A Layout Optimization Method for Deformation Monitoring of Large Deployable Structures

Abstract

The present invention belongs to the technical field of structural member strain monitoring, and relates to a layout optimization method for deformation monitoring of large deployable structures, including the following steps: establishing a finite element model for the large deployable structure; carrying out theoretical modal analysis of the large deployable structure for the finite element model, uniformly setting dense sensing measurement points on the surface of the structure, and constructing an error compensation model according to the strain transfer efficiency of the fiber optic sensor; obtaining the corresponding mass matrix [M] and stiffness matrix [K] at all measurement points, and obtaining the modal vibration modes of each measurement point and the vibration mode matrix of the entire system; calculating the orthogonality of each order of modes of each multi-degree-of-freedom structure according to the vibration mode matrix; realizing the update of the modal orthogonality fitness function through selection, crossover, and mutation steps to optimize the position of the sensor measurement points; and optimizing the position of the sensing measurement points. After determining the measurement point positions, a fitness function is constructed with the goal of minimizing the spacing between all sensing measurement points to obtain the final serial connection order of the fiber optic measurement points. The method of the present invention has less operation time.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural member strain monitoring, and relates to a method for accurate measurement of optical fiber signals and optimized layout of measuring points, and particularly relates to an optimized layout method for deformation monitoring of large deployable structures. Background Art

[0002] Large deployable structures are widely used in the fields of aerospace, civil engineering, and heavy machinery, and are a common large-scale structure. Under the long-term action of fatigue vibration, alternating impact, dynamic wind load, and temperature and humidity changes, the mechanical properties of large deployable structures are prone to deterioration, forming major safety hazards. Advanced sensing means need to be adopted to monitor the deployable structure in real time, and maintenance strategies need to be adopted to ensure the service life and avoid catastrophic accidents. Optical fiber sensors are very suitable for the real-time sensing requirements of large-scale structures due to their advantages of anti-electromagnetic interference, high precision, and easy multi-channel multiplexing. Since there is a measurement error between the measured value of the sensor and the actual physical quantity of the structure during the actual on-site monitoring process, and the current monitoring schemes for large deployable structures often adopt regular layouts, with strong empiricism, weak theoretical guidance, and low data quality. Therefore, it is necessary to study a sensing layout optimization and error compensation method that comprehensively considers the dynamic information of large-size large deployable structures and the characteristics of optical fiber monitoring. Summary of the Invention

[0003] The present invention aims to propose an optimized layout method for deformation monitoring of large deployable structures to solve any of the above problems. Aiming at the deficiencies in the current research, the present invention proposes an error compensation scheme based on strain transfer efficiency and a two-step method for optimizing the sensing layout of optical fiber distributed measurement for the real-time monitoring requirements of large deployable structures.

[0004] Specifically, the present invention provides an optimized layout method for deformation monitoring of large deployable structures, including the following steps:

[0005] Step 1: Establish a finite element model of the large deployable structure according to the mechanical properties, loading conditions, and service conditions of the actual engineering structure;

[0006] Step 2: Conduct a theoretical modal analysis of the large deployable structure for the finite element model, uniformly set dense sensing measurement points on the surface of the arrayed column skeleton structure, establish a strain transfer model according to the encapsulation configuration of the optical fiber sensor, perform error compensation, and calculate the structural deformation at the measured position after obtaining the structural modulus; obtain the corresponding mass matrix [M] and stiffness matrix [K] at all measurement points;

[0007] Step 3: Take the first order vibration modes for analysis according to the multi-degree-of-freedom system structural dynamics analysis method, and set the load condition as the time-history surface force wind load perpendicular to the extension direction of the column skeleton; obtain the modal vibration mode of the deployable structure under the excitation of the wind load through the initial optical fiber layout and the mode shape matrix of the entire system ;

[0008] Step 4: According to the mode shape matrix , calculate the orthogonality of each order of mode of each multi-degree-of-freedom structure; characterize the distributed measurement point layout strategy through multiple binary coding vectors, and construct an optimization fitness function with the maximum modal orthogonality as the goal; update the modal orthogonality fitness function through selection, crossover, and mutation steps to achieve the optimization of the sensor measurement point position;

[0009] Step 5: After determining the measurement point positions, establish the overall spatial distance model of the distributed measurement points; construct a fitness function with the minimum distance between all sensing measurement points as the goal; when the fitness of the optimal chromosome individual reaches the involved threshold, abort the iteration process to obtain the final fiber optic measurement point series connection order;

[0010] Step 6: According to the distributed measurement point series connection order obtained in Step 5, use the spline interpolation function to obtain the fiber optic measurement point series connection path, and the entire layout optimization process ends.

[0011] In one embodiment, the specific operation of Step 2 is to uniformly set dense sensing measurement points on the structure surface , where m is the number of rows and n is the number of columns. Considering the structural load direction and constraint conditions comprehensively, conduct dynamic calculations by taking the degrees of freedom in the direction perpendicular to the surface of the column skeleton; obtain the mass matrix and the stiffness matrix of each measurement point and truncate them in the axis direction to calculate the overall mass matrix and the stiffness matrix of the dense sensing measurement points.

[0012] In one embodiment, the mode shape matrix of the entire system is

[0013]

[0014] where and are the degrees of freedom and the order of the mode shape of the deployable structure system. In a real-time monitoring system for large deployable structures including sensors and acquisition devices, since the fiber optic sensor can only measure the strain state of a single degree of freedom in the axial direction, the fiber optic measurement point data is the same as the degrees of freedom, represents the number of fiber optic measurement points. takes values corresponding to the natural frequencies of each order one by one. Assuming that the first order fundamental frequencies of the system are selected for analysis, the mode shapes corresponding to the natural frequencies of each order are , where .

[0015] In one embodiment, the number of measurement points required for the fiber optic sensor network is determined in step 4 , and the optimization objective function and fitness of the measurement point layout position are determined according to the Modal Assurance Criterion (MAC).

[0016] In one embodiment, let , , then the fitness function is

[0017]

[0018] where ,

[0019] In the formula is the number of natural frequencies of the system taken, is the sum of the non-diagonal elements of the MAC matrix, and are respectively the vibration modes of the system at the , th order.

[0020] In one embodiment, the sensing layout measurement points are encoded using a binary bit sequence, and the number of binary digits is the same as the total number of initial sensing measurement points .

[0021] In one embodiment, according to the set fitness function, the fitness of different individuals in the population is calculated , where .

[0022] In one embodiment, the selection probability and cumulative probability of different individuals in the population are determined and , in a population of size , the selection probability corresponding to the th individual and the cumulative probability can be expressed as:

[0023]

[0024] where and are respectively the selection probability and cumulative probability corresponding to the th individual.

[0025] In one embodiment, step 4 further includes calculating the fitness value of the current population and determining whether the iteration termination condition is satisfied; if not, repeat the execution; if satisfied, output the final binary encoding , which represents the optimal sensing arrangement position.

[0026] In one embodiment, the binary code of the measurement points optimized by combining step 4 and the spatial coordinate information of the distributed measurement points can determine the layout position of the fiber optic sensors on the large deployable structure.

[0027] The solution of the present invention has the following effects.

[0028] This method analyzes the mechanical properties of the array skeleton structure under uniformly distributed loads, determines the initial layout position of the sensors, determines the transfer relationship between the measured structure and the fiber optic signal according to the fiber optic sensor packaging configuration, and performs error compensation. Taking the number, position of the fiber optic grating measurement points and the fiber optic laying path as variables, and the orthogonality of the structural modal vibration modes and the total length of the fiber optic path as the set optimization objectives, the optimal sensing layout solution suitable for large deployable structures is determined through the iteration of the algorithm of the present invention. The proposed method has less operation time, fast algorithm convergence speed, and can provide an effective solution for the design and laying of fiber optic sensing networks for large structures.

[0029] The layout optimization solution proposed by the present invention first performs a load analysis on the column skeleton to determine the mechanical characteristics under service conditions, and determines the initial number of measurement points and the monitoring positions according to the normal stress analytical formula. Perform modal analysis to obtain the vibration mode matrix corresponding to the distributed measurement points under the condition of uniform layout. Analyze the influence law of the fiber optic sensor packaging configuration on the monitoring signal error, and realize the accurate measurement of the strain of the deployable structure according to the strain transfer error compensation model. Subsequently, the fiber optic measurement points are binary coded, and the sensing layout under different restrictions on the number of measurement points is optimized. After determining the optimal layout, the optimal fiber optic connection path is obtained by solving the traveling salesman problem. Brief Description of the Drawings

[0030] Figure 1 is a schematic flow chart of the layout method of the present invention;

[0031] Figure 2 is a schematic diagram of the large deployable structure of the present invention;

[0032] Figure 3 is a finite element model of the large deployable structure of the present invention;

[0033] Figure 4 is a schematic diagram of the fiber optic sensor used for strain measurement of the large deployable structure of the present invention;

[0034] Figure 5 is a schematic diagram of the force characteristics of the column skeleton of the large deployable structure of the present invention;

[0035] Figure 6 is with the bending moment diagram and stress diagram of the column skeleton varying with the

[0036] Figure 7Schematic diagram of the initial layout of densely distributed measurement points with large deployable structures in the present invention;

[0037] Figure 8a Graph showing the relationship between the number of different measurement points and the sensor measurement point numbers under the optimization results, Figure 8b Curve showing the relationship between the number of measurement points and the fitness value under the optimization results;

[0038] Figure 9 Spatial distribution of the fiber optic measurement points obtained by the optimization of the present invention;

[0039] Figure 10 Arrangement orientations and fitness values of the fiber optic measurement points under the requirements of different target sensor numbers in the present invention; among them, (a), (b), (c), (d), (e), and (f) are the arrangement orientations with the number of measurement points being 16, 8, 24, 36, 40, and 48 respectively;

[0040] Figure 11 Variation of the total length of the fiber optic path with the number of optimization iterations in the present invention; among them, (a) is the optimal series connection measurement strategy; (b), (c), (d), and (e) are multiple sub - optimal series connection strategies;

[0041] Figure 12 Schematic diagram of the fiber optic path in the present invention, (a) before optimization and (b) after optimization;

[0042] Figure 13 Schematic diagram of the fiber optic path obtained by cubic spline interpolation in the present invention, (a) before optimization and (b) after optimization. Detailed implementation manners

[0043] In order to make the technical solutions and advantages of the present invention clearer, the present invention will be described in detail below with reference to the attached drawings and specific embodiments. Some professional terms and technical terms involved in the text have the same meanings as those understood by the general practitioners in the technical field to which this application belongs.

[0044] As Figure 1 shown, a layout optimization method for large deployable structure deformation monitoring in the present invention includes the following steps:

[0045] Step 1: Establish a finite element model for the large deployable structure according to the mechanical properties, loading conditions, and service conditions of the actual engineering structure.

[0046] Step 2: Conduct a theoretical modal analysis of the large deployable structure for the finite element model, uniformly set dense sensing measurement points on the surface of the structure, and construct an error compensation model according to the strain transfer efficiency of the fiber optic sensor. Obtain the corresponding mass matrix [M] and stiffness matrix [K] at all measurement points.

[0047] Step 3: According to the multi - degree - of - freedom system structural dynamics analysis method, take the first Analyze the first-order mode shape to obtain the modal mode shapes of each measurement point and the mode shape matrix of the entire system .

[0048] Step 4: According to the mode shape matrix , calculate the orthogonality of each order of mode of each multi-degree-of-freedom structure; characterize the distributed measurement point layout strategy through multiple binary coding vectors, and construct an optimization fitness function with the maximum modal orthogonality as the goal; update the modal orthogonality fitness function through selection, crossover, and mutation steps to realize the optimization of the sensor measurement point position.

[0049] Step 5: After determining the measurement point positions, establish a total spatial distance model for the distributed measurement points; construct a fitness function with the minimum distance between all sensing measurement points as the goal; when the fitness of the optimal chromosome individual reaches the involved threshold, abort the iteration process to obtain the final series connection order of the optical fiber measurement points;

[0050] Step 6: According to the series connection order of the distributed measurement points obtained in Step 5, use the spline interpolation function to obtain the series connection path of the optical fiber measurement points, and the entire layout optimization process ends.

[0051] Adopting the solution of the present application, a sensing position optimization fitness function can be constructed based on the distributed modal information of the large deployable structure and the multi-measurement point spatial distance model, and a distributed optical fiber measurement point arrangement method with the optimal system orthogonality and the shortest overall sensing path can be obtained. The present invention is verified through the specific implementation manner of the finite element simulation example, and through the execution process of selection, crossover, and mutation, a binary chromosome coding representing the optimal sensing layout is obtained, which is an intelligent layout optimization method.

[0052] In one embodiment, Step 2 is specifically to uniformly set dense sensing measurement points on the structure surface , comprehensively considering the structural load direction and constraint conditions, perform dynamic calculations by taking the degrees of freedom in the direction perpendicular to the surface of the column skeleton; obtain the mass matrix and the stiffness matrix of each measurement point, and truncate in the axis direction to calculate the overall mass matrix and the stiffness matrix of the dense sensing measurement points, where m and n are the number of rows and columns of the sensing measurement point matrix formed by the sensing measurement points respectively.

[0053] In one embodiment, Step 2 considers the strain transfer efficiency introduced by the optical fiber sensor packaging configuration, and ensures the optical fiber monitoring accuracy through compensation. The schematic diagram of the optical fiber sensor is as Figure 4 .

[0054] The fiber optic sensor includes a substrate 10, an adhesive 20, and an optical fiber 30. The optical fiber 30 includes a core 301 and a protective layer 302. The protective layer 302 surrounds the core 301 and is connected to the substrate 10 through the adhesive 20. A grating region 303 is provided on the optical fiber 30. The length of the grating strain measurement point region of the optical fiber is 2L, and the radii of the core 301 and the protective layer 302 are respectively and , and the fiber optic sensor is always subject to axial strain.

[0055] Specifically

[0056] Establish a force balance equation along the axis of the fiber optic sensor :

[0057]

[0058] Transforming formula (1), the following expression can be obtained:

[0059]

[0060] Simplifying the above formula, we can get:

[0061]

[0062] Since the length of the fiber optic sensor is much larger than the diameter of the core 301, that is . Therefore, the first term in formula (3) can be ignored, and the shear stress at any point between the protective layer 302 and the core 301 can be expressed as:

[0063]

[0064] This shear stress value can also be determined by the compatibility condition of the axial deformation of the optical fiber, as shown in the following formula:

[0065]

[0066] In the formula, , and are the deformation amounts of the measured substrate 10, the core 301 of the optical fiber, and the protective coating respectively. The above formula shows that the displacement of the substrate is the sum of the shear deformation of the protective coating and the axial displacement of the optical fiber. Since all materials are within the linear elastic range, using Hooke's theorem, we can get:

[0067]

[0068] Where , is the shear strain and shear modulus of the protective layer 302.

[0069] According to the knowledge of elasticity , where and are the Young's modulus and Poisson's ratio of the material of the protective layer 302 respectively. Under the assumption of small deformation, the shear strain of the protective layer 302 can be obtained as . Combining with formula (5), the deformation of the protective layer 302 can be expressed as follows:

[0070]

[0071] The axial stresses of the matrix 10 and the core 301 are as follows. In the formula , , and , , are the stress, elastic modulus and strain of the matrix 10 and the core 301 respectively.

[0072]

[0073] By integrating the strains of the two along the axial direction, the axial deformations of the matrix and the core 301 can be obtained:

[0074]

[0075] In the formula is the axial tension received by the core 301, which can be obtained by the following formula:

[0076]

[0077] Substitute the right-side expressions of formulas (7), (10), and (11) into the deformation compatibility equation (5) and simplify it to obtain the following integral equation:

[0078]

[0079] Differentiate the above formula to obtain:

[0080]

[0081] According to the strain compatibility condition, it can be known that . Therefore, the leftmost and the last two terms in the above formula can be cancelled out, and then we can get:

[0082]

[0083] Differentiate the above formula to obtain the following formula:

[0084]

[0085] Among them:

[0086]

[0087] The above equation is a typical second-order homogeneous linear differential equation with constant coefficients. According to the solution method of this type of differential equation, its general solution is as follows:

[0088]

[0089] Since the strain sensitive section of the fiber Bragg grating sensor is concentrated in the middle of the grating area 303, the boundary condition of the axial tension of the optical fiber can be obtained as follows:

[0090]

[0091] The above boundary conditions indicate that the strain of the fiber Bragg grating core 301 at its symmetry axis (and the middle part of the sensor) is the same as the strain of the substrate 10, and gradually decreases to zero at the ends on both sides. Substituting equations (19) and (20) into equation (18), solving the simultaneous equations, we can get the integral constant: and for:

[0092]

[0093] Will be obtained and Substituting the general solution (18) into the shear stress distribution function describing the interface between the fiber core 301 and the optical fiber protective layer 302 can be obtained:

[0094]

[0095] Substituting the above formula into the axial tension formula, the axial tension expression of the core 301 can be obtained:

[0096]

[0097] Therefore, the axial tension per unit area is:

[0098]

[0099] By dividing the left and right sides of the formula by the elastic modulus of the fiber core 301, the transfer rate formula between the axial strain of the fiber core 301 and the matrix strain can be obtained as follows:

[0100]

[0101] set up The value range is , then the average transmission rate of the fiber Bragg grating strain sensitive area can be obtained :

[0102]

[0103] As shown above, the final strain transfer modulus of the fiber Bragg grating sensor can be expressed by the following equations

[0104]

[0105] Let be the strain measured by the fiber optic sensor, be the actual strain of the deployable structure, then the actual surface strain of the structure can be expressed as:

[0106]

[0107] In the formula, the common parameters of the fiber Bragg grating are , , , , then . The average strain transfer rate is .

[0108] Then, .

[0109] In one embodiment, the following steps are adopted in step 3. The undamped vibration equation of the multi-degree-of-freedom structure is:

[0110]

[0111] According to the simple harmonic vibration hypothesis, the displacement function of the structure changing with time can be expressed as

[0112]

[0113] In the formula represents the vibration mode of the system that does not change with time, is the vibration frequency, is the phase. By taking the second derivative, the acceleration expression can be obtained:

[0114]

[0115] Furthermore, it can be obtained:

[0116]

[0117] Eliminating the terms that are not always zero, it can be obtained:

[0118]

[0119] The generalized eigenvalue problem of the above formula can be expressed as:

[0120]

[0121] By solving the eigenvalues, the spectral matrix and mode shape matrix of the entire system can be obtained:

[0122]

[0123]

[0124] In the above formula, is the natural frequency corresponding to different orders. For the row and column mode shape matrix , each column of it corresponds to the natural frequencies of each order of the structural system. Taking the first column and the first row in the matrix as an example, represents the degrees of freedom in the first-order mode shape, is the relative vibration amplitude of the first degree of freedom in the order mode shape.

[0125] In one embodiment, step 4 specifically includes:

[0126] 4.1 Determine the number of measurement points required for the fiber optic sensor network , and determine the optimization objective function and fitness of the measurement point layout position according to the Modal Assurance Criterion (MAC). The expression of MAC is:

[0127]

[0128] where , .

[0129] Since the algorithm optimization process is to maximize the fitness function, take the negative of the sum of the non-diagonal elements of the matrix as the fitness function , which can be expressed as:

[0130] (38)

[0131] Step 4.2: Encode the sensing layout measurement points using binary bit sequences. The number of binary bits is the same as the total number of initial sensing measurement points . The th sensing measurement point is numbered , where . Encoding 1 means retaining the sensor at that measurement point position, and encoding 0 means removing the sensor at that measurement point.

[0132] Step 4.3: Initialize the population size parameter , and form the initial population . Set the value range of the independent variable parameters.

[0133] Step 4.4: Calculate the fitness of different individuals in the population according to the set fitness function ,in .

[0134] Step 4.5: Determine the selection probability of different individuals in the population and cumulative probability , which can be expressed as:

[0135]

[0136] Step 4.6: Perform selection operations, copy the selected population, and perform exchange and mutation operations.

[0137] Step 4.7: Get the new individuals, forming a new population .

[0138] Step 4.8: Calculate the fitness value of the current population and determine whether the iteration termination condition is met. If not, repeat steps 4.3-4.7. If satisfied, output the final binary code , the binary code represents the optimal sensor layout position.

[0139] In one embodiment, step 5 specifically comprises:

[0140] Step 5.1: Combine the binary encoding of the measurement points obtained by step 4 optimization The spatial coordinate information of the distributed measuring points can be used to determine the layout of the fiber optic sensor on a large display. The Traveling Salesman Problem (TSP) is used to model multiple sensing points. The sensing points are marked as ,in . Then the source sensor point and target sensing points The spacing can be set to ,in and For the real-time monitoring of large deployable structures, it is hoped that the total path of the optical fiber laying will be minimized, so the minimum value of the sum of the spacings between all sensing points is Assuming it as the optimization goal, we can get the following formula:

[0141] (41)

[0142] In the above formula, For measuring point and The distance between To judge the weight, it can be expressed as:

[0143]

[0144] In the above formula, , and , The measuring points and In European space The horizontal and vertical coordinate values in .

[0145] Step 5.2: Use a similar process to steps 4.3-4.8 to optimize the TSP problem. In the path optimization problem, the meaning of the individuals and populations represented by the binary sequence is different from that in the layout optimization problem. After the optimization is completed, the decimal encoding vector corresponding to the optimal path is output .

[0146] In one embodiment, the step 6 uses a cubic spline interpolation function (CSIF) to calculate the optical fiber path.

[0147] Specifically, CSIF can obtain the third-order polynomial function between multiple nodes, and its expression is:

[0148]

[0149] In the above formula, , , and are coefficients of different orders. There are a total of sensing points spacing and need to be unknown coefficients. Determine the calculation step size After that, the simultaneous equations with the same first-order derivative and second-order derivative at different nodes are used to solve the problem. , , and It can be expressed as:

[0150]

[0151] In the above formula is a tridiagonal matrix. The node values and endpoint conditions are substituted into the matrix equation and Gaussian elimination method is used to obtain it. After obtaining the interpolation path, the entire fiber optic sensor layout optimization process is completed.

[0152] In one embodiment, in order to optimize the layout position of the sensor, save components, and improve efficiency, this application considers that the large deployable truss structure can be regarded as a simply supported beam structure under uniformly distributed load. According to the theory of mechanics of materials and elasticity, the bending moment diagram and stress diagram of each section of the truss under external load are analyzed with respect to the direction change, and the initial number of measurement points and the initial layout position of the fiber Bragg grating sensors are determined according to the quadratic curve solution conditions.

[0153] Specifically, each truss uniformly distributed on the main beam can be regarded as a simply supported beam. During the actual service process of the large deployable structure, it is often affected by wind load. Therefore, the truss can be analyzed according to the simply supported beam under uniformly distributed load. Let the uniformly distributed load be , and it can be known from the theory of elasticity that is a constant that does not change with . Therefore, the bending stress also does not change with , and it can be set that is a function of :

[0154]

[0155] Let be the stress function, and the following can be obtained:

[0156]

[0157] Performing the first and second integrations gives:

[0158]

[0159] After substituting the above formula into the compatibility equation, the normal stress, bending stress, and shear stress expressions, the following can be obtained

[0160]

[0161] Since and are even functions of , and is an odd function of . Therefore, in the above formula . By considering the upper and lower boundary problems , and , as well as the left and right boundary conditions , and . After substituting into the above formula, the following can be obtained , , , , , . After sorting, the following can be obtained:

[0162]

[0163] Optical fiber sensors are arranged axially on the column skeleton. Therefore, the normal stress is analyzed to determine the initial layout of the column skeleton sensors. For a beam structure, the bending moment on any cross-section can be set as , and the moment of inertia of a rectangular beam is known as . Then the normal stress in the above formula can be expressed as:

[0164]

[0165] Since the optical fiber sensors are arranged on the surface of the column skeleton to monitor the normal stress and strain, taking the expression of the maximum normal stress on any cross-section of the beam can be obtained:

[0166]

[0167] It is known that the bending moment varying with the direction on a simply supported beam is . Then the maximum normal stress on the cross-section varying with the direction can be given by the following formula:

[0168]

[0169] The above formula is a specific solution of the general form of a quadratic curve . The discriminant of the general form is . Fixing to obtain the equation of the normalized general form, the parabola needs to satisfy . After substituting it into the general form equation, we can get:

[0170]

[0171] It can be seen from the above formula that at least 4 coordinate points are required to determine the analytical formula of any parabola. Therefore, in the initial layout, at least 4 optical fiber sensors are arranged on each column skeleton. The stress value of the simply supported beam is the largest at the symmetry axis of its parabolic bending moment diagram. At least two optical fiber sensors are arranged near the symmetry axis at two positions with a relatively close distance, and at least two measuring points are arranged at the left and right ends of the parabola.

[0172] Adopting such a scheme, in the initial layout, fewer sensors and better layout positions can be used, which can greatly save the calculation amount and improve the efficiency. And finally, accurate measurement of the deployable structure can be realized with fewer optical fiber sensors, saving costs and improving efficiency.

[0173] The following combines a specific embodiment to illustrate the layout method of the present invention.

[0174] 1. Determine the parameters of the large deployable structure and create a finite element model

[0175] Figure 2 The established three-dimensional model of the large deployable structure of the deployable antenna consists of a scissor structure 100, a column skeleton 200, a telescopic arm 300, and a fixed end 400. The finite element model of the large deployable structure established via ANSYS is as shown in Figure 3 the figure. The length, width, and thickness of the scissor structure 100 in this simulation example are 8540 mm and 6000 mm respectively. The structural 45 steel material is selected as the property of the structure, and the specific parameters are shown in Table 1. The entire structure is meshed using the solid element SOLID185, and the number of meshes is 54021. Candidate sensing measurement points are evenly selected on 12 column skeletons to form a distributed measurement point.

[0176] Table 1 Material properties

[0177]

[0178] II. Structural modal analysis and candidate measurement point selection

[0179] For this example, the total number of measurement points is 48. The simplified load-bearing state of the column skeleton 200 is as shown in Figure 5 the figure. According to the structural dimension parameters, the bending moment and normal stress distribution curves of the cantilever main beam and the simply supported column skeleton varying with the direction are as shown in Appendix Figure 6 the figure. Four positions of , , and are respectively selected as the initial layout of the fiber optic sensors on each column skeleton, and the initial sensor layout of the entire deployable structure is as shown in Appendix Figure 7 the figure.

[0180] After determining the fixed end constraint conditions, the overall structural modal analysis is carried out to obtain the mass matrix of the measurement point axial direction degree of freedom and the stiffness matrix . The mode shape matrix is calculated according to the process described in Eqs. (29)-(36). .

[0181] III. Optimize the positions of the large deployable fiber optic measurement points

[0182] The fitness function for optimizing the sensing position is as shown in Eq. (38). For this example, the number of measurement points satisfies , the mode shape order is taken as , the population size is 100, the crossover probability and the mutation probability Take 0.8 and 0.1 respectively, and the total number of iterations is equal to 70. Since the algorithm has a fast convergence speed and a short operation time, when it is difficult to determine in advance, the optimal positions under different measurement points can be obtained by traversing and solving, and the MAC values under different layouts can be comprehensively compared and then the optimal one can be selected.

[0183] III. Optimize the connection order of fiber Bragg gratings between measurement points

[0184] The fitness function for fiber optic path optimization modeled according to the TSP problem is shown in Equation (41). The population size for the path optimization algorithm is 100, the crossover probability and the mutation probability take 0.8 and 0.05. The measurement points are compiled in the form of positive number coding. The numbers in the individual represent the connection order of the fiber optic measurement points, and the total number of iterations is 60.

[0185] IV. Obtain the fiber optic path through cubic spline interpolation

[0186] Regard the measurement points at different positions in space as nodes in the CSIF, and substitute the measurement point information into the matrix equation to solve the coefficients , , and , and finally determine the piecewise cubic spline interpolation function . The curve given is the final fiber optic laying path.

[0187] V. Results and Analysis

[0188] For the task of optimizing the sensing layout position, the relationship between the number of different measurement points, the sensing measurement point numbers and the fitness values is as shown in Figure 8a 、 8b . As the number of fiber optic measurement points increases, the fitness value optimized by the invention algorithm rapidly increases to a certain peak and then gradually decreases, and reaches the maximum at which is 0.8417. Since the fitness function is established through the modal assurance criterion MAC, the larger its value, the stronger the modal orthogonality between orders, and the higher the quality of the fiber optic sensing network composed of multiple measurement points. Therefore, the total number of measurement points of the sensing network is determined to be 16, and the subsequent fiber optic path optimization is carried out based on this.

[0189] Table 2 Fitness optimized under different numbers of measurement points conditions

[0190]

[0191] For Optimize the optical fiber path for the optimal measuring point positions obtained under the conditions. The relative positional relationships of all measuring points in space are as Figure 9 shown. Figure 10 Lists the layout orientations of the optical fiber measuring points under several different requirements for the number of target sensors (the number of sensors is 16, 8, 24, 32, 40, and 48 respectively). Calculated according to formula (10), the corresponding fitness values are shown in Table 2. It can be seen that the number of measuring points is not positively correlated with the modal orthogonality index. When the number of measuring points is 48, the fitness value is 0.6843, and the redundancy of the sensor network is relatively large. Considering comprehensively, the optimal number of measuring points is 16.

[0192] Obtain the fitness function of the total distance between measuring points through the Euclidean distance, and perform cyclic iterative search for the optimal connection sequence. During the optimization process, the total distance decreases significantly from 63.19 m with the number of iterations, as Figure 11 shown.

[0193] Figure 11 (a) is the optimal connection strategy after 40 iterations of the algorithm. Its connection sequence is 5→4→3→2→1→7→10→12→13→14→15→16→11→9→8→6, and the total path distance is 22.72 meters Figure 11 (b)-(f) are multiple sub-optimal connection strategies with 20 iterations. The distances range from 29.29 m to 36 m. Figure 11 The connection sequence of (b) is 15→14→13→12→11→10→7→6→1→2→3→4→5→8→9→16, and the total connection distance is 32.53 meters. Figure 11 The connection sequence of (c) is 16→11→9→8→1→2→5→3→4→6→7→10→12→13→14→15, and the total connection distance is 30.05 meters. Figure 11 The connection sequence of (d) is 14→15→16→11→8→5→1→2→3→4→6→7→9→10→12→13, and the total connection distance is 32.02 meters. Figure 11 The connection sequence of (e) is 10→12→13→14→15→16→5→1→4→3→2→6→9→8→7, and the total connection distance is 36.07 meters. Figure 11 The connection sequence of (f) is 9→11→16→15→14→13→12→10→7→6→5→4→3→2→1→8, and the total connection distance is 29.29 meters.

[0194] Figure 12 and 13After determining the measuring point positions, the schematic diagrams of the sensing paths before and after optimization are given respectively. For the same sensing measuring point positions, the series connection paths before and after optimization are short and easy to route, and are more suitable for the high-reliability and long-term real-time monitoring scenarios of large structures. Since it is difficult to make a straight series connection in the actual environment, cubic spline interpolation is used to obtain the optical fiber path in the order shown in Figure 12 (b). During the deployment of the optical fiber measurement system for large deployable structures, the optical fibers can be connected in series according to the sensing measuring point positions and connection order shown in Figure 13 (b). The proposed method for optimizing the optical fiber measuring point positions and paths of large deployable structures can provide a guiding basis for the selection of points, layout, and routing of the actual sensing network, and can be applied to objects such as space deployable mechanisms, large ground arrays, and heavy deployable telescopic arms, which has great theoretical innovation and engineering practical significance.

[0195] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A layout optimization method for deformation monitoring of large deployable structures, characterized in that, Including the following steps: Step 1: Establish a finite element model for the large deployable structure according to its actual mechanical properties, wind load conditions, and service conditions. Step 2: Conduct a theoretical modal analysis of the large deployable structure for the finite element model. Uniformly set dense sensing measurement points on the surface of the arrayed column skeleton structure. Establish a strain transfer model based on the encapsulation configuration of the fiber optic sensors, perform error compensation, and obtain the corresponding mass matrix [M] and stiffness matrix [K] at all measurement points. Step 3: According to the multi-degree-of-freedom system dynamics analysis method, take the first several vibration modes for analysis, and set the load condition as the time-history surface force wind load perpendicular to the extension direction of the column skeleton; obtain the modal vibration modes of the large deployable structure under the excitation of the wind load through the initial optical fiber layout and the vibration mode matrix of the entire system ; Step 4: According to the mode shape matrix , calculate the orthogonality of each order of mode of each multi-degree-of-freedom structure; represent the distributed measuring point layout strategy through multiple binary coding vectors, and construct an optimization fitness function with the maximum modal orthogonality as the goal; realize the update of the modal orthogonality fitness function through the steps of selection, crossover, and mutation, and realize the optimization of the sensor measuring point position; Step 5: After determining the measurement point positions, establish a general spatial distance model for the distributed measurement points; construct a fitness function with the goal of minimizing the distance between all sensing measurement points. When the fitness of the optimal chromosome individual reaches the involved threshold, terminate the iterative process to obtain the final serial connection order of the fiber optic measurement points. Step 6: According to the serial connection order of the distributed measurement points obtained in Step 5, use the spline interpolation function to obtain the serial connection path of the fiber optic measurement points, and the entire layout optimization process ends.

2. The layout optimization method for large deployable structure deformation monitoring according to claim 1, characterized in that: The specific operation of step 2 is to uniformly set dense sensing measurement points on the structure surface , considering the structural load direction and constraint conditions, conduct dynamic calculations for the degrees of freedom in the direction perpendicular to the surface of the column skeleton; obtain the mass matrix of each measurement point and the stiffness matrix and truncate them in the axis direction to calculate the overall mass matrix and stiffness matrix of the dense sensing measurement points, where m is the number of rows and n is the number of columns 3. A layout optimization method for large deployable structure deformation monitoring according to claim 2, characterized in that: The mode shape matrix of the entire system is as follows: Among them, and are the degrees of freedom and vibration mode orders of the deployable structure system; in the real-time monitoring system of large deployable structures including sensors and acquisition devices, since fiber optic sensors can only measure the strain state of a single axial degree of freedom, the fiber optic measurement point data is the same as the degrees of freedom; to prevent confusion, use to represent the number of fiber optic measurement points; takes values corresponding one by one to the natural frequencies of each order. Assume that the first order fundamental frequencies of the system are analyzed, and the vibration modes corresponding to the natural frequencies of each order are , where .

4. A layout optimization method for deformation monitoring of large deployable structures according to claim 3, characterized in that: Determine the number of measurement points required for the fiber optic sensor network in step 4 , and determine the optimization objective function and fitness of the measurement point layout position according to the Modal Assurance Criterion (MAC).

5. The layout optimization method for large deployable structure deformation monitoring according to claim 4, characterized in that: Let , , then the fitness function is Among them, , where is the number of the natural frequencies of the system taken, is the sum of the non-diagonal elements of the MAC matrix, and are respectively the , th order mode shapes of the system.

6. The layout optimization method for large deployable structure deformation monitoring according to claim 5, characterized in that: Encoding the sensing layout measurement points using a binary bit sequence, where the number of binary bits is the same as the initial number of sensing measurement points before optimization is the same.

7. A layout optimization method for deformation monitoring of large deployable structures according to claim 6, characterized in that: Calculate the fitness of different individuals in the population according to the set fitness function , where .

8. A layout optimization method for deformation monitoring of large deployable structures according to claim 7, characterized in that: Determine the selection probabilities and cumulative probabilities of different individuals in the population, which can be expressed as: wherein and are respectively the selection probability and the cumulative probability corresponding to the th individual.

9. The layout optimization method for large deployable structure deformation monitoring according to claim 8, characterized in that: Step 4 further includes calculating the fitness value of the current population and determining whether the iteration termination condition is satisfied; if not, repeat the execution; if satisfied, output the final binary coding , and this binary coding represents the optimal sensing arrangement position.

10. A layout optimization method for deformation monitoring of large deployable structures according to claim 1, characterized in that: The binary code of the measurement points optimized by combining Step 4 and the spatial coordinate information of the distributed measurement points, the installation position of the fiber optic sensor on the large deployable structure can be determined.

Images