Efficient underwater acoustic radiation estimation method for longitudinal-transverse reinforced conical shell structure

Abstract

The present application relates to a kind of longitudinal and transverse reinforced conical shell structure underwater sound radiation efficient estimation method, S1, the inherent circular frequency of underwater of longitudinal and transverse reinforced conical shell structure optimized model is calculated;S2, the relationship between air velocity response and underwater velocity response of longitudinal and transverse reinforced conical shell structure is established;S3, the relationship between underwater velocity response and sound radiation is established;S4, estimate the underwater sound radiation of longitudinal and transverse reinforced conical shell structure.The present application utilizes system identification method, perturbation model construction method and model correction method, and the underwater vibration response is quickly estimated by the vibration response in the air of longitudinal and transverse reinforced conical shell structure;Utilize system identification method and perturbation model construction method, and the underwater sound radiation of structure is quickly estimated by the underwater vibration response of longitudinal and transverse reinforced conical shell structure;Solve the problem of low efficiency of underwater vibration response and underwater sound radiation solution;Only need to complete once underwater sound vibration coupling solution calculation, i.e., can indirectly evaluate underwater sound radiation by the frequency domain response in the air of longitudinal and transverse reinforced conical shell structure.

Description

Technical Field

[0001] This invention relates to the field of low-radiation noise design technology for underwater structures, specifically to an efficient method for estimating underwater acoustic radiation of a longitudinally and transversely reinforced conical shell structure. Background Technology

[0002] To achieve low-radiated noise design for underwater structures, a combination of parametric finite element modeling and iterative optimization algorithms is typically used to design the key parameters of the underwater structure. However, if only the vibration response of the underwater structure in air is used as the objective function for optimization, the acoustic radiation efficiency of different modes of the underwater structure will be ignored, making it difficult to achieve the design goal of minimizing radiated noise. Furthermore, using the acoustic radiation of the underwater structure as the objective function, traditional finite element or boundary element analysis methods consume significant computational resources and require repeated solutions during the optimization process, resulting in low optimization efficiency.

[0003] The paper "Research on Rapid Prediction of Vibration and Acoustic Radiation of Large Underwater Structures" developed a rapid prediction method for acoustic radiation based on adaptive cross approximation, which improved the calculation speed by about 40%. However, this method is more suitable for large structures and still requires boundary element analysis, which cannot fundamentally solve the problem of low efficiency in optimization design. The paper "Research on Ship Vibration and Noise Prediction Method Based on Transfer Matrix" treats the underwater structure as equivalent to 26 beam elements, which has certain advantages in roughly predicting the overall acoustic radiation of the underwater structure in the scheme design stage, but cannot be used for the fine design of underwater structures. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide an efficient method for estimating underwater acoustic radiation of a longitudinally and transversely stiffened conical shell structure, which addresses the shortcomings of the existing technology. This method only requires one underwater finite element or boundary element method acoustic-vibration coupling solution calculation, and can indirectly evaluate the underwater acoustic radiation of the longitudinally and transversely stiffened conical shell structure through the structure's frequency domain response in air. This solves the problem of repeatedly performing underwater acoustic-vibration coupling solutions in the iterative optimization design of underwater structures, and improves the computational efficiency of iterative optimization design.

[0005] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0006] An efficient method for estimating underwater acoustic radiation of a longitudinally and transversely reinforced conical shell structure includes the following steps:

[0007] S1. Calculate the underwater natural circular frequencies of the optimized model of the longitudinally and transversely stiffened conical shell structure:

[0008] The first two modes, which contribute the most to the underwater acoustic radiation of the longitudinally and transversely stiffened conical shell structure, are defined as the first and second target optimization modes, respectively. The shell nodes corresponding to the tail end and midpoint of the longitudinally and transversely stiffened conical shell structure axis are defined as typical nodes characterizing the vibration response of the longitudinally and transversely stiffened conical shell structure, respectively, and are defined as the first node and the second node. The underwater natural circular frequencies of the optimized model of the longitudinally and transversely stiffened conical shell structure are calculated by using the equivalent modal mass and equivalent modal stiffness of the first and second nodes of the initial model of the longitudinally and transversely stiffened conical shell structure in air, the underwater natural circular frequencies of the initial model of the longitudinally and transversely stiffened conical shell structure, and the equivalent modal mass and equivalent modal stiffness of the first and second nodes of the optimized model of the longitudinally and transversely stiffened conical shell structure in air.

[0009] S2. Establish the relationship between the air velocity response and underwater velocity response of a longitudinally and transversely stiffened conical shell structure:

[0010] A systematic identification method was used to identify the state-space equation G between the load input at the first node and the air velocity responses at the first and second nodes of the finite element model of the longitudinally and transversely stiffened conical shell structure under optimization. Using the calculated underwater natural circular frequencies of the longitudinally and transversely stiffened conical shell structure under optimization, a perturbation model construction method was employed to construct the state-space equation G between the load input at the first node and the underwater velocity responses at the first and second nodes of the finite element model of the longitudinally and transversely stiffened conical shell structure under optimization.

[0011] S3. Establish the relationship between underwater velocity response and acoustic radiation:

[0012] A system identification method is used to identify the state-space model W between the underwater velocity response and acoustic radiation power of the first and second nodes. This state-space model is a two-input, single-output system, with the underwater velocity responses of the first and second nodes serving as model inputs and the radiated acoustic power of the longitudinally and transversely stiffened conical shell structure serving as model output. A perturbation model construction method is then used to construct the perturbation state-space model of W.

[0013] S4. Estimate the underwater acoustic radiation of a longitudinally and transversely reinforced conical shell structure:

[0014] The transfer function expression for the load input and underwater radiated acoustic power at the first node of the optimized finite element model of the longitudinally and transversely stiffened conical shell structure is as follows: The amplitude-frequency characteristic is the frequency response function between the load input at the first node and the underwater radiated acoustic power.

[0015] In the above scheme, step S1 specifically includes the following steps:

[0016] S1.1 Complete the modal analysis of the initial model of the longitudinally and transversely stiffened conical shell structure in air and underwater, the structural vibration frequency response analysis in air, and the acoustic-vibration coupling response analysis underwater;

[0017] S1.2. Based on the underwater modal results and underwater acoustic radiation of the initial model of the longitudinally and transversely stiffened conical shell structure, the first two modes that contribute the most to the underwater acoustic radiation of the longitudinally and transversely stiffened conical shell structure are identified. The first two modes that contribute the most to the underwater acoustic radiation of the longitudinally and transversely stiffened conical shell structure are taken as the target optimization modes, and are defined as the first target optimization mode n1 and the second target optimization mode n2, respectively. The analysis frequency band is 10Hz to 100Hz, and the step size is 1Hz.

[0018] S1.3 Identify the air modes N1 and N2 that are the same as the underwater modes n1 and n2 of the initial model of the longitudinally and transversely stiffened conical shell structure;

[0019] S1.4. The nodes on the shell corresponding to the tail end point and midpoint of the longitudinal and transverse stiffened conical shell structure are used as typical nodes to characterize the vibration response of the longitudinal and transverse stiffened conical shell structure. They are defined as the first node and the second node, respectively. The node numbers of the first node A and the second node B are extracted respectively.

[0020] S1.5 Extracting the mass matrix M in the air from the initial model of the longitudinally and transversely stiffened conical shell structure. 0 Stiffness matrix K 0 , mode array Φ 0 ; and according to the mass matrix M 0 Stiffness matrix K 0 , mode array Φ 0 Calculate the equivalent modal masses of the first node A and the second node B in air for modes N1 and N2 of the initial model of the longitudinally and transversely stiffened conical shell structure. With equivalent modal stiffness

[0021] S1.6 Complete the modal analysis of the optimized model of the longitudinally and transversely stiffened conical shell structure, and the frequency response analysis of the structure vibration in air;

[0022] S1.7 Extract the mass matrix M, stiffness matrix K, and mode shape matrix Φ of the optimized model of the longitudinally and transversely stiffened conical shell structure in air; and calculate the equivalent modal mass M of the first node A and the second node B of the optimized model of the longitudinally and transversely stiffened conical shell structure in air for modes N1 and N2 based on the mass matrix M, stiffness matrix K, and mode shape matrix Φ. 11 M 21 M 12 M 22 With equivalent modal stiffness K 11 K 21 K 12 K 22 ;

[0023] S1.8, the optimized model of the longitudinally and transversely reinforced conical shell structure has an underwater natural circular frequency of ω. i for:

[0024]

[0025]

[0026] Where the subscript i represents the corresponding modal order, j represents the corresponding node, and l i This represents the ratio of the underwater equivalent modal mass to the air equivalent modal mass. The initial underwater natural circular frequency of the model calculated using the boundary element method. and These are the equivalent modal mass and equivalent modal stiffness of the first node A and the second node B of the initial model in air for modes N1 and N2, respectively.

[0027] In the above scheme, in S1.5, the equivalent modal mass at the j-th node in the i-th mode is... and equivalent modal stiffness The solution formula is:

[0028]

[0029]

[0030] in, These are the normalized mode matrix vectors of the initial model; i = 1, 2; j = 1, 2.

[0031] In the above scheme, in S1.7, the equivalent modal mass M at the j-th node in the i-th mode is... ji and equivalent modal stiffness K ji The solution formula is:

[0032] M ji ={X ji} T M{X ji}

[0033] K ji ={X ji} T K{X ji}

[0034] Among them, {X ji} represents the normalized mode matrix vector of the optimized model; i = 1, 2; j = 1, 2.

[0035] In the above scheme, step S2 specifically includes the following steps:

[0036] S2.1. Using a systematic identification method, identify the state-space equation G between the load input F at the first node and the air velocity response at the first node A and the second node B of the optimized finite element model of the longitudinally and transversely stiffened conical shell structure:

[0037]

[0038] Where A, B, C, and D are the system matrix, input matrix, output matrix, and direct transfer matrix of the state-space equation G, respectively; and x, u, and y are the state vector, control vector, and output vector of the state-space equation G, respectively.

[0039] The frequency domain response of the state-space model must match the actual model by more than 90%.

[0040] Decompose the system matrix A:

[0041] A = VΛV -1

[0042] In the formula, V is the eigenvector of system matrix A, and Λ is the eigenvalue matrix of system matrix A;

[0043] S2.2. Using the calculated underwater natural circular frequencies of the optimized model of the longitudinally and transversely stiffened conical shell structure, the state-space equations between the load input F at the first node and the underwater velocity responses at the first node A and the second node B are constructed using the perturbation model construction method.

[0044]

[0045] in: For the perturbation state-space model of G; State-space equations The state vector, control vector, and output vector; The perturbated system matrix can be expressed as: Λ+ΔΛ is the perturbation eigenvalue matrix of system matrix A; The corrected output matrix is ​​obtained by correcting the elements of the output matrix C corresponding to modes n1 and n2 based on the amplitude difference of the velocity frequency response in air and underwater in the initial model.

[0046] In the above scheme, step S3 specifically includes the following steps:

[0047] S3.1. Using the system identification method, the state-space model W between the underwater velocity response and radiated acoustic power of the first node A and the second node B can be identified as follows:

[0048]

[0049] Among them, A w B w C w D w These are the system matrix, input matrix, output matrix, and direct transfer matrix of the state-space model W, respectively; x w u w y w These are the state vector, control vector, and output vector of the state-space model W, respectively.

[0050] The state-space model is a two-input single-output system. The underwater velocity responses of the first and second nodes are used as model inputs, and the radiated acoustic power of the longitudinally and transversely stiffened conical shell structure is used as model output. The frequency domain response of the state-space model must match the actual model by more than 90%.

[0051] S3.2, Regarding the system matrix A w Decompose it.

[0052]

[0053] In the formula, V w For system matrix A w eigenvectors, Λ w For system matrix A w The eigenvalue matrix of W; construct the perturbation state-space model of W.

[0054]

[0055] in, State-space model The state vector, control vector, and output vector; The perturbated system matrix can be expressed as: Λ w +ΔΛ w For the system matrix The perturbation eigenvalue matrix.

[0056] In the above scheme, the specific steps of S4 are as follows:

[0057] The transfer function expression for the load input F and underwater radiated acoustic power at the first node of the optimized model of the longitudinally and transversely stiffened conical shell structure is as follows: The amplitude-frequency characteristic is the frequency response function between the load input F at the first node and the underwater radiated acoustic power.

[0058] The beneficial effects of this invention are as follows:

[0059] 1. This invention utilizes system identification, perturbation model construction, and model correction methods to rapidly estimate the underwater vibration response of a longitudinally and transversely stiffened conical shell structure by analyzing its air vibration response, thus solving the problem of low efficiency in underwater vibration response calculation. Furthermore, by employing system identification and perturbation model construction methods, it rapidly estimates the underwater acoustic radiation of the structure by analyzing its underwater vibration response, solving the problem of low efficiency in underwater acoustic radiation calculation. In other words, this invention's efficient estimation method only requires one underwater acoustic-vibration coupling calculation to indirectly evaluate underwater acoustic radiation through the frequency domain response of the longitudinally and transversely stiffened conical shell structure in the air, solving the problem of repeatedly performing underwater acoustic-vibration coupling calculations in optimization algorithms and improving the computational efficiency of the optimized design of longitudinally and transversely stiffened conical shell structures.

[0060] 2. The efficient estimation method of the present invention is applicable to the tail structure optimization design of underwater structures. Attached Figure Description

[0061] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0062] Figure 1 This is a schematic diagram of a longitudinally and transversely reinforced conical shell structure;

[0063] Figure 2 This is a comparison diagram of the efficient estimation algorithm and the boundary element algorithm in the embodiments of the present invention. Detailed Implementation

[0064] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0065] This invention provides an efficient method for estimating underwater acoustic radiation of a longitudinally and transversely reinforced conical shell structure, comprising the following steps:

[0066] S1. Calculate the underwater natural circular frequencies of the optimized model of the longitudinally and transversely stiffened conical shell structure:

[0067] The first two modes, which contribute the most to the underwater acoustic radiation of the longitudinally and transversely stiffened conical shell structure, are defined as the first and second target optimization modes, respectively. The shell nodes corresponding to the tail end and midpoint of the longitudinally and transversely stiffened conical shell structure axis are defined as typical nodes characterizing the vibration response of the longitudinally and transversely stiffened conical shell structure, respectively, and are defined as the first node and the second node. The underwater natural circular frequency of the optimized model of the longitudinally and transversely stiffened conical shell structure is calculated by using the equivalent modal mass and equivalent modal stiffness of the first and second nodes of the initial model of the longitudinally and transversely stiffened conical shell structure in air, the underwater natural circular frequency of the initial model of the longitudinally and transversely stiffened conical shell structure, and the equivalent modal mass and equivalent modal stiffness of the first and second nodes of the optimized model of the longitudinally and transversely stiffened conical shell structure in air.

[0068] S1 specifically includes the following steps:

[0069] S1.1 Complete the modal analysis of the initial model of the longitudinally and transversely stiffened conical shell structure in air and underwater, the structural vibration frequency response analysis in air, and the acoustic-vibration coupling response analysis underwater;

[0070] S1.2. Based on the underwater modal results and underwater acoustic radiation of the initial model of the longitudinally and transversely stiffened conical shell structure, the first two modes that contribute the most to the underwater acoustic radiation of the longitudinally and transversely stiffened conical shell structure are identified. The first two modes that contribute the most to the underwater acoustic radiation of the longitudinally and transversely stiffened conical shell structure are taken as the target optimization modes, and are defined as the first target optimization mode n1 and the second target optimization mode n2, respectively. The analysis frequency band is 10Hz to 100Hz, and the step size is 1Hz.

[0071] S1.3 Identify the air modes N1 and N2 that are the same as the underwater modes n1 and n2 of the initial model of the longitudinally and transversely stiffened conical shell structure;

[0072] S1.4. The nodes on the shell corresponding to the tail end point and midpoint of the longitudinal and transverse stiffened conical shell structure are used as typical nodes to characterize the vibration response of the longitudinal and transverse stiffened conical shell structure. They are defined as the first node and the second node, respectively. The node numbers of the first node A and the second node B are extracted respectively.

[0073] S1.5 Extracting the mass matrix M in the air from the initial model of the longitudinally and transversely stiffened conical shell structure. 0 Stiffness matrix K 0 , mode array Φ 0 ; and according to the mass matrix M 0 Stiffness matrix K 0 , mode array Φ 0 Calculate the equivalent modal masses of the first node A and the second node B in air for modes N1 and N2 of the initial model of the longitudinally and transversely stiffened conical shell structure. With equivalent modal stiffness Equivalent modal mass at node j in the i-th mode and equivalent modal stiffness The solution formula is:

[0074]

[0075]

[0076] in, These are the normalized mode matrix vectors of the initial model; i = 1, 2; j = 1, 2;

[0077] S1.6 Complete the modal analysis and air vibration frequency response analysis of the optimized model of the longitudinally and transversely stiffened conical shell structure; the optimized model is the model generated after iterative optimization of the initial model. S1.7 Extract the mass matrix M, stiffness matrix K, and mode shape matrix Φ of the optimized model of the longitudinally and transversely stiffened conical shell structure in air; and calculate the equivalent modal mass M of the first node A and the second node B of the optimized model of the longitudinally and transversely stiffened conical shell structure in air for modes N1 and N2 based on the mass matrix M, stiffness matrix K, and mode shape matrix Φ. 11 M 21 M 12 M 22 With equivalent modal stiffness K 11 K 21 K 12 K 22 The equivalent modal mass M at the j-th node in the i-th mode. ji and equivalent modal stiffness K ji The solution formula is:

[0078] M ji ={X ji} T M{X ji}

[0079] K ji ={X ji} T K{X ji}

[0080] Among them, {X ji} represents the normalized mode shape matrix vector of the optimized model; i = 1, 2; j = 1, 2;

[0081] S1.8, the optimized model of the longitudinally and transversely reinforced conical shell structure has an underwater natural circular frequency of ω. i for:

[0082]

[0083]

[0084] Where the subscript i represents the corresponding modal order, j represents the corresponding node, and l i This represents the ratio of the underwater equivalent modal mass to the air equivalent modal mass. The initial underwater natural circular frequency of the model calculated using the boundary element method. and These are the equivalent modal mass and equivalent modal stiffness of the first node A and the second node B of the initial model in air for modes N1 and N2, respectively.

[0085] S2. Establish the relationship between the air velocity response and underwater velocity response of a longitudinally and transversely stiffened conical shell structure:

[0086] A systematic identification method was used to identify the state-space equation G between the load input at the first node and the air velocity responses at the first and second nodes of the finite element model of the longitudinally and transversely stiffened conical shell structure under optimization. Using the calculated underwater natural circular frequencies of the longitudinally and transversely stiffened conical shell structure under optimization, a perturbation model construction method was employed to construct the state-space equation G between the load input at the first node and the underwater velocity responses at the first and second nodes of the finite element model of the longitudinally and transversely stiffened conical shell structure under optimization.

[0087] S2 specifically includes the following steps:

[0088] S2.1. Using a systematic identification method, identify the state-space equation G between the load input F at the first node and the air velocity response at the first node A and the second node B of the optimized finite element model of the longitudinally and transversely stiffened conical shell structure:

[0089]

[0090] Where A, B, C, and D are the system matrix, input matrix, output matrix, and direct transfer matrix of the state-space equation G, respectively; and x, u, and y are the state vector, control vector, and output vector of the state-space equation G, respectively.

[0091] The frequency domain response of the state-space model must match the actual model by more than 90%.

[0092] Decompose the system matrix A:

[0093] A = VΛV -1

[0094] In the formula, V is the eigenvector of the system matrix A, and Λ is the eigenvalue matrix of the system matrix A.

[0095] S2.2. Using the calculated underwater natural circular frequencies of the optimized model of the longitudinally and transversely stiffened conical shell structure, the state-space equations between the load input F at the first node and the underwater velocity responses at the first node A and the second node B are constructed using the perturbation model construction method.

[0096]

[0097] in: For the perturbation state-space model of G; State-space equations The state vector, control vector, and output vector; The perturbated system matrix can be expressed as: Λ+ΔΛ is the perturbation eigenvalue matrix of system matrix A; The corrected output matrix is ​​obtained by correcting the elements of the output matrix C corresponding to modes n1 and n2 based on the amplitude difference of the velocity frequency response in air and underwater in the initial model.

[0098] S3. Establish the relationship between underwater velocity response and acoustic radiation:

[0099] A system identification method is used to identify the state-space model W between the underwater velocity response and acoustic radiation power of the first and second nodes. This state-space model is a two-input, single-output system, with the underwater velocity responses of the first and second nodes serving as model inputs and the radiated acoustic power of the longitudinally and transversely stiffened conical shell structure serving as model output. A perturbation model construction method is then used to construct the perturbation state-space model of W.

[0100] The specific steps for S3 are as follows:

[0101] S3.1. Using the system identification method, the state-space model W between the underwater velocity response and radiated acoustic power of the first node A and the second node B can be identified as follows:

[0102]

[0103] Among them, A w B w C w D w These are the system matrix, input matrix, output matrix, and direct transfer matrix of the state-space model W, respectively; x w u w y w These are the state vector, control vector, and output vector of the state-space model W, respectively.

[0104] The state-space model is a two-input single-output system. The underwater velocity responses of the first and second nodes are used as model inputs, and the radiated acoustic power of the longitudinally and transversely stiffened conical shell structure is used as model output. The frequency domain response of the state-space model must match the actual model by more than 90%.

[0105] S3.2, Regarding the system matrix A w Decompose it.

[0106]

[0107] In the formula, V w For system matrix A w eigenvectors, Λ w For system matrix A w eigenvalue matrix.

[0108] Construct a perturbation state-space model of W

[0109]

[0110] in, State-space model The state vector, control vector, and output vector; The perturbated system matrix can be expressed as: Λ w +ΔΛ w For the system matrix The perturbation eigenvalue matrix.

[0111] S4. Estimate the underwater acoustic radiation of a longitudinally and transversely reinforced conical shell structure:

[0112] The transfer function expression for the load input and underwater radiated acoustic power at the first node of the optimized finite element model of the longitudinally and transversely stiffened conical shell structure is as follows: The amplitude-frequency characteristic is the frequency response function between the load input at the first node and the underwater radiated acoustic power.

[0113] The specific steps for S4 are as follows:

[0114] The transfer function expression for the load input F and underwater radiated acoustic power at the first node of the optimized model of the longitudinally and transversely stiffened conical shell structure is as follows: The amplitude-frequency characteristic is the frequency response function between the load input F at the first node and the underwater radiated acoustic power.

[0115] by Figure 2Taking the example shown, the length is 7m, the diameter at the large end is 5m, the diameter at the small end is 0.8m, the material is steel, the weight is about 7.3 tons, and there are 8 longitudinal ribs and 13 ring ribs; the boundary element mesh is about 6500, and the CPU is an Intel 8-core E5-1630 v4. The calculation time was reduced from 25 minutes to 6 minutes; the radiated sound power amplitude is basically the same, the frequency error is about 1Hz, and the calculation accuracy basically meets the requirements of optimization design.

[0116] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A highly efficient method for estimating underwater acoustic radiation of a longitudinally and transversely reinforced conical shell structure, characterized in that, Includes the following steps: S1. Calculate the underwater natural circular frequencies of the optimized model of the longitudinally and transversely stiffened conical shell structure: The first two modes that contribute the most to the underwater acoustic radiation of the longitudinally and transversely stiffened conical shell structure are taken as the target optimization modes, and are defined as the first target optimization mode and the second target optimization mode, respectively. The nodes on the shell corresponding to the tail end and midpoint of the axis of the longitudinally and transversely stiffened conical shell structure are used as typical nodes to characterize the vibration response of the longitudinally and transversely stiffened conical shell structure, and are defined as the first node and the second node, respectively. The underwater natural circular frequencies of the optimized model of the longitudinally and transversely stiffened conical shell structure are calculated by using the equivalent modal mass and equivalent modal stiffness of the first and second nodes in the first and second target optimization modes in air, the underwater natural circular frequencies of the initial model of the longitudinally and transversely stiffened conical shell structure, and the equivalent modal mass and equivalent modal stiffness of the first and second nodes in the first and second target optimization modes in air of the optimized model of the longitudinally and transversely stiffened conical shell structure. S2. Establish the relationship between the air velocity response and underwater velocity response of a longitudinally and transversely stiffened conical shell structure: The system identification method is used to identify the state-space equation G between the load input at the first node and the air velocity response at the first and second nodes of the optimized model of the longitudinally and transversely stiffened conical shell structure. Using the calculated underwater natural circular frequencies of the optimized model of the longitudinally and transversely stiffened conical shell structure, a perturbation model construction method is employed to construct the state-space equations between the load input at the first node and the underwater velocity responses at the first and second nodes of the optimized finite element model of the longitudinally and transversely stiffened conical shell structure. ; S3. Establish the relationship between underwater velocity response and acoustic radiation: A system identification method is used to identify the state-space model W between the underwater velocity response and acoustic radiation power of the first and second nodes. This state-space model is a two-input, single-output system, with the underwater velocity responses of the first and second nodes serving as model inputs and the acoustic radiation power of the longitudinally and transversely stiffened conical shell structure serving as model output. A perturbation model construction method is then used to construct the perturbation state-space model of W. ; S4. Estimate the underwater acoustic radiation of a longitudinally and transversely reinforced conical shell structure: The transfer function expression for the load input and underwater acoustic radiation power at the first node of the optimized model of the longitudinally and transversely stiffened conical shell structure is as follows: ; The amplitude-frequency characteristic is the frequency response function between the load input at the first node and the underwater acoustic radiation power.

2. The efficient estimation method for underwater acoustic radiation of a longitudinally and transversely reinforced conical shell structure according to claim 1, characterized in that, Step S1 specifically includes the following steps: S1.1 Complete the modal analysis of the initial model of the longitudinally and transversely stiffened conical shell structure in air and underwater, the structural vibration frequency response analysis in air, and the acoustic-vibration coupling response analysis underwater; S1.

2. Based on the underwater modal results and underwater acoustic radiation of the initial model of the longitudinally and transversely stiffened conical shell structure, the two modes that contribute the most to the underwater acoustic radiation of the longitudinally and transversely stiffened conical shell structure are identified. These two modes are then defined as the first target optimization modes. n 1 and second objective optimization modes n 2. The analysis frequency band is 10Hz~100Hz, with a step size of 1Hz; S1.3 Identify the underwater modes of the initial model of the longitudinally and transversely reinforced conical shell structure. n 1. n 2 air modes with the same vibration mode N 1. N 2; S1.

4. The nodes on the shell corresponding to the tail end point and midpoint of the longitudinal and transverse stiffened conical shell structure are used as typical nodes to characterize the vibration response of the longitudinal and transverse stiffened conical shell structure. They are defined as the first node and the second node, respectively, and the node numbers of the first node and the second node are extracted. S1.5 Extracting the mass matrix M in the air from the initial model of the longitudinally and transversely stiffened conical shell structure. 0 Stiffness matrix K 0 , mode array Φ 0 ; and according to the mass matrix M 0 Stiffness matrix K 0 , mode array Φ 0 Calculate the air modes of the first and second nodes of the initial model of the longitudinally and transversely stiffened conical shell structure. N 1. N Equivalent modal mass of 2 , , , With equivalent modal stiffness , , , ; S1.6 Complete the modal analysis of the optimized model of the longitudinally and transversely stiffened conical shell structure, and the frequency response analysis of the structure vibration in air; S1.7 Extract the mass matrix M, stiffness matrix K, and mode shape matrix Φ of the optimized model of the longitudinally and transversely stiffened conical shell structure in air; and calculate the air modes of the first and second nodes of the optimized model of the longitudinally and transversely stiffened conical shell structure based on the mass matrix M, stiffness matrix K, and mode shape matrix Φ. N 1. N Equivalent modal mass of 2 , , , With equivalent modal stiffness , , , ; S1.8, the optimized model of the longitudinally and transversely reinforced conical shell structure has the following underwater natural circular frequency: ω i for: Among them, subscript i For the corresponding modal order, j For the corresponding node, This represents the ratio of the underwater equivalent modal mass to the air equivalent modal mass. The initial underwater natural circular frequency of the model calculated using the boundary element method. and These are the air modes of the first and second nodes of the initial model, respectively. N 1. N The equivalent modal mass and equivalent modal stiffness of 2.

3. The efficient estimation method for underwater acoustic radiation of a longitudinally and transversely reinforced conical shell structure according to claim 2, characterized in that, In S1.5, the first i The first mode j Equivalent modal mass at the node and equivalent modal stiffness The solution formula is: in,{ } represents the normalized mode shape matrix vectors of the initial model; i =1,2; j =1,2.

4. The efficient estimation method for underwater acoustic radiation of a longitudinally and transversely reinforced conical shell structure according to claim 3, characterized in that, In S1.7, the first i The first mode j Equivalent modal mass at the node and equivalent modal stiffness The solution formula is: in,{ X ji } represents the normalized mode shape matrix vector of the optimized model; i =1,2; j =1,2.

5. The efficient method for estimating underwater acoustic radiation of a longitudinally and transversely reinforced conical shell structure according to claim 2, characterized in that, Step S2 specifically includes the following steps: S2.

1. Using a systematic identification method, identify the load input at the first node of the finite element model of the longitudinally and transversely stiffened conical shell structure to be optimized. F The state-space equation G between the velocity responses in the air at the first and second nodes is: in, A , B , C , D These are the system matrix, input matrix, output matrix, and direct transfer matrix of the state-space equation G, respectively. x , u , y These are the state vector, control vector, and output vector of the state-space equation G, respectively. The state-space equation must have a greater than 90% agreement with the frequency domain response of the actual model; For system matrix A Decompose: In the formula, V For the system matrix A eigenvectors, Λ For the system matrix A eigenvalue matrix; S2.

2. Using the calculated underwater natural circular frequencies of the longitudinally and transversely stiffened conical shell structure, the finite element model of the optimized model of the longitudinally and transversely stiffened conical shell structure is constructed using the perturbation model construction method. Load input at the first node. F State-space equations between the first node and the underwater velocity response of the second node : in: For the perturbation state-space model of G; , , State-space equations The state vector, control vector, and output vector; The perturbated system matrix is ​​represented as follows: , For the system matrix The perturbation eigenvalue matrix; The corrected output matrix is ​​obtained by adjusting the modal frequency response based on the amplitude difference between the initial model's velocity frequency response in air and underwater. n 1. n 2 corresponding output matrix C The elements are modified.

6. The efficient estimation method for underwater acoustic radiation of a longitudinally and transversely reinforced conical shell structure according to claim 1, characterized in that, Step S3 specifically includes the following steps: S3.

1. Using the system identification method, identify the state-space model W between the underwater velocity response and acoustic radiation power of the first and second nodes, expressed as: in, A w , B w , C w , D w These are the system matrix, input matrix, output matrix, and direct transfer matrix of the state-space model W, respectively. x w , u w , y w These are the state vector, control vector, and output vector of the state-space model W, respectively. The state-space model is a two-input single-output system. The underwater velocity responses of the first and second nodes are used as model inputs, and the acoustic radiation power of the longitudinally and transversely stiffened conical shell structure is used as model output. The frequency domain response of this state-space model must have a greater than 90% agreement with the actual model. S3.2, System Matrix A w Decompose it. In the formula, V w For the system matrix A w eigenvectors, Λ w For the system matrix A w eigenvalue matrix; Construct a perturbation state-space model of W : in, , , State-space model The state vector, control vector, and output vector; The perturbated system matrix is ​​represented as follows: , For the system matrix The perturbation eigenvalue matrix.

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