A method for reconstructing global responses of offshore structures based on limited measurement information

Abstract

The application relates to the technical field of structural state monitoring, in particular to a marine structure global response reconstruction method based on limited measuring point information, which comprises the following steps: 1, model establishment and response acquisition: obtaining the unoptimized target to-be-reconstructed measuring point response based on Chebyshev polynomial dynamic response expansion technology; 2, orthogonal base acquisition: according to an orthogonal base optimization selection strategy of a permutation genetic algorithm, Gram-Schmidt orthogonalization is carried out on the base function to decompose the time domain response of a prior model, response expansion is carried out on a numerical model, and the orthogonal base is optimized and selected in combination with the permutation genetic algorithm; 3, response reconstruction: according to the optimal orthogonal base of the target measuring point obtained by the permutation genetic algorithm, the acceleration response is measured, the response of any virtual measuring point of the target marine structure is obtained, and the global response of the structure is reconstructed, and the application has the effects of not depending on accurate modal information and analytical parameters for the response reconstruction of the marine structure and low calculation cost.

Description

Technical Field

[0001] This invention relates to the field of structural condition monitoring technology, and specifically to a method for reconstructing the global response of marine structures based on limited measurement point information. Background Technology

[0002] Currently, marine engineering structures are the main engineering equipment for marine resource development, and their operational safety is of paramount importance. However, the fixed and limited response of measurement points in marine engineering cannot effectively reflect the dynamic changes in the overall performance of the structure. Moreover, hot spots in marine engineering structures are usually located below the water surface and at flange connections, and traditional response measurement methods cannot effectively determine the state at these locations, affecting the structural service safety. By using a global response reconstruction method based on limited measurement point information, response information at key locations can be captured, thereby providing a more comprehensive understanding of the structural service status. Current research on technologies for obtaining the global response of structures mainly focuses on: expanding and estimating the response through model reduction and expansion, but this requires obtaining accurate structural modal information or structural parameters (mass and stiffness) of the analytical model, and the error between the created model and the actual structure will seriously affect the expansion accuracy; and constructing structural twins through finite element model correction, but due to the huge number of degrees of freedom of the target structure, the iterative analysis calculation cost is high, and its application in practical engineering is still some distance away.

[0003] A patent application with publication number CN115186379A protects a method for reconstructing the uncertainty response of a thermal protection structure based on Bayesian theory. The method includes: constructing a reduced-order analysis model, which takes load uncertainty variables as input and reduced-order global structural response data as output, and is built based on a neural network; selecting one uncertainty variable and its corresponding variable range from the load uncertainty variables, and randomly sampling sample points using the Monte Carlo method to ensure the selected uncertainty variable satisfies a Gaussian distribution within its corresponding variable range; inputting the sample point data into the reduced-order analysis model and outputting the corresponding structural response data; obtaining the prior probability density distribution of the structural response data as the prior distribution of the response for subsequent Bayesian inversion; experimentally obtaining the actual distribution of the selected uncertainty variable, and using the response prior distribution and the actual distribution as inputs to the Bayesian formula to perform Bayesian probability inversion to obtain the reconstructed structural response posterior distribution of the uncertainty variable.

[0004] In the above-mentioned technical solutions, the traditional response reconstruction method relies heavily on accurate modal information and analytical parameters of the structure, but the calculation process for both is complex and costly. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method for reconstructing the global response of marine structures based on limited measurement point information.

[0006] The technical solution of this invention is as follows:

[0007] This invention provides a method for reconstructing the global response of marine structures based on limited measurement point information, comprising the following steps:

[0008] I. Model Establishment and Response Acquisition: Based on the geometric shape and size of the target structure, the structure is discretized according to the target augmented measurement point number, and a numerical model is established using finite element solution software. Dynamic solutions are then performed under pulsed load excitation to obtain the dynamic response at each node of the numerical prior model structure. Sparse measurement points are selected as known measurement points, and the rest are selected as measurement points to be reconstructed. The model is divided along the generatrix, and the space is unfolded into a two-dimensional plane. Subsequently, the unoptimized target measurement point response to be reconstructed is obtained based on the dynamic response extension technique of Chebyshev polynomial.

[0009] II. Orthogonal basis acquisition: Based on the orthogonal basis optimization selection strategy of the permutation genetic algorithm, the basis functions are Gram-Schmidt orthogonalized to decompose the time-domain response of the prior model. The response is extended on the numerical model and the orthogonal basis is optimized by combining the permutation genetic algorithm.

[0010] III. Response Reconstruction: Based on the optimal orthogonal basis of the target measurement points obtained by the permutation genetic algorithm, and combined with the measured acceleration response, the response of any virtual measurement point of the target marine structure is obtained, and the global response of the structure is reconstructed.

[0011] The beneficial effects achieved by this invention are: it enables the response reconstruction of marine structures without relying on accurate modal information and analytical parameters, resulting in lower computational costs.

[0012] Furthermore, the model building and response acquisition also include:

[0013] The dynamic response at sparse measurement points is decomposed into a series of orthogonal polynomial mode shape functions and their corresponding weighting coefficients: ,

[0014] In the formula, U(x, y, ξ) represents the dynamic response of the structure at time ξ, and x and y are spatial coordinate points; C i (x,y) is a polynomial shape function that depends only on the spatial coordinates of sparse measurement points. Mathematically, the shape function is represented as a two-dimensional polynomial, determined by structural geometry information. i These are the weighting coefficients of the corresponding shape functions, where the subscript i indicates the order of the shape function included in the summation; coefficient a i Represented as: ,

[0015] The orthogonality of shape functions is expressed as: ,

[0016] In the formula, <.,> represents the inner product operation;

[0017] The dynamic response of the augmented measuring point can be derived from the shape function of the augmented measuring point. and their corresponding weighting coefficients get: ,

[0018] The coefficient a of the shape function of sparse measurement points i (ξ) After scaling, the coefficient a corresponding to the shape function of the augmented measurement point is obtained. i (ξ).

[0019] The above scheme divides the numerical prior model along the generatrix and unfolds it into a two-dimensional plane, thus solving the problem of lack of boundary conditions caused by the sensor arrangement of marine engineering structures along a single straight line.

[0020] Furthermore, the model building and response acquisition also include:

[0021] Will Replace Ci(x, y) in the original text with Obtain the unscaled extended response U unscaled (x, y, ξ) is represented as: ,

[0022] Weights are assigned based on the distance from the augmented measurement point to each sparse measurement point, with greater weights for points closer to the sparse measurement point. This yields: , ,

[0023] In the formula, φ s l is the scaling factor for the s-th sparse measurement point; s φ is the straight-line distance between the s-th sparse measurement point and the target extended measurement point; φ≠s is the scaling factor of the target extended measurement point; the extended dynamic response obtained at the augmented measurement point is: ,

[0024] Using a two-dimensional Chebyshev polynomial as its shape function, the two-dimensional Chebyshev polynomial C i (x) is the product of two one-dimensional Chebyshev polynomials T, expressed as: ,

[0025] Substitute the values ​​to obtain the unoptimized target measurement point response to be reconstructed.

[0026] Using the above scheme, a shape function based on Chebyshev polynomials can be constructed based on the position information of each node. At the same time, the dynamic response characteristics of the prior model provide an optimization target for response expansion.

[0027] Furthermore, the acquisition of orthogonal bases also includes:

[0028] Based on the dynamic response obtained from the numerical prior model and the aforementioned response extension method, an optimization objective function is determined. To ensure that the reconstructed response matches the original response of the numerical model to the greatest extent possible, an orthogonal basis is formed by further Schmitt orthogonalization by changing the polynomial arrangement order. Then, the RMS value of the goodness of fit is selected as the optimization objective for response reconstruction. The closer the value is to 1, the higher the reconstruction accuracy, expressed as: ,

[0029] In the formula, This is the original response. For refactoring the response;

[0030] The constraint is that the number of measurement points is known. The number of polynomials is determined by the number of measurement points along the X and Y axes of the plane. The order of the one-dimensional polynomial is also limited by the number of sparse points along each axis.

[0031] Using the selection operator and the individual replacement strategy, the individual with the highest fit in the previous generation is replaced with the individual with the lowest fit in the next generation. The individual with the highest fit is then directly passed on to the next generation, resulting in a relatively optimal orthogonal basis.

[0032] The above scheme establishes an optimization objective based on the fit of the reconstructed response of the numerical prior model by iteratively optimizing the polynomial arrangement order. The use of the permutation genetic algorithm avoids the situation where the best individual cannot be inherited and replicated, which is conducive to the evolution and optimization of the population.

[0033] Furthermore, the response reconstruction:

[0034] For actual structures with the same geometric dimensions as the numerical model, the optimal orthogonal basis of the target measurement points and the measured structural response obtained after optimization by the permutation genetic algorithm are used again to reconstruct each unknown measurement point in turn, thereby enabling global response reconstruction of the measured marine structure.

[0035] Using the above scheme, the optimal orthogonal basis obtained by numerical prior model and permutation genetic algorithm optimization method can reconstruct the global dynamic response of marine structures with only a small number of measurement points.

[0036] The global response reconstruction method for marine structures based on finite measurement point information of the present invention has the following advantages:

[0037] 1. The numerical prior model is divided along the generatrix and unfolded into a two-dimensional plane to solve the problem of lack of boundary conditions caused by the distribution of marine engineering structure sensors along a single straight line; based on the position information of each node, a shape function based on Chebyshev polynomials can be constructed, and the dynamic response characteristics of the prior model provide an optimization target for response expansion.

[0038] 2. By iteratively optimizing the polynomial arrangement, an optimization objective based on the fit of the reconstructed response from the numerical prior model was established. The substitution genetic algorithm was adopted to avoid the situation where the optimal individual cannot be inherited and replicated, which is conducive to the evolution and optimization of the population.

[0039] 3. The optimal orthogonal basis obtained by using numerical prior models and permutation genetic algorithm optimization methods can reconstruct the global dynamic response of marine structures with only a small number of measurement points. Detailed Implementation

[0040] This invention provides a method for reconstructing the global response of marine structures based on limited measurement point information, the specific steps of which are as follows:

[0041] Step 1: Model Building and Response Acquisition

[0042] For the geometric shape and size of the target structure, the structure is discretized according to the target augmented measurement point number and a numerical model is established using finite element solution software. Dynamic solution is performed under pulsed load excitation to obtain the dynamic response at each node of the numerical prior model structure. Sparse measurement points are selected as known measurement points, and the rest are selected as measurement points to be reconstructed. The model is divided along the generatrix, and the space is unfolded into a two-dimensional plane. Then, the unoptimized target measurement point response to be reconstructed is obtained based on the dynamic response extension technique of Chebyshev polynomial.

[0043] Specifically, this includes: decomposing the dynamic response of sparse measurement points into a series of orthogonal polynomial mode shape functions and their corresponding weighting coefficients. ,

[0044] In the formula, U(x, y, ξ) represents the dynamic response of the structure at time ξ, and x and y are spatial coordinate points; C i (x,y) is a polynomial shape function that depends only on the spatial coordinates of sparse measurement points. Mathematically, the shape function is represented as a two-dimensional polynomial, determined by structural geometry information. i These are the weighting coefficients of the corresponding shape functions, where the subscript i indicates the order of the shape function included in the summation; coefficient a i Represented as: ,

[0045] The orthogonality of shape functions is expressed as: ,

[0046] In the formula, <.,> represents the inner product operation;

[0047] The dynamic response of the augmented measuring point can be derived from the shape function of the augmented measuring point. and their corresponding weighting coefficients get: ,

[0048] The coefficient a of the shape function of sparse measurement points i (ξ) After scaling, the coefficient a corresponding to the shape function of the augmented measurement point is obtained. i (ξ).

[0049] Will C in i (x, y) replaced with Obtain the unscaled extended response U unscaled (x, y, ξ) is represented as: ,

[0050] At sparse measurement points, the measured dynamic response and the corresponding unscaled extended response U can be utilized. unscaled (x, y, t) is used to determine the scaling factor of the extended response at sparse measurement points. The scaling factor at sparse measurement points can predict the scaling factor of the extended response outside of sparse measurement points. Any unknown scaling factor at augmented measurement points can be represented as the sum of the weighted scaling factors of sparse measurement points. Weights are assigned based on the distance from the augmented measurement point to each sparse measurement point, with larger weights for closer points. This yields: , ,

[0051] In the formula, φ s l is the scaling factor for the s-th sparse measurement point; s φ is the straight-line distance between the s-th sparse measurement point and the target extended measurement point; φ≠s is the scaling factor of the target extended measurement point; the extended dynamic response obtained at the augmented measurement point is: ,

[0052] Using a two-dimensional Chebyshev polynomial as its shape function, the two-dimensional Chebyshev polynomial C i (x) is the product of two one-dimensional Chebyshev polynomials T, expressed as: ,

[0053] Substitute the values ​​to obtain the unoptimized target measurement point response to be reconstructed.

[0054] The numerical prior model is segmented along the generatrix and unfolded into a two-dimensional plane to address the lack of boundary conditions caused by the linear distribution of sensors on marine structures. Based on the positional information of each node, a shape function based on Chebyshev polynomials can be constructed, while the dynamic response characteristics of the prior model provide an optimization target for response extension.

[0055] Step 2: Obtaining the orthogonal basis:

[0056] Based on the orthogonal basis optimization selection strategy of the permutation genetic algorithm, the basis functions are Gram-Schmidt orthogonalized to decompose the time-domain response of the prior model. The response is then extended on the numerical model, and the orthogonal basis is optimized by combining the permutation genetic algorithm.

[0057] Specifically, this includes: determining the objective function based on the dynamic response obtained from the numerical prior model and the aforementioned response extension method; to ensure the reconstructed response closely matches the original response of the numerical model, further Schmitt orthogonalization is performed by changing the polynomial arrangement to form an orthogonal basis; and then the RMS value of the goodness of fit is selected as the optimization objective for response reconstruction. The closer the RMS value is to 1, the higher the reconstruction accuracy, expressed as: ,

[0058] In the formula, This is the original response. For refactoring the response.

[0059] The constraint is that the number of measurement points is known. The number of polynomials is determined by the number of measurement points along the X and Y axes of the plane. The order of the one-dimensional polynomial is also limited by the number of sparse points along each axis.

[0060] For the selection operator, an individual replacement strategy is used to address the problem of highly fitted individuals being eliminated. The individual with the highest fit from the previous generation directly replaces the individual with the lowest fit in the next generation, and the individual with the highest fit is directly passed on to the next generation, ultimately obtaining a relatively optimal orthogonal basis.

[0061] By iteratively optimizing the polynomial arrangement, an optimization objective based on the fit of the reconstructed response from the numerical prior model was established. The substitution genetic algorithm was adopted to avoid the situation where the best individual cannot be inherited and replicated, which is conducive to the evolution and optimization of the population.

[0062] Step 3: Response Restructuring

[0063] Based on the optimal orthogonal basis of the target measurement points obtained by the permutation genetic algorithm, and combined with the measured acceleration response, the response of any virtual measurement point of the target marine structure is obtained, and the global response of the structure is reconstructed.

[0064] Specifically, this includes: for actual structures with the same geometric dimensions as the numerical model, based on the optimal orthogonal basis of the target measurement points and the measured structural response obtained after optimization by the permutation genetic algorithm, the response extension method based on Chebyshev polynomials is used again to reconstruct each unknown measurement point in sequence, thereby enabling global response reconstruction of the measured marine structure.

[0065] The optimal orthogonal basis obtained by using numerical prior models and permutation genetic algorithm optimization methods can reconstruct the global dynamic response of marine structures with only a small number of measurement points.

[0066] The present invention provides a method for reconstructing the global response of marine structures based on limited measurement point information. The advantages of this method are as follows: the present invention addresses the technical difficulty of traditional response reconstruction methods requiring accurate structural information and boundary conditions. It uses response data obtained from numerical simulation as prior information, employs dynamic response extension technology based on Chebyshev polynomials and permutation genetic algorithm to obtain the spatially optimal orthogonal basis, and then combines a small amount of measured acceleration information to reconstruct the global response of marine structures in real time, thus eliminating the dependence on accurate modal information and analytical parameters of the structure.

[0067] The embodiments of the present invention described above do not constitute a limitation on the scope of protection of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for reconstructing the global response of marine structures based on finite measurement point information, characterized in that, Includes the following steps: I. Model Establishment and Response Acquisition: Based on the geometric shape and size of the target structure, the structure is discretized according to the target augmented measurement point number, and a numerical model is established using finite element solution software. Dynamic solutions are then performed under pulsed load excitation to obtain the dynamic response at each node of the numerical prior model structure. Sparse measurement points are selected as known measurement points, and the rest are selected as measurement points to be reconstructed. The model is divided along the generatrix, and the space is unfolded into a two-dimensional plane. Subsequently, the unoptimized target measurement point response to be reconstructed is obtained based on the dynamic response extension technique of Chebyshev polynomial. II. Orthogonal basis acquisition: Based on the orthogonal basis optimization selection strategy of the permutation genetic algorithm, the basis functions are Gram-Schmidt orthogonalized to decompose the time-domain response of the prior model. The response is extended on the numerical model and the orthogonal basis is optimized by combining the permutation genetic algorithm. III. Response Reconstruction: Based on the optimal orthogonal basis of the target measurement points obtained by the permutation genetic algorithm, and combined with the measured acceleration response, the response of any virtual measurement point of the target marine structure is obtained, and the global response of the structure is reconstructed.

2. The method for reconstructing the global response of marine structures based on finite measurement point information according to claim 1, characterized in that, The model building and response acquisition also include: The dynamic response at sparse measurement points is decomposed into a series of orthogonal polynomial mode shape functions and their corresponding weighting coefficients: ， In the formula, U(x, y, ξ) represents the dynamic response of the structure at time ξ, and x and y are spatial coordinates; Ci(x, y) is a polynomial shape function that depends only on the spatial coordinates of sparse measurement points. Mathematically, the shape function is represented as a two-dimensional polynomial, determined by the structural geometry. i These are the weighting coefficients of the corresponding shape functions, where the subscript i indicates the order of the shape function included in the summation; coefficient a i Represented as: ， The orthogonality of shape functions is expressed as: ， In the formula, <., > denote the dot product of vectors; The dynamic response of the augmented measuring point can be derived from the shape function of the augmented measuring point. and their corresponding weighting coefficients get: ， The coefficient a of the shape function of sparse measurement points i (ξ) After scaling, the coefficient a corresponding to the shape function of the augmented measurement point is obtained. i (ξ).

3. The method for reconstructing the global response of marine structures based on finite measurement point information according to claim 2, characterized in that: The model building and response acquisition also include: Will Replace Ci(x, y) in the original text with Obtain the unscaled extended response U unscaled (x, y, ξ) is represented as: ， Weights are assigned based on the distance from the augmented measurement point to each sparse measurement point, with greater weights for points closer to the sparse measurement point. This yields: ， ， In the formula, φ s l is the scaling factor for the s-th sparse measurement point; s φ is the straight-line distance between the s-th sparse measurement point and the target extended measurement point; φ≠s is the scaling factor of the target extended measurement point; the extended dynamic response obtained at the augmented measurement point is: ， Using a two-dimensional Chebyshev polynomial as its shape function, the two-dimensional Chebyshev polynomial C i (x) is the product of two one-dimensional Chebyshev polynomials T, expressed as: ， Substitute the values ​​to obtain the unoptimized target measurement point response to be reconstructed.

4. The method for reconstructing the global response of marine structures based on finite measurement point information according to claim 1, characterized in that, The acquisition of orthogonal bases also includes: Based on the dynamic response obtained from the numerical prior model and the aforementioned response extension method, an optimization objective function is determined. To ensure that the reconstructed response matches the original response of the numerical model to the greatest extent possible, an orthogonal basis is formed by further Schmitt orthogonalization by changing the polynomial arrangement order. Then, the RMS value of the goodness of fit is selected as the optimization objective for response reconstruction. The closer the value is to 1, the higher the reconstruction accuracy, expressed as: ， In the formula, This is the original response. For refactoring the response; The constraint is that the number of measurement points is known. The number of polynomials is determined by the number of measurement points along the X and Y axes of the plane. The order of the one-dimensional polynomial is also limited by the number of sparse points along each axis. Using the selection operator and the individual replacement strategy, the individual with the highest fit in the previous generation is replaced with the individual with the lowest fit in the next generation. The individual with the highest fit is then directly passed on to the next generation, resulting in a relatively optimal orthogonal basis.

5. The method for reconstructing the global response of marine structures based on finite measurement point information according to claim 1, characterized in that, The response reconstruction: For actual structures with the same geometric dimensions as the numerical model, the optimal orthogonal basis of the target measurement points and the measured structural response obtained after optimization by the permutation genetic algorithm are used again to reconstruct each unknown measurement point in turn, thereby enabling global response reconstruction of the measured marine structure.

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