CN-121997657-A - NSGA-II-based multi-objective optimization method for fiber bragg grating sensor layout

CN121997657ACN 121997657 ACN121997657 ACN 121997657ACN-121997657-A

Abstract

The invention provides a multi-target optimization method for fiber grating sensor layout based on NSGA-II, which comprises the steps of obtaining a global strain field, a displacement field and a stress field of a tested structure under typical load through finite element simulation, generating an initial population, wherein each individual in the initial population represents a group of sensor layout coordinates, intersecting and mutating a parent population to obtain a child population, merging the parent population and the child population, calculating deformation measurement errors, fatigue life and uniformity coverage corresponding to each population individual, carrying out rapid non-dominant sorting on all population individuals, sorting population individuals in the same front edge according to crowding degree distances, adopting an elite strategy to select a new population, and repeatedly executing multi-target calculation operation and population updating operation until a preset iteration termination condition is reached. The invention effectively balances the measurement error, the fatigue life and the uniformity coverage, and realizes the comprehensive optimization layout of the fiber bragg grating sensor.

Inventors

LV JIAMING
ZHU YUNHONG
ZHANG YONG
Peng Anxu
LOU XIAOPING

Assignees

北京信息科技大学

Dates

Publication Date: 20260508
Application Date: 20260123

Claims (7)

1. An NSGA-II-based fiber bragg grating sensor layout multi-objective optimization method is characterized by comprising the following steps: acquiring a global strain field, a displacement field and a stress field of a tested structure under a typical load through finite element simulation; Generating an initial population, each individual in the initial population representing a set of sensor layout coordinates on a structure under test; the multi-objective calculation operation comprises the steps of intersecting and mutating a current population as a parent population to obtain a child population, combining the parent population and the child population, and calculating deformation measurement errors, fatigue life and uniformity coverage corresponding to individuals of each population; The population updating operation comprises the steps of carrying out rapid non-dominant sorting on all population individuals, dividing the population individuals into non-dominant fronts with different grades according to dominant relations, sorting the population individuals in the same fronts according to crowding distances, and selecting a new population by adopting elite strategies; And repeatedly executing the multi-target calculation operation and the population updating operation until a preset iteration termination condition is reached, and taking the population individuals in the obtained new population as the optimal solution of the sensor layout.
2. The method of claim 1, wherein the deformation measurement error is achieved by: acquiring position coordinates of each sensor corresponding to individuals in the current population; Based on the global strain field obtained by finite element simulation and the position coordinates of each sensor, obtaining the strain value of each sensor point position on the surface of the structure to be measured, and calculating the reconstruction displacement field of the structure to be measured based on a preset deformation reconstruction algorithm; Calculating to obtain deformation measurement errors corresponding to individuals of the current population according to the reconstructed displacement field of the tested structure and the displacement field obtained by finite element simulation: , In the above formula, er represents deformation measurement error, Z (x, y) represents displacement field obtained by finite element simulation, Indicating the desire for the absolute amplitude of the displacement field, Representing the expectation of absolute error between the reconstructed displacement field and the displacement field obtained by finite element simulation.
3. The method of claim 1, wherein the fatigue life is achieved by: Obtaining a stress extremum of a point position of a target sensor, wherein the stress extremum comprises a maximum stress and a minimum stress of the point position of the target sensor; Calculating average stress and stress amplitude of the target sensor point based on the stress extremum of the target sensor point: , In the above-mentioned method, the step of, Representing the maximum stress of the target sensor spot, Representing the minimum stress of the target sensor spot, Representing the average stress of the target sensor sites, Representing stress amplitude values of the target sensor points; Calculating the equivalent stress amplitude of the point position of the target sensor based on the stress amplitude of the point position of the target sensor: , In the above-mentioned method, the step of, Representing the corrected equivalent stress amplitude of the target sensor spot, Representing the ultimate tensile strength of the target sensor; Obtaining the fatigue life of the target sensor according to a 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 by fatigue experiments; According to the fatigue life calculation of the sensors of each sensor point position in the individuals of the current population, the fatigue life corresponding to the individuals of the current population is obtained: , In the above-mentioned method, the step of, Indicating the fatigue life of the individuals of the current population, N indicating the number of sensors, The fatigue life of the i-th sensor is indicated, i=1, 2,..n.
4. The method of claim 1, wherein the uniformity coverage is achieved by: calculating and obtaining the average value of the distance between any two sensors in the individuals in the current population: , In the above-mentioned method, the step of, Representing the average value of the distance between any two sensors, and N represents the number of the sensors; Representing the total combination number of pairwise pairs of sensors; Representing any two sensors And The distance between them, wherein, ; Calculating to obtain standard deviation of the distance between any two sensors: , In the above-mentioned method, the step of, Representing the standard deviation of the distance between any two sensors; Calculating the uniformity coverage of individuals in the current population based on the mean value and standard deviation of the distance between any two sensors: , In the above equation, UCI represents uniformity coverage, and d max represents the theoretically achievable maximum distance between any two sensors.
5. The method of claim 1, wherein said rapid non-dominant ranking of all populations of individuals, dividing them into different levels of non-dominant fronts by dominant relationship comprises: S41, respectively taking the measurement error, the fatigue life and the uniformity coverage as objective functions, and judging that the individual p dominates the individual q if the values of the individual p on all objective functions are not worse than the individual q in the population and are strictly better than the individual q on at least one objective function; S42, traversing all individual pairs (p, q) in the population, and acquiring, for each individual p in the population, the number of individuals n p that dominate the individual p, and an individual set S p that is dominated by the individual p; S43, identifying all individuals with n p value of 0 as a first non-dominant front; S44, traversing each individual q in the S p set of each individual p in the currently identified non-dominant front, and subtracting 1 from the n p value of q, wherein if the n p value of q is 0 after subtracting 1, q is identified as the next non-dominant front; S45, executing the step S44 in a circulating way until all individuals in the population are divided into corresponding non-dominant fronts.
6. The method of claim 5, wherein the sorting the population of individuals within the same non-dominant front by crowdedness distance comprises: Sorting individuals in the current leading edge according to the values of the individuals in the current leading edge on the mth objective function; calculating the crowding degree distance of the sequenced individual i on the mth objective function: , In the above-mentioned method, the step of, And (3) with Representing the values on the mth objective function of individuals adjacent to the ith individual, And (3) with Representing the maximum and minimum of the mth objective function in the current leading edge respectively, Representing the crowding degree of the individual i on the mth objective function; the total crowding distance of the individual i on all objective functions is calculated as follows: , in the above formula, M is the number of objective functions, Indicating the total crowding distance of individual i.
7. The method of claim 6, wherein selecting a new population using elite strategy comprises: sequentially adding population individuals in each non-dominant front to the next generation population from the optimal non-dominant front; When adding a certain non-dominant front leads to the quantity in the next generation population exceeding the individual quantity threshold value of the population, sorting the current non-dominant front in descending order according to the crowding degree distance; Preferably, population individuals with larger crowding distances are selected to be added into the next generation population until the number of individuals in the next generation population reaches the threshold number of individuals in the population.

Description

NSGA-II-based multi-objective optimization method for fiber bragg grating sensor layout Technical Field The invention relates to the technical field of optical fiber sensing, in particular to a multi-objective optimization method for an optical fiber grating sensor layout based on NSGA-II. Background As a core component of the structural health monitoring system, the sensors can monitor state parameters of key structural components, such as stress, strain, displacement and acceleration, in real time, and provide necessary data support for fault detection, fatigue life prediction and maintenance decision. As an emerging sensor, an optical Fiber Bragg Grating (FBG) sensor, which uses the optical characteristic change of light transmitted by an optical fiber under external stimulus to realize accurate measurement of a plurality of physical quantities, has light weight, compact size, strong environmental robustness and electromagnetic interference resistance, and is easy to multiplex into a sensor network, and has been widely applied to structural health monitoring in various fields. The performance of the fiber bragg grating sensing system is limited by the fiber bragg grating sensor, and the comprehensive performance of the fiber bragg grating sensing system is directly determined by the sensor layout, so that optimization of the sensor layout is needed. Most of the existing researches focus on single performance index optimization, such as measurement accuracy or reconstruction errors, and the methods ignore simultaneous optimization of multiple key performance indexes. Whereas existing multi-objective optimization methods typically only consider trade-offs between accuracy, cost, number of sensors, fatigue life and uniformity coverage have not been integrated into a unified multi-objective optimization framework. Therefore, how to improve the stability and reliability of the fiber bragg grating sensing system in a complex application environment in the aspect of the sensor network layout is still a technical bottleneck to be broken through. Disclosure of Invention The invention provides a multi-objective optimization method for a fiber grating sensor layout based on NSGA-II so as to overcome or partially overcome the problems. The invention provides a multi-objective optimization method for a fiber grating sensor layout based on NSGA-II, which comprises the following steps: acquiring a global strain field, a displacement field and a stress field of a tested structure under a typical load through finite element simulation; Generating an initial population, each individual in the initial population representing a set of sensor layout coordinates on a structure under test; the multi-objective calculation operation comprises the steps of intersecting and mutating a current population as a parent population to obtain a child population, combining the parent population and the child population, and calculating deformation measurement errors, fatigue life and uniformity coverage corresponding to individuals of each population; The population updating operation comprises the steps of carrying out rapid non-dominant sorting on all population individuals, dividing the population individuals into non-dominant fronts with different grades according to dominant relations, sorting the population individuals in the same fronts according to crowding distances, and selecting a new population by adopting elite strategies; And repeatedly executing the multi-target calculation operation and the population updating operation until a preset iteration termination condition is reached, and taking the population individuals in the obtained new population as the optimal solution of the sensor layout. Further, the deformation measurement error is realized by the following steps: acquiring position coordinates of each sensor corresponding to individuals in the current population; Based on the global strain field obtained by finite element simulation and the position coordinates of each sensor, obtaining the strain value of each sensor point position on the surface of the structure to be measured, and calculating the reconstruction displacement field of the structure to be measured based on a preset deformation reconstruction algorithm; Calculating to obtain deformation measurement errors corresponding to individuals of the current population according to the reconstructed displacement field of the tested structure and the displacement field obtained by finite element simulation: , In the above formula, er represents deformation measurement error, Z (x, y) represents displacement field obtained by finite element simulation, Indicating the desire for the absolute amplitude of the displacement field,Representing the expectation of absolute error between the reconstructed displacement field and the displacement field obtained by finite element simulation. Further, the fatigue life is achieved by: Obtaining a stress extremum of a point pos