Large-area distributed ice load quasi-static identification mathematical model morbid elimination method

Abstract

The invention relates to the field of ice load identification of an ice region ship structure, and discloses a large-area distributed ice load quasi-static identification mathematical model morbidity elimination method, which comprises the following steps of: firstly, establishing a high-dimensional initial mathematical model containing massive redundant measurement point information; and then carrying out dimensionality reduction and optimization on a transfer matrix of the model by adopting an innovative regional discrete retrieval method. According to the method, an optimal measurement point combination is screened out from tens of thousands of initial measurement channels by iteratively searching in divided sub-domains and taking matrix condition number minimization as a target, so that an optimized transfer matrix with remarkably reduced dimensionality and good performance is obtained, and the optimal physical layout of the sensor is synchronously determined. Finally, an enhanced mathematical model is constructed based on the optimization matrix for solving, the number of sensors is greatly reduced, the cost is reduced, interference of measurement noise is effectively overcome, and the stability and accuracy of an ice load identification result are ensured.

Description

Technical Field

[0001] The present invention relates to the field of ice load identification for ship structures in ice areas, and in particular to a method for eliminating pathological conditions in a mathematical model for quasi-static identification of large-area distributed ice loads. Background Art

[0002] With the increasing global development of polar resources and utilization of Arctic shipping routes, the structural safety of polar-navigating ships and offshore platforms has attracted much attention. Throughout the life cycle of such structures, their complex interaction with sea ice will generate huge ice loads, which pose a severe test to the integrity of the structure and navigation safety. Accurate monitoring of ice loads is a prerequisite for structural safety assessment and optimization. Ice load monitoring methods are mainly divided into two categories: direct measurement and indirect identification. The direct measurement method requires the installation of sensors on the hull's outer plate, but in harsh environments, the sensors are easily damaged, the signals are severely interfered with by noise, and the maintenance cost is high. Therefore, the indirect identification method of placing sensors in relatively safe positions inside the hull and reversely inferring external loads by measuring structural responses has become the current mainstream technical path.

[0003] Research has shown that although ship-ice interaction is a dynamic process, its load energy is primarily concentrated in the low-frequency range, far below the natural frequency of the hull structure. Therefore, the process can often be simplified as a series of quasi-static mechanical problems. Mathematically, the indirect identification of ice loads is a typical inverse problem of structural dynamics, and the initially established mathematical models often exhibit severe "ill-conditioning" or "ill-posedness." This ill-conditioning primarily stems from the high redundancy and linear correlation of the mapping matrix (i.e., the transfer matrix) between loads and responses. This problem is particularly prominent when large-scale, high-density sensor arrays are employed to accurately describe the load distribution. An ill-conditioned mathematical model is extremely sensitive to the inevitable noise in the measurements, and even minimal perturbations can be dramatically amplified during the solution process, resulting in severe distortion and lack of reliability in the final identified load results.

[0004] To address this core challenge, existing technologies typically address it from two perspectives. One approach, at the algorithmic level, employs methods such as Tikhonov regularization and truncated singular value decomposition (SVD) to smooth the solution by introducing constraints or filtering, thereby reducing the impact of ill-posedness. A more fundamental approach involves optimizing the initial mathematical model before solving. This approach focuses on optimizing the sensor layout and directly reducing the ill-conditioned nature of the transfer matrix by selecting an optimal set of measurement point combinations. For example, methods such as C-optimal design (COD), D-optimal design (DOD), and improved simulated annealing (ISAA) have been used to perform this type of dimensionality reduction optimization. However, when dealing with extremely high-dimensional matrices composed of a vast number of initial measurement points, these existing optimization algorithms typically rely on a single, direct dimensionality reduction optimization process. The randomness and path-dependence of this single-shot optimization make it difficult to guarantee stable convergence to the global optimal solution within a vast search space. The optimization results are often uncertain, making it difficult to effectively and reliably address the challenges posed by the selection of extremely large measurement points. Summary of the Invention

[0005] The technical problem to be solved by the present invention is that in the existing large-area distributed ice load identification method, the initial mathematical model used to describe the load-response relationship usually exhibits high pathological properties due to excessive dimensionality and information redundancy, which leads to serious ill-conditioning in the model inversion process, thereby affecting the accuracy and stability of the load identification results.

[0006] To address the aforementioned technical issues, the first aspect of the present invention provides a method for eliminating ill-conditioning in a mathematical model for quasi-static identification of large-area distributed ice loads. This method uses a specific optimization algorithm to reduce the dimensionality and optimize the initial transfer matrix, significantly reducing the degree of ill-conditioning in the mathematical model and thus laying the foundation for subsequent accurate load identification.

[0007] The technical solution provided by the present invention comprises the following steps: S1. Establish an ice load equivalent mechanical model to describe the effects of ice loads, and a sensor placement method to define the strain measurement point acquisition method. The ice load equivalent mechanical model uses concentrated ice extrusion forces acting perpendicularly to the outer surface of the hull structure to represent the spatial distribution of ice loads. The sensor placement method, based on the structural characteristics of the hull, places sensors at key load-bearing components such as ribs, longitudinal girders, and some outer plating, with the strain gauges aligned with the principal stress direction of the structural features.

[0008] S2. Determine the specific ice load information to be identified and the initial measurement point layout based on the ice load equivalent mechanical model and sensor layout method. Specifically, the ice load information to be identified is a limited number of equivalent nodal ice loads distributed in an array within a predetermined area where the bow shell interacts with the ice. The initial measurement point layout involves placing a large number of initial measurement points in an array within the inner area of the bow shell, covering the ribs, longitudinal girders, and shell areas.

[0009] S3. Based on the ice load information to be identified and the initial measurement point layout, a unit pressure analysis is performed to obtain an initial transfer matrix. Specifically, this process involves sequentially applying a unit normal concentrated pressure to each node where the ice load is applied. Structural strain response data for all initial measurement points is extracted through finite element analysis or other methods. The initial transfer matrix is then constructed based on the linear mapping relationship between load and response.

[0010] S4. Establish a time sample statics system discretized in time substeps, and establish an initial mathematical model containing the initial transfer matrix. Since the dynamic response of the hull structure can be ignored, the time-varying process of the hull dynamic icebreaking is equivalently discretized into a series of static processes in time substeps, with each moment corresponding to an independent static mechanical system. The initial mathematical model of this system can be expressed as: ,in, is the ice load vector to be identified, is the response vector collected for all initial measurement points, is the initial transfer matrix.

[0011] S5. Dimensionality reduction optimization is performed on the initial transfer matrix using a regional discrete search method to reduce the ill-posedness of the initial mathematical model and obtain an optimized transfer matrix and sensor layout optimization. This step is the core of the present invention. The regional discrete search method aims to screen a row vector combination from the high-dimensional initial transfer matrix so that the target dimensional matrix it forms has the lowest degree of pathological condition. The specific execution process is as follows: (a) Taking the initial transfer matrix as the overall matrix, setting the number of target sensors to p, and setting the maximum number of iterations to q; (b) In each iteration, the current overall matrix is divided into p sub-search domains according to the row vector, and a row vector is initialized from each sub-search domain to form a candidate target dimension matrix; (c) locally optimizing each row of the candidate target dimension matrix, that is, keeping other rows unchanged, replacing them with other row vectors in the corresponding sub-search domain, and retaining the replacement result that minimizes the condition number of the candidate target dimension matrix; (d) After an iteration, the optimization result obtained in the iteration is stored, and its row vector is removed from the overall matrix to update the overall matrix; (e) Repeat steps (b) to (d) until q iterations are completed, and retrieve the target matrix with the minimum condition number from the optimization results of all iterations as the final optimized transfer matrix.

[0012] In this method, the condition number of the matrix is used as the objective function to evaluate the ill-conditioned characteristics of the matrix. The condition number is defined as: ; in, is the matrix to be evaluated, is the 2-norm of the matrix, is the Moore-Penrose generalized inverse of the matrix. The smaller the condition value, the less ill-conditioned the matrix is.

[0013] The sensor arrangement scheme is optimized by comparing the position of each row element in the optimized transfer matrix with the position in the initial transfer matrix, and reversely locating the corresponding initial measurement point arrangement position, thereby obtaining a combination composed of optimal measurement points.

[0014] S6. Obtain an enhanced mathematical model using the optimized transfer matrix, and solve the enhanced mathematical model to obtain a load identification result. The enhanced mathematical model is obtained by replacing the initial transfer matrix and initial response vector in the initial mathematical model with the optimized transfer matrix and the response vector determined according to the optimized measurement point position, and its expression is: ; in, is the ice load vector to be identified, is the optimized transfer matrix, The response vector is composed of the response data corresponding to the measurement points determined by the optimization of the sensor arrangement scheme. Finally, the Moore-Penrose inverse method is used to solve the enhanced mathematical model, and the solution vector is the load identification result.

[0015] The present invention provides a method for eliminating pathological conditions in a quasi-static identification mathematical model for large-area distributed ice loads. It has the following beneficial effects: 1. The regional discrete retrieval method provided by the present invention divides the high-dimensional initial transfer matrix into multiple sub-search domains and performs replacement and local optimization within these lower-dimensional sub-domains. This avoids the global traversal of all possible combinations of sensor measurement points and the calculation of massive high-dimensional matrix condition numbers, significantly reducing the computational cost of the optimization process and making the optimization of large-scale initial measurement point solutions computationally possible.

[0016] 2. The regional discrete search method of this invention involves multiple iterative optimizations and a secondary optimization process. By executing multiple independent discrete optimizations and retrieving the final matrix with the minimum condition number from the optimization results of all rounds, this method effectively reduces the instability of the results caused by a single random optimization, ensures the stability and reliability of the optimization results, and can obtain a less pathological transfer matrix.

[0017] 3. The present invention uses the optimized transfer matrix to construct an enhanced mathematical model, which is much less pathological than the initial mathematical model. Therefore, when the enhanced mathematical model is subsequently solved using the Moore-Penrose inverse method, the numerical stability of the solution process is significantly enhanced, and the interference of measurement noise on the solution results can be effectively suppressed, thereby obtaining a more accurate distributed ice load identification result. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 This is a schematic diagram of the overall process of a method for eliminating pathological conditions in a mathematical model for quasi-static identification of large-area distributed ice loads according to an embodiment of the present invention; Figure 2 This is a schematic diagram of a distributed ice load equivalent mechanical model according to an embodiment of the present invention; Figure 3 A schematic diagram of an initial measurement point arrangement and a sensor arrangement method according to an embodiment of the present invention; Figure 4 A schematic diagram of ice load distribution at a node to be identified according to an embodiment of the present invention; Figure 5 A schematic diagram of an execution flow of a regional discrete search method according to an embodiment of the present invention; Figure 6 A schematic diagram of an optimized sensor arrangement scheme according to an embodiment of the present invention; Figure 7 This is a schematic diagram of the ice load identification results of the present invention. DETAILED DESCRIPTION

[0019] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the present specification. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0020] Please refer to the attached Figure 1 , Figure 1 The figure is a schematic diagram of the overall process of eliminating pathological conditions in a large-area distributed ice load quasi-static identification mathematical model according to an embodiment of the present invention. The method provided by the present invention may include the following steps: S1. Establish an ice load equivalent mechanical model to describe the ice load effect, and define the sensor arrangement method for strain measurement point acquisition; S2. Determine specific ice load information to be identified and an initial measurement point arrangement plan based on the ice load equivalent mechanical model and sensor arrangement method; S3. Based on the ice load information to be identified and the initial measurement point arrangement plan, perform unit pressure analysis to obtain an initial transfer matrix; S4, establishing a time sample statics system discrete in time sub-steps, and establishing an initial mathematical model including the initial transfer matrix; S5. Performing dimensionality reduction optimization on the initial transfer matrix using a regional discrete retrieval method to reduce the ill-posedness of the initial mathematical model and obtain an optimized transfer matrix and sensor layout scheme; S6. Obtaining an enhanced mathematical model using the optimized transfer matrix, and solving the enhanced mathematical model to obtain a load identification result.

[0021] The overall technical concept of this method is to first capture comprehensive structural response information by establishing a mechanical model and deploying a large number of initial measurement points. This allows the construction of an initial mathematical model that fully describes the load-response relationship. While this initial model is comprehensive, it exhibits significant pathological characteristics due to the high dimensionality and redundancy of its transfer matrix.

[0022] Next, to address the ill-posed nature of this initial mathematical model, a specific regional discrete search method was employed to reduce and optimize the high-dimensional initial transfer matrix. The goal of this optimization process was to identify an optimized transfer matrix composed of the optimal measurement point response row vectors, with significantly reduced dimensionality and minimal ill-conditioning. This process also determined the optimal sensor placement.

[0023] Finally, the optimized transfer matrix is used to replace the ill-conditioned matrix in the initial mathematical model, thereby constructing a well-behaved enhanced mathematical model. Solving this enhanced model yields stable and accurate distributed ice load identification results. Through these steps, the original ill-conditioned mathematical model is effectively eliminated while maintaining identification accuracy.

[0024] Please refer to the attached Figure 2 , Figure 2 Attached is a schematic diagram of a distributed ice load equivalent mechanical model according to an embodiment of the present invention. Figure 2 The region where the ship structure interacts with the ice is shown in Figure 2. In this region, the continuously distributed actual ice load is equivalent to a set of concentrated ice extrusion forces acting on discrete nodes.

[0025] In the implementation of this invention, establishing the mathematical relationships required for load identification first requires an accurate mathematical description of the physical loads acting on the structure. Actual ice loads typically act on the outer surface of the hull structure in the form of a complex, continuously distributed pressure, with the precise distribution function and action boundaries unknown.

[0026] To effectively identify this unknown load, this embodiment establishes an ice load equivalent mechanical model. This model spatially discretizes the continuously distributed ice pressure into a series of concentrated ice extrusion forces acting on a finite number of predefined nodes. These predefined nodes are located within regions where the hull structure and the ice layer may interact.

[0027] To further demonstrate the rationale for this equivalent model, it is important to point out that the bow plating of an icebreaker is the primary structure bearing the random ice extrusion forces during the continuous icebreaking process. The resulting ice extrusion forces acting continuously on the hull plating within a specific region can be decoupled into the process of ice loads acting perpendicularly to the outer surface of the hull structure along the normal direction. Given the significant spatial distribution of ice loads during icebreaking, using multi-point concentrated normal pressure as the target for identification of localized ice loads is a feasible equivalent method.

[0028] Each concentrated ice extrusion force acts perpendicularly to the shell structure's surface, along the normal to the outer surface at its point of application. This equivalence transforms the problem of identifying a complex, continuous pressure distribution function into solving an unknown force vector composed of a finite number of concentrated forces. This lays the foundation for the subsequent construction of a discrete, linear load-response mathematical model.

[0029] In a specific example, the equivalent nodal ice load to be identified is selected in the area where the flat ice interacts with the bow shell. Figure 4 The action positions are distributed in an array, covering the range of the outer plate, ribs and longitudinal girders. The node ice loads are evenly arranged with a spacing of 0.4m in the x-direction (the direction of the ship's length) and staggered with a spacing of 0.25m in the z-direction (the direction of the ship's height), ultimately forming a rectangular array with a size of 1.0m×11.2m, with a total coverage area of 11.2m. 2 The array is located outside the bow plating, 4.3 to 15.5 meters from the bow tip in the x-direction and 6.1 to 7.1 meters from the bottom in the z-direction. A total of 102 nodal ice loads are identified, with the identified load components being those normal to the plating pointing inwards towards the hull.

[0030] Refer to the attached Figure 3 and attached Figure 4 . Figure 3FIG. 4 is a schematic diagram of an initial measurement point arrangement and a sensor arrangement method according to an embodiment of the present invention. Figure 4 FIG. 4 is a schematic diagram of ice load distribution at a node to be identified according to an embodiment of the present invention.

[0031] In the specific implementation of the present invention, in order to collect the response of the structure under ice load, it is first necessary to establish a sensor arrangement method. Figure 3 As shown in the figure, the scheme arranges a large number of dense initial measurement points in the form of an array on the inner structure of the bow. The coverage of the initial measurement point array includes the ribs, longitudinal girders and outer plate areas in the target area, thus forming a The initial measurement set of measurement points.

[0032] The specific basis for this sensor placement method is that the ribs and longitudinal girders on the bow side are the main load-bearing components under ice loads, and the structural response of the outer plate is most obvious, so the sensors are preferentially placed in these locations. Under the action of ice loads, the main form of strain in the hull structure is shear strain. In order to monitor larger strain values and improve the signal-to-noise ratio, the arrangement direction of the strain gauges must be consistent with the principal stress direction of different structural features. Therefore, this embodiment adopts the following arrangement scheme: the outer plate strain gauges are installed at 0° and 90°, and the strain gauges on the ribs and longitudinal girder structures are installed at ±45°.

[0033] Based on this method, in order to obtain the most complete information, a high-density initial measurement point layout plan was developed in this example. The initial measurement points cover a 11.2m×4.2m rectangular area on the inner side of the bow outer plate (4m to 15.2m from the bow in the x-direction and 4.6m to 8.8m from the bottom of the ship in the z-direction), with a total area of 53.76m. 2 The measuring points are distributed in an array with a spacing of 0.1m.

[0034] The specific array design rules are: The distance between the edge of the measuring point array and the ribs and longitudinal girders in the outer plate area is controlled to be 0.1m; The measurement point array design for the ribs and stringers requires that the array edges be aligned with the neutral axis, and the spacing between the other edges and the flanges and other structural connections is also 0.1m. In all areas, the measurement points are distributed in two perpendicular directions at 0.1m intervals.

[0035] According to this plan, the total number of initial measurement points designed is 10,200, and two mutually perpendicular channels are installed at each measurement point, covering a total of 20,400 initial measurement channels.

[0036] Corresponding to the initial measurement point arrangement scheme, refer to Figure 4, the distribution of the node ice loads to be identified is defined in the preset action area of the hull structure outer plate. These node ice loads to be identified are distributed in the form of an array, which together constitutes The high-density initial measurement point arrangement scheme and the definition of the ice load on the nodes to be identified together provide the necessary data basis for the subsequent construction of the initial transfer matrix and the screening of the optimal measurement point combination through the regional discrete search method.

[0037] After determining the distribution of ice loads at the nodes to be identified and the layout of the initial measurement points, this embodiment performs a unit pressure analysis to obtain an initial transfer matrix describing the relationship between structural loads and responses. This process is based on an established finite element model that accurately reflects the physical characteristics of the hull structure.

[0038] The specific steps of unit pressure analysis are as follows: First, the defined The first point of ice load in the node to be identified is subjected to a concentrated pressure of unit size along the normal direction of the shell surface at that point, while all other points are The node loads are kept at zero.

[0039] Under this unit load condition, all pre-arranged The structural strain response values at the initial measurement points. This group contains The response vector of the strain values constitutes the first column of the initial transfer matrix.

[0040] Then, the unit pressure on the first point of action is canceled and the same unit normal concentrated pressure is applied to the second point of action. All the The strain response values of the initial measuring points are obtained, and this set of response vectors is used as the second column of the initial transfer matrix.

[0041] Repeat the above steps until all The ice load action points of the nodes to be identified are all applied with a unit pressure in turn. Through this process, a total of groups of response vectors are obtained, each group contains Strain value.

[0042] Put this The group response vectors are arranged in order to form a dimension of The initial transfer matrix . Each element of this matrix The physical meaning is: the action on Unit ice load on the node, This initial transfer matrix completely establishes the linear mapping relationship between the load vector to be identified and the initial measurement point response vector.

[0043] The interaction between a ship's hull and ice is a physically dynamic process. However, for large-mass ship structures subjected to quasi-static ice loads, low-order modal responses dominate the overall response, while high-frequency dynamic response components can be neglected. Based on this, the present invention discretizes this continuous, time-varying dynamic physical process in the time dimension, establishing a time-sampled statics system.

[0044] The system treats the continuous dynamic process as a time sequence of independent static mechanical processes occurring at discrete time substeps. At any time substep, there is a definite ice load distribution and a corresponding static strain response of the structure.

[0045] Based on this time sample static system, and combined with the initial transfer matrix obtained in the previous steps , we can establish an initial mathematical model that describes the load-response relationship in the static mechanical system. This model is a set of linear equations, and its specific form is as follows: ,in, is a dimension of The ice load vector to be identified is , whose elements are at the current time substep, The size of the ice load at the node to be identified. is a dimension of The initial response vector of , whose elements are at the current time step, is given by The structural strain response values collected at the initial measuring points. That is, the dimension obtained in the previous step is The initial transfer matrix.

[0046] Taking the specific numerical values of this example as an example, after establishing a When the time sample system is used, we obtain the collision response data and real load data at that moment from the time history signal and establish the initial mathematical model. Initial measurement point channel The model expression is:

[0047] in, is the response vector at that moment, is the ice load vector to be identified, is the initial transfer matrix.

[0048] Although the initial mathematical model contains all the information of the initial measurement points, the number of initial measurement points is limited. Usually much larger than the number of loads to be identified , and there is a high degree of linear correlation and information redundancy between the response information collected at each measuring point, resulting in the initial transfer matrix The model exhibits high dimensionality and high condition number characteristics, which make it severely ill-conditioned when used for inverse solution of load identification. The solution process is extremely sensitive to measurement noise, making it difficult to obtain a stable and reliable solution.

[0049] To quantitatively assess the degree of ill-conditioning of the initial mathematical model and provide a clear target for the subsequent optimization process, this paper uses the matrix condition number as the objective function for evaluating the ill-conditioning characteristics of the transfer matrix. The condition number is an important indicator for measuring the stability of the numerical solution of a linear system of equations.

[0050] In linear algebra, the condition number of a matrix reflects how sensitive its output is to small perturbations in its input data. A matrix with a condition number close to 1 is called well-conditioned, while a matrix with a large condition number is called ill-conditioned.

[0051] In the technical solution of the present invention, the specific definition of the condition number adopts a form based on the matrix 2-norm, and its mathematical expression is as follows: ,in, is the transfer matrix to be evaluated, such as the initial transfer matrix or any candidate matrix in the optimization process. Represents the 2-norm of the matrix, also known as the spectral norm, whose value is the largest singular value of the matrix. Representation matrix Moore-Penrose generalized inverse.

[0052] In solving the inverse problem of load identification, the condition number of the transfer matrix is directly related to the stability of the solution. A low condition number means that the response vector caused by measurement errors is A small change in the condition number will only result in a correspondingly small change in the load vector being solved. Conversely, a very high condition number means that even very small measurement noise may be severely amplified, resulting in large deviations or even complete distortion of the load solution.

[0053] Therefore, the core optimization goal of the subsequent regional discrete retrieval method of the present invention is to obtain the initial transfer matrix of row vectors, filter out one by The optimal subset of row vectors, which constitutes the optimal transfer matrix has the smallest conditional value.

[0054] Please refer to the attached Figure 5 , Figure 5 This is a schematic diagram of the execution process of the regional discrete search method according to an embodiment of the present invention. Perform dimensionality reduction optimization to obtain a vector with a lower condition number and dimension The optimized transfer matrix .in, is the total number of initial measurement points, is the total number of loads to be identified, is the number of sensors determined after optimization and satisfies and .

[0055] In this example, the initial transfer matrix The dimension of is 20400×102, and its condition number is as high as 2011, which is seriously ill-conditioned. Based on mathematical theory, when the transfer matrix is a square matrix (i.e. ), the solution is the most stable. Therefore, the optimization goal of this example is to obtain a square matrix with a dimension of 102×102, that is, the number of target sensors .

[0056] The specific implementation process of the regional discrete retrieval method is as follows: Step 501: Initialize the algorithm. The initial transfer matrix As the overall matrix to be optimized. Set two key parameters: the number of target sensors , which defines the target number of rows in the final optimization transfer matrix; the maximum number of iterations , this parameter controls the search depth and breadth of the algorithm.

[0057] Step 502: Iteration starts and subdomains are divided. The algorithm enters the main iteration loop, which executes At the beginning of each iteration, the current overall matrix is divided into For example, in the first iteration, the initial transfer matrix containing row vectors Divided into subdomains.

[0058] Step 503: Initialization of the candidate matrix. From each sub-search domain divided in step 502, select a row vector, totaling row vector. The row vectors are combined to form a vector of dimension The candidate target dimension matrix of is used as the starting point for local optimization in this iteration.

[0059] Step 504: Local iterative optimization. Optimize the candidate target dimension matrix generated in step 503 row by row. The specific process is: OK When processing the first row, keep the other The row remains unchanged, then In the sub-search domain corresponding to the row, traverse all other row vectors that have not been selected to replace the current row vector. OK.

[0060] For each replacement, a temporary Matrix and calculate its condition number. After all the replacement options in the sub-search domain, the row vector that can minimize the condition number of the temporary matrix is formally determined as the new first row of the candidate target dimension matrix. This process is repeated until all the candidate target dimension matrices are All rows have undergone a round of optimization.

[0061] Step 505: Store the iteration results and update the overall matrix. After completing a complete local iterative optimization (i.e., after step 504), the currently obtained, optimized candidate target dimension matrix and its corresponding minimum condition number are stored as the optimization result of this main iteration. The row vectors are removed from the current overall matrix, forming a new one with fewer rows. The overall matrix of is used for calculation of the next main iteration.

[0062] Step 506: Iteration judgment and final selection. Determine whether the number of main iterations has reached the preset maximum number of iterations. If not, then return to step 502 and start a new round of iteration using the updated overall matrix. If it has been reached, then the main loop of the algorithm ends.

[0063] Finally, from all Stored in the next major iteration Optimization results (i.e. The dimensions are The matrix with the smallest condition number is selected as the final optimized transfer matrix. This matrix is the target matrix with the lowest degree of pathology to be obtained in the entire optimization process.

[0064] Specifically in the example given, the process of the present invention is: first, the initial matrix of 20400×102 The 20400 row vectors are evenly divided into 102 sub-search domains, each containing 200 row vectors. Set the maximum number of iterations This method calculates the optimal target dimension matrix obtained by the replacement matrix starting from each subdomain, compares the optimization results of a large number of different starting points, and finally retrieves the optimal matrix among all the optimization process calculation results as the final optimization result by continuously executing 102 iterations. , which is the optimal efficient row vector combination.

[0065] Refer to the attached Figure 6 , Figure 6 Schematic diagram of the optimized sensor arrangement scheme according to one embodiment of the present invention. The optimized transfer matrix with the lowest condition number is obtained by the regional discrete search method. Finally, the present invention further determines the corresponding optimal arrangement scheme of the physical sensors.

[0066] The basis of this determination process is to optimize the transfer matrix The initial transfer matrix is In the initial transfer matrix In the equation, each row vector has a unique and definite correspondence with an initial measurement point, that is, The row vector represents the The response set of the initial measurement points under all unit load conditions.

[0067] Therefore, the specific steps to determine the optimal sensor layout are: All By recording or querying these row vectors in the original initial transfer matrix To identify these optimal row vectors, we use the row index numbers in .

[0068] Each identified original row index number directly corresponds to a specific physical measurement point location in the initial measurement point layout plan. The combination of the identified physical measurement point positions constitutes the final sensor optimization layout plan.

[0069] like Figure 6 As shown, the optimization scheme consists of a set of The distribution of the measurement points is relatively sparse. Figure 3 Compared with the high-density initial measurement point array shown in , this optimization scheme significantly reduces the number of sensors used while retaining the measurement point combination that is most effective for load identification and has the lowest information redundancy, thus providing a physical basis for the subsequent establishment of a well-performing reinforcement mathematical model.

[0070] The optimal transfer matrix with the lowest condition number is obtained by the regional discrete search method. The present invention then utilizes the optimization results to establish a reinforced mathematical model with significantly improved properties.

[0071] The enhanced mathematical model is based on the same time sample static system as the initial mathematical model, which is discretized in time substeps. The establishment process is to use the optimized transfer matrix obtained in the previous step Replace the initial transfer matrix in the initial mathematical model The resulting enhanced mathematical model is also a set of linear equations, and its specific form is as follows: ,in, The dimension is The ice load vector to be identified is the same as that defined in the initial mathematical model. It is obtained by optimizing the regional discrete retrieval method, and its dimension is The optimized transfer matrix. is a dimension of The optimized response vector of . The elements of this vector are all the responses determined by the optimal placement of sensors at the current time step. The vector is composed of the actual structural strain response values collected at the physical measurement points. A subvector of .

[0072] The enhanced mathematical model established in the above way uses the transfer matrix With much lower initial transfer matrix The condition number is reduced, and the ill-conditioned degree of the model is significantly reduced. This process transforms an ill-posed inverse problem into a well-posed inverse problem, providing the necessary foundation for subsequent stable and accurate load solutions.

[0073] Refer to the attached Figure 7 , Figure 7After establishing a well-behaved enhanced mathematical model, the present invention uses the Moore-Penrose generalized inverse method to solve the model to obtain the ice load vector to be identified. Since the optimized transfer matrix The dimension is , which is usually a non-square matrix and cannot be solved by conventional matrix inversion methods. Moore-Penrose generalized inverse provides an effective way to solve such mathematical models consisting of overdetermined or underdetermined linear equations.

[0074] The specific solution process is to optimize the transfer matrix Moore-Penrose generalized inverse Left multiply both sides of the mathematical model equation. Load identification result vector The calculation formula is as follows: ,in, The dimension is The load identification result vector, each element of which is the load identification result vector calculated by this method at the current time sub-step The magnitude of the ice load at each node. is the optimized transfer matrix Moore-Penrose generalized inverse. After optimization The strain response vector actually measured by each sensor at the current time sub-step.

[0075] Due to the optimization transfer matrix used in the strengthening mathematical model With a low condition number, the above solution process is effective for optimizing the response vector The sensitivity of the measurement noise in the load identification result vector is low, which makes the load identification result vector It is stable.

[0076] By optimizing the response vector of all continuous time steps including the complete process of the hull and the ice layer By repeatedly executing the above solution calculation, we can obtain the complete history of the ice load changes over time at each node to be identified during the entire action period. Figure 7 A set of ice load identification results obtained by the method of the present invention is presented, which visualizes the magnitude and spatial distribution of the ice load acting on the hull structure at a specific time sub-step, demonstrating the technical feasibility of the method provided by the present invention.

[0077] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A method for eliminating ill-conditioning in a mathematical model for quasi-static identification of large-area distributed ice loads, characterized by: The following steps are involved: S1. Establish an ice load equivalent mechanical model to describe the ice load effect, and define the sensor arrangement method for strain measurement point acquisition; S2. Determine specific ice load information to be identified and an initial measurement point arrangement plan based on the ice load equivalent mechanical model and sensor arrangement method; S3. Based on the ice load information to be identified and the initial measurement point arrangement plan, perform unit pressure analysis to obtain an initial transfer matrix; S4, establishing a time sample statics system discrete in time sub-steps, and establishing an initial mathematical model including the initial transfer matrix; S5. Performing dimensionality reduction optimization on the initial transfer matrix using a regional discrete retrieval method to reduce the ill-posedness of the initial mathematical model and obtain an optimized transfer matrix and sensor layout scheme; S6. Obtaining an enhanced mathematical model using the optimized transfer matrix, and solving the enhanced mathematical model to obtain a load identification result.

2. The method for eliminating pathological conditions of a quasi-static identification mathematical model for large-area distributed ice loads according to claim 1 is characterized in that: In step S1, the ice load equivalent mechanical model is: It is represented by the multi-point concentrated ice extrusion force acting perpendicularly on the outer surface of the shell structure along the normal direction; The sensor arrangement method is: The sensors are arranged at the ribs, longitudinal girders and part of the outer plate, and the strain gauges are arranged in the same direction as the principal stress of the structural characteristics.

3. The method for eliminating pathological conditions of a quasi-static identification mathematical model for large-area distributed ice loads according to claim 1 is characterized in that: In step S2, the ice load information to be identified is: A limited number of equivalent nodal ice loads to be identified are selected in the area where the smooth ice interacts with the bow shell, and their action positions are distributed in an array form; The initial measurement point arrangement scheme is: A large number of initial measurement points are arranged in an array on the inner side of the bow outer plate, covering the ribs, longitudinal girders and outer plate areas.

4. The method for eliminating pathological conditions of a quasi-static identification mathematical model for large-area distributed ice loads according to claim 1 is characterized in that: In step S3, the unit pressure analysis is: A unit normal concentrated pressure is applied to each action point of the ice load to be identified, and the structural strain response data of all initial measurement points are extracted. According to the mapping relationship of the transfer matrix, the initial transfer matrix is obtained.

5. The method for eliminating pathological conditions of a quasi-static identification mathematical model for large-area distributed ice loads according to claim 1 is characterized in that: In step S4, the time sample statics system is: The time-varying process of dynamic icebreaking of the ship is equivalently discretized into a time sequence arrangement of the static process of ice extrusion force in time sub-steps, and each moment corresponds to an independent static mechanical system.

6. The method for eliminating pathological conditions of a quasi-static identification mathematical model for large-area distributed ice loads according to claim 1 is characterized in that: In step S5, the region discrete search method specifically includes: (a) Taking the initial transfer matrix as the overall matrix, setting the number of target sensors to p, and setting the maximum number of iterations to q; (b) In each iteration, the current overall matrix is divided into p sub-search domains according to the row vector, and a row vector is initialized from each sub-search domain to form a candidate target dimension matrix; (c) locally optimizing each row of the candidate target dimension matrix, that is, keeping other rows unchanged, replacing them with other row vectors in the corresponding sub-search domain, and retaining the replacement result that minimizes the condition number of the candidate target dimension matrix; (d) After an iteration, the optimization result obtained in the iteration is stored, and its row vector is removed from the overall matrix to update the overall matrix; (e) Repeat steps (b) to (d) until q iterations are completed, and retrieve the target matrix with the minimum condition number from the optimization results of all iterations as the final optimized transfer matrix.

7. The method for eliminating pathological conditions of a quasi-static identification mathematical model for large-area distributed ice loads according to claim 6 is characterized in that: The regional discrete search method uses the condition number of the matrix as the objective function for evaluating the ill-conditioned characteristics of the matrix. The condition number is defined as: ； in, is the matrix to be evaluated, is the 2-norm of the matrix, is the Moore-Penrose generalized inverse of the matrix.

8. The method for eliminating ill-conditioning of a large-area distributed ice load quasi-static identification mathematical model according to claim 1 is characterized in that: In step S5, the sensor arrangement scheme is optimized as follows: By comparing the position of each row element in the optimized transfer matrix with the position in the initial transfer matrix, the corresponding initial measurement point arrangement position is reversely located, thereby obtaining the optimal measurement point combination.

9. The method for eliminating ill-conditioning of a quasi-static identification mathematical model for large-area distributed ice loads according to claim 1 is characterized in that: In step S6, the enhanced mathematical model is: ； in, is the ice load vector to be identified, is the optimized transfer matrix, It is a response vector composed of response data corresponding to the measurement points determined by optimizing the sensor arrangement scheme.

10. The method for eliminating ill-conditioning of a quasi-static identification mathematical model for large-area distributed ice loads according to claim 1, characterized in that: In step S6, the solution of the enhanced mathematical model is: The Moore-Penrose inverse method is used to solve the strengthening mathematical model, and the solution vector is the load identification result.

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