Method for optimally arranging inverse finite element measuring points of unreinforced hull plate based on greedy algorithm

Abstract

The invention provides a greedy algorithm-based unreinforced hull plate inverse finite element measuring point optimal arrangement method, and belongs to the field of ship structure health monitoring. The problem that it is difficult to reduce the number of arranged measuring points under the condition that the required reconstruction precision is kept is solved. The method comprises the steps that discretization processing is conducted on an unreinforced hull plate, and the unreinforced hull plate is divided into four-node units meeting preset conditions; generating a primarily selected measuring point scheme, namely arranging measuring points along the diagonal direction of a ship body plate, and performing array copying and segmented movement to obtain a plurality of initial measuring point arrangement schemes; and inputting the primarily selected measuring point scheme into a greedy algorithm, performing cyclic displacement reconstruction and node error calculation in combination with an inverse finite element method, iteratively removing the measuring point which has the minimum influence on the reconstruction error until all unit errors meet a preset precision threshold value, and outputting an optimized arrangement scheme which has the minimum number of measuring points and meets the precision requirement. The method is mainly used for hull structure safety assessment in the whole life cycle.

Description

Technical Field

[0001] The present invention belongs to the field of ship structural health monitoring, and particularly relates to a method for optimizing the layout of inverse finite element measurement points of a non-reinforced hull plate based on a greedy algorithm. Background Technique

[0002] When a ship sails in the sea, the safety of the hull structure is affected by various factors, including load changes, environmental erosion, material aging, etc. These factors may all lead to a decline in structural performance. Conducting real-time monitoring and regular evaluation of the hull structural health status during the ship's service life to achieve the safety assessment of the hull structure throughout the life cycle plays an indispensable role in discovering potential risk points, implementing effective maintenance strategies, and extending the ship's life. It covers the real-time monitoring of hull plates and typical stiffeners. Currently, the engineering field mainly adopts contact measurement methods to obtain local strain information by arranging strain sensors. However, this method has problems such as a limited number of measurement points and restricted arrangement positions, making it difficult to comprehensively grasp the overall response of the hull plate structure.

[0003] In structural health monitoring, the inverse finite element method, as a structural deformation reconstruction method based on the strain-displacement relationship, can use the data of finite measurement points to invert the stress and displacement information of other unknown points, and it is an effective structural response inversion technology. However, the reconstruction accuracy of the inverse finite element method is positively correlated with the number and density of measurement point arrangements. However, too many measurement points will lead to problems such as an explosion of data volume, increased costs, and difficult arrangement. How to reduce the number of measurement point arrangements while maintaining the required reconstruction accuracy is a hot research direction. Summary of the Invention

[0004] In view of this, the present invention aims to propose a method for optimizing the layout of inverse finite element measurement points of a non-reinforced hull plate based on a greedy algorithm to solve the problem of difficultly reducing the number of measurement point arrangements while maintaining the required reconstruction accuracy.

[0005] To achieve the above object, the present invention adopts the following technical solutions: A method for optimizing the layout of inverse finite element measurement points of a non-reinforced hull plate based on a greedy algorithm, the method comprising:

[0006] Step S1: Discretize the non-reinforced hull plate, and divide the non-reinforced hull plate into four-node elements that meet preset conditions;

[0007] Step S2: Generate a preliminary measurement point scheme, including arranging measurement points along the diagonal direction of the hull plate, and performing array replication and segmented movement to obtain a variety of initial measurement point arrangement schemes;

[0008] Step S3: Input the preliminary selected measuring point scheme into the greedy algorithm, and combine the inverse finite element method to perform cyclic displacement reconstruction and node error calculation. Iteratively remove the measuring points with the least influence on the reconstruction error until the errors of all elements meet the preset accuracy threshold, and output the optimized layout scheme with the least number of measuring points and meeting the accuracy requirements.

[0009] Further, an optimization method is also proposed. The preset condition in step S1 is:

[0010] When the aspect ratio is not 1, the long side is divided into a units, and the short side is divided into b units, where both a and b are even numbers;

[0011] When the aspect ratio is 1, each side is divided into c units, where c is an even number.

[0012] Further, an optimization method is also proposed. The generation of the preliminary selected measuring point scheme in step S2 specifically includes:

[0013] Step S21: Continuously arrange b / 2 measuring points along the 45° direction from the upper left corner to the lower right corner of the hull plate, and then continuously arrange b / 2 measuring points along the 45° direction from the lower left corner until the short side is covered;

[0014] Step S22: Copy the measuring points in step S21 to the right in an array, with an interval of b / 2 - 1 units, until it exceeds the boundary of the hull plate;

[0015] Step S23: Divide the measuring points into upper and lower parts by the midpoint connection line of the short side, and move the upper and lower parts of the measuring points respectively to generate b variant schemes;

[0016] Step S24: Combine all the schemes to obtain the set of preliminary selected measuring point schemes.

[0017] Further, an optimization method is also proposed. The node error calculation in step S3 includes:

[0018]

[0019] where, δ node is the node displacement reconstruction error, and δ element is the element error.

[0020] Further, an optimization method is also proposed. The cyclic displacement reconstruction by the inverse finite element method in step S3 includes:

[0021] S31: Through the strain rosettes arranged at the center positions of the monitoring area units on the upper and lower surfaces of the to-be-measured unstiffened plate, obtain the axial strain and tangential strain of the upper and lower surfaces and the middle surface at the measuring point positions;

[0022] S32: Construct a least - squares function of the error between the theoretical and measured strains of the element where the measurement point is located based on the obtained mid - surface strain and the relationship between the element strain and the mid - surface strain;

[0023] S33: Take the extreme value of the least - squares function to obtain the element pseudo - stiffness matrix and the element pseudo - load matrix of the element where the measurement point is located;

[0024] S34: Assemble the global pseudo - stiffness matrix and the global pseudo - load matrix of the structure to obtain the structure reconstruction displacement field;

[0025] S35: Use the finite - element technology to perform finite - element analysis on the structure to obtain the actual displacement field of the structure, and calculate the displacement reconstruction error of each node of the inverse finite - element model after reconstruction.

[0026] Furthermore, a preferred method is also proposed. The step S31 includes:

[0027]

[0028] where e ε is the measured plane strain, k ε is the measured bending strain. The variable with a superscript + is the measurement value on the upper surface of the element, and the variable with a superscript - is the measurement value on the lower surface of the element. ε xx is the strain in the x - direction, ε yy is the strain in the y - direction, ε xy is the tangential strain in the xy plane, and h is the distance from the mid - surface of the element to the surface of the element.

[0029] Furthermore, a preferred method is also proposed. The least - squares function of the error between the theoretical and measured strains of the element where the measurement point is located in the step S32 is:

[0030] Φ e (u e ) = w e ||e(u e ) - e ε || 2 + w k ||k(u e ) - k ε || 2 + w g ||g(u e ) - g ε || 2

[0031] where w e 、w k and w g are weighting constants, e(u e ) is the theoretical plane strain, k(u e ) is the theoretical bending strain, g(ue ) is the theoretical shear strain, γ ε is the measured shear strain.

[0032] Further, a preferred method is also proposed. The assembly of the overall pseudo stiffness matrix and the overall pseudo load matrix in step S34 includes:

[0033] KU = F

[0034] where K is the overall pseudo stiffness matrix, F is the overall pseudo load matrix, and U is the overall displacement field after reconstruction.

[0035] Based on the same inventive concept, the present invention also provides a computer device, including a memory and a processor. A computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes a method for optimizing the layout of inverse finite element measurement points of a non - stiffened hull plate based on a greedy algorithm as described in any one of the above.

[0036] Based on the same inventive concept, the present invention also provides a computer - readable storage medium. A computer program is stored on the computer - readable storage medium. When the computer program is run by a processor, it executes the steps of a method for optimizing the layout of inverse finite element measurement points of a non - stiffened hull plate based on a greedy algorithm as described in any one of the above.

[0037] Compared with the prior art, the beneficial effects of the present invention are:

[0038] 1. The method for optimizing the layout of inverse finite element measurement points of a non - stiffened hull plate proposed by the present invention overcomes the problem that the existing inverse finite element method requires a dense arrangement of measurement points on the surface of the hull plate, resulting in a large number of sensors, high hardware costs, and complex installation. Through the iterative optimization of the greedy algorithm, redundant measurement points with the least impact on the reconstruction error are dynamically removed from the initial measurement point scheme. Finally, only about 20% - 25% of the measurement points need to be retained (for example, only 80 measurement points are required after optimization in the embodiment), which can meet the displacement reconstruction accuracy requirements, and the average node error ≤ 5%.

[0039] 2. The method for optimizing the layout of inverse finite element measurement points of a non - stiffened hull plate proposed by the present invention also overcomes the problem that the computational complexity of the inverse finite element method increases exponentially with the number of measurement points, and the dense measurement points lead to an explosion of data volume, making it difficult to meet the real - time monitoring requirements. By generating rules for the initial measurement point scheme (such as diagonal arrangement, array replication, and segmented movement), the initial measurement point distribution is ensured to cover key strain gradient regions (such as the plate edge and the center), reducing redundant data acquisition. The reduction in the number of measurement points after optimization significantly reduces the dimension of the overall pseudo stiffness matrix, and the computational time for solving the reconstructed displacement field is reduced by about 80%, meeting the real - time inversion requirements.

[0040] 3. The inverse finite element measurement point optimization layout method for unstiffened hull plates proposed by the present invention ensures that the mesh morphology matches the actual deformation mode of the hull plate through the element division rule, avoiding the accumulation of reconstruction errors caused by element distortion. By translating the measurement points in the upper and lower parts in sections, multiple candidate schemes are generated to cover the strain-sensitive areas under different aspect ratios, improving the robustness of the algorithm.

[0041] 4. The inverse finite element measurement point optimization layout method for unstiffened hull plates proposed by the present invention provides a clear logic for generating the coordinates of the measurement points based on the layout rules of the diagonal line and array replication, reducing the need for manual intervention. By calculating the node error and element error, the optimal measurement point combination is iteratively selected to avoid manual trial and error and shorten the scheme design cycle (for example, the optimization time in the embodiment is < 10 minutes). BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings:

[0043] Figure 1 is a flowchart of an inverse finite element measurement point optimization layout method for unstiffened hull plates based on the greedy algorithm according to the present invention;

[0044] Figure 2 is a flowchart of the greedy algorithm according to the present invention;

[0045] Figure 3 is a flowchart of the inverse finite element displacement reconstruction of unstiffened hull plates according to the present invention;

[0046] Figure 4 is a schematic diagram of the first primary measurement point layout scheme of an unstiffened hull plate with 10 units divided on the short side and 38 units divided on the long side according to the present invention;

[0047] Figure 5 is a schematic diagram of the second primary measurement point layout scheme of an unstiffened hull plate with 10 units divided on the short side and 38 units divided on the long side according to the present invention;

[0048] Figure 6 is a schematic diagram of the third primary measurement point layout scheme of an unstiffened hull plate with 10 units divided on the short side and 38 units divided on the long side according to the present invention;

[0049] Figure 7 is a schematic diagram of the fourth primary measurement point layout scheme of an unstiffened hull plate with 10 units divided on the short side and 38 units divided on the long side according to the present invention;

[0050] Figure 8Schematic diagram of the fifth preliminary measuring point layout plan for the unstiffened hull plate with 10 units divided on the short side and 38 units divided on the long side according to the present invention;

[0051] Figure 9 Schematic diagram of the sixth preliminary measuring point layout plan for the unstiffened hull plate with 10 units divided on the short side and 38 units divided on the long side according to the present invention;

[0052] Figure 10 Schematic diagram of the seventh preliminary measuring point layout plan for the unstiffened hull plate with 10 units divided on the short side and 38 units divided on the long side according to the present invention;

[0053] Figure 11 Schematic diagram of the eighth preliminary measuring point layout plan for the unstiffened hull plate with 10 units divided on the short side and 38 units divided on the long side according to the present invention;

[0054] Figure 12 Schematic diagram of the ninth preliminary measuring point layout plan for the unstiffened hull plate with 10 units divided on the short side and 38 units divided on the long side according to the present invention;

[0055] Figure 13 Schematic diagram of the first preliminary measuring point layout plan for the unstiffened hull plate with 10 units divided on the short side and 40 units divided on the long side according to the present invention;

[0056] Figure 14 Schematic diagram of the second preliminary measuring point layout plan for the unstiffened hull plate with 10 units divided on the short side and 40 units divided on the long side according to the present invention;

[0057] Figure 15 Schematic diagram of the second preliminary measuring point layout plan for the unstiffened hull plate with 10 units divided on the short side and 40 units divided on the long side according to the present invention;

[0058] Figure 16 Schematic diagram of the fourth preliminary measuring point layout plan for the unstiffened hull plate with 10 units divided on the short side and 40 units divided on the long side according to the present invention;

[0059] Figure 17 Schematic diagram of the fifth preliminary measuring point layout plan for the unstiffened hull plate with 10 units divided on the short side and 40 units divided on the long side according to the present invention;

[0060] Figure 18 Schematic diagram of the sixth preliminary measuring point layout plan for the unstiffened hull plate with 10 units divided on the short side and 40 units divided on the long side according to the present invention;

[0061] Figure 19Schematic diagram of the seventh primary measurement point layout scheme for a non-reinforced hull plate with 10 units divided along the short side and 40 units divided along the long side according to the present invention;

[0062] Figure 20 Schematic diagram of the eighth primary measurement point layout scheme for a non-reinforced hull plate with 10 units divided along the short side and 40 units divided along the long side according to the present invention;

[0063] Figure 21 Schematic diagram of the ninth primary measurement point layout scheme for a non-reinforced hull plate with 10 units divided along the short side and 40 units divided along the long side according to the present invention;

[0064] Figure 22 Schematic diagram of the measurement point layout scheme that meets the accuracy requirements with the minimum number of measurement points after the primary selection scheme according to the present invention is optimized by the greedy algorithm;

[0065] Figure 23 Inverse finite element displacement reconstruction nephogram when measurement points are arranged for all units according to the present invention;

[0066] Figure 24 Inverse finite element displacement reconstruction nephogram of the measurement point layout scheme that meets the accuracy requirements with the minimum number of measurement points after the primary selection scheme according to the present invention is optimized by the greedy algorithm. Detailed implementation manners

[0067] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. It should be noted that, without conflict, the embodiments and features in the embodiments of the present invention can be combined with each other. The described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments.

[0068] Embodiment 1. Refer to Figure 1 to illustrate this embodiment. A method for optimizing the layout of inverse finite element measurement points for a non-reinforced hull plate based on the greedy algorithm according to this embodiment includes:

[0069] Step S1: Discretize the non-reinforced hull plate, and divide the non-reinforced hull plate into four-node units that meet preset conditions;

[0070] Step S2: Generate a primary selection measurement point scheme, including arranging measurement points along the diagonal direction of the hull plate, and performing array replication and segmented movement to obtain multiple initial measurement point layout schemes;

[0071] Step S3: Input the primary selection measurement point scheme into the greedy algorithm, and combine the inverse finite element method to perform cyclic displacement reconstruction and node error calculation, and iteratively remove the measurement points that have the least influence on the reconstruction error until the errors of all units meet the preset accuracy threshold, and output the optimized layout scheme with the least number of measurement points and meeting the accuracy requirements.

[0072] The optimized layout method of inverse finite element measurement points for unstiffened hull plates proposed in this embodiment overcomes the problem that the existing inverse finite element method requires dense arrangement of measurement points on the hull plate surface, resulting in a large number of sensors, high hardware costs, and complex installation. Through iterative optimization of the greedy algorithm, redundant measurement points with the least influence on the reconstruction error are dynamically removed from the initial measurement point scheme. Finally, only about 20%-25% of the measurement points need to be retained to meet the displacement reconstruction accuracy requirements, and the average node error ≤ 5%.

[0073] The optimized layout method of inverse finite element measurement points for unstiffened hull plates proposed in this embodiment also overcomes the problem that the computational complexity of the inverse finite element method increases exponentially with the number of measurement points, and dense measurement points lead to an explosion of data volume, making it difficult to meet the real-time monitoring requirements. By generating rules for the initial measurement point scheme (such as diagonal arrangement, array replication, and segmented movement), it is ensured that the initial measurement point distribution covers key strain gradient regions (such as plate edges and centers), reducing redundant data acquisition. The reduction in the number of optimized measurement points significantly reduces the dimension of the overall pseudo-stiffness matrix, and the computational time for solving the reconstructed displacement field is reduced by about 80%, meeting the real-time inversion requirements.

[0074] The optimized layout method of inverse finite element measurement points for unstiffened hull plates proposed in this embodiment ensures that the mesh shape matches the actual deformation mode of the hull plate through element division rules, avoiding the accumulation of reconstruction errors caused by element distortion. By translating the upper and lower part measurement points in segments, multiple candidate schemes are generated to cover the strain-sensitive regions under different aspect ratios, improving the robustness of the algorithm.

[0075] The optimized layout method of inverse finite element measurement points for unstiffened hull plates proposed in this embodiment provides a clear logic for generating measurement point coordinates based on the diagonal and array replication layout rules, reducing the need for manual intervention. By calculating the node error and element error, the optimal measurement point combination is iteratively screened, avoiding manual trial and error and shortening the scheme design cycle.

[0076] In this embodiment, a double-precision guarantee mechanism is also used, that is, the initial scheme ensures the basic accuracy by covering high-strain gradient regions (such as diagonal arrangement); the greedy algorithm gradually eliminates non-critical measurement points based on the node error, and the final scheme meets the preset error threshold.

[0077] Embodiment 2: This embodiment further limits a method for optimizing the layout of inverse finite element measurement points for unstiffened hull plates based on the greedy algorithm. The preset conditions in step S1 are as follows:

[0078] When the aspect ratio is not 1, the long side is divided into a units and the short side is divided into b units, where both a and b are even numbers;

[0079] When the aspect ratio is 1, each side is divided into c units, where c is an even number.

[0080] In the prior art, any arbitrary division is likely to generate long and narrow elements (such as triangles or quadrilaterals with a high aspect ratio), resulting in the accumulation of strain interpolation errors in the inverse finite element method (such as shear locking phenomenon). In this embodiment, regular elements are set to make the calculation of strain gradient more accurate, reduce the non-physical oscillation of the reconstructed displacement field, and the node displacement error is reduced by about 30%. Evenly dividing the long / short sides into even-numbered elements ensures a clear structural center line, providing a geometric symmetry reference for the diagonal measurement point layout in step 2. At the same time, the even division makes the measurement points naturally form a symmetric distribution after being arranged along the diagonal, covering the high strain gradient region.

[0081] Embodiment 3: This embodiment further limits a method for optimizing the layout of inverse finite element measurement points for a non-reinforced hull plate based on the greedy algorithm described in Embodiment 1. The generation of the initial measurement point scheme in step S2 specifically includes:

[0082] Step S21: Continuously arrange b / 2 measurement points along the 45° direction from the upper left corner to the lower right corner of the hull plate, and then continuously arrange b / 2 measurement points along the 45° direction from the lower left corner until the short side is covered;

[0083] Step S22: Copy the measurement points in step S21 to the right in an array, with an interval of b / 2 - 1 elements, until it exceeds the boundary of the hull plate;

[0084] Step S23: Divide the measurement points into upper and lower parts with the midpoint connection line of the short side, and move the upper and lower parts of the measurement points respectively to generate b variant schemes;

[0085] Step S24: Combine all the schemes to obtain a set of initial measurement point schemes.

[0086] In this embodiment, by arranging the measurement points along the diagonal direction of the hull plate (the 45° direction from the upper left corner to the lower right corner and the 45° direction from the lower left corner to the upper right corner), it can ensure that the measurement points are evenly distributed on the surface of the hull plate, covering the entire area of the hull plate. By copying the measurement points in an array with an interval of b / 2 - 1 elements, it can ensure that the distance between the measurement points is appropriate, avoiding the situation of overly dense or sparse measurement points, and improving the calculation efficiency. By dividing the measurement points into upper and lower parts and moving them respectively, multiple variant schemes are generated. In this way, different measurement point layout methods can be considered, making the initial measurement point scheme more diverse and improving the flexibility of the optimization algorithm when selecting the optimal measurement points. The generated b variant schemes can cover different reconstruction requirements and fit the specific situation of the actual project. Combining all the variant schemes forms a complete set of initial measurement point schemes. By combining multiple schemes, the limitations that may be brought by a single layout scheme can be avoided, ensuring the wide applicability of the measurement point layout scheme in different hull design situations.

[0087] Embodiment 4. This embodiment further limits a method for optimizing the layout of inverse finite element measurement points for an un-reinforced hull plate based on the greedy algorithm described in Embodiment 1. The node error calculation in step S3 includes:

[0088]

[0089] where δ node is the node displacement reconstruction error, δ element is the element error, and is the mean reconstruction error of the included nodes.

[0090] Embodiment 5. This embodiment further limits a method for optimizing the layout of inverse finite element measurement points for an un-reinforced hull plate based on the greedy algorithm described in Embodiment 1. The cyclic displacement reconstruction by the inverse finite element method in step S3 includes:

[0091] S31: Obtain the axial strain and tangential strain on the upper and lower surfaces and the middle surface of the measurement point position through the strain rosettes arranged at the center positions of the monitoring area elements on the upper and lower surfaces of the un-reinforced plate to be measured;

[0092] S32: Construct a least-squares function of the theoretical and measured strain errors of the element where the measurement point is located according to the obtained middle surface strain and the relationship between the element strain and the middle surface strain;

[0093] S33: Take the extreme value of the least-squares function to obtain the element pseudo-stiffness matrix and element pseudo-load matrix of the element where the measurement point is located;

[0094] S34: Assemble the overall pseudo-stiffness matrix and overall pseudo-load matrix of the structure to obtain the structure reconstruction displacement field;

[0095] S35: Use finite element technology to perform finite element analysis on the structure to obtain the actual displacement field of the structure, and calculate the displacement reconstruction error of each node of the inverse finite element model after reconstruction.

[0096] In this embodiment, by arranging strain rosettes at the center of the monitoring area elements on the upper and lower surfaces of the un-reinforced plate to be measured, accurate strain data can be obtained. By constructing a least-squares function of the theoretical and measured strain errors of the element where the measurement point is located, precise correction and optimization of the measurement point data are realized, thereby improving the accuracy of inverse finite element analysis. The layout of the measurement points is optimized using the greedy algorithm. By iteratively and gradually selecting the optimal measurement point layout strategy, it is ensured that the layout of the measurement points can not only cover the key areas of the hull plate but also minimize the measurement error to ensure that a more accurate reconstruction can be obtained for the entire structure's inversion model. The element pseudo-stiffness matrix and pseudo-load matrix are calculated by the least-squares method, and further the overall pseudo-stiffness matrix and pseudo-load matrix are constructed, effectively improving the accuracy of the reconstruction displacement field and optimizing the reliability of the structure analysis results.

[0097] Embodiment 6. This embodiment further limits a method for optimizing the layout of inverse finite element measurement points of a non-reinforced hull plate based on the greedy algorithm described in Embodiment 5. The step S31 includes:

[0098]

[0099] where e ε is the measured plane strain, k ε is the measured bending strain. The variable with a superscript + is the measurement value on the upper surface of the element, and the variable with a superscript - is the measurement value on the lower surface of the element. ε xx is the strain in the x direction, ε yy is the strain in the y direction, ε xy is the tangential strain in the xy plane, and h is the distance from the mid-surface of the element to the surface of the element.

[0100] Embodiment 7. This embodiment further limits a method for optimizing the layout of inverse finite element measurement points of a non-reinforced hull plate based on the greedy algorithm described in Embodiment 6. The least squares function of the theoretical and measured strain errors of the measurement points in the unit where the measurement points are located in the step S32 is:

[0101]

[0102] where w e , w k and w g are weighted constants, e(u e ) is the theoretical plane strain, k(u e ) is the theoretical bending strain, g(u e ) is the theoretical shear strain, and g ε is the measured shear strain.

[0103] Embodiment 8. This embodiment further limits a method for optimizing the layout of inverse finite element measurement points of a non-reinforced hull plate based on the greedy algorithm described in Embodiment 6. Assembling the overall pseudo-stiffness matrix and the overall pseudo-load matrix in the step S34 includes:

[0104] KU = F

[0105] where K is the overall pseudo-stiffness matrix, F is the overall pseudo-load matrix, and U is the overall displacement field after reconstruction.

[0106] Embodiment 9. A computer device described in this embodiment includes a memory and a processor. A computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes a method for optimizing the layout of inverse finite element measurement points of a non-reinforced hull plate based on the greedy algorithm described in any one of Embodiments 1 to 8.

[0107] Embodiment 10. A computer-readable storage medium described in this embodiment. A computer program is stored on the computer-readable storage medium, and when the computer program is run by a processor, it executes the steps of a method for optimizing the layout of inverse finite element measurement points of a non-reinforced hull plate based on a greedy algorithm as described in any one of Embodiments 1 to 8.

[0108] Embodiment 11. Refer to Figures 2 to 24 This embodiment is described. This embodiment provides a specific example for a method for optimizing the layout of inverse finite element measurement points of a non-reinforced hull plate based on a greedy algorithm described in Embodiment 1, and is also used to explain Embodiments 2 to 9. Specifically:

[0109] This embodiment provides a method for optimizing the layout of inverse finite element measurement points of a non-reinforced hull plate based on a greedy algorithm. Taking a specific non-reinforced plate structure as an example, the structural dimensions of the non-reinforced plate are 2400mm×600mm×22mm, the material is structural steel, the yield limit is 450MPa, the boundary condition is rigid fixation around, and the load condition is a uniform load distributed on the entire plate surface, with a magnitude of 1MPa.

[0110] Step S101. Discretize the non-reinforced hull plate to determine the structural element division.

[0111] Specifically, according to the conditions that the element division should meet, the structural element division in this embodiment uses iQS4 elements. Each element contains 4 nodes, and each node has 6 degrees of freedom in different directions. It is divided into 40 elements along the long side and 10 elements along the short side, for a total of 400 elements;

[0112] Step S102. Determine the initial selection measurement point scheme input for the greedy algorithm, including:

[0113] Step S201. The left and right sides of the structure are short sides, and the upper and lower sides are long sides. Starting from the upper left corner of the structure, continuously arrange b / 2 measurement points along a 45° angle to the lower right corner, and then continuously arrange b / 2 measurement points along a 45° angle to the lower left corner until reaching the lower left corner of the structure;

[0114] Step S202. Copy the measurement points arranged in Step S201 to the right as a whole in an array, with an interval of (b / 2 - 1) elements, until the arrangement position of the measurement points is outside the structure;

[0115] Step S203. Divide the measurement points into upper and lower parts by the midpoint connection line of the left and right short sides of the structure. First, keep the lower part unchanged, and move the upper part to the right by 1, 2,..., b / 2 elements respectively to obtain b / 2 measurement point arrangement schemes. Then, keep the upper part unchanged, and move the lower part to the right by 1, 2,..., b / 2 elements respectively to obtain another b / 2 measurement point arrangement schemes;

[0116] Step S204: Take the (b + 1) solutions obtained in Steps 202 and 203 as the preliminary selected measuring point solutions.

[0117] For easy understanding, take an unstiffened hull plate with 10 units divided along the short side and 40 and 38 units divided along the long side respectively as an example. Each division method contains 9 measuring point layout solutions. After the preliminary selection solutions are determined, as Figures 4 to 21 shown.

[0118] Step S103: Input the preliminary selection solutions into the greedy algorithm program, and use the inverse finite element method to perform cyclic displacement reconstruction of the hull plate to obtain an optimized layout solution of the measuring points that meets the accuracy requirements.

[0119] It should be noted that the greedy algorithm program is as Figure 2 shown. Using the inverse finite element method to perform hull plate displacement reconstruction includes the following steps:

[0120] Step S301: Obtain the axial strain and tangential strain on the upper and lower surfaces and the middle surface of the measuring point positions through the strain rosettes arranged at the center positions of the monitoring area units on the upper and lower surfaces of the unstiffened plate to be measured.

[0121] Step S302: Construct a least - square function of the theoretical and measured strain errors of the unit where the measuring point is located according to the obtained middle - surface strain and the relationship between the element strain and the middle - surface strain.

[0122] Step S303: Take the extreme value of the least - square function to obtain the unit pseudo - stiffness matrix and unit pseudo - load matrix of the unit where the measuring point is located.

[0123] Step S304: Assemble the overall structure pseudo - stiffness matrix and overall pseudo - load matrix to obtain the structure reconstruction displacement field.

[0124] Step S305: Use finite element technology to perform finite element analysis on the structure to obtain the actual displacement field of the structure, and calculate the displacement reconstruction error of each node of the inverse finite element model after reconstruction.

[0125] It should be noted that in this embodiment, the least - square function of the theoretical and measured strain errors of the unit where the measuring point is located is:

[0126] Φ e (u e ) = w e ||e(u e ) - e ε || 2 + w k ||k(u e ) - k ε || 2 + w g ||g(u e ) - gε || 2

[0127] The least - squares function of the element where no measuring points are arranged is:

[0128] Φ e (u e ) = 10 -4 ·||e(u e )|| 2 + 10 -4 ·||k(u e )|| 2 + 10 -4 ·||g(u e )|| 2

[0129] Where u e is the displacements of the 4 nodes included in the element, e ε is the measured plane strain, k ε is the measured bending strain, e(u e ) is the theoretical plane strain, k(u e ) is the theoretical bending strain, g(u e ) is the theoretical shear strain, and g ε is the measured shear strain.

[0130] It should also be noted that the element pseudo - stiffness matrix in this embodiment is:

[0131]

[0132] Where A e is the entire area of the element, w e , w k and w g are the weighting constants. When measuring points are arranged on the element surface, the weighting constants w e = w k = w g = 1; when no measuring points are arranged on the element surface, w e = w k = w g = 0, B m is the theoretical plane strain matrix, B b is the theoretical bending strain matrix, B[[ID=8�0]] s is the theoretical shear strain matrix, and h is the distance from the mid - surface to the upper and lower surfaces.

[0133] The element pseudo - load matrix is:

[0134]

[0135] The overall pseudo - stiffness matrix is:

[0136]

[0137] Among them, T e is the coordinate transformation matrix.

[0138] The overall pseudo-load matrix is:

[0139]

[0140] The balance equation of the overall pseudo-load matrix and the overall pseudo-stiffness matrix is:

[0141] KU = F

[0142] Among them, U is the overall displacement field after reconstruction

[0143] In order to describe the advantages and disadvantages of the measuring point scheme, a node displacement reconstruction error is set, and its calculation formula is as follows:

[0144]

[0145] Among them, i is the node number, u is the total node displacement, the data with the subscript "all" is the reconstructed displacement when measuring points are arranged for all elements, and the data with the subscript "part" is the reconstructed displacement of the measuring point scheme.

[0146] The measuring point scheme that meets the accuracy conditions optimized by the greedy algorithm based on the initially selected measuring point scheme in this embodiment is as Figure 22 shown. The maximum value of the node displacement reconstruction error is 4.956%, and the average value of the node displacement reconstruction error is 1.298%. Figure 23 is the inverse finite element displacement reconstruction nephogram when measuring points are arranged for all elements in the embodiment, with the unit of millimeters. Figure 24 is the inverse finite element displacement reconstruction nephogram of the measuring point arrangement scheme that meets the accuracy requirements with the minimum number of measuring points after the initially selected scheme in the embodiment is optimized by the greedy algorithm, with the unit of millimeters; compared with the scheme of arranging measuring points for all elements, the measuring point scheme obtained by this scheme can ensure that the maximum error and the average error are within a certain range, and only need to arrange measuring points at 96 element measuring points, effectively reducing the cost of measuring point layout and improving the efficiency of inverse finite element reconstruction.

[0147] Those skilled in the art should understand that the embodiments of the present disclosure can be provided as a method, a system, or a computer program product. Therefore, the present disclosure can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present disclosure can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0148] This disclosure is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the disclosure. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to produce a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices produce a means for realizing the functions specified in one process Figure 1 one process or multiple processes and / or blocks Figure 1 or multiple blocks. These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing devices to work in a specific manner, such that the instructions stored in the computer-readable memory produce a manufactured article including an instruction means that realizes the functions specified in one process Figure 1 one process or multiple processes and / or blocks Figure 1 or multiple blocks.

[0149] These computer program instructions can also be loaded onto a computer or other programmable data processing devices, such that a series of operation steps are executed on the computer or other programmable devices to produce a computer-implemented process, and thus the instructions executed on the computer or other programmable devices provide steps for realizing the functions specified in one process Figure 1 one process or multiple processes and / or blocks Figure 1 or multiple blocks.

[0150] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present disclosure rather than to limit the scope of its protection. Although the present disclosure has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: after reading the present disclosure, those skilled in the art can still make various changes, modifications, or equivalent replacements to the specific implementation manners of the invention, but these changes, modifications, or equivalent replacements are all within the scope of the claims of the pending disclosure.

Claims

1. An inverse finite element measuring point optimization layout method for an unstiffened hull plate based on a greedy algorithm, characterized in that, The method includes: Step S1: Discretize the unstiffened hull plate, and divide the unstiffened hull plate into four-node elements that meet the preset conditions; Step S2: Generate a preliminary measurement point scheme, including arranging measurement points along the diagonal direction of the hull plate, and performing array replication and segmented movement to obtain multiple initial measurement point arrangement schemes; Step S3: Input the preliminary measurement point scheme into the greedy algorithm, and combine the inverse finite element method to perform cyclic displacement reconstruction and node error calculation. Iteratively remove the measurement points that have the least influence on the reconstruction error until the errors of all elements meet the preset accuracy threshold, and output the optimized arrangement scheme with the least number of measurement points and meeting the accuracy requirements.

2. The inverse finite element measurement point optimization layout method for a non-reinforced hull plate based on the greedy algorithm according to claim 1, wherein The preset conditions in the step S1 are: When the aspect ratio is not 1, the long side is divided into a units, and the short side is divided into b units, where both a and b are even numbers; When the aspect ratio is 1, each side is divided into c units, where c is an even number.

3. A method for optimizing the layout of inverse finite element measurement points of a non-reinforced hull plate based on the greedy algorithm according to claim 1, characterized in that The generation of the preliminary measurement point scheme in the step S2 specifically includes: Step S21: Continuously arrange b / 2 measurement points along the 45° direction from the upper left corner to the lower right corner of the hull plate, and then continuously arrange b / 2 measurement points along the 45° direction from the lower left corner until the short side is covered; Step S22: Copy the measurement points in step S21 to the right in an array, with an interval of b / 2 - 1 units, until it exceeds the boundary of the hull plate; Step S23: Divide the measurement points into upper and lower parts by the midpoint connection line of the short side, and move the upper and lower part measurement points respectively to generate b variant schemes; Step S24: Combine all the schemes to obtain a set of preliminary measurement point schemes.

4. A method for optimizing the layout of inverse finite element measurement points of an un-reinforced hull plate based on a greedy algorithm according to claim 1, characterized in that The node error calculation in the step S3 includes: where, δ node is the node displacement reconstruction error, and δ element is the element error.

5. A method for optimizing the layout of inverse finite element measurement points of an unstiffened hull plate based on the greedy algorithm according to claim 1, characterized in that The inverse finite element method for cyclic displacement reconstruction in the step S3 includes: S31: Obtain the axial strain and tangential strain of the upper and lower surfaces and the middle surface at the measurement point positions through the strain rosettes arranged at the center positions of the monitoring area elements on the upper and lower surfaces of the unstiffened plate to be measured; S32: Construct a least squares function of the theoretical and measured strain errors of the unit where the measurement point is located according to the obtained middle surface strain and the relationship between the unit strain and the middle surface strain; S33: Take the extreme value of the least squares function to obtain the unit pseudo stiffness matrix and unit pseudo load matrix of the unit where the measurement point is located; S34: Assemble the overall pseudo stiffness matrix and overall pseudo load matrix of the structure to obtain the structure reconstruction displacement field; S35: Use the finite element technology to perform finite element analysis on the structure to obtain the actual displacement field of the structure, and calculate the displacement reconstruction error of each node of the inverse finite element model after reconstruction.

6. A method for optimizing the layout of inverse finite element measurement points of an unstiffened hull plate based on a greedy algorithm, characterized in that, The step S31 includes: Among them, e ε is the measured plane strain, k ε is the measured bending strain. The variable with a superscript + is the measurement value on the upper surface of the element, and the variable with a superscript - is the measurement value on the lower surface of the element. ε xx is the strain in the x direction, ε yy is the strain in the y direction, ε xy is the tangential strain in the xy plane, and h is the distance from the mid-plane of the element to the surface of the element.

7. A method for optimizing the layout of inverse finite element measurement points of an unstiffened hull plate based on the greedy algorithm according to claim 6, characterized in that The least squares function of the theoretical and measured strain errors of the unit where the measurement point is located in the step S32 is: Φ e (u e ) = w e ||e(u e ) - e ε || 2 + w k ||k(u e ) - k ε || 2 + w g ||g(u e ) - g ε || 2 where, w e , w k and w g are weighting constants, e(u e ) is the theoretical plane strain, k(u e ) is the theoretical bending strain, g(u e ) is the theoretical shear strain, and g ε is the measured shear strain.

8. A method for optimizing the layout of inverse finite element measurement points of a non-reinforced hull plate based on a greedy algorithm, characterized in that, The assembly of the overall pseudo stiffness matrix and overall pseudo load matrix of the structure in the step S34 includes: KU = F Where K is the overall pseudo stiffness matrix, F is the overall pseudo load matrix, and U is the overall displacement field after reconstruction.

9. A computer device, characterized in that: It includes a memory and a processor. A computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes a method for optimizing the arrangement of inverse finite element measurement points of an unstiffened hull plate based on a greedy algorithm according to any one of claims 1 - 8.

10. A computer-readable storage medium, characterized in that, A computer program is stored on the computer-readable storage medium. When the computer program is run by a processor, it executes the steps of a method for optimizing the layout of inverse finite element measurement points of a non-reinforced hull plate based on a greedy algorithm as described in any one of claims 1-8.

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