# Study and Design Optimization of Fiber Bragg Grating Based Wind Pressure Sensor

Authors: Danhui Dan; Rong Xiao; Wulong Bai; XueLei Wen
Journal: International Journal of Distributed Sensor Networks
 (2015)

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## Abstract

A Fiber Bragg Grating (FBG) based wind pressure sensor (WPS) for structural surfaces is introduced, and wind pressure-strain conversion model as well as temperature compensation method is established. By using finite element analysis, the design of the wind-bearing carrier of the WPS is optimized such that the nominal measured values by the FBGs are maximized under the action of fundamental wind pressures suggested in codes. Furthermore, sensing characteristics of the WPS, as well as its static wind safety, pressure stability, and dynamic stability during operation, are investigated. Results demonstrate that the design scheme for the WPS, which is of good object sensing properties and working performance, is technically feasible. The final prototype of WPS is developed according to the proposed optimized design scheme.


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## Body

## 1. Introduction

Evaluation of the effects of wind loads on modern super-high-rise buildings and long-span bridges is an important design consideration. Some extreme events have shown that wind loads can cause excessive vibration, static deflection, and even damage. These have a significant impact on the safety and reliability of structures. Therefore, it is important to accurately monitor wind loads acting on structures during their service life for evaluation of safety and for the purposes of structural control [1]. Monitoring wind loads thus becomes an important component of structural health monitoring [2].Currently, wind tunnel experiments, numerical wind tunnel simulations with computational fluid dynamics (CFD), and field measurements are the main methods to assess wind loads on structural surfaces. The first two approaches establish the relationship between wind field (wind) and wind loads to achieve an indirect estimation of the wind loads acting on real structures. However, due to the “scale effect” of wind tunnel experiments [3–5] and lack of simulation methods for CFD based numerical wind tunnel studies [6–8], the accurate wind loads are difficult to be acquired. On the other hand, the field measurement, which is the most reliable, direct, and effective way, includes measurements of wind speeds and direction and structural surface pressures. Since sensors need to be attached to structural surfaces, it is still difficult to obtain accurate measurements of wind speeds and directions [9]. In contrast, monitoring structural surface pressures, which not only simplifies measuring procedures, but also overcomes the drawbacks during wind speed and direction measurements, is a very efficient field measuring approach [10–12].Field wind pressure measurement generally can be classified into two categories, namely, buried-tubing pressure measurement system and front-end pressure sensor measurement system (PSMS). The former is based on the principle of wind tunnel experiments, where holes need to be drilled on structural surfaces. This method not only damages surfaces but also creates more difficulties such as wire distribution, instrument installation, and system calibration. As a result, it is only appropriate for wind load monitoring of experimental structures, but not that of real structures [13, 14]. In contrast, PSMS has the advantages of prevention of wire distribution, easy installation, and no damage to surfaces. Therefore, it is a highly efficient wind pressure monitoring technology. It can measure the structural surface pressure directly so as to improve the quality of measurements [8, 15]. Unfortunately, at present, there are no mature front-end pressure sensor technologies which are suitable for adverse exposure conditions.We developed a new FBG based WPS [16, 17], which does not have the limitations of conventional monitoring systems. In this paper, the prototype design of the WPS is introduced and its sensing mechanism is studied followed by numerical analysis on mechanical characterization of proposed wind-bearing barrier, with the aim to demonstrate the technical feasibility of proposed WPS.


## 2. Conceptual Design of FBG Based WPS

### 2.1. Design Optimization for Basic Structure of Sensor

Wind pressures on civil engineering structural surfaces are in a micropressure range and have the characteristics of fluctuating. Thus, there are many factors influencing WPS design, such as temperature, waterproofing, stability of reference pressure, installation method, and data transmission. These factors must be considered in pressure sensor design. Therefore, sensors, which have a micropressure measuring range, can measure positive and negative pressures, and are suitable for adverse exposure conditions, are adopted for WPS systems.Studies have shown that FBG sensors have the advantages of antielectromagnetic interference, anti-zero-drift, repeatability, good reliability, durability, and excellent performance in hostile environments. Furthermore, these sensors can achieve multiparameter and (quasi)distributed measurements. Thus, they are well suited for long-term and real-time monitoring of structure wind pressures. In this study, an FBG based WPS [16] which is suitable for real-time monitoring and consists of force-bearing system, sensing system, and displacement-limiting system, is developed as shown in Figure 1.Figure 1
Diagram of the WPS structure (1: shell, 2: fiber and spring, and 3: base).The FBG based WPS is based on the principle of curved arch structures. Deep thin spherical shell (DTSS) is used as the main force-bearing structure that directly bears wind pressure. This sensor consists of a base, wind-bearing surface (thin spherical shell), and transition system, which is composed of spring and FBGs. The DTSS is attached to the base by a fixed connection system (fixed bearings and expansion bearings). The basic principle is that the spring is extended or shortened by deformation of the DTSS under the action of wind pressures, and strains can be sensed by the FBGs connected. Thereby, the wind pressures can be calculated by mechanical relationship between pressures and strains.In order to simultaneously measure the attack angle of wind, the transition system was designed as shown in Figure2, three FBGs intersect at an angle of 60° in the center of DTSS bottom, and three groups of fixed bearings and expansion bearings are arranged apart from each other. The attack angle of wind can be estimated by the differences among the measured values of three strains of FBGs.Figure 2
Arrangement of FBGs and layout of fixed and expansion bearings.Generally speaking, sensors should work in linear range and its conversion relationship should remain linear within its work scope. For proposed WPS, it means the large deflection of DTSS should be limited to a neglected extent and the relationship of force-strain should maintain linearity. The design of DTSS should meet the requirement of linearity firstly. As numerical analytical tools, the finite element model of WPS should also have the ability to deal with nonlinearity behavior. By simulation with this nonlinear FEM model, we can obtain the right parameters of DTSS which have a linear conversion relationship within the range of nature wind speed.The SHELL63 in ANSYS has both bending and membrane capabilities. Both in-plane and normal loads are permitted. Stress stiffening and large deflection capabilities are also included. A consistent tangent stiffness matrix option is available for use in large deflection (finite rotation) analyses. Accordingly, the DTSS was modeled using the shell element SHELL63, and the FBGs were modeled using the link element LINK8, which ensure that the model has the ability to consider the geometric nonlinearity.The fundamental parameters of the wind-bearing surface of the DTSS are shown in Figure3(a). Finite element model of the WPS was developed in ANSYS (Figure 3(b)).Figure 3
Diagrams of geometric parameters of WPS structure and finite element numerical model.
(a)
Geometric parameters of WPS structure
(b)
Finite element modelAccording to the wind-bearing characteristics of the sensor, the spatial wind load,q, at any angle is decomposed into three orthogonal-direction loads, q1, q2, and q3. Wind load q1 is perpendicular to the bottom of the spherical shell; q2 and q3 are parallel to the bottom of the spherical shell. Wind load q2 is perpendicular to q3 and is parallel to the FBG, G1, as shown in Figure 4.Figure 4
Sketch of the action of decomposed wind loads at any angles.Let us assume thatε1, ε2, and ε3 are the strains of FBGs, G1, G2, and G3 under the load, q, respectively, ε11, ε21, and ε31 are the strains of FBGs, G1, G2, and G3 under the individual load, q1, respectively, ε12, ε22, and ε32 are the strains of FBGs, G1, G2, and G3 under the individual load, q2, respectively, and ε13, ε23, and ε33 are the strains of FBGs, G1, G2, and G3 under the individual load, q3, respectively.When doing optimization design, we set perpendicular wind pressureq1 to a series of values q1i, i=1,2,…,n, and let q11=0, q2=q2=0.According to the “General Code for Design of Highway Bridge and Culverts (JTG D60-2004),” the designed fundamental wind pressure positively acting on WPS was 500 Pa, and the extreme wind speed in nature is 80 m/s. So we letq1m be the mth wind pressure, which is equal to the basic wind pressure, 500 Pa, and let q1n be the theoretical full-scale output of WPS, which is the extreme wind pressure value in nature, corresponding to the extreme wind speed of 80 m/s.Correspondingly, we can get a series of simulated strain responses ofε11i by FEM analysis, which can be expressed as(1)ε11i=fFEMθ,q1i,where θ=L,t,α,E,μ is the fundamental parameters of DTSS.And the valuesε11n and ε11m are corresponding to the full-scale output and the output under basic wind pressure, ε111=0. Then, we define one of objective functions for optimization as follows:(2)fθ,q1m=ε11m.Another objective function brings the definition of degree of linearity of simulated WPSδ;(3)δ=gθ,q1i=Δεmaxε11n×100%,where Δεmax is the maximum difference between the result calculated by FEM and the value calculated by function of endpoint baseline:(4)Δεmax=max⁡ε11i-ε11nq1n·q1i.Considering the requirements for monitoring sensitivity of fundamental wind pressures, processing technology, the linear force-stain conversion relationship, and the limitations of selectable engineering materials, a reasonable range of values of the fundamental design parameters was considered; let us denote this design parameters feasible region asΘ. So, the design of WPS can be written as the following optimization problem, and the optimal design parameters θopt comes from(5)θopt=θθ∈Θmax⁡fθ,q1m,min⁡gθ,q1iunder the constraint conditions as follows:(6)σmax=E·ε11n≤0.3fy,where E, fy are the material elastic modulus and field strength of DTSS.When the values of the fundamental parameters change, the corresponding strains of three FBGs can be calculated by using the finite element model and the values of the objective function can be determined. Furthermore, the parameters can be optimized by the first-order optimization algorithm. In this study, aluminum alloy was adopted as the wind-bearing surface material due to its mechanical characteristics and metal processing properties. The optimized configuration of fundamental parameters of the WPS is shown in Table1.Table 1
Optimized configuration of fundamental parameters of the WPS.
Design variables
Unit
Range of values
Optimized results
Span of spherical shell (L)
mm
50~100
80 mm
Central angle of spherical shell (α)
°
45~90
45°
Thickness of spherical shell (t)
mm
0.1~0.5
0.1 mm
Elastic modulus of spherical shell (E)
GPa
70~130
70 GPa
Poisson’s ratio (µ)
/
0.2~0.4
0.3It is worth mentioning that the constraint condition ensures that no material nonlinearity can be occurring during the normal work scope of WPS. And the optimization on second objective function ensures that no geometric nonlinearity can occur during the normal work scope of WPS. The optimization on first objective function ensures the best sensitivity of the designed WPS. So the final optimized design of WPS (or DTSS) will take a good linear force-deformation conversion relationship theoretically, as shown in Figure5.Figure 5
Relationships between components of wind pressures and corresponding independent strains.


### 2.2. Mathematical Model for Wind Pressure-Strain Conversion of Optimal Designed WPS

Now let us give a mathematical model for wind pressure-strain conversion of the above optimal designed WPS, which can be obtained using mechanical analysis.Consider the most general case that the wind pressure with arbitrary direction is applied to the surface of DTSS. For the linear elastic structure,(7)ε11+ε12+ε13=ε1ε21+ε22+ε23=ε2ε31+ε32+ε33=ε3.Taking into account the symmetry of structure and loads,(8)ε11=ε21=ε31ε22=-ε32ε12=0ε23=ε33,which indicates that there are only four independent variables, that is, ε11, ε22, ε13, and ε23, among the nine independent strains of the FBGs.The effect of wind loads in any direction can be determined from the individual loads in the above three directions. Furthermore, since under natural conditions the maximum wind speed does not exceed 80 m/s, wind pressures (q1, q2, and q3) are approximatively proportional to the four independent variables as follows:(9)ε11=a·q1ε22=b·q2ε13=c·q3ε23=d·q3,where a, b, c, and d are the proportionality coefficients. Consequently, for any wind direction, the relationship between the strains and the corresponding components of wind pressures can be expressed by the following equation, by substituting (9) and (8) into (7):(10)a0cabda-bdq1q2q3=ε1ε2ε3.Upon calculation of the three components of the pressure from the above equation, the pressure in any direction can be computed as(11)q=q12+q22+q32.Thereby, the angle,θ1, between any wind pressure, q, and direction perpendicular to sensor base, and the angle, θ2, between q and q3 are determined by(12)tan⁡θ1=q22+q32q1tan⁡θ2=q2q3.The wind pressure-strain conversion model of the WPS is defined by (10), (11), and (12).The relationship between strain and wind pressure was obtained as shown in Figure5, through finite element analyses using the optimized parameters of the design variables given in Table 1. It is evident that the sensor has good linear performing characteristics. By curve fitting, the proportionality coefficients a, b, c, and d are 0.1318, 0.063, −0.073, and 0.036 με/Pa, respectively.


### 2.3. Implementation of Temperature Self-Compensation

The FBG sensing technology utilizes the photosensitive properties of optical fibers to embed in the measurand by a change in the fiber-optical wavelength. If coupled effects are ignored, the change in the FBG wavelength caused by the temperature and axial force can be expressed as(13)Δλελε=βadd+βTΔT+βεε,where λε and Δλε are the central wavelength and changes in the wavelength of grating strains, respectively, βT and βε are the temperature sensitivity and strain sensitivity of gratings with strains, respectively, given by optical and thermal properties of materials, and βadd is the additional sensitivity coefficient determined by βadd=βεαH-α, where α and αH are the thermal expansion coefficients of gratings with strains and the measurand (attachment structures), respectively. In this paper, the strain grating in this design does not adhere to the base, so βadd value is zero.A temperature compensated gratingGT which is only affected by temperature can be arranged outside the three gratings with strains shown in Figure 2. Assuming that the central wavelength and wavelength changes of the GT are λT and ΔλT, respectively, the relationship between changes in the wavelength and that in the temperature can be described by(14)ΔλTλT=βT′ΔT,where βT′ is the temperature sensitivity of the GT.During doing temperature compensation of each gratings strain, if the wavelength changes due to the temperature change are deducted, the wavelength changes caused by the actual strains of structures can be obtained by(15)ε=Δλε/λε-ψ·ΔλT/λTβε,where ψ=βadd+βT/βT′=βT/βT′.


## 2.1. Design Optimization for Basic Structure of Sensor

Wind pressures on civil engineering structural surfaces are in a micropressure range and have the characteristics of fluctuating. Thus, there are many factors influencing WPS design, such as temperature, waterproofing, stability of reference pressure, installation method, and data transmission. These factors must be considered in pressure sensor design. Therefore, sensors, which have a micropressure measuring range, can measure positive and negative pressures, and are suitable for adverse exposure conditions, are adopted for WPS systems.Studies have shown that FBG sensors have the advantages of antielectromagnetic interference, anti-zero-drift, repeatability, good reliability, durability, and excellent performance in hostile environments. Furthermore, these sensors can achieve multiparameter and (quasi)distributed measurements. Thus, they are well suited for long-term and real-time monitoring of structure wind pressures. In this study, an FBG based WPS [16] which is suitable for real-time monitoring and consists of force-bearing system, sensing system, and displacement-limiting system, is developed as shown in Figure 1.Figure 1
Diagram of the WPS structure (1: shell, 2: fiber and spring, and 3: base).The FBG based WPS is based on the principle of curved arch structures. Deep thin spherical shell (DTSS) is used as the main force-bearing structure that directly bears wind pressure. This sensor consists of a base, wind-bearing surface (thin spherical shell), and transition system, which is composed of spring and FBGs. The DTSS is attached to the base by a fixed connection system (fixed bearings and expansion bearings). The basic principle is that the spring is extended or shortened by deformation of the DTSS under the action of wind pressures, and strains can be sensed by the FBGs connected. Thereby, the wind pressures can be calculated by mechanical relationship between pressures and strains.In order to simultaneously measure the attack angle of wind, the transition system was designed as shown in Figure2, three FBGs intersect at an angle of 60° in the center of DTSS bottom, and three groups of fixed bearings and expansion bearings are arranged apart from each other. The attack angle of wind can be estimated by the differences among the measured values of three strains of FBGs.Figure 2
Arrangement of FBGs and layout of fixed and expansion bearings.Generally speaking, sensors should work in linear range and its conversion relationship should remain linear within its work scope. For proposed WPS, it means the large deflection of DTSS should be limited to a neglected extent and the relationship of force-strain should maintain linearity. The design of DTSS should meet the requirement of linearity firstly. As numerical analytical tools, the finite element model of WPS should also have the ability to deal with nonlinearity behavior. By simulation with this nonlinear FEM model, we can obtain the right parameters of DTSS which have a linear conversion relationship within the range of nature wind speed.The SHELL63 in ANSYS has both bending and membrane capabilities. Both in-plane and normal loads are permitted. Stress stiffening and large deflection capabilities are also included. A consistent tangent stiffness matrix option is available for use in large deflection (finite rotation) analyses. Accordingly, the DTSS was modeled using the shell element SHELL63, and the FBGs were modeled using the link element LINK8, which ensure that the model has the ability to consider the geometric nonlinearity.The fundamental parameters of the wind-bearing surface of the DTSS are shown in Figure3(a). Finite element model of the WPS was developed in ANSYS (Figure 3(b)).Figure 3
Diagrams of geometric parameters of WPS structure and finite element numerical model.
(a)
Geometric parameters of WPS structure
(b)
Finite element modelAccording to the wind-bearing characteristics of the sensor, the spatial wind load,q, at any angle is decomposed into three orthogonal-direction loads, q1, q2, and q3. Wind load q1 is perpendicular to the bottom of the spherical shell; q2 and q3 are parallel to the bottom of the spherical shell. Wind load q2 is perpendicular to q3 and is parallel to the FBG, G1, as shown in Figure 4.Figure 4
Sketch of the action of decomposed wind loads at any angles.Let us assume thatε1, ε2, and ε3 are the strains of FBGs, G1, G2, and G3 under the load, q, respectively, ε11, ε21, and ε31 are the strains of FBGs, G1, G2, and G3 under the individual load, q1, respectively, ε12, ε22, and ε32 are the strains of FBGs, G1, G2, and G3 under the individual load, q2, respectively, and ε13, ε23, and ε33 are the strains of FBGs, G1, G2, and G3 under the individual load, q3, respectively.When doing optimization design, we set perpendicular wind pressureq1 to a series of values q1i, i=1,2,…,n, and let q11=0, q2=q2=0.According to the “General Code for Design of Highway Bridge and Culverts (JTG D60-2004),” the designed fundamental wind pressure positively acting on WPS was 500 Pa, and the extreme wind speed in nature is 80 m/s. So we letq1m be the mth wind pressure, which is equal to the basic wind pressure, 500 Pa, and let q1n be the theoretical full-scale output of WPS, which is the extreme wind pressure value in nature, corresponding to the extreme wind speed of 80 m/s.Correspondingly, we can get a series of simulated strain responses ofε11i by FEM analysis, which can be expressed as(1)ε11i=fFEMθ,q1i,where θ=L,t,α,E,μ is the fundamental parameters of DTSS.And the valuesε11n and ε11m are corresponding to the full-scale output and the output under basic wind pressure, ε111=0. Then, we define one of objective functions for optimization as follows:(2)fθ,q1m=ε11m.Another objective function brings the definition of degree of linearity of simulated WPSδ;(3)δ=gθ,q1i=Δεmaxε11n×100%,where Δεmax is the maximum difference between the result calculated by FEM and the value calculated by function of endpoint baseline:(4)Δεmax=max⁡ε11i-ε11nq1n·q1i.Considering the requirements for monitoring sensitivity of fundamental wind pressures, processing technology, the linear force-stain conversion relationship, and the limitations of selectable engineering materials, a reasonable range of values of the fundamental design parameters was considered; let us denote this design parameters feasible region asΘ. So, the design of WPS can be written as the following optimization problem, and the optimal design parameters θopt comes from(5)θopt=θθ∈Θmax⁡fθ,q1m,min⁡gθ,q1iunder the constraint conditions as follows:(6)σmax=E·ε11n≤0.3fy,where E, fy are the material elastic modulus and field strength of DTSS.When the values of the fundamental parameters change, the corresponding strains of three FBGs can be calculated by using the finite element model and the values of the objective function can be determined. Furthermore, the parameters can be optimized by the first-order optimization algorithm. In this study, aluminum alloy was adopted as the wind-bearing surface material due to its mechanical characteristics and metal processing properties. The optimized configuration of fundamental parameters of the WPS is shown in Table1.Table 1
Optimized configuration of fundamental parameters of the WPS.
Design variables
Unit
Range of values
Optimized results
Span of spherical shell (L)
mm
50~100
80 mm
Central angle of spherical shell (α)
°
45~90
45°
Thickness of spherical shell (t)
mm
0.1~0.5
0.1 mm
Elastic modulus of spherical shell (E)
GPa
70~130
70 GPa
Poisson’s ratio (µ)
/
0.2~0.4
0.3It is worth mentioning that the constraint condition ensures that no material nonlinearity can be occurring during the normal work scope of WPS. And the optimization on second objective function ensures that no geometric nonlinearity can occur during the normal work scope of WPS. The optimization on first objective function ensures the best sensitivity of the designed WPS. So the final optimized design of WPS (or DTSS) will take a good linear force-deformation conversion relationship theoretically, as shown in Figure5.Figure 5
Relationships between components of wind pressures and corresponding independent strains.


## 2.2. Mathematical Model for Wind Pressure-Strain Conversion of Optimal Designed WPS

Now let us give a mathematical model for wind pressure-strain conversion of the above optimal designed WPS, which can be obtained using mechanical analysis.Consider the most general case that the wind pressure with arbitrary direction is applied to the surface of DTSS. For the linear elastic structure,(7)ε11+ε12+ε13=ε1ε21+ε22+ε23=ε2ε31+ε32+ε33=ε3.Taking into account the symmetry of structure and loads,(8)ε11=ε21=ε31ε22=-ε32ε12=0ε23=ε33,which indicates that there are only four independent variables, that is, ε11, ε22, ε13, and ε23, among the nine independent strains of the FBGs.The effect of wind loads in any direction can be determined from the individual loads in the above three directions. Furthermore, since under natural conditions the maximum wind speed does not exceed 80 m/s, wind pressures (q1, q2, and q3) are approximatively proportional to the four independent variables as follows:(9)ε11=a·q1ε22=b·q2ε13=c·q3ε23=d·q3,where a, b, c, and d are the proportionality coefficients. Consequently, for any wind direction, the relationship between the strains and the corresponding components of wind pressures can be expressed by the following equation, by substituting (9) and (8) into (7):(10)a0cabda-bdq1q2q3=ε1ε2ε3.Upon calculation of the three components of the pressure from the above equation, the pressure in any direction can be computed as(11)q=q12+q22+q32.Thereby, the angle,θ1, between any wind pressure, q, and direction perpendicular to sensor base, and the angle, θ2, between q and q3 are determined by(12)tan⁡θ1=q22+q32q1tan⁡θ2=q2q3.The wind pressure-strain conversion model of the WPS is defined by (10), (11), and (12).The relationship between strain and wind pressure was obtained as shown in Figure5, through finite element analyses using the optimized parameters of the design variables given in Table 1. It is evident that the sensor has good linear performing characteristics. By curve fitting, the proportionality coefficients a, b, c, and d are 0.1318, 0.063, −0.073, and 0.036 με/Pa, respectively.


## 2.3. Implementation of Temperature Self-Compensation

The FBG sensing technology utilizes the photosensitive properties of optical fibers to embed in the measurand by a change in the fiber-optical wavelength. If coupled effects are ignored, the change in the FBG wavelength caused by the temperature and axial force can be expressed as(13)Δλελε=βadd+βTΔT+βεε,where λε and Δλε are the central wavelength and changes in the wavelength of grating strains, respectively, βT and βε are the temperature sensitivity and strain sensitivity of gratings with strains, respectively, given by optical and thermal properties of materials, and βadd is the additional sensitivity coefficient determined by βadd=βεαH-α, where α and αH are the thermal expansion coefficients of gratings with strains and the measurand (attachment structures), respectively. In this paper, the strain grating in this design does not adhere to the base, so βadd value is zero.A temperature compensated gratingGT which is only affected by temperature can be arranged outside the three gratings with strains shown in Figure 2. Assuming that the central wavelength and wavelength changes of the GT are λT and ΔλT, respectively, the relationship between changes in the wavelength and that in the temperature can be described by(14)ΔλTλT=βT′ΔT,where βT′ is the temperature sensitivity of the GT.During doing temperature compensation of each gratings strain, if the wavelength changes due to the temperature change are deducted, the wavelength changes caused by the actual strains of structures can be obtained by(15)ε=Δλε/λε-ψ·ΔλT/λTβε,where ψ=βadd+βT/βT′=βT/βT′.


## 3. Mechanical Behavior Analyses and Parameter Optimization of Wind-Bearing Component of WPS

Although the optimized WPS has a linear and predictable performance, it is worth the effort to further investigate the safety and stability under long-term effects of static and fluctuating wind.


### 3.1. Safety Analysis of Wind-Bearing Surface of WPS under Static Wind Loads

Safety analysis of the wind-bearing shell under static wind loads can be conducted by applying wind pressures in three directions in the finite element model discussed above. Taking into account possible maximum wind speed in nature being less than 80 m/s (pressure less than 3,920 Pa), the pressures in three directions, that is,q1, q2, and q3, are classified into different levels, respectively, which are then applied to the numerical model to analyze the corresponding maximum stress of the DTSS.Figure6 shows Von Mises stresses of the spherical shell under the maximum levels of wind pressures in three directions. It is clear from Figure 6 that, under the action of q1, the maximum stresses appear near the base of the spherical shell. Furthermore, the stresses of fixed bearings are greater than that of expansion bearings. Under the action of q2, greater stresses appear at the edge of the spherical shell except for some areas between endpoints of G2 and G3, and the maximum stress appears near the base. Under the action of q3, greater stresses appear at the edge of the spherical shell except for some areas on both sides of endpoints of G1, and the maximum stress appears near the base, too. Since most of the stress concentrates at the base and the edge of the spherical shell, these parts are vulnerable to damage and should be strengthened appropriately. For the entire multilevel loading process, the locations where maximum stresses appear remain unchanged during linear elastic stages.Figure 6
Von Mises stresses of the spherical shell under the maximum level loads of wind pressure (3920 Pa).
(a)
q
1
(b)
q
2
(c)
q
3Figure7 shows the relationship between maximum stresses of the spherical shell and the corresponding pressures under all levels of pressure loads, q1, q2, and q3. It is apparent from the figure that the maximum stresses are positively proportional to the pressures. Under the action of once-in-a-century wind pressure, the maximum stress of the spherical shell is less than 100 MPa, while yield strength of aluminum alloy is, according to the different grades, between 195 MPa and 503 MPa. Therefore, the WPS has sufficient safety margin stresses during operation.Figure 7
Relationship between maximum stresses and corresponding wind pressures.


### 3.2. Elastic Buckling Analysis of Wind-Bearing Device under Static Wind Pressure

In order to investigate the stability of the optimized structure of the WPS and to avoid buckling failure, stability analysis of the structure under the wind loads in three directions was carried out by assuming the maximum wind pressure of 3,920 Pa (design fundamental wind pressure is 500 Pa). The first fourth-order stability coefficients of the structure and the first-order buckling mode are shown in Table2 and Figure 8, respectively. These results indicate that the stability coefficients of the structure are very high and the buckling failure does not occur. Therefore, the structure is safe and highly stable under the action of wind loads from all directions.Table 2
Stability coefficients of WPS structure.
Mode order
1
2
3
4
Stability coefficients
q1 direction
4.92
5.08
5.08
6.39
q2 direction
8.34
9.25
12.13
12.56
q3 direction
9.83
10.58
11.01
13.68
Note. Stability coefficient = ultimate wind load of structure buckling failure/design wind load.Figure 8
First-order buckling modes of directions ofq1, q2, and q3 of WPS.
(a)
q
1 direction
(b)
q
2 direction
(c)
q
3 direction


### 3.3. Vibration Stability Analysis of Shell under Fluctuating Wind

Vibration will occur when the wind-bearing barrier of the WPS is excited by fluctuating wind component. In extreme cases, the resonance takes place, which not only affects the quality of wind pressure monitoring data, but also, more seriously, causes dynamic instability resulting in the damage of wind-bearing barrier. Therefore, vibration characteristics of the design-optimized WPS structure must be investigated. For this purpose, modal analysis was carried out using the finite element model described above. The results of first fourth-order modal frequencies and mode shapes of variation are shown in Table3 and Figure 9, respectively. They show that the natural frequencies of the wind-bearing barrier are much higher than that of fluctuating wind in nature. Consequently, the possibility of the occurrence of resonance is very low, which demonstrates that the dynamic stability of the design-optimized WPS meets the engineering requirements.Table 3
Modal frequencies of WPS structure.
Mode order
1
2
3
4
Frequency (Hz)
787
787
808
868Figure 9
The first fourth-order modes of variations of WPS structure.
(a)
First-order mode of variation
(b)
Second-order mode of variation
(c)
Third-order mode of variation
(d)
Fourth-order mode of variation


## 3.1. Safety Analysis of Wind-Bearing Surface of WPS under Static Wind Loads

Safety analysis of the wind-bearing shell under static wind loads can be conducted by applying wind pressures in three directions in the finite element model discussed above. Taking into account possible maximum wind speed in nature being less than 80 m/s (pressure less than 3,920 Pa), the pressures in three directions, that is,q1, q2, and q3, are classified into different levels, respectively, which are then applied to the numerical model to analyze the corresponding maximum stress of the DTSS.Figure6 shows Von Mises stresses of the spherical shell under the maximum levels of wind pressures in three directions. It is clear from Figure 6 that, under the action of q1, the maximum stresses appear near the base of the spherical shell. Furthermore, the stresses of fixed bearings are greater than that of expansion bearings. Under the action of q2, greater stresses appear at the edge of the spherical shell except for some areas between endpoints of G2 and G3, and the maximum stress appears near the base. Under the action of q3, greater stresses appear at the edge of the spherical shell except for some areas on both sides of endpoints of G1, and the maximum stress appears near the base, too. Since most of the stress concentrates at the base and the edge of the spherical shell, these parts are vulnerable to damage and should be strengthened appropriately. For the entire multilevel loading process, the locations where maximum stresses appear remain unchanged during linear elastic stages.Figure 6
Von Mises stresses of the spherical shell under the maximum level loads of wind pressure (3920 Pa).
(a)
q
1
(b)
q
2
(c)
q
3Figure7 shows the relationship between maximum stresses of the spherical shell and the corresponding pressures under all levels of pressure loads, q1, q2, and q3. It is apparent from the figure that the maximum stresses are positively proportional to the pressures. Under the action of once-in-a-century wind pressure, the maximum stress of the spherical shell is less than 100 MPa, while yield strength of aluminum alloy is, according to the different grades, between 195 MPa and 503 MPa. Therefore, the WPS has sufficient safety margin stresses during operation.Figure 7
Relationship between maximum stresses and corresponding wind pressures.


## 3.2. Elastic Buckling Analysis of Wind-Bearing Device under Static Wind Pressure

In order to investigate the stability of the optimized structure of the WPS and to avoid buckling failure, stability analysis of the structure under the wind loads in three directions was carried out by assuming the maximum wind pressure of 3,920 Pa (design fundamental wind pressure is 500 Pa). The first fourth-order stability coefficients of the structure and the first-order buckling mode are shown in Table2 and Figure 8, respectively. These results indicate that the stability coefficients of the structure are very high and the buckling failure does not occur. Therefore, the structure is safe and highly stable under the action of wind loads from all directions.Table 2
Stability coefficients of WPS structure.
Mode order
1
2
3
4
Stability coefficients
q1 direction
4.92
5.08
5.08
6.39
q2 direction
8.34
9.25
12.13
12.56
q3 direction
9.83
10.58
11.01
13.68
Note. Stability coefficient = ultimate wind load of structure buckling failure/design wind load.Figure 8
First-order buckling modes of directions ofq1, q2, and q3 of WPS.
(a)
q
1 direction
(b)
q
2 direction
(c)
q
3 direction


## 3.3. Vibration Stability Analysis of Shell under Fluctuating Wind

Vibration will occur when the wind-bearing barrier of the WPS is excited by fluctuating wind component. In extreme cases, the resonance takes place, which not only affects the quality of wind pressure monitoring data, but also, more seriously, causes dynamic instability resulting in the damage of wind-bearing barrier. Therefore, vibration characteristics of the design-optimized WPS structure must be investigated. For this purpose, modal analysis was carried out using the finite element model described above. The results of first fourth-order modal frequencies and mode shapes of variation are shown in Table3 and Figure 9, respectively. They show that the natural frequencies of the wind-bearing barrier are much higher than that of fluctuating wind in nature. Consequently, the possibility of the occurrence of resonance is very low, which demonstrates that the dynamic stability of the design-optimized WPS meets the engineering requirements.Table 3
Modal frequencies of WPS structure.
Mode order
1
2
3
4
Frequency (Hz)
787
787
808
868Figure 9
The first fourth-order modes of variations of WPS structure.
(a)
First-order mode of variation
(b)
Second-order mode of variation
(c)
Third-order mode of variation
(d)
Fourth-order mode of variation


## 4. Prototype Trial

According to the optimized configuration of fundamental parameters of the WPS above, we give a prototype trial by choosing Aluminum alloy 1060 as the optimal material for the pressure-bearing DTSS and its processing, which has the best metal processing properties, was finally adopted and meets the requirements of conventional processing (stamping and stretching). Stamping technique by using stamping mould was adopted for the alloy processing. And then, prelocating FBGs, gluing, and heat curing are required to achieve the bonding of FBGs and connecting-aluminum. In order to simultaneously measure pressures and suctions, during adhering connecting-aluminum to the spherical shell, pretensioning of the FBGs should be conducted.All the FBGs (including unstressed one for temperature compensation) were welded to each other in series via tail fibers and coiled around and fixed underneath the DTSS. Figure10 shows the optical circuit with FBGs, the base, and the final prototype of WPS.Figure 10
The prototype of WPS.
(a)
Optical circuit
(b)
Base
(c)
Finished WPSOn the basis of prototype of WPS shown in Figure10, the next study should focus on its corresponding calibration scheme, and its sensing mechanism and performance should also be investigated experimentally in order to verify its technical feasibility.


## 5. Conclusions

Monitoring wind pressures acting on surfaces of engineering structures is of vital significance in assessment and control of structural suitability and safety during their service life. In this paper, an FBG based WPS for the monitoring of wind pressures on structures was introduced. Finite element analysis was used to establish the wind pressure-strain conversional model, the methodology for temperature compensation, and the design optimization of the wind-bearing device. Furthermore, sensing characteristics of the WPS were investigated, and its static wind safety, pressure stability, and dynamic stability during operation were verified.Results showed that the design-optimized WPS has the ability to simultaneously measure wind pressure as well as the attack angle and has a very good temperature-compensation capability due to the existence of unstressed temperature grating. Meanwhile, within wind speed range in nature, the sensor has good linear-proportional sensing properties. Furthermore, its wind-bearing device is safe under static wind action, even under extreme pressure conditions, and buckling failure does not occur. The possibility of resonance occurring under the excitation of fluctuating winds is also very low and dynamic stability is high. This indicates that the design-optimized WPS presented in the paper has a good sensing function and working performance, so that the design scheme is technically feasible and can be a reference for further research and development of prototypes.



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*Source: 745346-2015-06-08.xml*