mean of the frequency of the actual structure of the offshore platform, represents the th order mean standard deviation of the finite element model frequency, represents the th order standard deviation of the frequency of the actual structure of the offshore platform, .

[0032] In some embodiments of the present invention, the method for optimizing and correcting the mean and standard deviation of the correction parameters based on the optimization objective includes:

[0033] Taking the optimization and correction of the parameter mean and standard deviation of the correction parameters as the solution objective, substituting the distance objective function into the multi-objective optimization algorithm, using the optimization algorithm to solve the mean and standard deviation of the correction parameters, setting a correction target threshold, and when the output result of the mean objective function is less than the correction target threshold and the output result of the standard deviation objective function is less than the correction target threshold, stop the correction, and use the mean and standard deviation at this time as the mean and standard deviation of the correction parameters after optimization and correction.

[0034] In some embodiments of the present invention, the method for constructing the distribution objective function includes:

[0035]

[0036] Wherein, is the mean of the finite element model frequencies, is the mean of the actual frequencies of the offshore platform, is the frequency covariance matrix of the finite element model , is the actual frequency covariance matrix of our platform.

[0037] The step-by-step rapid stochastic model correction method for offshore platform structures proposed by the present invention, compared with the prior art, the beneficial effects of the technical solution of the present invention are as follows:

[0038] A distributed model correction method is proposed. Aiming at the problem of poor correction effect for the structural frequency distribution difference, the model correction is divided into two-step correction processes. The first correction process is the distance correction for the distance objective function, and the second correction process is the distribution difference correction based on the distribution objective function. Compared with the direct stochastic correction method, the step-by-step stochastic correction method has fewer effective iteration times than the direct method, high stochastic model correction efficiency, and more stable correction effects on the mean and standard deviation of the structural parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the embodiments or the description of the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0040] Figure 1 is the flowchart of the step-by-step rapid stochastic model correction method for offshore platform structures provided by the present invention;

[0041] Figure 2 Graph for comparing the effects of correcting the parameter mean value between the direct method and the distributed method;

[0042] Figure 3 Graph for comparing the effects of correcting the parameter standard deviation between the direct method and the distributed method;

[0043] Figure 4 Graph for comparing the correction effects of the mean value and standard deviation correction errors of the first five-order frequencies between the direct method and the distributed method under different working conditions;

[0044] Figure 5 Graph of the confidence ellipse of the corrected frequency of the finite element model and the measured frequency - effect diagram of the step-by-step stochastic correction method;

[0045] Figure 6 Graph of the confidence ellipse of the corrected frequency of the finite element model and the measured frequency - effect diagram of the direct stochastic correction method;

[0046] Figure 7 Graph for comparing the average effective iteration times under each working condition;

[0047] Figure 8 Graph for comparing the effects of the correction errors of the parameter mean value between the direct and step-by-step model correction methods; (a) is the graph for comparing the effects of the correction errors of the parameter mean value of the direct model correction method; (b) is the graph for comparing the effects of the correction errors of the parameter mean value of the step-by-step model correction method.

[0048] Figure 9 Graph for comparing the effects of the correction errors of the parameter standard deviation between the direct and step-by-step model correction methods; (a) is the graph for comparing the effects of the correction errors of the parameter standard deviation of the direct model correction method; (b) is the graph for comparing the effects of the correction errors of the parameter standard deviation of the step-by-step model correction method. Detailed implementation manner

[0049] In order to make the technical problems, technical solutions and beneficial effects to be solved by 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.

[0050] In the embodiments of the present application, prefix words such as "first" and "second" are only used to distinguish different described objects, and have no limiting effect on the position, order, priority, quantity or content of the described objects, etc. The use of ordinal words and other prefix words for distinguishing described objects in the embodiments of the present application does not constitute a limitation on the described objects. The statements of the described objects refer to the description in the claims or the context of the embodiments, and should not constitute redundant limitations because of the use of such prefix words. In addition, in the description of this embodiment, unless otherwise specified, "a plurality of" means two or more.

[0051] The technical solutions in the embodiments of the present application will be described below with reference to the accompanying drawings in the embodiments of the present application. Among them, in the description of the embodiments of the present application, unless otherwise specified, " / " means "or". For example, A / B may represent A or B; "and / or" herein is only a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B may represent: A exists alone, A and B exist simultaneously, and B exists alone.

[0052] In several embodiments provided in the embodiments of the present application, it should be understood that the disclosed systems and methods can be implemented in other ways. For example, the device embodiments described above are only illustrative. For example, the division of the units is only a logical function division, and there can be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point, the displayed or discussed coupling or direct coupling or communication connection between each other can be through some interfaces, and the indirect coupling or communication connection of the device or unit can be in electrical, mechanical or other forms.

[0053] Based on this, the present invention proposes a step-by-step rapid random model updating method for an offshore platform structure, referring to Figure 1 , which specifically includes the following steps. S1: Step of establishing an initial finite element model of the offshore platform.

[0054] According to the design parameters of the offshore platform, an initial finite element model of the offshore platform is established, and each design parameter corresponds to the structural parameter or dimensional parameter of the offshore platform.

[0055] Among them, the design parameters of the offshore platform include structural parameters and material parameters. The structural parameters reflect the structural design characteristics of the offshore platform, and the material parameters reflect what parameters are adopted for the main structure part of the offshore platform.

[0056] S2: Step of selecting correction parameters.

[0057] Among the design parameters of the offshore platform, the parameters to be corrected are selected , and the maximum value and minimum value of each correction parameter are determined . Among them, is an integer greater than 1. The maximum value of the parameter and the minimum value of the parameter are determined based on the design scheme and design requirements of the offshore platform.

[0058] The purpose of the step of determining the correction parameters is to extract some parameters from numerous offshore platform design parameters for correction to modify the model of the offshore platform. Since the number of offshore platform design parameters is large, using all parameters for model correction has low efficiency and may carry the risk of large correction errors. In order to be able to correct the initial finite element model according to the design parameters, in the step of selecting the parameters to be corrected, a sensitivity index is used to select the parameters to be corrected.

[0059] In the embodiment of the present invention, sensitivity analysis is performed on the design parameters, and the parameters with high sensitivity are selected as the parameters to be corrected.

[0060] The analysis of parameter sensitivity is used to evaluate the sensitivity of the model output to parameter changes. High sensitivity means that a slight modification of the correction parameter can obtain a relatively obvious output response; low sensitivity means that modifying the correction coefficient results in little change in the output response and effective model correction cannot be achieved. Regarding the analysis method of parameter sensitivity, it can be carried out in combination with the specific actual situation of the offshore platform structure and by using the local analysis method and global analysis method in the prior art. The local method is suitable for quickly evaluating the influence of parameters near a specific point, while the global method is more suitable for comprehensively analyzing the role of parameters in the entire space. In practical applications, multiple methods can be combined to obtain more comprehensive results. Details are not elaborated here.

[0061] S3: Parameter sampling step.

[0062] Perform samplings on the maximum and minimum values of each parameter to be corrected to obtain the correction parameter matrix , and each correction parameter vector contains correction parameters.

[0063] In a specific embodiment, perform Latin hypercube samplings on the maximum and minimum values of each correction parameter to obtain the correction parameter matrix , where is the correction parameter vector obtained from the th Latin hypercube sampling, and each correction parameter vector contains correction parameters. Among them, is an integer greater than 1.

[0064] In the specific implementation process, other sampling methods can also be used. Details are not elaborated here.

[0065] S4: Step of establishing the Kriging model.

[0066] The Kriging model assumes that the data is generated by a Gaussian process. Its core idea is to use the spatial correlation between known data points to predict the values of unknown points. As a powerful interpolation and prediction tool, the Kriging model is particularly suitable for spatial data analysis and engineering optimization.

[0067] Substitute the modified parameter matrix obtained by Latin hypercube sampling into the initial finite element model, update the structural parameters or dimensional parameters corresponding to the modified parameters in the modified parameter matrix to obtain an updated finite element model, perform modal analysis or finite element analysis on the updated finite element model, input the modified parameter vector into the finite element model, and obtain the structural frequency vectors corresponding to the modified parameter vectors; establish a Kriging model based on the modified parameter vectors and their corresponding structural frequency vectors. ; Establish a Kriging model based on the modified parameter vector and its corresponding structural frequency vector.

[0068] In some embodiments of the present invention, the steps of establishing a Kriging model include: recording each group of modified parameter vectors and corresponding structural frequencies as a group of sample data, and obtaining a total of groups of sample data; select the first 80% of the sample data as the training set, and the remaining sample data as the test set to establish a Kriging model. The steps of establishing a Kriging model belong to the prior art and will not be elaborated here.

[0069] In some embodiments of the present invention, after establishing the Kriging model, the following steps are further included:

[0070] Use the effectiveness evaluation indicators determination coefficient R2 and relative root mean square error RMSE to verify the established Kriging model and set the model verification accuracy;

[0071] If the accuracy of the Kriging model meets the model verification accuracy requirements, use the established Kriging model to continue calculating the frequencies of the initial finite element model. If the accuracy of the Kriging model does not meet the model verification accuracy requirements, repeat the Latin hypercube sampling step, substitute the modified parameter matrix obtained by Latin hypercube sampling into the initial finite element model again, and re-establish the Kriging model until the accuracy of the Kriging model meets the model verification accuracy requirements.

[0072] S5: Initial finite element model frequency calculation step.

[0073] Calculate the frequencies of the initial finite element model based on the modified parameters and the Kriging model ; where is an integer greater than 1.

[0074] Specifically, calculate the initial mean and standard deviation of each correction parameter, and perform the -th Monte Carlo sampling to obtain the parameter samples of the finite element model , where represents the initial mean of the -th order correction parameter, represents the standard deviation of the -th order correction parameter, is the vector of the initial mean and standard deviation of the correction parameter obtained from the -th Monte Carlo sampling; substitute the parameter samples into the Kriging model to obtain the initial finite element model frequency .

[0075] S6: Construct the distance objective function step.

[0076] Utilize the measured frequency of the offshore platform and the initial finite element model frequency to construct the distance objective function. Among them, the measured frequency of the offshore platform is obtained according to the actual working environment of the offshore platform.

[0077] The distance objective function includes the mean objective function and the standard deviation objective function. In the embodiments of the present invention, the Euclidean norm is used as the distance objective function. The Euclidean norm is an index for measuring the distance between these two vectors and is usually used to calculate the similarity or difference degree between vectors. The Euclidean norms of the structural frequency mean and standard deviation are:

[0078] ;

[0079] ;

[0080] where: represents the mean objective function, represents the standard deviation objective function, represents the frequency order, represents the mean of the -th order finite element model frequency, represents the mean of the -th order actual structure frequency of the offshore platform, represents the mean standard deviation of the -th order finite element model frequency, represents the standard deviation of the -th order actual structure frequency of the offshore platform. . The calculation steps of the mean and standard deviation belong to well-known technologies and will not be elaborated.

[0081] S7: Optimize the distance objective function and perform the first correction of the mean and standard deviation.

[0082] The first correction is based on the distance objective function correction.

[0083] The distance objective function is constructed using the measured frequency of the offshore platform and the frequency of the initial finite element model. Among them, the distance objective function includes the mean objective function and the standard deviation objective function, and the mean and standard deviation of the correction parameters are optimized and corrected based on the optimization objective.

[0084] In some embodiments of the present invention, the method for optimizing and correcting the mean and standard deviation of the correction parameters based on the optimization objective includes:

[0085] Taking the parameter mean and standard deviation for optimizing and correcting the correction parameters as the solution objective, substituting the distance objective function into the multi-objective optimization algorithm, and using the optimization algorithm to solve the mean and standard deviation of the correction parameters. Set the correction target threshold. When the output result of the mean objective function is less than the correction target threshold and the output result of the standard deviation objective function is less than the correction target threshold, stop the correction, and use the mean and standard deviation at this time as the mean and standard deviation of the correction parameters after optimization and correction: . Among them, is the th mean after the first optimization and correction, is the th standard deviation after the first optimization and correction.

[0086] S8: Construct the distribution objective function.

[0087] Substitute the mean and standard deviation after the first correction into the Kriging model, calculate the frequency of the finite element model after the first correction, and construct the distribution objective function using the KL divergence based on the measured frequency of the offshore platform and the frequency of the corrected finite element model. Perform the second correction on the mean and standard deviation of the correction parameters based on the optimization objective.

[0088] Specifically, substitute the mean and standard deviation of the first optimization and correction parameters into the Kriging model to obtain the frequency of the distance-corrected model ; based on the measured frequency of the offshore platform and the frequency of the distance-corrected finite element model , construct the distribution objective function using the KL divergence.

[0089] Compared with the Bhattacharyya distance index, the KL divergence (Kullback-Leibler divergence) index can better quantify the differences between the distributions of small-sample data. Calculate the finite element model frequency and the actual structure frequency respectively, and obtain the mean of the finite element model frequency as and the actual frequency mean of the offshore platform , the frequency covariance matrix of the finite element model and the actual frequency covariance matrix of the platform , then the reverse KL divergence index between the finite element model and the actual structure frequency is:

[0090] .

[0091] That is, it serves as the distribution objective function.

[0092] S9: Optimize the distribution function and perform the second distance correction.

[0093] The second correction is based on the distribution objective function.

[0094] Substitute the mean and standard deviation after the first correction into the Kriging model, calculate the frequency of the finite element model after the first correction, construct a distribution objective function using the KL divergence based on the measured frequency of the offshore platform and the frequency of the corrected finite element model, and perform the second correction on the mean and standard deviation of the correction parameters based on the optimization objective.

[0095] Taking the mean and standard deviation of the correction parameters as the solution objectives, substitute the distribution objective function into the multi-objective optimization algorithm. The input of the optimization algorithm is the population size, the number of iterations, the fitness deviation value, and the initial frequency of the finite element model, and continue the optimization solution. Stop the solution when the convergence condition is met, and obtain the mean and standard deviation of the corrected correction parameters . Among them, is the mean after the nd second optimization correction, is the standard deviation after the th second optimization correction.

[0096] S10: Check the correction accuracy error.

[0097] Substitute the mean and standard deviation of the parameters after the second optimization correction obtained in step S9 into the frequency of the corrected finite element model, calculate the error between the frequency of the corrected finite element model and the measured frequency at this time. If the accuracy requirement is met, the corrected finite element model is obtained. If the accuracy requirement is not met, repeat steps S7 to S9 until the accuracy is met.

[0098] Next, taking the step-by-step stochastic model correction of the jacket platform as an example, the effect of the model correction method provided by the present invention is described. In the embodiment of the present invention, for the same jacket platform, the direct model correction method and the step-by-step model correction method are used to perform model correction, and the model correction effects of the two methods are compared.

[0099] First, 100 groups of modified parameter vectors are obtained by Monte Carlo sampling according to the mean and standard deviation of the initial finite element model modification parameters, and the first five natural frequencies of the structure corresponding to each parameter vector are substituted into the finite element model as the natural frequencies of the initial finite element model;

[0100] Subsequently, the Euclidean norm and KL divergence of the finite element model natural frequencies and the measured natural frequencies are constructed as the distance modification index and the distribution difference index respectively;

[0101] Then, the population size in the optimization algorithm is set to 200, the number of iterations is 100, and the fitness deviation value is 1×10 -6 , and the input is the measured natural frequencies, the mean and standard deviation of the initial finite element model modification parameters;

[0102] Furthermore, the distance between the two is corrected by using the Euclidean norm of the finite element model natural frequencies and the measured natural frequencies, and the distance index between the two frequency distributions is calculated simultaneously. When the distance index is less than 10 4 , the distance correction is stopped, and the objective function is changed to the KL divergence to continue the optimization solution; finally, the optimization algorithm outputs the mean and standard deviation of the modified finite element model modification parameters.

[0103] Compare the correction errors of the direct method and the step-by-step method for the mean and standard deviation of the modified parameters. The correction error of the step-by-step method for the mean of the modified parameters is not greater than 0.01%, and the correction error of the direct method for the mean of the modified parameters is between 0.009% and 0.015%. The correction error of the step-by-step method for the standard deviation of the parameters is about 5.0%, which is less than the correction error of the direct method for the standard deviation of the parameters. This also shows that the correction effect of the step-by-step method is better than that of the direct method. To sum up: for the correction errors of the structural parameter mean and standard deviation, referring to Figure 2 and Figure 3 , it can be seen that the correction effects of the step-by-step method and the direct method are similar, and there is no obvious decrease in the correction error of the structural parameters.

[0104] Referring to Figure 4 , to study the mean and standard deviation of the correction of the first five natural frequencies of the modified finite element model, the errors of the first five natural frequencies corrected by the direct method and the step-by-step method are visualized as a bar chart. It can be seen that the correction error of the direct method for the mean of the structural natural frequencies is 0.012% - 0.018%, and the correction error of the standard deviation is about 6% - 7%; the correction error of the step-by-step method for the mean of the structural natural frequencies has a significant decrease compared with the direct method. The correction error of its frequency mean is 0.001% - 0.008%, and the correction error of the standard deviation is 2% - 2.5%. Therefore, it can be concluded that the step-by-step method has a good correction effect on the structural modification parameters and frequency response, and has good correction stability.

[0105] To study the stochastic model updating effects of two correction strategies under different degrees of noise influence, small noises of 0.15% and 1% and large noises of 3% and 5% were respectively added to the measured frequencies, and the stochastic model updating was carried out by the direct method and the step-by-step method. Both methods used the NSGA-II optimization algorithm for iterative solution. The parameter settings were the same as those in the previous text, that is, the population size was 200, the number of iterations was 100, the fitness deviation value was 1×10-6, the output results of the optimization algorithm were the mean and standard deviation of the updated parameters, and the surrogate model was the active learning Kriging model. To avoid contingency, the stochastic model updating was carried out 20 times for different noise levels by both methods, and their averages were taken to observe the updating effects of the mean and standard deviation of the structural updated parameters.

[0106] To observe the correction of the distribution difference between the frequencies of the finite element model and the measured frequencies by the step-by-step correction method, the confidence ellipses of the first two-order frequencies of the updated finite element model and the measured frequencies under the influence of 0.15% noise were drawn. It can be seen that: the central points of the confidence ellipse of the updated frequencies and the confidence ellipse of the measured frequencies almost completely coincide, indicating that the correction effect of the mean value of the finite element model frequencies is good; the lengths of the major and minor axes of the two ellipses are similar, indicating that the correction effect of the frequency standard deviation is good. Compared with the direct correction effect, the inclination angles of the two ellipses obtained by the step-by-step method are less different, and the overall fitting degree of the two ellipses has been significantly improved, proving the superiority of the step-by-step method for the correction effect of the frequency distribution difference.

[0107] Reference Figure 5 and Figure 6 The step-by-step stochastic model updating method proposed by the present invention has a similar correction effect on the mean and standard deviation of the structural parameters to the direct stochastic model updating method, but the step-by-step method is very superior in the correction effect of the frequency distribution difference of the finite element model. The confidence ellipse of the updated frequencies of the finite element model and the confidence ellipse of the measured frequencies almost completely coincide, and the overall correction effect is better than that of the direct stochastic model updating method.

[0108] The step-by-step method divides the direct method into distance correction and distribution difference correction, changing the one-time optimization calculation of the direct method into two times. If the number of iterations is too large, it will affect the efficiency of the structural stochastic model updating. The working conditions were set to carry out 20 times of model updating by the step-by-step method and the direct method respectively. The population size of the multi-objective optimization algorithm was set to 200, and the average number of iterations of the four working conditions was statistically analyzed. The number of iterations when the KL divergence value between the frequencies of the finite element model and the measured frequencies appeared at the minimum value was taken as the final effective number of iterations. The average effective number of iterations of each working condition is as Figure 7 shown.

[0109] For the direct method, the average effective number of iterations in working condition E1 is 9.6 times, which is the least among the four working conditions. The average effective number of iterations in working condition E2 is 10.1 times, and that in working condition E3 is 10 times. The working condition with the most iterations is E4, with an average effective number of iterations of 10.4 times.

[0110] For the step-by-step method, the average effective number of iterations in the four working conditions has decreased significantly compared with the direct method. The average effective number of iterations in working condition E1 is 5.1 times, and that in working condition E2 is 5 times. The working condition with the most iterations is E3, with an average effective number of iterations of 5.2 times. Working condition E4 has the least average effective number of iterations among the four working conditions, which is 4.9 times.

[0111] In summary: The optimized performance of the step-by-step random model correction method proposed by the present invention is stronger and it is not easy to fall into local optimal solutions. Although the step-by-step method divides the optimization process into two steps, the number of iterations has decreased significantly compared with the direct method, indicating that the step-by-step method can be better applied to the random model correction of actual structures.

[0112] Through the previous research on the random model correction effects of the direct method and the step-by-step method, it is found that there will be a small number of abnormal correction effects during multiple tests. To be closer to the actual engineering application scenario, the finite element model frequencies with 0.15% noise added to working condition E1 are selected as the measured frequencies, and the direct method and the step-by-step method are respectively used for 100 times of model correction, and the mean values and standard deviation errors of the corrected structural parameters are observed.

[0113] Reference Figure 8 , it can be seen that: for the mean values of the structural correction parameters, the fluctuations of the direct method in the test are very obvious, while the correction results of the step-by-step method in the test are relatively stable. At the same time, the stability of the model correction results can also be measured by the standard deviation of the mean correction errors of the 100 test parameters. Among them, the standard deviations of the mean correction errors of the elastic modulus E, density D, and the outer diameter DLP of the lower half column of the direct method are 0.017%, 0.016%, and 0.011% respectively, and the standard deviations of the mean correction errors of the elastic modulus E, density D, and the outer diameter DLP of the lower half column of the step-by-step method are 0.0034%, 0.004%, and 0.0026% respectively. Thus, it can be seen that the step-by-step method has a more stable correction effect on the mean values of the structural parameters.

[0114] The standard deviation errors of the corrected structural parameters are plotted as Figure 9As shown. The fluctuations of the direct method in the test are still very obvious, and the correction results of the step-by-step method in the test are relatively stable. The stability of the model correction results is measured by the standard deviation of the mean correction error of 100 test parameters. Among them, the standard deviation of the correction error of the standard deviation of the elastic modulus E, density D, and the outer diameter DLP of the lower half column of the direct method are 6.86%, 7.52%, and 8.27% respectively, and the standard deviation of the correction error of the standard deviation of the elastic modulus E, density D, and the outer diameter DLP of the lower half column of the step-by-step method are 1.456%, 1.51%, and 1.72% respectively. Thus, it can be seen that: the correction effect of the step-by-step method on the standard deviation of the structural parameters is more stable.

[0115] In summary: The step-by-step correction method proposed by the present invention has better stability compared with the traditional direct method.

[0116] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. It should be noted that for those of ordinary skill in the art, any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the patent application of the present application shall be subject to the protection scope of the appended claims.

Claims

1. A rapid stochastic model updating method for a stepped offshore platform structure, characterized in that The steps include: Establish an initial finite element model of the offshore platform according to the design parameters of the offshore platform; Among the said design parameters, select parameters to be corrected, and determine the maximum and minimum values of each parameter to be corrected; Perform subsampling on the maximum and minimum values of each parameter to be corrected to obtain a corrected parameter matrix , where each corrected parameter vector contains corrected parameters; Substitute the correction parameter matrix into the initial finite element model to obtain an updated finite element model, perform modal analysis or finite element analysis on the updated finite element model, and obtain the structural frequency vector corresponding to the correction parameter vector; Establish a Kriging model based on the correction parameter vector and its corresponding structural frequency vector; Calculate the frequency of the initial finite element model based on the correction parameter vector and the Kriging model; Construct a distance objective function based on the mean and standard deviation of the initial finite element model frequency, as well as the mean and standard deviation of the measured frequency of the offshore platform, and perform the first correction on the mean and standard deviation of the correction parameters based on the optimization objective; Substitute the mean and standard deviation after the first correction into the Kriging model, calculate the frequency of the finite element model after the first correction, construct a distribution objective function using the KL divergence based on the measured frequency of the offshore platform and the frequency of the corrected finite element model, and perform the second correction on the mean and standard deviation of the correction parameters based on the optimization objective; Substitute the mean and standard deviation of the correction parameters after the second correction into the Kriging model to obtain the frequency of the finite element model after the second correction, calculate the error between the frequency of the finite element model after the second correction and the measured frequency of the offshore platform. If the error meets the accuracy requirement, obtain the corrected finite element model of the offshore platform based on the frequency of the finite element model after the second correction.

2. The rapid stochastic model updating method for the step-type offshore platform structure according to claim 1, characterized in that The step of selecting the parameters to be corrected includes: Conduct a sensitivity analysis on the design parameters, and select the parameters with high sensitivity as the parameters to be corrected.

3. The step-by-step rapid stochastic model updating method for the offshore platform structure according to claim 1 or 2, characterized in that, The design parameters of the offshore platform include structural parameters and material parameters.

4. The rapid stochastic model updating method for the step-type offshore platform structure according to claim 1, wherein The steps of establishing a Kriging model include: Each set of corrected parameter vectors and corresponding structural frequencies is recorded as a set of sample data, and a total of sets of sample data are obtained; 80% of the sample data is selected as the training set, and the remaining sample data is used as the test set to establish a Kriging model.

5. The rapid stochastic model updating method for the step-type offshore platform structure according to claim 1 or 4, characterized in that, After establishing the Kriging model, the following steps are further included: Verify the established Kriging model using the effectiveness evaluation indexes determination coefficient R2 and relative root mean square error RMSE, and set the model verification accuracy; If the accuracy of the Kriging model meets the model verification accuracy requirement, use the established Kriging model to continue calculating the frequency of the initial finite element model. If the accuracy of the Kriging model does not meet the model verification accuracy requirement, repeat the Latin hypercube sampling step, and substitute the correction parameter matrix obtained by Latin hypercube sampling into the initial finite element model again to re - establish the Kriging model until the accuracy of the Kriging model meets the model verification accuracy requirement.

6. The rapid stochastic model updating method for the step-type offshore platform structure according to claim 1, characterized in that The steps of calculating the initial finite element frequency include: Calculate the initial mean and standard deviation of each correction parameter, and perform times of Monte Carlo sampling on the initial mean and standard deviation of each correction parameter to obtain the finite element model parameter samples , where is the vector of the initial mean and standard deviation of the correction parameter obtained by the -th Monte Carlo sampling; substitute the parameter samples into the Kriging model to obtain the initial finite element model frequency .

7. The rapid stochastic model updating method for the step-type offshore platform structure according to claim 1 or 6, characterized in that, The distance objective function includes a mean objective function and a standard deviation objective function. The steps of constructing the distance objective function include: ； ； Wherein: represents the mean objective function, represents the standard deviation objective function, represents the frequency order, represents the mean value of the frequency of the th-order finite element model, represents the mean value of the frequency of the actual structure of the th-order offshore platform, represents the mean standard deviation of the frequency of the th-order finite element model, represents the standard deviation of the frequency of the actual structure of the .

8. The step-by-step rapid stochastic model updating method for the offshore platform structure according to claim 7, characterized in that, The method of optimizing and correcting the mean and standard deviation of the correction parameters based on the optimization objective includes: Taking the mean and standard deviation of the correction parameters optimized and corrected as the solution objectives, substituting the distance objective function into the multi-objective optimization algorithm, using the optimization algorithm to solve the mean and standard deviation of the correction parameters, setting a correction target threshold, when the output result of the mean objective function is less than the correction target threshold, and the output result of the standard deviation objective function is less than the correction target threshold, stop the correction, and use the mean and standard deviation at this time as the mean and standard deviation of the correction parameters after optimization and correction.

9. The rapid stochastic model updating method for the step-type offshore platform structure according to claim 1, characterized in that The method for constructing the distribution objective function includes: Among them, is the mean value of the finite element model frequency, is the actual mean value of the ocean platform frequency, is the frequency covariance matrix of the finite element model , is the actual frequency covariance matrix of the platform.

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