Large-area distributed random ice load frequency domain identification mathematical model morbid elimination method

Abstract

The invention relates to the field of ship structure safety evaluation, and discloses a large-area distributed random ice load frequency domain identification mathematical model morbidity elimination method, which comprises the following steps: firstly, by establishing a finite element model comprising a ship hull plate, a rib and a stringer structure, converting an ice load effect into an equivalent concentrated force model; the method comprises the following steps: firstly, constructing a structure, arranging multiple strain response measuring points on the surface of the structure, then obtaining frequency response data by applying simple harmonic excitation, forming a frequency response function matrix, optimizing a high morbid frequency through a multiple expansion retrieval algorithm, screening out a submatrix with the minimum condition number, reconstructing a frequency domain identification model, and finally, identifying the high morbid frequency according to the frequency domain identification model. And based on the optimized frequency response function sub-matrix, combining a structure response spectrum and an inverse problem theory, and solving by utilizing a generalized inverse method to obtain an ice load power spectral density function. A frequency response function matrix is optimized through a multiple expansion retrieval algorithm and a generalized inverse method, the stability and recognition precision of the model are remarkably improved, and the problem of discomfort caused by high ill-conditioned frequency in an existing method is solved.

Description

Technical Field

[0001] The present invention relates to the field of ship structure safety assessment, and specifically to a method for eliminating the ill - conditioning of a mathematical model for the frequency - domain identification of large - area distributed random ice loads. Background Art

[0002] With the development of shipping in ice - covered waters, the dynamic ice loads generated by ship - ice collisions pose a severe challenge to the safety of ship structures. To effectively monitor ice loads, the indirect identification method of inverse - solving loads through structural responses has become the mainstream technology due to its advantages such as safety and convenience.

[0003] However, during high - speed icebreaking, the ship will encounter non - stationary random ice loads with complex time - frequency characteristics, which poses higher requirements for the accuracy of load identification, especially in the frequency domain. The core technical problem faced by current frequency - domain load identification techniques is that the mathematical models they rely on are severely ill - conditioned during the solution process. This problem is caused by the ill - conditioned characteristics of the frequency response function matrix in the model, which leads to low accuracy and poor stability of the load identification results.

[0004] To solve this problem, the existing technologies mainly adopt two types of methods: one is algorithms such as Tikhonov regularization, but its effect is not good when dealing with complex random ice loads; the other is to reduce the condition number of the frequency response function matrix by optimizing the sensor layout, such as the C - optimal or D - optimal design methods. However, these optimization methods only have an obvious improvement effect on the matrix ill - conditioning at a single frequency point, and have limitations in controlling the global ill - conditioning within the entire working frequency band. It is difficult to effectively suppress the ill - conditioning problems commonly existing in the wide - frequency domain and cannot meet the accurate and stable identification requirements of large - area distributed random ice loads.

[0005] Therefore, there are obvious technical gaps in how to effectively eliminate the global ill - conditioning of the mathematical model for the frequency - domain identification of wide - band and large - area random ice loads in the existing technologies, and new solutions are urgently needed. Summary of the Invention

[0006] In view of the deficiencies of the existing technologies, the present invention provides a method for eliminating the ill - conditioning of a mathematical model for the frequency - domain identification of large - area distributed random ice loads, and solves the problem of ill - posed inversion caused by the high ill - conditioning and excessive condition number of the frequency response function matrix in the ice load identification of ship structures.

[0007] To achieve the above objectives, the present invention is realized through the following technical solutions: A method for eliminating the ill - conditioning of a mathematical model for the frequency - domain identification of large - area distributed random ice loads, including the following steps: S1. Establish a finite - element model including the outer hull plate, ribs, and longitudinal girders of the ship, construct an equivalent concentrated - force model under the action of ice loads, and arrange multi - point strain - response measurement points on the structure surface as the initial sensor array; S2. Set multiple nodes in the ice load acting area, apply a harmonic excitation with a unit amplitude to each node one by one, obtain the strain response frequency data at the structural measurement points, and thereby establish a frequency response function matrix to form a frequency-domain structural identification model; S3. In the frequency-domain identification model, based on the ill-condition analysis of the frequency response function matrix, identify the frequency point corresponding to the maximum condition number, and extract the high-ill-condition frequency response matrix; S4. Apply the multiple expansion retrieval algorithm to the high-ill-condition matrix, screen out the sub-matrix with the minimum condition number from multiple measurement point combinations, form an optimized frequency response sub-matrix, and determine the corresponding optimized measurement point layout plan; S5. Use the optimized frequency response function sub-matrix to reconstruct the structural frequency-domain identification model, collect the measured strain responses of the optimized measurement points, and construct the response power spectral density function; S6. Based on the inverse problem theory and the generalized inverse matrix solution method, combine the enhanced identification model with the structural response spectrum to identify the ice load power spectral density function, which is used to reflect the random excitation intensity distribution of each load node in the frequency domain.

[0008] Preferably, in step S1, the equivalent concentrated force model is constructed by discretizing the ice extrusion force into multiple concentrated normal nodal forces acting on the hull shell surface. The nodes are evenly arranged along the bow outer plate area to form a two-dimensional grid arrangement, so as to simulate the spatial distribution characteristics of the actual ice-breaking load.

[0009] Preferably, the sensor layout method in step S1 includes the following content: The strain gauges of the sensors in the outer plate area are arranged along the structural axial and transverse directions respectively, and the directions are 0 degrees and 90 degrees; The strain gauges of the sensors in the rib and longitudinal girder areas are arranged at angles of plus and minus 45 degrees; The overall sensor array is arranged at equal intervals in a rectangular manner to form a multi-channel structural response observation network.

[0010] Preferably, in step S2, the frequency response function matrix is a complex-domain matrix, whose row dimension is the number of sensors, the column dimension is the number of ice load nodes, and the matrix elements are the complex strain responses at a certain sensor position generated by a unit harmonic excitation acting on a certain load node at a given frequency.

[0011] Preferably, the identification method based on the ill-condition analysis of the frequency response function matrix in step S3 is: within a preset frequency scanning range, calculate the condition number of the frequency response function matrix at each frequency. The condition number is the product of the matrix norm and the norm of its generalized inverse matrix, and take the frequency with the maximum condition number as the high-ill-condition frequency.

[0012] Preferably, the multiple expansion retrieval algorithm in step S3 includes the following steps: Select a set of initial row vector combinations from the high ill-conditioned frequency response matrix as the starting measurement point set; Generate several candidate submatrices by replacing the starting combination row by row, and recalculate the condition number after each replacement; Adopt a full combination traversal strategy to traverse all possible combinations of measurement point arrangements; Select the submatrix with the smallest condition number as the optimized frequency response submatrix, and record the measurement point positions corresponding to its row indices to form the final optimized layout plan.

[0013] Preferably, the optimized frequency response submatrix in step S5 is used to reconstruct the structural frequency domain identification model, where the model input is the ice load power spectral density matrix at each frequency, and the output is the strain response spectrum of the optimized measurement points, which is constructed through the structural power transfer relationship.

[0014] Preferably, the construction method of the response power spectral density function in step S5 includes: Collect the strain time series of the optimized measurement points under the actual ice load excitation; Perform discrete Fourier transform on the strain series to obtain the frequency domain strain response; Calculate the auto-correlation and cross-correlation spectral densities between each response channel to form the structural response spectrum matrix.

[0015] Preferably, the solution steps of the ice load power spectral density function in step S6 include: Based on the structural response spectrum matrix and the optimized frequency response function submatrix, construct a frequency domain inverse problem model; Use the Moore-Penrose generalized inverse method to solve the input spectral matrix; The recognition result is the diagonal element of the spectral matrix, representing the auto-power spectral density at each ice load node, which is used as the final output.

[0016] The present invention provides a method for eliminating the ill-conditioning of the mathematical model for the frequency domain identification of large-area distributed random ice loads. It has the following beneficial effects: 1. The present invention can provide better optimization results for high ill-conditioned matrices than the C-optimal design method and the D-optimal design method. By optimizing the high ill-conditioned frequencies in the frequency response function matrix through multiple extended search algorithms, the effect of significantly reducing the condition number at this frequency is achieved. Compared with the C-optimal design method and the D-optimal design method, which only optimize a single frequency and lead to an increase in the condition numbers of other frequencies, the present invention can perform a more comprehensive optimization for high ill-conditioned matrices, effectively alleviating the negative impact of high ill-conditioned frequencies on the model stability and identification accuracy.

[0017] 2. The present invention can provide an optimized frequency response function matrix with lower global condition numbers compared to the C-optimal design method and the D-optimal design method. During the optimization process, it not only focuses on the condition numbers of individual frequencies but also reduces the condition numbers of the entire frequency response function matrix through a global optimization scheme, improving the numerical stability of the matrix. Compared with the traditional C-optimal and D-optimal design methods that only optimize the condition numbers of specific frequencies, the present invention can achieve lower global condition numbers throughout the frequency domain, thereby enhancing the stability of the inversion process and the accuracy of the results.

[0018] 3. The present invention can achieve more flexible control of the computational cost compared to the C-optimal design method and the D-optimal design method. During the optimization process at multiple frequency points, the optimization method of the present invention can flexibly adjust the complexity of the optimization calculation according to needs. Compared with the fixed calculation strategies of the C-optimal design method and the D-optimal design method, the solution of the present invention provides a more flexible control method, which can adjust the degree of optimization according to the actual computational resources and the requirements of identification accuracy, reducing unnecessary computational burdens.

[0019] 4. The identification results of the present invention show more obvious accuracy advantages compared to those obtained by using the C-optimal design method and the D-optimal design method. Since the present invention combines multiple extended retrievals and the generalized inverse method during the optimization process of the frequency response function matrix, the optimized matrix can provide more stable and accurate identification results during the inversion process. Compared with the C-optimal design method and the D-optimal design method, the optimization results of the present invention show obvious accuracy advantages. Especially when facing highly ill-conditioned frequencies, it can effectively improve the accuracy of model inversion, thus providing a more reliable basis for the safety assessment of ship structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 is a schematic diagram of the overall process of the present invention; Figure 2 is the equivalent mechanical model of random ice loads of the present invention; Figure 3 is a schematic diagram of the initial measurement point layout and sensor layout method of the present invention; Figure 4 is a schematic diagram of the ice load distribution at the nodes to be identified of the present invention; Figure 5 is a flowchart of the optimization algorithm of the present invention; Figure 6 is the result of eliminating the ill-conditioning of the mathematical model of the present invention; Figure 7 is a schematic diagram of the optimized sensor layout scheme of the present invention; Figure 8 is the ice load spectrum identification result of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0021] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0022] Please refer to the attached Figure 1 - attached Figure 8 , the embodiment of the present invention provides a method for eliminating the ill-condition of the mathematical model for the frequency-domain identification of large-area distributed random ice loads, including the following steps: S1. Establish a finite element model including the hull outer plate, ribs and longitudinal girders, construct an equivalent concentrated force model under the action of ice loads, and arrange multi-point strain response measuring points on the structure surface as the initial sensor array; Before constructing the frequency-domain mathematical model for identifying the random dynamic ice loads borne by the hull structure in the ice area environment, it is necessary to first model the hull structure and its loading environment. In this embodiment, the bow area of the icebreaker is taken as the research object, and an initial mechanical system covering the ice load action distribution and the structural response observation network is established.

[0023] Generally, to improve the spatial resolution and practical adaptability of the identification results, it is necessary to construct a finite element model that can characterize the ice-ship coupling behavior, supplemented by a multi-point measurement point array for the subsequent calculation of the frequency response function matrix. In this embodiment, the model includes the main load-bearing structures such as the bow outer plate, ribs and longitudinal girders.

[0024] In this embodiment, to characterize the actual action distribution formed by the ice extrusion load on the structure surface, the ice load is regarded as a multi-point concentrated normal force, and an equivalent mechanical model is constructed by discretization means. The ice extrusion force is simplified to a concentrated force acting vertically at the nodes of the structure outer plate, and the direction is distributed along the normal direction of the hull outer plate. The construction form is as follows: In a specific implementation, let the total number of load nodes be , and these nodes are arranged regularly in the bow outer plate area, covering the flat ice contact zone. The node spacing in the x direction (transverse) is 0.4 m, and the spacing in the z direction (vertical) is 0.3 m, finally forming a node array of about 1.2 m × 10.4 m, and the total number of nodes is 133.

[0025] The ice load nodes can be defined as: ; where represents the concentrated ice load at the th node, with the unit of N; = 133 represents the total number of nodes. All nodes act along the normal direction, forming a two-dimensional space discrete field, approximately simulating the random loading of the actual ice block.

[0026] As an option, to ensure the identifiability of the frequency response function, in this embodiment, strain gauges are reasonably arranged inside the structure to form a response observation network. The arrangement of the measuring points follows the principle of the principal stress direction of the structure to improve the directional sensitivity of the strain response.

[0027] Specifically: In the outer plate area, the strain gauges are arranged along two directions of 0° (the axial direction of the hull) and 90° (the transverse direction); In the rib and longitudinal girder areas, the arrangement angle of the strain gauges is ±45°, used to capture the shear strain; The measuring point array is arranged in a rectangular uniform manner, the distance between the measuring points is 0.1 m, covering the inner area of 11.2 m × 4.2 m, and finely covering all areas with significant forces.

[0028] In a possible implementation, let the total number of measuring points be m, and the measuring point numbers are denoted as: ; Among them, represents the arrangement position corresponding to the th sensor, and the unit is the position coordinate vector. The arrangement of the measuring points covers the ribs, longitudinal girders and the inside of the outer plate. The distance between the points in the outer plate area from the structure edge is 0.1 m to ensure the observation sensitivity.

[0029] In order to establish a frequency domain model later, a unit amplitude harmonic excitation needs to be applied to the structural model to simulate the single-point ice load input, and record the strain response frequencies at all measuring points to form a frequency response function. This process will be carried out in the subsequent step S2.

[0030] Generally, in order to ensure the stability of the inverse problem solution, it is necessary to pay attention to the ill-conditioning characteristics of the frequency response function matrix, and it is necessary to ensure that the number and position of the measuring points have sufficient linear independence for the formation of the frequency response matrix. In this embodiment, a certain redundancy is reserved in the arrangement of the measuring points to provide a data basis for subsequent dimensionality reduction optimization.

[0031] S2. Set multiple nodes in the ice load acting area, apply a unit amplitude harmonic excitation to each node one by one, obtain the strain response frequency data at the structural measuring points, and thus establish a frequency response function matrix to form a frequency domain structural identification model; After the structural model and the observation network are constructed, in order to establish a model that can accurately reflect the frequency-domain response characteristics of the structure under ice loads, it is necessary to further identify the dynamic response behavior of the structure when excited at each ice load node. By applying a harmonic excitation signal with a unit amplitude at the preset ice load nodes and combining the strain measurement results at the observation points, the response mapping relationship of the structure in the frequency domain can be established, and finally a frequency response function matrix is formed to characterize the frequency-domain dynamic characteristics of the structure.

[0032] Generally, ice loads show random uncertainty in the actual process, and it is difficult to directly obtain their time-domain distribution characteristics. Therefore, using the frequency-domain modeling method is more convenient for extracting the system response characteristics and is used for subsequent inversion identification. In this embodiment, the establishment of the frequency-domain structure identification model is completed through the construction of the frequency response function matrix.

[0033] In this embodiment, the frequency response function (FRF) matrix is constructed in the following way: First, a plurality of nodes within the ice load action area are set, and a harmonic excitation with a unit amplitude is applied to each node in turn. The form of this excitation signal is: ; where, represents the excitation function applied to the th ice load node, represents the excitation angular frequency, with the unit of rad / s, is the total number of ice load nodes. The harmonic excitation is applied with a unit amplitude, and the direction is perpendicular to the outer hull of the ship and consistent.

[0034] While applying the excitation to each node, the response signal is recorded through strain measurement points arranged on the inner surface of the structure. For any excitation point and any measurement point , the strain response at this frequency can be obtained, which is in complex form and is used to simultaneously characterize the amplitude and phase information of the response.

[0035] Therefore, the constructed frequency response function matrix is expressed as: ; where, is the frequency response function matrix, is the total number of strain measurement points, is the total number of ice load nodes, and the matrix element is the value when the frequency is , and the unit harmonic excitation acting on the th load node causes the The complex strain responses at each measurement point.

[0036] In a possible implementation, for the measurement of the frequency response function, a swept-frequency method or a multi-frequency excitation technique is adopted, and point-by-point sampling is carried out within the concerned frequency range. For example: The frequency range is rad / s, corresponding to 1 Hz to 50 Hz; Sampling is carried out every 0.25 Hz to obtain 200 sets of independent frequency points; For each frequency point, the above process of unit excitation and response recording is repeated; At each frequency point, a matrix is constructed.

[0037] Generally, the structural response is greatly affected by the layout direction of the measurement points. Therefore, in actual measurement, it should be ensured that the direction of the strain gauge is consistent with the direction of the principal stress to improve the sensitivity and accuracy of response identification. For the diagonal layout in the rib and longitudinal girder areas, the strain response usually includes a shear component, which should be included in the calculation process of the complex response.

[0038] As an option, to avoid the problem of severe ill-conditioning of the frequency response function matrix, singular value analysis means can be introduced to evaluate the matrix. The rank of the frequency response function matrix affects the stability of the structural input-output mapping. A low-rank matrix may lead to non-unique subsequent load identification. Therefore, the measurement points should be arranged to cover multiple structural directions to ensure the linear independence between the column vectors of the matrix.

[0039] Specifically, in this embodiment, the number of measurement points adopted is m = 9100, the number of load nodes is n = 133, and the response matrix is a complex-domain matrix of 9100×133.

[0040] At some frequencies, if it is found that the matrix rank is insufficient, it is necessary to further increase the observation dimension. For example: Densify the measurement point layout in the outer plate area; Increase the number of strain gauges in the vertical direction; Expand the observation area to the adjacent cabin section structure.

[0041] In addition, to balance the computational efficiency and identification accuracy, in some embodiments, a frequency-domain window function or a noise filtering method is introduced to enhance the robustness of the FRF measurement. Common methods include Gaussian window, Hamming window or weighted average technique.

[0042] The finally constructed frequency response function matrix will be used as the core input for subsequent ice load inversion analysis and structural characteristic identification, running through the entire identification process.

[0043] S3. In the frequency-domain identification model, based on the ill-condition analysis of the frequency response function matrix, identify the frequency point corresponding to the largest condition number, and extract the high-ill-condition frequency response matrix; After obtaining the complete frequency response function matrix, to further improve the stability and inversion accuracy of structure identification, it is necessary to quantitatively analyze the ill-condition of the matrix at different frequencies. By identifying the frequency point with the most severe ill-condition and deeply processing the frequency response function matrix at this frequency, it can provide a basic basis for subsequent observation point optimization and data dimensionality reduction.

[0044] Generally, the frequency response function matrix may exhibit characteristics such as rank deficiency and enhanced linear correlation at certain frequency points, resulting in unstable structure input-output mapping. Such frequencies often correspond to system resonance frequencies, modal dense regions, or weak response regions of structural characteristics. Therefore, identifying the ill-condition frequency points in the frequency domain is an important step in constructing a highly robust inversion model.

[0045] In this embodiment, the ill-condition analysis method uses the matrix condition number as the evaluation index. Let a certain frequency point The corresponding frequency response function matrix is: ; Its condition number Is defined as the product of the norm of the matrix and the norm of its generalized inverse matrix, and the expression is: ; Among them, Represents the matrix norm, taking the 2-norm (i.e., the largest singular value); Represents the matrix Moore-Penrose generalized inverse; The larger it is, the more ill-conditioned the matrix is.

[0046] In a possible implementation, the selected frequency scanning range is rad / s, with a step of 0.25 Hz, and calculate the condition number corresponding to each frequency point in turn. Finally, determine the frequency point Corresponding to the largest condition number: ; After obtaining the high-ill-condition frequency , extract the corresponding frequency response function matrix , as the analysis basis for subsequent observation point combination optimization.

[0047] To further improve the numerical stability of the structure response matrix, this embodiment introduces a combination optimization algorithm based on a multiple expansion retrieval strategy to extract sub-matrices for the high-ill-condition frequency response matrix.

[0048] Specifically, the algorithm includes the following steps: In the initial stage, select from rows to form a submatrix, denoted as , where , as the starting observation subset. The initial submatrix can be determined by random selection, principal component selection, or modal coverage principle.

[0049] As an option, the initial combination can be set as the row index sequence , and its corresponding submatrix is denoted as: ; where represents the th row vector in the original matrix.

[0050] Based on the initial combination index sequence , add rows one by one from the remaining row vector reserve space to obtain a high-dimensional matrix with the minimum condition number until the expansion part ends after obtaining the target dimension matrix.

[0051] Subsequently, the method of replacing rows one by one is used to generate candidate sub-combinations. While keeping original rows unchanged, replace a new row vector to generate a new submatrix, and recalculate its condition number: ; This process is continuously iterated until all possible row combinations are traversed to form a combination set . The total number of the entire combination space is , and the efficiency can be improved by pruning or parallel computing.

[0052] Finally, select the submatrix with the minimum condition number from all candidate combinations, and its corresponding combination is recorded as the final measurement point optimization scheme. Its condition number is denoted as: ; where represents the submatrix corresponding to the combination .

[0053] Generally, this method can effectively avoid the ill-conditioned dimension of the frequency response function matrix and provide a stable and anti-interference input-output mapping structure for subsequent load inversion.

[0054] Specifically, the finally selected optimization combination in this embodiment is 133 strain measurement points, and its corresponding submatrix , at the high ill-conditioned frequency The condition number is the lowest under the following conditions, and the numerical stability is significantly enhanced.

[0055] As an extended method, mechanisms such as combinatorial sparsity constraints and structural topology information weighting can be further introduced to impose prior restrictions on the combination process, improving the physical interpretability and computational efficiency.

[0056] S4. For a highly ill-conditioned matrix, use the multiple extension retrieval algorithm to screen out the submatrix with the smallest condition number from multiple measurement point combinations, form the optimized frequency response submatrix, and determine the corresponding optimized measurement point layout plan; After identifying the highly ill-conditioned frequency points and extracting the corresponding frequency response function matrix, it is still necessary to further screen and reconstruct the composition of the row vectors of the observation points in the original response matrix. Since there are response redundancies or linear dependencies at some measurement points in the structural system, screening the optimal measurement point combination through the multiple extension retrieval algorithm helps to improve the numerical stability of the submatrix and avoid the ill-posed inversion problem caused by too large a condition number.

[0057] Generally, directly performing inversion or load identification in the full response matrix will face problems such as high dimensionality, high noise sensitivity, and poor solution convergence. Therefore, realizing the compression of the observation dimension through the optimized frequency response submatrix is a key link in structural identification modeling. This step optimizes the combination of the row vectors of the observation points in the aforementioned highly ill-conditioned matrix to obtain the final optimized measurement point layout plan.

[0058] In this embodiment, the multiple extension retrieval algorithm is based on the aforementioned constructed highly ill-conditioned frequency response function matrix , where is the total number of initial observation points, is the number of load nodes, is the frequency point with the strongest ill-condition.

[0059] First, set the target number of observation points after compression to , satisfying , and select row vectors from to form a candidate submatrix: ; Among them, represents the response row vector corresponding to the th observation point in the original matrix, and the row index combination is the current measurement point selection scheme.

[0060] To screen out the optimal sub-combination, based on a group of initial combinations, use the method of one-by-one replacement and recursive extension to construct multiple candidate combinations, and calculate the condition number of the submatrix corresponding to each group of combinations: ; wherein, is the condition number of the current candidate sub-matrix, and the smaller it is, the higher the numerical stability of the sub-matrix; is the Moore-Penrose generalized inverse of; the matrix norm still takes the 2-norm, that is, the largest singular value.

[0061] In a possible implementation manner, all possible combinations of measurement points are exhaustively searched by the full combination traversal method. To reduce the calculation amount, the algorithm introduces a layer-by-layer pruning mechanism, and only the locally optimal combinations are retained to enter the next round of expansion. For example, only the first K combinations with the smallest condition numbers (such as K = 50) are retained in each round of expansion, and replacement attempts are continued based on these combinations in subsequent rounds.

[0062] Specifically, for the sub-matrix obtained after each replacement, the condition number is recalculated: ; Finally, the one with the smallest condition number is selected from all feasible combinations: ; The corresponding row index set is the optimized observation point layout scheme, denoted as .

[0063] As an option, in actual deployment, the positions of the observation points can be converted into two-dimensional coordinate mappings to facilitate the corresponding actual layout diagram of the structure. Combining the structure panel numbers with the rib positions and section divisions, the final observation point layout scheme can be output in the form of structure coordinates.

[0064] In this embodiment, the initial number of measurement points is m = 9100, the finally selected number of observation points is r = 133, and the dimension of the corresponding optimized frequency response sub-matrix is 133×133, where 133 is the number of ice load nodes. The ill-conditioning of the original matrix is significantly reduced by the optimized combination of measurement points, and its corresponding condition number is significantly smaller than that of the original matrix, and the numerical stability is stronger.

[0065] In some embodiments, to further improve the search efficiency, a greedy strategy or a dynamic programming method based on the eigenvalue change rate can also be combined to heuristically prune the combination space. Such methods can be used as a supplement to the full combination strategy to improve the scalability of the algorithm in large-scale structure identification tasks.

[0066] S5. Reconstruct the structural frequency domain identification model by using the optimized frequency response function sub-matrix, collect the measured strain responses of the optimized measurement points, and construct the response power spectral density function; After completing the optimization and screening of the high-pathological frequency response matrix and obtaining the optimal measurement point layout plan, it is necessary to further reconstruct the frequency-domain structural identification model based on the selected measurement points to ensure the accuracy and stability of the physical response mapping of the model. Since the frequency response function sub-matrix has achieved measurement point compression and pathological mitigation, the reconstructed model can significantly improve the inversion performance while retaining the main structural dynamic characteristics. The model construction process needs to combine the actually collected strain response data, and establish the response power spectral density function through frequency-domain analysis as the structural output expression.

[0067] Generally, the structural frequency-domain model can be established through the convolution relationship between the frequency response function and the excitation power spectral density. Among them, the ice load power spectral density matrix is used as the input, and the strain response power spectral density function is the output, and the two are connected through the power spectral transfer relationship. Due to the characteristics of low redundancy and high recognition of the corresponding measurement points of the optimized sub-matrix, the output mapping of this model is more representative.

[0068] In this embodiment, the structural frequency-domain identification model is reconstructed in the following power transfer form: ; Where: : represents the strain response power spectral density matrix corresponding to the optimized measurement points; : is the optimized frequency response function sub-matrix obtained in step S4; : represents the input excitation power spectral density matrix corresponding to each ice load node; : represents The conjugate transpose matrix of; is the angular frequency, with the unit of rad / s.

[0069] In a possible implementation, can be estimated through prior scenario simulation or ice excitation statistical model, and can also be used as a parameter to be estimated in the inverse identification process. The corresponding then comes from the processing of the measured response data of the optimized measurement points.

[0070] To construct the response power spectral density matrix, it is necessary to first collect the strain time series of the optimized measurement points under the actual ice load conditions. Assume that the strain time series of a certain measurement point is , the sampling duration is , the sampling frequency is , and a total of point data are collected.

[0071] Perform Fourier transform on the strain time series of each channel to obtain the frequency-domain response: ; Among them, ; , is the th frequency component; , is the frequency-domain strain response of the th channel.

[0072] Subsequently, by statistically processing the frequency-domain response, autocorrelation and cross-correlation power spectral density functions are constructed: ; Among them, is the cross-correlation power spectrum between channel and channel at frequency ; represents the complex conjugate; if , this expression degenerates into the auto-power spectral density.

[0073] In this way, a complete response spectrum matrix at frequency point can be constructed: ; Specifically, the obtained has a Hermitian structure, that is, it satisfies the conjugate symmetry property: ; This structure ensures the physical consistency and numerical invertibility of the subsequent inversion and estimation processes.

[0074] In some embodiments, to avoid window function leakage and frequency aliasing problems, preprocessing methods such as the Hanning window and Welch's overlapping segment averaging technique can be introduced in the Fourier transform process to improve the stability of spectral density estimation.

[0075] As an option, the structural response spectrum matrix can be repeatedly collected and averaged under multiple measurement point groups and multiple ice load excitation conditions, and finally a statistical expression of the frequency-domain structural response under multiple scenarios is obtained, providing an input basis for ice load inversion or spectral decoupling analysis in the next stage.

[0076] S6. Based on the inverse problem theory and the generalized inverse matrix solution method, combined with the enhanced identification model and the structural response spectrum, the ice load power spectral density function is identified to reflect the random excitation intensity distribution of each load node in the frequency domain.

[0077] After completing the optimization of the frequency response function sub-matrix, the construction of the response power spectrum, and the preliminary establishment of the frequency-domain identification model, the next step is the inverse identification process of the ice load power spectral density function. This step utilizes the theory of inverse problems, constructs a frequency-domain inverse problem model, and combines the generalized inverse matrix solution method to identify the power spectral density function of each ice load node. Through this process, the excitation intensity distribution of each node in the frequency domain can be reflected, and it provides an effective input for subsequent structural response analysis.

[0078] In general, the solution of an inverse problem involves the mapping relationship between the known output response and the system frequency response function. By using the generalized inverse matrix method, we can inversely deduce the input excitation power spectrum from the observed structural response spectrum. This process can effectively obtain the auto-power spectral density of each load node, which is further used to analyze and optimize the influence of the load.

[0079] In this embodiment, first, based on the optimized frequency response function sub-matrix obtained in the previous steps and the response power spectral density matrix , a frequency-domain inverse problem model is constructed. Specifically, it is assumed that the relationship between the structural response and the ice load excitation satisfies the following power spectrum transfer equation: ; where is the ice load power spectral density matrix to be identified, which contains the excitation intensity of each ice load node in the frequency domain. The goal of the inverse problem is to inversely deduce and from the known .

[0080] Specifically, this inverse problem is solved by the Moore-Penrose generalized inverse matrix method. The basic definition of the Moore-Penrose generalized inverse is: ; where is the solved ice load power spectral density matrix, is the pseudo-inverse matrix of , which can stably inversely deduce the ice load excitation information.

[0081] In one possible implementation, the solution process of the inverse problem includes solving band by band under the condition that the input is a combination of multiple frequency bands and multiple measurement points, and combining the spectral decoupling technology to improve the solution accuracy. Through this method, the ill-posedness in the solution process can be effectively avoided, and the stability of the ice load power spectrum can be ensured.

[0082] Finally, for the identified ice load power spectral density matrix , by extracting its diagonal elements, the auto-power spectral density at each ice load node is obtained, that is: ; These diagonal elements represent the random excitation intensity distributions of each ice load node at different frequencies and serve as the final output of the power spectral density of that node.

[0083] As an option, if there are multiple load nodes or multiple excitation conditions, the obtained power spectral density matrix can be weighted and averaged to further improve the robustness and accuracy of the results.

[0084] Through the method described in this embodiment, the relationship between the structural response and the excitation spectrum in the frequency domain is successfully deduced in reverse, thereby obtaining the power spectral density functions of each ice load node in the structure, providing an important basis for structural analysis and optimization.

[0085] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. Method for eliminating ill-condition of mathematical model for frequency-domain identification of large-area distributed random ice loads, characterized in that, It includes the following steps: S1. Establish a finite element model including the hull outer plate, ribs and longitudinal girders, construct an equivalent concentrated force model under ice load, and arrange multi-point strain response measuring points on the structure surface as the initial sensor array; S2. Set multiple nodes in the ice load acting area, apply a harmonic excitation with a unit amplitude to each node one by one, obtain the strain response frequency data at the structure measuring points, and thereby establish a frequency response function matrix to form a frequency-domain structure identification model; S3. In the frequency-domain identification model, based on the ill-condition analysis of the frequency response function matrix, identify the frequency point corresponding to the maximum condition number, and extract the high-ill-condition frequency response matrix; S4. Apply the multiple extended search algorithm to the high-ill-condition matrix, screen out the sub-matrix with the minimum condition number from multiple measuring point combinations to form an optimized frequency response sub-matrix, and determine the corresponding optimized measuring point layout scheme; S5. Use the optimized frequency response function sub-matrix to reconstruct the structure frequency-domain identification model, collect the measured strain responses of the optimized measuring points, and construct the response power spectral density function; S6. Based on the inverse problem theory and the generalized inverse matrix solution method, combine the enhanced identification model with the structure response spectrum to identify the ice load power spectral density function, which is used to reflect the random excitation intensity distribution of each load node in the frequency domain.

2. The method for eliminating the ill-condition of the mathematical model for frequency-domain identification of large-area distributed random ice loads according to claim 1, characterized in that In the S1 step, the equivalent concentrated force model is constructed by discretizing the ice extrusion force into multiple concentrated normal node forces acting on the hull surface. The nodes are evenly arranged along the bow outer plate area to form a two-dimensional grid arrangement to simulate the spatial distribution characteristics of the actual ice-breaking load.

3. The method for eliminating the ill-conditioning of the mathematical model for the frequency-domain identification of large-area distributed random ice loads according to claim 1, wherein, The sensor layout method in the S1 step includes the following contents: In the outer plate area, the sensor strain gauges are arranged along the axial and transverse directions of the structure, and the directions are 0 degrees and 90 degrees; In the rib and longitudinal girder areas, the sensor strain gauges are arranged at angles of plus and minus 45 degrees; The sensor array is arranged in a rectangular equal-spacing manner as a whole to form a multi-channel structure response observation network.

4. The method for eliminating the ill - conditioning of the mathematical model for identifying the frequency - domain of large - area distributed random ice loads according to claim 1, characterized in that, In the S2 step, the frequency response function matrix is a complex-domain matrix, whose row dimension is the number of sensors, and the column dimension is the number of ice load nodes. The matrix elements are the complex strain responses at a certain sensor position generated by a unit harmonic excitation acting on a certain load node at a given frequency.

5. The method for eliminating the ill - conditioning of the mathematical model for frequency - domain identification of large - area distributed random ice loads according to claim 1, wherein, The identification method based on the ill-condition analysis of the frequency response function matrix in the S3 step is: within the preset frequency scanning range, calculate the condition number of the frequency response function matrix at each frequency. The condition number is the product of the matrix norm and the norm of its generalized inverse matrix, and the frequency with the maximum condition number is taken as the high-ill-condition frequency.

6. The method for eliminating the ill-conditioning of the mathematical model for identifying the frequency domain of large-area distributed random ice loads according to claim 1, characterized in that The multiple extended search algorithm in the S3 step includes the following steps: Select a group of initial row vector combinations from the high-ill-condition frequency response matrix as the starting measuring point set; Replace the starting combination row by row to generate several candidate sub-matrices, and recalculate the condition number after each replacement; Adopt a full combination traversal strategy to traverse all possible combinations of measuring point arrangements; Select the sub-matrix with the minimum condition number as the optimized frequency response sub-matrix, and record the measuring point positions corresponding to its row indices to form the final optimized layout scheme.

7. The method for eliminating the ill-conditioning of the mathematical model for frequency-domain identification of large-area distributed random ice loads according to claim 1, characterized in that In the S5 step, the optimized frequency response sub-matrix is used to reconstruct the structural frequency-domain identification model, where the model input is the ice load power spectral density matrix at each frequency, and the output is the strain response spectrum of the optimized measurement points, which is constructed through the structural power transfer relationship.

8. The method for eliminating the ill-conditioning of the mathematical model for the frequency-domain identification of large-area distributed random ice loads according to claim 1, wherein, The construction method of the response power spectral density function in the S5 step includes: Collect the strain time series of the optimized measurement points under the actual ice load excitation; Perform discrete Fourier transform on the strain series to obtain the frequency-domain strain response; Calculate the auto-correlation and cross-correlation spectral densities between each response channel to form the structural response spectrum matrix.

9. The method for eliminating the ill-conditioning of the mathematical model for frequency-domain identification of large-area distributed random ice loads according to claim 1, characterized in that, The solution steps of the ice load power spectral density function in the S6 step include: Based on the structural response spectrum matrix and the optimized frequency response function sub-matrix, construct a frequency-domain inverse problem model; Use the Moore-Penrose generalized inverse method to solve the input spectral matrix; The identification result is the diagonal element of the spectral matrix, representing the auto-power spectral density at each ice load node, which is used as the final output.

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