NSGA-II-based fiber grating sensor layout multi-objective optimization method

Abstract

The invention provides a fiber grating sensor layout multi-objective optimization method based on NSGA-II. The method comprises the following steps: acquiring a global strain field, a displacement field and a stress field of a measured structure under a typical load through finite element simulation; generating an initial population, wherein each individual in the initial population represents a group of sensor layout coordinates; performing crossover and variation on the parent population to obtain a filial population, combining the parent population and the filial population, and calculating a deformation measurement error, fatigue life and uniformity coverage corresponding to each population individual; performing rapid non-dominated sorting on all population individuals, sorting the population individuals in the same front edge according to the congestion degree distance, and selecting a new population by adopting an elitist strategy; and repeatedly executing the multi-target calculation operation and the population updating operation until a preset iteration termination condition is met. According to the invention, the measurement error, the fatigue life and the uniformity coverage are effectively balanced, and the comprehensive optimization layout of the fiber grating sensor is realized.

Description

Technical Field

[0001] This invention relates to the field of fiber optic sensing technology, and in particular to a multi-objective optimization method for the layout of fiber optic grating sensors based on NSGA-II. Background Technology

[0002] As a core component of structural health monitoring systems, sensors can monitor the state parameters of key structural components in real time, such as stress, strain, displacement, and acceleration, providing necessary data support for fault detection, fatigue life prediction, and maintenance decisions. Fiber Bragg grating (FBG) sensors, as an emerging type of sensor, utilize the changes in the optical properties of light transmitted through optical fibers under external stimuli to achieve precise measurement of multiple physical quantities. Compared with traditional sensors, FBG sensors are lightweight, compact, highly environmentally robust, resistant to electromagnetic interference, and easily reused in sensor networks, and have been widely used in structural health monitoring across various fields.

[0003] The performance of fiber Bragg grating (FBG) sensing systems is constrained by the FBG sensors themselves, and the sensor layout directly determines their overall performance. Therefore, optimizing the sensor layout is crucial. Existing research largely focuses on optimizing single performance indicators, such as measurement accuracy or reconstruction error, neglecting the simultaneous optimization of multiple key performance indicators. Furthermore, existing multi-objective optimization methods typically only consider trade-offs between accuracy, cost, and the number of sensors, failing to integrate fatigue life and uniform coverage into a unified multi-objective optimization framework. Thus, improving the stability and reliability of FBG sensing systems in complex application environments at the sensor network layout level remains a critical technical bottleneck that needs to be overcome. Summary of the Invention

[0004] This invention proposes a multi-objective optimization method for fiber optic grating sensor layout based on NSGA-II, in order to overcome or partially overcome the above-mentioned problems.

[0005] This invention provides a multi-objective optimization method for fiber Bragg grating sensor layout based on NSGA-II, the method comprising: The global strain field, displacement field, and stress field of the structure under test under typical loads are obtained through finite element simulation. An initial population is generated, where each individual in the initial population represents a set of sensor layout coordinates on the structure under test; Multi-objective computation operation: The current population is used as the parent population for crossover and mutation to obtain the offspring population. The parent population and the offspring population are then merged, and the deformation measurement error, fatigue life and uniformity coverage corresponding to each individual in the population are calculated. Population update operation: Perform a fast non-dominated sort on all population individuals, divide them into different levels of non-dominated fronts according to their dominance relationship, sort the population individuals within the same front according to their crowding distance, and select a new population using an elite strategy. Repeatedly perform multi-objective computation and population update operations until the preset iteration termination condition is met, and use the population individuals in the new population as the optimal solution for sensor layout.

[0006] Furthermore, the deformation measurement error is achieved through the following steps: Obtain the position coordinates of each sensor corresponding to an individual in the current population; Based on the global strain field and position coordinates of each sensor obtained by finite element simulation, the strain values ​​of each sensor point on the surface of the tested structure are obtained, and the reconstructed displacement field of the tested structure is calculated based on the preset deformation reconstruction algorithm. The deformation measurement error corresponding to the current individual in the population is calculated based on the reconstructed displacement field of the measured structure and the displacement field obtained from finite element simulation. , In the above formula, Er represents the deformation measurement error, and Z(x,y) represents the displacement field obtained from finite element simulation. This represents the expected value of the absolute amplitude of the displacement field. This represents the expected absolute error between the reconstructed displacement field and the displacement field obtained from the finite element simulation.

[0007] Furthermore, the fatigue life is achieved through the following steps: Obtain the stress extreme values ​​at the target sensor location, whereby the stress extreme values ​​include the maximum and minimum stress at the target sensor location; Calculate the average stress and stress amplitude at the target sensor point based on the stress extreme values ​​at the target sensor point: , In the above formula, This indicates the maximum stress at the target sensor location. This represents the minimum stress at the target sensor location. This represents the average stress at the target sensor location. This indicates the stress amplitude at the target sensor location; Based on the stress amplitude at the target sensor location, calculate the equivalent stress amplitude at the target sensor location: , In the above formula, This represents the corrected equivalent stress amplitude at the target sensor location. Indicates the ultimate tensile strength of the target sensor; The fatigue life of the target sensor is obtained based on the pre-obtained stress-life curve of the target sensor; wherein, the stress-life curve of the target sensor is expressed as: , In the above formula, A and B are material constants determined through fatigue experiments; The fatigue life of each individual in the current population is calculated based on the fatigue life of the sensors at each sensor location. , In the above formula, This represents the fatigue life of an individual in the current population; N represents the number of sensors. Let represent the fatigue life of the i-th sensor, i=1,2,…,N.

[0008] Furthermore, the uniformity of coverage is achieved through the following steps: Calculate the mean distance between any two sensors in the current population: , In the above formula, This represents the average distance between any two sensors, and N represents the number of sensors. This represents the total number of combinations of pairwise sensor pairings; Represents any two sensors and The distance between them, ; Calculate the standard deviation of the distance between any two sensors: , In the above formula, The standard deviation of the distance between any two sensors; Calculate the uniformity coverage of the current population based on the mean and standard deviation of the distance between any two sensors: , In the above formula, UCI represents uniformity coverage; d max This represents the theoretically achievable maximum distance between any two sensors.

[0009] Furthermore, the step of performing rapid non-dominated ordination on all individuals in the population and dividing them into different levels of non-dominated fronts according to their dominance relationships includes: S41. Taking measurement error, fatigue life and uniformity coverage as objective functions respectively, if individual p is no worse than individual q in all objective functions and is strictly better than individual q in at least one objective function, then individual p is determined to dominate individual q. S42. Iterate through all pairs of individuals (p, q) in the population. For each individual p in the population, obtain the number n individuals that dominate individual p. p and the set of individuals S dominated by individual p p ; S43, put all n p Individuals with a value of 0 are identified as the first non-dominated frontier; S44. For each individual p in the currently identified non-dominated frontier, traverse its S... p For each individual q in the set, the n of q p The value is reduced by 1; if after reducing by 1, the value of n of q is reduced by 1. p If the value becomes 0, then q is identified as the next non-dominated frontier; S45. Repeat step S44 until all individuals in the population have been assigned to the corresponding non-dominated frontier.

[0010] Furthermore, the sorting of individuals within the same non-dominated front according to crowding distance includes: For the m-th objective function, sort the individuals in the current frontier according to their values ​​on that objective function; Calculate the crowding distance of the sorted individual i on the m-th objective function: , In the above formula, and Let represent the values ​​of the individuals adjacent to the i-th individual on the m-th objective function, respectively. and Let represent the maximum and minimum values ​​of the m-th objective function at the current frontier, respectively. This represents the crowding degree of individual i on the m-th objective function; The total crowding distance of individual i across all objective functions is calculated as follows: , In the above formula, M is the number of objective functions. This represents the total crowding distance for individual i.

[0011] Furthermore, the selection of a new population using an elite strategy includes: Starting from the optimal non-dominated front, individuals from each non-dominated front are sequentially added to the next generation of the population; When adding a non-dominated front causes the number of individuals in the next generation to exceed the population's individual size threshold, the current non-dominated fronts are sorted in descending order based on their crowding distance. Individuals with greater crowding distance are preferentially selected to join the next generation of the population until the number of individuals in the next generation reaches the population size threshold.

[0012] This invention provides a multi-objective optimization method for fiber optic grating sensor layout based on NSGA-II. This method obtains the global strain, displacement, and stress fields of the measured structure under typical loads through finite element simulation, providing necessary data support for subsequent sensor layout optimization. The parent population is crossovered and mutated to obtain offspring. The parent and offspring populations are merged for multi-objective optimization evaluation, calculating the deformation measurement error, fatigue life, and uniformity coverage for each individual. All individuals are subjected to rapid non-dominated sorting, dividing them into different levels of non-dominated fronts according to their dominance relationships. Individuals within the same front are sorted by crowding distance, prioritizing individuals with lower front levels and higher crowding distances to form a new population, balancing quality and diversity, ensuring that the generated population approximates the Pareto front while covering a wider area. To retain as many excellent individuals as possible, an elite strategy is used to update the population. When the maximum number of iterations is reached, the loop terminates, and the optimal solution is output. This method effectively balances measurement error, fatigue life, and uniformity coverage, improves the efficiency of solving multi-objective optimization problems, has stronger global search capabilities, avoids local optima, and realizes the comprehensive optimization layout of fiber Bragg grating sensors, thereby improving the overall performance of fiber Bragg grating sensing systems.

[0013] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0014] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. In the drawings: Figure 1 This is a flowchart illustrating a multi-objective optimization method for fiber optic grating sensor layout based on NSGA-II, according to an embodiment of the present invention. Figure 2 This is a network architecture diagram of a multi-objective optimization method for fiber optic grating sensor layout based on NSGA-II, according to an embodiment of the present invention. Figure 3 This is a finite element simulation diagram of the deformation of the tested structure provided in an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the relationship between stress amplitude and fatigue life of a fiber optic grating sensor provided in an embodiment of the present invention. Figure 5 This is a schematic diagram of the elite strategy provided in an embodiment of the present invention; Figure 6 These are simulation results provided by an embodiment of the present invention when the number of fiber Bragg grating sensors is 10; Figure 7 These are simulation results of the deformation of the tested structure under different fiber Bragg grating sensor layout schemes provided in the embodiments of the present invention; Figure 8 These are physical experimental diagrams provided in the embodiments of the present invention; Figure 9 These are experimental results of flat plate deformation under different fiber Bragg grating sensor layout schemes provided in the embodiments of the present invention. Detailed Implementation

[0015] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0016] See Figure 1 and Figure 2 As shown in the figure, the multi-objective optimization method for fiber optic grating sensor layout based on NSGA-II disclosed in this embodiment of the invention specifically includes the following steps: S1. Obtain the global strain field, displacement field, and stress field of the structure under test under typical loads through finite element simulation; In a specific embodiment of the present invention, a finite element simulation model of a flat plate sample made of 7075-T6 aluminum alloy is established, and finite element simulation analysis is performed on the distribution of strain field, displacement field, and stress field. The simulation is performed using the solid mechanics module in COMSOL, and the dimensions of the flat plate sample are 500 mm × 500 mm × 2 mm. Regarding boundary conditions, one edge is fixed, and a concentrated load of 10 N is applied vertically downwards (i.e., in the -z direction) at the point (500 mm, 500 mm) to simulate a load (e.g., plate bending caused by a local impact). Figure 3 This is a finite element simulation diagram of the plate deformation provided in this embodiment of the invention, showing the strain, displacement, and stress field obtained from the finite element simulation, providing reference data for subsequent optimization of the fiber Bragg grating sensor layout. Based on the simulation results, the surface information of the plate is extracted as input parameters to evaluate the measurement error of the fiber Bragg grating sensor and predict its fatigue life, providing necessary data support for the proposed multi-objective optimization method based on NSGA-II.

[0017] S2. Generate an initial population, where each individual in the initial population represents a set of sensor layout coordinates on the structure under test; In this embodiment of the invention, in addition to generating the initial population, it is also necessary to set the NSGA-II core parameters, including the number of sensors M, the population size N, and the maximum number of iterations i. max Crossover probability (CR) and mutation probability (MR) are used, where each individual in the population represents a set of sensor layout coordinates on the structure being measured.

[0018] S3. Multi-objective calculation operation: The current population is used as the parent population for crossover and mutation to obtain the offspring population. The parent population and the offspring population are merged, and the deformation measurement error, fatigue life and uniformity coverage corresponding to each individual in the population are calculated. In this embodiment of the invention, the existing technology of applying genetic operators such as selection, crossover, and mutation to the parent population to obtain the offspring population as NSGA-II is not described in detail in this invention.

[0019] S4. Population update operation: Perform a fast non-dominated sort on all population individuals, divide them into different levels of non-dominated fronts according to their dominance relationship, sort the population individuals within the same front according to their crowding distance, and select a new population using an elite strategy. S5. Repeat the multi-objective calculation operation and population update operation until the preset iteration termination condition is reached, and use the population individuals in the new population as the optimal solution for sensor layout.

[0020] The embodiments of the present invention, based on NSGA-II, have significant advantages in solving large-scale, multi-objective, and complex coupling optimization problems by comprehensively considering the deformation measurement error, fatigue life, and uniformity coverage of sensor layout.

[0021] Furthermore, Table 1 shows the values ​​of various parameters in a specific embodiment of the present invention.

[0022] Table 1: Parameter Symbols and Values ​​Reference Table

[0023] Furthermore, in step S3, the deformation measurement error is achieved based on the following steps: S311. Obtain the position coordinates of each sensor corresponding to an individual in the current population; S312. Based on the global strain field and position coordinates of each sensor obtained by finite element simulation, obtain the strain values ​​of each sensor point on the surface of the tested structure, and calculate the reconstructed displacement field of the tested structure based on the preset deformation reconstruction algorithm. In this embodiment of the invention, the reconstructed displacement field can be expressed by the following formula: (1) In the above formula, Indicates the reconstructed displacement field; This represents the strain value at the position (x,y). The deformation reconstruction algorithm is described in the specific embodiments of the present invention. The deformation reconstruction algorithm reconstructs the displacement field from the strain field. The deformation reconstruction algorithm includes, but is not limited to, the direct integration method, the radial basis function interpolation method, the polynomial function interpolation method, and the inverse finite element method.

[0024] S313. Calculate the deformation measurement error corresponding to the current population individual based on the reconstructed displacement field of the measured structure and the displacement field obtained from finite element simulation: (2) In the above formula, Er represents the deformation measurement error, and Z(x,y) represents the displacement field obtained from finite element simulation. This represents the expected value of the absolute amplitude of the displacement field. This represents the expected absolute error between the reconstructed displacement field and the displacement field obtained from the finite element simulation.

[0025] This invention reconstructs the displacement field from the strain field obtained by finite element simulation, compares it with the displacement field obtained by simulation, and then obtains the deformation measurement error. Compared with obtaining the strain value at the measurement point based on fiber optic grating, this method ensures the absolute consistency between the strain field and the displacement field, avoids measurement errors caused by external factors, and improves the calculation accuracy of deformation measurement error.

[0026] Furthermore, in step S3, the fatigue life is achieved through the following steps: S321. Obtain the stress extreme values ​​at the target sensor point, wherein the stress extreme values ​​include the maximum stress and minimum stress at the target sensor point; In this embodiment of the invention, the target sensor point is a sensor point in a population of individuals whose fatigue life is to be calculated that is currently participating in the calculation. This sensor point corresponds to a coordinate on the surface of the junction to be tested, and the stress extrema are the maximum and minimum stress values ​​at that coordinate location.

[0027] S322. Calculate the average stress and stress amplitude at the target sensor point based on the stress extreme values ​​at the target sensor point: (3) In the above formula, This indicates the maximum stress at the target sensor location. This represents the minimum stress at the target sensor location. This represents the average stress at the target sensor location. This indicates the stress amplitude at the target sensor location; S323. Based on the stress amplitude at the target sensor location, calculate the equivalent stress amplitude at the target sensor location: (4) In the above formula, This represents the corrected equivalent stress amplitude at the target sensor location. Indicates the ultimate tensile strength of the target sensor; S324. Obtain the fatigue life of the target sensor based on the pre-obtained stress-life curve of the target sensor; wherein, the stress-life curve of the target sensor is expressed as: (5) In the above formula, A and B are material constants determined through fatigue experiments; Figure 4 This is a schematic diagram illustrating the relationship between stress amplitude and fatigue life of a fiber Bragg grating sensor according to a specific embodiment of the present invention. It can be seen that the two are negatively correlated.

[0028] S325. Calculate the fatigue life of each individual in the current population based on the fatigue life of the sensors at each sensor location: (6) In the above formula, This represents the fatigue life of an individual in the current population; N represents the number of sensors. Let represent the fatigue life of the i-th sensor, i=1,2,…,N.

[0029] It should be noted that fiber Bragg grating sensors, subjected to repeated loading due to structural deformation, will suffer fatigue damage. Therefore, it is necessary to evaluate their fatigue life based on the load at their location to guide layout optimization and extend the effective working life of the entire sensor network. In this embodiment of the invention, the stress extrema at each point can be obtained through finite element simulation. Based on the sensor's own material constant, the sensor lifetime at each sensor point within the target population can be obtained through steps S321 to S324. Finally, the fatigue life of the entire target population can be calculated based on step S325. This, in turn, can guide the sensor layout.

[0030] Further, in step S3, the uniformity coverage is obtained through the following steps: S331. Calculate the mean distance between any two sensors in the current population: (7) In the above formula, This represents the average distance between any two sensors, and N represents the number of sensors. This represents the total number of combinations of pairwise sensor pairings; Represents any two sensors and The distance between them, ; The distance between any two sensors is represented as: (8) S332. Calculate the standard deviation of the distance between any two sensors: (9) In the above formula, The standard deviation of the distance between any two sensors; S333. Calculate the uniformity coverage of the current population individuals based on the mean and standard deviation of the distance between any two sensors: (10) In the above formula, UCI represents uniformity coverage; d max This represents the theoretically achievable maximum distance between any two sensors.

[0031] In this embodiment of the invention, uniformity coverage (UCI) reflects the density and spatial coverage of sensor distribution. It is one of the important indicators for optimizing sensor layout schemes and directly affects the overall performance of the sensor network. This invention uses uniformity coverage as another evaluation indicator for sensor layout, further optimizing the overall layout of the sensors.

[0032] Furthermore, in this embodiment of the invention, the step of performing rapid non-dominated ordination on all individuals in the population and dividing them into different levels of non-dominated fronts according to their dominance relationships includes: S41. Taking measurement error, fatigue life and uniformity coverage as objective functions respectively, if individual p is no worse than individual q in all objective functions and is strictly better than individual q in at least one objective function, then individual p is determined to dominate individual q. In this embodiment of the invention, the measurement error Er will be minimized and the fatigue life will be extended to the maximum extent. With maximizing uniformity coverage (UCI) as the optimization objective, individuals in the population are divided into different levels of non-dominated frontiers according to their dominance relationship. Specifically, if individual p has a deformation measurement error no greater than that of individual q, and is no less than that of individual q in both fatigue life and uniformity coverage, and is strictly superior to q in at least one of the objectives, then individual p is considered to dominate individual q.

[0033] S42. Iterate through all pairs of individuals (p, q) in the population. For each individual p in the population, obtain the number n individuals that dominate individual p. p and the set of individuals S dominated by individual p p ; S43, put all n p Individuals with a value of 0 are identified as the first non-dominated frontier; S44. For each individual p in the currently identified non-dominated frontier, traverse its S... p For each individual q in the set, the n of q p The value is reduced by 1; if after reducing by 1, the value of n of q is reduced by 1. p If the value becomes 0, then q is identified as the next non-dominated frontier; S45. Repeat step S44 until all individuals in the population have been assigned to the corresponding non-dominated frontier.

[0034] Based on the above dominance relationship determination, the population can be divided into multiple non-dominated fronts. The first layer of fronts contains the solution with the best overall performance in terms of deformation measurement accuracy, structural fatigue life, and coverage uniformity, which is the optimal non-dominated front. In this process, only one comparison is needed between each pair of individuals, requiring a total of O(N²) comparisons. Each comparison requires comparing M objective function values, so the time complexity of NSGA-II can be written as O(MN²). 2 This is significantly lower than the time complexity O(MN) of the traditional non-dominated sorting genetic algorithm NSGA. 3 This improves algorithm efficiency.

[0035] Furthermore, in step S4, the crowding distance is used as the ranking criterion for individuals within the same non-dominated front. By estimating the relative distance between an individual and its neighbors in the target space, solutions located in sparse regions are preferentially retained, thereby preventing the solution set from converging prematurely or concentrating in local areas. Specifically, the ranking of population individuals within the same non-dominated front according to crowding distance includes: S411. For the m-th objective function, sort the individuals in the current frontier according to their values ​​on the objective function; In a specific embodiment of the present invention, the total number of objective functions is 3. The individuals in the population are sorted according to their values ​​on the objective function; for example, for measurement errors, the individuals can be sorted in ascending order of measurement errors.

[0036] S422. Calculate the crowding distance of the sorted individual i on the m-th objective function: (11), In the above formula, and Let represent the values ​​of the individuals adjacent to the i-th individual on a specific objective function. and These represent the maximum and minimum values ​​of the objective function at the current frontier, respectively. This represents the crowding degree of individual i on the m-th objective function; The total crowding distance of individual i across all objective functions is calculated as follows: (12), In the above formula, M is the number of objective functions. This represents the total crowding distance for individual i.

[0037] The method in this invention prioritizes individuals with larger crowding distances to maintain the diversity of the solution set. To ensure that boundary individuals are preferentially retained in the selection, their crowding degree is assigned to infinity.

[0038] Furthermore, in this embodiment of the invention, the selection of a new population using an elite strategy includes: starting from the optimal non-dominated front, sequentially adding individuals from each non-dominated front to the next generation population; when adding a certain non-dominated front causes the number of individuals in the next generation population to exceed the population's individual size threshold, sorting the current non-dominated fronts in descending order according to their crowding distance; preferentially selecting individuals from the population with larger crowding distances to add to the next generation population, until the number of individuals in the next generation population reaches the population's individual size threshold.

[0039] Specifically, such as Figure 5 As shown, this is a schematic diagram of the elite strategy provided in an embodiment of the present invention. In each generation, the parent population (preferably converted to subscript form) P t and offspring population Q t They were merged into a temporary group R. t For the temporary group R t Perform a fast non-dominated sort to obtain the frontiers F1, F2, ..., and add the best frontiers to the next generation parent P in order. t+1 The process continues until the population limit is reached. The frontier containing the population limit (e.g., F3) is sorted by crowding distance, with individuals having larger crowding distances being retained first until the population limit is reached; the remaining individuals are discarded. This elite strategy ensures that individuals with higher levels and greater diversity are prioritized, thus balancing solution quality and diversity. This strategy also ensures that individuals with high non-dominant levels and located in sparse regions are prioritized, balancing solution quality and diversity. This not only enhances the retention of excellent solutions but also contributes to improving the global convergence of the search process.

[0040] Furthermore, in step S5, the iteration termination condition can be reaching the maximum number of iterations or finding an optimal solution that meets the requirements. In a specific embodiment of the present invention, when the maximum number of iterations i is reached... max When the loop terminates, the Pareto solution is output, and the Pareto front in the Pareto solution space is obtained.

[0041] Furthermore, Figure 6This is the simulation result provided by an embodiment of the invention when the number of fiber Bragg grating sensors is 10. The red dots represent Pareto solutions, each solution corresponding to a set of fiber Bragg grating sensor layout schemes, i.e., a set of coordinates for the 10 fiber Bragg grating sensors. All red dots together constitute the Pareto front. Compared to non-Pareto solutions, the sensor layout schemes on the Pareto front are superior in at least one objective. Therefore, layout schemes on the Pareto front should be given priority to achieve a balanced optimization of performance.

[0042] The point P1 on the Pareto front achieves optimal performance for the measurement error optimization objective. Figure 6 The corresponding coordinates are (0.0143, 46.7079, 0.3736); point P2 achieves optimal performance in terms of fatigue life optimization objective. Figure 6 The corresponding coordinates are (0.1659, 82.6056, 0.3026); point P3 achieves the best performance in terms of uniformity coverage optimization objective. Figure 6 The corresponding coordinates are (0.0465, 57.3441, 0.3898).

[0043] Furthermore, Figure 7 These are the simulation results of flat panel deformation for the fiber Bragg grating sensor layout schemes corresponding to points P1, P2, and P3 provided in this embodiment of the invention. In the simulation results for flat panel deformation at point P1, the simulated value is closest to the measured value, with a measurement error of only 0.0143. In the simulation results for flat panel deformation at point P2, the measurement error is 0.1659. In the simulation results for flat panel deformation at point P3, the measurement error is 0.0465.

[0044] Furthermore, Figure 8 This is a physical experimental diagram provided in an embodiment of the present invention. The experimental sample is an aerospace 7075-T6 aluminum alloy plate, whose dimensions and material properties are consistent with the finite element simulation model. One edge of the aluminum alloy plate is kept fixed, while the other three edges are not fixed or constrained.

[0045] Ten fiber Bragg grating strain sensors are arranged on the surface of the aluminum alloy plate, with sensor coordinates corresponding to the results of each optimized arrangement. The central Bragg wavelength range of the ten fiber Bragg grating sensors is 1530nm to 1550nm, with a spacing of 5nm, and two fiber Bragg grating sensors per wavelength. Each fiber Bragg grating sensor is 10mm long. A temperature-compensated fiber Bragg grating sensor with a central wavelength of 1543nm is also included to correct for measurement errors caused by changes in ambient temperature.

[0046] A concentrated load of 10N is applied vertically downward at a point (500mm, 500mm) using standard weights to cause elastic deformation of the aluminum alloy plate.

[0047] Twenty-five uniformly distributed grid-like sampling points were set on the surface of the aluminum alloy plate. In order to obtain the actual displacement of the aluminum alloy plate surface, a handheld laser displacement meter was used to measure the displacement of each sampling point before and after loading. Then, an interpolation algorithm was used to reconstruct the actual displacement field of the entire aluminum alloy plate surface.

[0048] The deformation measurement error can be calculated by comparing the actual displacement field with the displacement field measured by the fiber Bragg grating strain sensor, and then the actual effectiveness of the proposed fiber Bragg grating sensor deployment method can be evaluated.

[0049] Furthermore, Figure 9 The experimental results of plate deformation for the fiber Bragg grating sensor layout scheme corresponding to points P1, P2, and P3 provided in this embodiment of the invention are shown. In the plate deformation experimental results corresponding to point P1, the simulated value is closest to the measured value, with a measurement error of only 0.0268. In the plate deformation simulation results corresponding to point P2, the measurement error is 0.1575. In the plate deformation simulation results corresponding to point P3, the measurement error is 0.0473. The trend of the experimental results agrees well with the simulation results, verifying the effectiveness of the proposed method and its feasibility under actual operating conditions.

[0050] Compared with existing technologies, the multi-objective optimization method for fiber Bragg grating sensor layout based on NSGA-II provided in this invention effectively balances measurement error, fatigue life, and uniformity coverage. By utilizing the NSGA-II algorithm, the efficiency of solving multi-objective optimization problems is improved, achieving comprehensive optimized layout of fiber Bragg grating sensors, thereby enhancing the overall performance of the fiber Bragg grating sensing system. Simulations and experiments have verified the feasibility and superiority of the proposed method. This method is particularly suitable for applications requiring high precision and high reliability, such as structural health monitoring of aerospace structures.

[0051] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art and should not be interpreted in an idealized or overly formal sense unless specifically defined.

[0052] For the sake of simplicity, the method embodiments are described as a series of actions. However, those skilled in the art should understand that the embodiments of the present invention are not limited to the described order of actions, because according to the embodiments of the present invention, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions involved are not necessarily essential to the embodiments of the present invention.

[0053] Furthermore, those skilled in the art will understand that although some embodiments herein include certain features included in other embodiments but not others, combinations of features from different embodiments are intended to be within the scope of the invention and form different embodiments. For example, any of the claimed embodiments can be used in any combination.

[0054] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-objective optimization method for fiber optic grating sensor layout based on NSGA-II, characterized in that, The method includes: The global strain field, displacement field, and stress field of the structure under test under typical loads are obtained through finite element simulation. An initial population is generated, where each individual in the initial population represents a set of sensor layout coordinates on the structure under test; Multi-objective computation operation: The current population is used as the parent population for crossover and mutation to obtain the offspring population. The parent population and the offspring population are then merged, and the deformation measurement error, fatigue life and uniformity coverage corresponding to each individual in the population are calculated. Population update operation: Perform a fast non-dominated sort on all population individuals, divide them into different levels of non-dominated fronts according to their dominance relationship, sort the population individuals within the same front according to their crowding distance, and select a new population using an elite strategy. Repeatedly perform multi-objective computation and population update operations until the preset iteration termination condition is met, and use the population individuals in the new population as the optimal solution for sensor layout.

2. The method according to claim 1, characterized in that, The deformation measurement error is corrected using the following steps: Obtain the position coordinates of each sensor corresponding to an individual in the current population; Based on the global strain field and position coordinates of each sensor obtained by finite element simulation, the strain values ​​of each sensor point on the surface of the tested structure are obtained, and the reconstructed displacement field of the tested structure is calculated based on the preset deformation reconstruction algorithm. The deformation measurement error corresponding to the current individual in the population is calculated based on the reconstructed displacement field of the measured structure and the displacement field obtained from finite element simulation. ， In the above formula, Er represents the deformation measurement error, and Z(x,y) represents the displacement field obtained from finite element simulation. This represents the expected value of the absolute amplitude of the displacement field. This represents the expected absolute error between the reconstructed displacement field and the displacement field obtained from the finite element simulation.

3. The method according to claim 1, characterized in that, The fatigue life is achieved through the following steps: Obtain the stress extreme values ​​at the target sensor location, whereby the stress extreme values ​​include the maximum and minimum stress at the target sensor location; Calculate the average stress and stress amplitude at the target sensor point based on the stress extreme values ​​at the target sensor point: ， In the above formula, This indicates the maximum stress at the target sensor location. This represents the minimum stress at the target sensor location. This represents the average stress at the target sensor location. This indicates the stress amplitude at the target sensor location; Based on the stress amplitude at the target sensor location, calculate the equivalent stress amplitude at the target sensor location: ， In the above formula, This represents the corrected equivalent stress amplitude at the target sensor location. Indicates the ultimate tensile strength of the target sensor; The fatigue life of the target sensor is obtained based on the pre-obtained stress-life curve of the target sensor; wherein, the stress-life curve of the target sensor is expressed as: ， In the above formula, A and B are material constants determined through fatigue experiments; The fatigue life of each individual in the current population is calculated based on the fatigue life of the sensors at each sensor location. ， In the above formula, N represents the fatigue life of individuals in the current population; N represents the number of sensors. Let represent the fatigue life of the i-th sensor, i=1,2,…,N.

4. The method according to claim 1, characterized in that, The uniform coverage is achieved through the following steps: Calculate the mean distance between any two sensors in the current population: ， In the above formula, This represents the average distance between any two sensors, and N represents the number of sensors. This represents the total number of combinations of pairwise sensor pairings; Represents any two sensors and The distance between them, ; Calculate the standard deviation of the distance between any two sensors: ， In the above formula, The standard deviation of the distance between any two sensors; Calculate the uniformity coverage of the current population based on the mean and standard deviation of the distance between any two sensors: ， In the above formula, UCI represents uniformity coverage; d max This represents the theoretically achievable maximum distance between any two sensors.

5. The method according to claim 1, characterized in that, The process of performing rapid non-dominated ordination on all individuals in the population and dividing them into different levels of non-dominated frontiers according to their dominance relationships includes: S41. Taking measurement error, fatigue life and uniformity coverage as objective functions respectively, if individual p is no worse than individual q in all objective functions and is strictly better than individual q in at least one objective function, then individual p is determined to dominate individual q. S42. Iterate through all pairs of individuals (p, q) in the population. For each individual p in the population, obtain the number n individuals that dominate individual p. p and the set of individuals S dominated by individual p. p ; S43, put all n p Individuals with a value of 0 are identified as the first non-dominated frontier; S44. For each individual p in the currently identified non-dominated frontier, traverse its S... p For each individual q in the set, the n of q p The value is reduced by 1; if after reducing by 1, the value of n of q is reduced by 1. p If the value becomes 0, then q is identified as the next non-dominated frontier; S45. Repeat step S44 until all individuals in the population have been assigned to the corresponding non-dominated frontier.

6. The method according to claim 5, characterized in that, The sorting of population individuals within the same non-dominated front according to crowding distance includes: For the m-th objective function, sort the individuals in the current frontier according to their values ​​on that objective function; Calculate the crowding distance of the sorted individual i on the m-th objective function: ， In the above formula, and Let represent the values ​​of the individuals adjacent to the i-th individual on the m-th objective function, respectively. and Let represent the maximum and minimum values ​​of the m-th objective function at the current frontier, respectively. This represents the crowding degree of individual i on the m-th objective function; The total crowding distance of individual i across all objective functions is calculated as follows: ， In the above formula, M is the number of objective functions. This represents the total crowding distance for individual i.

7. The method according to claim 6, characterized in that, The selection of a new population using an elite strategy includes: Starting from the optimal non-dominated front, individuals from each non-dominated front are sequentially added to the next generation of the population; When adding a non-dominated front causes the number of individuals in the next generation to exceed the population's individual size threshold, the current non-dominated fronts are sorted in descending order based on their crowding distance. Individuals with greater crowding distance are preferentially selected to join the next generation of the population until the number of individuals in the next generation reaches the population size threshold.

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