Development of a Large-Range FBG Strain Sensor Based on the NSGA-II Algorithm

Abstract

To monitor large deformations in dovetail tenon joints of Dong ethnic wooden drum towers, this study designs a large-range Fiber Bragg Grating (FBG) strain sensor based on the FBG sensing principle. The NSGA-II algorithm is utilized to optimize the packaging structure of FBG strain sensors. Consequently, an adaptive optimization methodology for its packaging configuration is proposed. This study sets the optimization objectives as a 5000 με measurement range and 0.1 pm/με sensitivity. It employs the NSGA-II algorithm to optimize the structural dimensions and material properties of the large-range FBG strain sensor. This process yields three combinations that meet the requirements for monitoring large deformations in dovetail tenon joints of Dong wooden drum towers. Subsequent linearity experiments were conducted to verify the sensitivity stability and measurement range of the three large-range FBG strain sensors. The results show that within the measurement range of 0–6000 με, all three sensors achieve a strain sensitivity of 0.099 pm/με, with a fitted linear correlation coefficient of 0.999.

1. Introduction

The wooden drum tower is a cultural treasure of China’s Dong ethnic architecture. During long-term service, its wooden components are prone to mortise-tenon joint detachment due to environmental loads and fatigue effects. In severe cases, this may even lead to collapse under strong winds. Therefore, long-term monitoring of its wooden structure is imperative for cultural heritage preservation. Fiber Bragg Grating (FBG) strain sensors are widely employed in monitoring multi-scale deformations (strain, deflection, inclination) in wooden structures, owing to their high sensitivity, corrosion resistance, high-temperature tolerance, and adaptability to harsh environments [1]. However, Roberto et al. [2], who used FBG sensors to monitor modal responses of a wooden building in Perugia, Italy, found that bare gratings are fragile and require complex packaging for protection. Moreover, wind-induced deformations at mortise-tenon joints of the Dong drum tower are large. This makes it necessary to improve the packaging structure to develop large-range FBG strain sensors. To address these issues, researchers have enhanced the range and sensitivity of FBG sensors by modifying the packaging configuration, material, and processing [3]. For instance, Kim et al. [4] coated FBG sensors with polyimide to extend the maximum strain range of those embedded in seven-core steel wires, achieving a 1.73% improvement over bare gratings. Guo et al. [5] developed a three-dimensional FBG sensor, extending its range to 5000 με. Sun et al. [6] doubled and quadrupled the range by adjusting the bracket clamping length in the protection device. Liu et al. [7] integrated a pre-relaxed FBG into the packaging: when the initial operational FBG reaches its limit, the pre-relaxed one activates, extending the maximum range to 18,923 με.

FBG strain sensors applied to on-site monitoring of Dong wooden drum towers require not only a large measurement range but also easy installation. Therefore, a packaging structure that is easy to install can be selected to protect bare gratings. Structural optimization analysis is then conducted according to the requirements of measurement range and sensitivity. Currently, commonly used structural optimization algorithms include Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Non-dominated Sorting Genetic Algorithm II (NSGA-II), etc. Delyová et al. [8] applied the genetic algorithm to the size optimization of truss structures. By combining the genetic algorithm with the finite element method, the structural weight was reduced. Wang et al. [9] used the genetic algorithm to perform multi-objective optimization of size, topology, and shape for steel space frame roof structures. Kociecki et al. [10] proposed a two-stage genetic algorithm to convert constrained optimization problems into unconstrained ones by defining fitness functions. Subsequently, Kociecki et al. [11] continued their research on the application of genetic algorithms in structural optimization and proposed a method for simultaneous optimization of size, topology, and shape of steel space frame roof structures. Kookalani et al. [12] used the multi-objective particle swarm optimization (MOPSO) algorithm to find the optimal geometric shape, with the objective functions of minimizing structural stress and the ratio of maximum displacement to self-weight. Sardone et al. [13] adopted multi-objective evolutionary algorithms (MOEAs) to find the optimal shape of hollow beams, aiming to minimize mass and tensile stress. Carbas et al. [14] carried out structural optimization design using five new nature-inspired meta-heuristic algorithms, including Tree-Seed Algorithm, Squirrel Search Algorithm, Water Strider Algorithm, Grey Wolf Algorithm, and Brain Storm Optimization Algorithm, and analyzed their advantages and disadvantages. Shan et al. [15] proposed a highly integrated method combining meta-heuristic algorithms and machine learning methods to optimize structural design through online model training, updating, and parameter adjustment. NSGA-II incorporates three core enhancements: efficient sorting, elitism preservation, and uniform distribution control. It outperforms early multi-objective optimization algorithms in computational efficiency, convergence behavior, and solution distributivity. As a result, it has established itself as the “benchmark algorithm” in the domain of multi-objective optimization. Stanković et al. [16] conducted multi-objective optimization based on the NSGA-II algorithm, considering constraints such as stress and displacement, with the objectives of minimizing structural mass and deflection.

The above research results indicate that the NSGA-II algorithm, a type of multi-objective optimization algorithm, can be adopted to improve the packaging structure of fiber Bragg grating sensors. Therefore, this paper proposes an adaptive optimization method for the packaging structure of FBG strain sensors. Based on the FBG sensing principle, the finite element analysis method is used to determine the sensitive parameters affecting the sensitivity and measurement range of the strain sensor. Sensitivity and measurement range are set as the objective conditions. Sensitive parameters serve as the analysis subgroups. The NSGA-II algorithm is then employed to optimize the structural parameters of the FBG strain sensor, enabling the intelligent development of fiber Bragg grating strain sensors with special functions. Ultimately, an FBG strain sensor capable of large-range measurement is developed to satisfy the requirement for real-time monitoring of large deformations at the mortise-tenon joints of Dong wooden drum towers.

2. Working Principle of Large-Range FBG Strain Sensor

2.1. FBG Sensing Principle

Figure 1 shows the basic structure of an FBG, of which the core layer is with periodic refractive index gratings and the operation relies on the Bragg condition [17]:

$${\lambda }_B=2n_{eff}\mathrm{\Lambda }$$

(1)

where λ_B (Bragg wavelength) is the reflected light wavelength, n_eff is the fiber’s effective refractive index, and Λ is the grating period. For sensing applications, temperature changes ΔT alter Λ (thermal expansion) and n_eff (thermo-optic effect), causing wavelength shifts Δλ_T, Strain ε (tension/compression) modifies Λ (mechanical deformation) and n_eff (photoelastic effect), leading to shifts: Δλε.

2.2. Structural Form of Large-Range FBG Strain Sensor

As a mature commercial packaging form of FBG strain sensors, the substrate type has advantages such as high sensitivity, small volume, and easy installation. The substrate-type FBG strain sensor protection device proposed in this paper mainly consists of a substrate, a strain measurement grating FBG1, and a temperature compensation grating FBG2 (Figure 2). Based on the relationship between the central wavelength shift of bare FBG versus temperature and strain [18,19], the shift of the central wavelength of the designed FBG strain sensor in Figure 1 can be given:

$${\displaystyle \frac{\mathrm{\Delta }{\lambda }_{\beta }}{{\lambda }_{\beta }}}=(1-{\mathrm{P}}_e)\epsilon +\left[{\alpha }_n+{\alpha }_{\mathrm{\Lambda }}+(1-{\mathrm{P}}_e)({\alpha }_{stru\mathrm{ct}}-{\alpha }_{\mathrm{\Lambda }})\right]\mathrm{\Delta }T$$

(2)

where α_Λ is thermal expansion coefficient; α_n is thermo-optic coefficient; P_e is effective photoelastic coefficient; α_struct is the thermal expansion of the structure, which is the key factor determining the sensing performance. By symmetrically cutting two rectangular cavities on both sides of the substrate, the stiffness of the substrate is reduced, and the measurement range of the FBG strain sensor is increased. To meet the installation requirements of the mortise-tenon joints of Dong wooden drum towers, the substrate structure of the FBG strain sensor proposed in this paper reserves four screw holes at the four corners of the substrate, and screws are used to fix the substrate-type FBG strain sensor at the mortise-tenon joints of Dong wooden drum towers. The working mechanism of the substrate-type FBG strain sensor proposed in this paper is as follows: when the mortise-tenon joints of the Dong wooden drum tower are detached, the movement of the screws at the four corners of the substrate causes axial displacement of the substrate. The concentrated stress inside the substrate leads to strain changes in the middle part of the substrate, which in turn causes an increase in the wavelength of the fiber grating inside the groove. Due to the cross-sensitivity of FBG to strain and temperature, the FBG strain sensor proposed in this paper is connected in series with a temperature compensation grating outside the substrate to separate the wavelength shifts of the fiber grating caused by strain and temperature.

2.3. Transmission Principle

During the service process of the substrate-type FBG strain sensor, its strain monitoring accuracy depends on the structural parameters of the substrate. It is also closely related to the interface transmission characteristics of strains between various layers of the FBG sensor. The strain transmission model of the substrate-type FBG strain sensor is shown in Figure 3, which consists of a glass fiber core, a coating layer, an adhesive layer, and a substrate.

At this point, the average strain at the optical fiber core ε_g(x) is given by [20]:

$${\epsilon }_g(x)={\left({\displaystyle \frac{2}{\beta E_g{r}_g}}\right)}^{1/2}{C}_1\exp \left[{\left({\displaystyle \frac{2}{\beta E_g{r}_g}}\right)}^{1/2}\left(L+x\right)\right]-{\left({\displaystyle \frac{2}{\beta E_g{r}_g}}\right)}^{1/2}{C}_2\exp \left[{\left({\displaystyle \frac{2}{\beta E_g{r}_g}}\right)}^{1/2}\left(L-x\right)\right]+{\epsilon }_m$$

(3)

where L denotes half the length of the substrate, E_g is the elastic modulus of the glass core, r_g is the radius of the glass core, and ε_m is the structural strain of the substrate. The parameter β in the equation can be expressed by the following formula:

$$\beta =r_g\left({\displaystyle \frac{1}{G_c}}\ln {\displaystyle \frac{r_c}{r_g}}+{\displaystyle \frac{1}{G_a}}\ln {\displaystyle \frac{r_a}{r_c}}\right)$$

(4)

In the equation, r_c is the outer radius of the coating layer, r_a is the outer radius of the adhesive layer, and G_a and G_c are the shear modulus of the adhesive and the shear modulus of the coating layer, respectively. The strain at both ends of the optical fiber core is equal to that at both ends of the substrate. Thus, the boundary conditions for Equation (3) are the displacement of the glass core at the origin u_g(0) = 0. And the strain ε_g (L) of the glass core at the position along the fiber length L is ε_m. Accordingly, the integral constants C₁ and C₂ in Equation (3) can be expressed as:

$$C_1=-1/\left\{\exp \left[L{\left({\displaystyle \frac{2}{\beta E_g{r}_g}}\right)}^{1/2}\right]+\exp \left[3L{\left({\displaystyle \frac{2}{\beta E_g{r}_g}}\right)}^{1/2}\right]\right\}$$

(5)

$$C_2=-\exp \left[2L{\left({\displaystyle \frac{2}{\beta E_g{r}_g}}\right)}^{1/2}\right]/\left\{\begin{array}{l}\exp \left[L{\left({\displaystyle \frac{2}{\beta E_g{r}_g}}\right)}^{1/2}\right]+\\ \exp \left[3L{\left({\displaystyle \frac{2}{\beta E_g{r}_g}}\right)}^{1/2}\right]\end{array}\right\}$$

(6)

Therefore, in practical engineering, the strain response of the substrate structure can be derived from the average strain at the optical fiber core and the material parameters of each layer of the optical fiber sensor. It can be seen from Equation (2) that the FBG strain sensor eliminates the temperature influence through the temperature compensation grating. The effect of the average strain at the optical fiber core on the shift of the FBG central wavelength can then be expressed as:

$$\mathrm{\Delta }\lambda =K_g{\epsilon }_g(x)$$

(7)

where K_g is the strain sensitivity coefficient of the bare grating. Therefore, when the strain transmission relationship K_ε between the structure to be measured and the substrate structure is known, the relationship between the strain ε_d(x) of the structure to be measured and the shift of the FBG central wavelength can be obtained by combining Equations (3) and (7) as:

$${\epsilon }_d\left(x\right)=K_{\epsilon }{\epsilon }_m\left(x\right)=K_{\epsilon }\left({\displaystyle \frac{△\lambda }{K_g}}-{\alpha }_c\right)$$

(8)

where

$$\begin{array}{l}{\alpha }_c={\left({\displaystyle \frac{2}{\beta E_g{r}_g}}\right)}^{1/2}{C}_1\exp \left[{\left({\displaystyle \frac{2}{\beta E_g{r}_g}}\right)}^{1/2}\left(L+x\right)\right]-\\ {\left({\displaystyle \frac{2}{\beta E_g{r}_g}}\right)}^{1/2}{C}_2\exp \left[{\left({\displaystyle \frac{2}{\beta E_g{r}_g}}\right)}^{1/2}\left(L-x\right)\right]\end{array}$$

(9)

3. Structural Optimization Method for Large-Range FBG Strain Sensor

This paper proposes a sensor packaging structure optimization method to realize the development of FBG strain sensors with special functions. This method first uses the finite element analysis method to find the packaging structure parameters (structural dimensions and material properties) that affect the monitoring sensitivity and measurement range of the FBG strain sensor. Through the relationship between each structural parameter and the sensitivity and measurement range of the FBG strain sensor, the structural optimization subgroup of the FBG strain sensor is determined. Subsequently, combined with Formula (8) in the strain transmission theory, the actual sensitivity requirement K_g is corrected to the sensitivity K_ε. The NSGA-II algorithm is used to take the corrected sensitivity K_ε and measurement range as the objective functions to track the structural optimization subgroup of the FBG strain sensor. Finally, multiple sets of algorithm results that meet the monitoring function requirements are selected based on the application scenarios. Taking the monitoring requirements of the mortise-tenon joints of the Dong wooden drum tower in this paper as an example, based on the proposed sensor packaging structure optimization method, by optimizing the parameters of the substrate-type packaging structure, the development of a large-range FBG strain sensor with a measurement range of 5000 με and a sensitivity monitoring function of 0.1 pm/με is finally realized.

3.1. Subgroup Analysis of Structural Optimization for Large-Range FBG Strain Sensor

Among the substrate structural parameters, some have the most significant impact on the sensitivity and measurement range of the FBG strain sensor. These key parameters mainly include the elastic modulus E of the substrate material, the substrate thickness t, the width b of the square-shaped opening, and the width h of the middle narrow part where the FBG fiber grating is arranged. Therefore, by changing these four parameters of the finite element model, the sensitivity of the substrate structure to the sensitivity and measurement range of the FBG strain sensor is studied. The finite element analysis method is used to conduct a sensitivity analysis on the structure of the large-range FBG strain sensor. The sensor structure is modeled using the Design Modeler module, where the model is divided into tetrahedral meshes with a mesh size of 1 mm. The finite element analysis model of the large-range FBG strain sensor is shown in Figure 4. In this model, the substrate thickness, t, is 2 mm, the width, b, of the square-shaped openings on both sides is 2.9 mm, and the width, h, of the middle narrow part where the FBG fiber grating is arranged is 4 mm. The Young’s modulus E of the structural material is 2.2 GPa, the Poisson’s ratio is 0.394, and the density is 1.1 g/cm³. At this time, the sensitivity coefficient of the sensor K_ε is 0.447 pm/με, and the measurement range is 9000 με.

As illustrated in Figure 5a, the sensitivity of the FBG strain sensor exhibits a positive correlation with the width b of the square-shaped opening. Conversely, it shows a negative correlation with the thickness t of the substrate structure and the width h of the middle narrow section where the FBG fiber grating is deployed. Within the allowable range of values, the width of the square-shaped opening and the middle width each exert an influence on the sensitivity with a range of approximately 0.05 pm/με. These values are significantly smaller than the influence range of the substrate thickness on the sensitivity, which stands at 0.5 pm/με. The measurement range of the FBG strain sensor is positively correlated with the thickness t of the substrate structure and the width h of the middle narrow part where the FBG fiber grating is arranged, and negatively correlated with the width b of the square-shaped opening. The three structural dimension parameters all have a relatively large influence range. When the width h of the middle narrow part where the FBG fiber grating is arranged reaches 4.8 mm, the measurement range of the FBG strain sensor can reach 10,000 με.

In the finite element analysis process, representative material types were selected for analysis. This was done to examine the influence of the elastic modulus of various materials on the sensitivity and measurement range of FBG sensors. Therefore, the selected elastic moduli are relatively scattered and uneven. As shown in Figure 5b, the relationship curve between material type (i.e., elastic modulus) and sensitivity presents an exponential form. However, the influence range is only 0.003 pm/με, which is still much smaller than the influence of substrate thickness on sensitivity.The elastic modulus of the material is positively correlated with the measurement range. When the elastic modulus is 225 GPa, the measurement range can reach 7000 με. From the above analysis, it can be known that among the four parameters, the influence of the square-shaped opening width b is relatively weak. The sensitivity of the FBG strain sensor is most sensitive to the thickness of the substrate structure, and the measurement range of the FBG strain sensor is most sensitive to the width h of the middle narrow section. These two parameters need to be focused on in the subsequent structural dimension optimization.

3.2. Structural Dimension Optimization of Large-Range FBG Strain Sensor

The specific optimization process is shown in Figure 6. NSGA-II is frequently employed for solving multi-objective optimization problems. It accomplishes this through the implementation of non-dominated sorting and other related operations on the population. Such operations enable the algorithm to rapidly converge toward the Pareto frontier. Simultaneously, it can output optimal solutions while preserving the diversity of the population. Multi-objective optimization problems can generally be formulated as:

$$\begin{array}{cc}\min /\max y=f(x)& =(f_1(x),f_2(x),\dots f_k(x)),k\ge 2\hfill \\ s.t\hfill & g_i(x)\le 0,i=1,2\dots ,k\hfill \\ & h_j(x)=0,j=1,2\dots ,m\hfill \end{array}$$

(10)

where x = (x₁, x₂, x_n) is an n-dimensional decision vector in x⊂Rⁿ, f_k(x) is the objective function, g_i(x) and h_j(x) are inequality constraints and equality constraints, respectively. The NSGA-II algorithm process mainly includes non-dominated sorting, crowding calculation, selection, crossover and mutation. Non-dominated sorting is the core of the algorithm, and the population is sorted by the Pareto dominance concept. In the multi-objective maximization problem, we say that x₁ dominates x₂ when the following conditions are satisfied.

$$\forall j=1,2,\dots ,k,f_j(x_1)\ge f_j(x_2)$$

(11)

$$\exists j=1,2,\dots ,k,f_j(x_1)>f_j(x_2)$$

(12)

The crowding distance is used to evaluate the density of other solutions around a particular solution. is defined as the average distance between the nearest two solutions along a specific target solution. Selection, crossover and mutation are closely linked algorithm processes in NSGA-II. The selection operator selects better population individuals to enter the next generation, and the selection rule is that the higher the pareto dominance level is preferred and the larger the crowding distance under the same level is preferred. Both crossover and mutation are effective means to increase population diversity. The crossover sets several crossover points in the individual population through the crossover operator, and swaps the parts on both sides of the crossover point. When the population is under the mutation probability, the genetic variation occurs in the selected individuals, and the individual part is replaced by the random value.

In the structural design process of FBG strain sensor, the sensitivity and range maximization are taken as the optimization objectives. Based on the calculation of Formula (7), when the sensitivity requirement of 0.1 pm/με is reached, the sensitivity target value in the optimization process should be set to 0.5 pm/με. At the same time, in order to meet the requirements of long-term service, the range target needs to be greater than 5000 με. Therefore, the optimization goal is set to 0.5 pm/με sensitivity and 6000 με range. Based on the structural optimization subgroup analysis of the large-range FBG strain sensor, the structural optimization analysis is aimed at the four populations of substrate thickness t, mouth-shaped width b, width h of the narrow part in the middle of the sensor and elastic modulus E of the material. In the process of crossover and mutation, individuals with high sensitivity but small range are selected to cross with individuals with low sensitivity but large range. For individuals with obvious defects after crossover, the mutation probability of the corresponding parameters of the defects will be increased, so as to improve the diversity of the population and guide the population to continuously approach the optimization goal.

As shown in Figure 6, the optimization process primarily involves determining the objective function and constraints based on optimization sensitivity targets, followed by initializing the population of sensor structural parameters within the parameter range. Individuals with high crowding distance or non-dominance rank in the parent population P_t are selected to undergo crossover operations at predefined probabilities, with crossover index distribution controlling parameter deviations from parent values. Subsequent mutation operations at specified probabilities P_m introduce minor variations to enhance population diversity and prevent local optimization traps. The resulting offspring population Q_t is merged with the parent population P_t to form a new population R_t of size 2N. All individuals in Rt are evaluated for sensitivity alignment, with higher-ranking individuals assigned non-dominance ranks. Differences in sensitivity between adjacent ranked individuals are accumulated into crowding indices until computation completion. The top N individuals are selected based on dominance rankings and crowding indices to form a new parent population. Subsequent iterations of selection, crossover, and mutation operations generate new offspring populations. Convergence checks are performed to identify Pareto optimal solutions (Pareto optimality) with sufficient target sensitivity. If converged, the resulting thickness t, mouth-shaped width b, and middle width h are output; otherwise, the process repeats until convergence is achieved.

Finally, considering the structural characteristics of the Dong wooden structure drum tower, three sets of FBG strain sensor packaging structure parameters are selected from the structural parameter optimization results. The three sets of structural parameters are shown in

Table 1. Structural parameters of large-range strain sensor.

	t/mm	b/mm	h/mm	E/Gpa
1#	1.85	2.98	4.25	70
2#	1.89	3.04	3.78	70
3#	1.9	2.85	3.90	70

.

4. Linearity Test

4.1. Test Design

This study aims to further verify the feasibility of the proposed structural optimization method. It also intends to determine the linearity and sensitivity stability of the proposed large-range FBG strain sensor. To achieve these goals, three types of large-range FBG strain sensors were fabricated according to the sensor structural parameters in Table 1. During the fabrication of the large-range FBG strain sensor, the same tensile force was first applied to both ends of the strain measurement grating until the grating wavelength shifted by 1 nm. Then, the grating was smoothly embedded into the groove of the protection device, and the optical fibers on both sides of the strain-sensing grating were bonded to the protection device using α-cyanoacrylate ethyl ester instant adhesive. It is necessary to ensure that the large-range FBG strain sensor can adapt to the harsh service environment of long-term monitoring of the Dong wooden drum tower. To protect the joints between the substrate and the optical fibers on both sides, white polyvinyl chloride (PVC) sleeves are used. The bare optical fibers on both sides of the FBG pass through two white polyvinyl chloride (PVC) sleeves, respectively, and the sleeves are embedded in the groove of the sensor substrate. The length of a single sleeve is 1 m, among which the length embedded in the groove of the sensor substrate is 5 mm. During packaging, ethyl α-cyanoacrylate instant adhesive is used: first, the optical fibers and sleeves in the groove are bonded and fixed; then, glue is applied to the contact part between the sleeves in the groove and the sensor substrate to ensure that the two are also firmly bonded.

As shown in Figure 7, Q235 steel was selected for the tension-compression specimen in this experiment. The specimen has a length of 225 mm, a width of 30 mm, and a thickness of 8 mm, with the middle part where the sensor is pasted being 50 mm in length and 10 mm in width. The large-range FBG strain sensor was fixed on the specimen by means of bolt connection.

The tension-compression test on the tension-compression specimen was carried out using a PA-200 electro-hydraulic servo fatigue static and dynamic testing machine, which has a maximum test force of 200 kN, an effective test space of 600 mm, and a maximum measuring displacement of 100 mm. The experimental setup is shown in Figure 8. A high-precision extensometer was used to measure the structural deformation of the tensile specimen, calibrate the relationship between the wavelength variation of the large-range FBG strain sensor and the structural deformation of the tensile specimen, and identify the sensitivity and measurement range of the large-range FBG strain sensor. The gauge length of the high-precision extensometer is 50 mm, and the maximum deformation is 5 mm. In this experiment, a home-made optical fiber grating network demodulator with a range from 1525 nm to 1570 nm, a wavelength resolution of 0.5 pm and a maximal speed of 20 kHz was used to collect the central wavelength changes in the strain measurement grating and the temperature compensation grating.

4.2. Tensile Experiment

The working conditions of this experiment are set to six levels: 1000 με, 2000 με, 3000 με, 4000 με, 5000 με, and 6000 με. After step-by-step loading, unloading is executed. Each working condition maintains the load for 1 min, and the process is repeated three times. The test results are presented in Figure 9, Figure 10 and Figure 11. The central wavelengths of the strain measurement gratings of the three large-range FBG strain sensors all first show a stepwise increase and then return to the initial wavelength step by step, exhibiting good repeatability. As indicated in the spectral diagram of the strain measurement grating FBG1 in Figure 9a, the initial wavelength of the strain measurement grating of the 1^# large-range FBG strain sensor is 1551.6 nm. When the strain of the tensile specimen reaches 1000 με, the initial wavelength of its strain measurement grating shifts to 1551.7 nm. By comparing the wavelength change diagram, it can be observed that it remains stable during the 1 min load-holding period, presenting a plateau phenomenon. However, during each load-holding plateau in the loading phase, the data will have an instantaneous drop at the initial stage of load holding. This is because the loading process of the PA-200 electro-hydraulic servo fatigue static and dynamic testing machine is not uniform. When it is about to reach the load-holding value, it will first exceed the load-holding value and then fall back to it. The same phenomenon also occurs in the unloading phase. Figure 10 and Figure 11 demonstrate that both the 2^# and 3^# large-range FBG strain sensors maintain high stability during the plateau period. This test is a short-term indoor experiment. The temperature compensation grating FBG2 in Figure 9, Figure 10 and Figure 11 has minimal change and basically remains a straight line.

The temperature influence in the central wavelength shift of the strain measurement grating was eliminated using the monitoring results from the temperature compensation grating.

The calculated wavelength shift was compared with the extensometer monitoring data to obtain the sensitivity and linearity of the large-range FBG strain sensor. As shown in Figure 12, the central wavelength shifts of the large-range FBG strain sensor under the same strain condition are basically coincident. After three tensile tests, all three types of large-range FBG strain sensors remained structurally intact and could still be reused. This phenomenon indicates that all three types of large-range FBG strain sensors can achieve a measurement range of 6000 με, and the sensors within the elastic deformation range exhibit high stability.

Fitting was performed on the central wavelength shifts of the large-range FBG strain sensors under various working conditions, with all fitting linear correlation coefficients reaching 0.999. This indicates that the large-range FBG strain sensors have small repeatability errors and high linearity. The sensitivities of the three types of large-range FBG strain sensors are 0.0996 pm/με, 0.0998 pm/με, and 0.1 pm/με, respectively. These values are slightly lower than the multi-objective optimization sensitivity target value of 0.1 pm/με. This is attributed to the difficulty in precisely controlling the sensor manufacturing process.

The sensitivities of the three types large-range FBG strain sensors are slightly lower than those optimized by the multi-objective method for sensors of the same size. However, the sensitivities of the proposed large-range FBG strain sensors in this paper can still meet the monitoring requirements of the mortise-tenon joints of the Dong wooden drum tower. Therefore, the proposed adaptive optimization method for FBG strain sensor packaging structures can be used to develop substrate-type FBG strain sensors with special functional requirements.

The comparison of the performance study between the proposed sensor and the other reported sensors is listed in

Table 2. Comparison of Measurement Range and Sensitivity of Existing Substrate-Type FBG Strain Sensors.

Sensor Type	Research Group	Sensitivity (pm/με)	Measurement Range (με)
Metal Substrate	Zhang et al. [21]	3.21	-
Metal Substrate	Yan et al. [22]	0.151	0–12,148
Metal Substrate	Liu et al. [23]	10.84	0–200
Composite Substrate	Li et al. [24]	1.5	−2000–2000
Composite Substrate	Hong et al. [25]	2.48	0–1000
Metal Substrate	This work	0.1	−4650–6000

. It can be seen from Table 2 that the large-range FBG strain sensor proposed in this paper maintains high sensitivity within a relatively wide measurement range, and thus can play an important role in the performance monitoring of mortise-tenon joints in wooden structures. Compared with other FBG strain sensors, this sensor has a smaller structural size, which makes it easy to install. Moreover, its relatively sturdy metal substrate enables it to meet the monitoring requirements of harsh outdoor service environments.

5. Monitoring Experiment on Mortise—Tenon Joints of Dong Drum Tower

5.1. Experimental Design

As can be seen from Figure 13, due to issues with fabrication techniques and long-term service, the beam-to-beam lap joints of the Dong wooden drum tower have large disengagement displacement, which requires focused attention during the monitoring of the Dong wooden drum tower. This study addresses the problem of wood structural deterioration in the bottom layer of the Congjiang Drum Tower, situated in Qiandongnan Prefecture, Guizhou Province. The 1^# large-range FBG strain sensor was installed at the midpoint of the boundary of the lap joint between the inner crossbeams (which form a regular quadrilateral) and the outer crossbeams, to conduct monitoring tests on the mortise-tenon joints of the Dong wooden drum tower. For this monitoring test, one day from each of the four seasons (spring, summer, autumn and winter) was selected, with the monitoring period set from 7:00 to 17:00 on each selected day. An optical fiber grating network demodulator was used to collect the central wavelength changes in the strain measurement grating and the temperature compensation grating. The sampling frequency is 10 Hz, and data are collected for 10 min every hour. Additionally, a one-year long-term monitoring test was performed. Its purpose is to verify the service performance of the proposed large-range FBG strain sensor in the monitoring process of the Dong wooden drum tower.

5.2. Experimental Results

Due to the large amount of monitoring data and the limited length of this paper, this paper presents only the monitoring data of the large-range FBG sensor within a single day in summer. On the measurement day, the lowest temperature throughout the day was 21 °C at 5:00 a.m. Subsequently, the temperature began to rise rapidly at 8:00 a.m. and had reached the daily maximum temperature of 33 °C by 9:00 a.m. Before 6:00 p.m., the temperature remained basically stable at 33 °C, after which it dropped sharply. As shown in Figure 14, as the temperature increased, the wavelengths of both the strain measurement FBG (FBG1) and the temperature-compensated FBG (FBG2) inside the large-range FBG sensor exhibited a positive drift phenomenon. At 9:00 a.m., with the sharp temperature rise, the wavelengths of both FBG1 and FBG2 showed a sudden upward trend. By comparing the wavelengths of FBG1 and FBG2, it can be found that the fluctuation range of FBG1’s wavelength was relatively small between 10:00 a.m. and 11:00 a.m., indicating that the wind conditions were relatively stable during this period. The average wind speed at this time was 0.83 m/s. Occasional increases in wind speed at other times led to a larger fluctuation range of FBG1’s wavelength. At 8:00 a.m., the central wavelength of the strain-measuring FBG (FBG1) changed abruptly, which was due to the sudden increase in wind speed to 4.01 m/s at that moment. In particular, a stepped upward phenomenon occurred at both 12:00 p.m. and 4:00 p.m. At these respective times, the average wind speed surged to 1.83 m/s and 2.63 m/s. It indicates that the mortise-tenon joint structure experienced a disengagement phenomenon due to the influence of wind load at these moments. The above phenomena indicate that in addition to ambient temperature, wind load has a significant impact on the mortise-tenon joints.

The wavelength data of the FBG strain sensing grating were processed and analyzed. In this experiment, the grating wavelength at the time of installation in summer was taken as the initial wavelength. The FBG strain sensing grating wavelength data were first subtracted by the initial wavelength. Then, the wavelength variation in the temperature compensation grating was subtracted from the result. Finally, the calculation result is divided by the sensitivity coefficient to obtain the strain monitoring data at the west beam-beam lap joint of Congjiang Drum Tower (Figure 15).

It can be seen from the figure that with the temperature changes throughout the year, the crack between the tenon and the mortise changes from opening in summer to shrinking in winter. In summer, the strain of the mortise-tenon joint occasionally fluctuates greatly as the wind speed increases. In other seasons, the wind conditions are relatively stable, and the strain curve is relatively smooth at this time. This phenomenon indicates that temperature is a long-term influencing factor for the damage of mortise-tenon joints. When the damage of mortise-tenon joints reaches the critical value, wind load will cause the sudden collapse of the Dong ethnic group’s wooden structure drum tower. The experimental results show that the special functional FBG strain sensor, which developed based on the sensor packaging structure optimization method proposed in this paper, has good service performance, which can be applied in practical engineering.

6. Conclusions

This paper proposes a sensor packaging structure optimization method to realize the development of FBG strain sensors with special functions. Firstly, the finite element analysis method is used to determine the structural optimization subgroups of the FBG strain sensor. Subsequently, the sensitivity coefficient is corrected in combination with the strain transfer theory. The NSGA-II algorithm is adopted to optimize the structural parameters of the FBG strain sensor.

To meet the monitoring requirements for the mortise-tenon joints of the Dong ethnic group’s wooden drum towers, this paper takes a measurement range of 5000 με and a sensitivity of 0.1 pm/με as the objective functions. Three-dimensional parameters of the packaging structure and packaging structure material properties are taken as the optimization subsets. The development of a large-range FBG strain sensor is finally realized based on the proposed sensor packaging structure optimization method. The linearity experiment results show that within the measurement range of 0–6000 με, the strain sensitivities of the three large-range strain sensors all reach 0.099 pm/με, with a fitting linear correlation coefficient of 0.999. By installing the large-range strain sensors at the mortise-tenon joints of the Dong wooden drum tower, the long-term service performance of the large-range FBG strain sensors is verified based on the monitoring data within one year, which indicates that the FBG sensor structure optimization method proposed in this paper has practical engineering significance.