Numerical investigation and optimal design of fiber Bragg grating based wind pressure sensor

Abstract

A wind pressure sensor based on fiber Bragg grating (FBG) for engineering structure was investigated in this paper. We established a transaction model of wind pressure to strain and proposed a method of temperature compensation. By finite element analysis, the basic parameters of the sensor were optimized with the aim of maximum strain under the basic wind pressure proposed in relative design code in China taking geometrical non-linearity into consideration. The result shows that the wind pressure sensor we proposed is well performed and have good sensing properties, which means it is a technically feasible solution.

Keywords

wind pressure measurement / wind pressure sensor / fiber Bragg grating / optimal design

Introduction

Evaluation of the effects of wind loads on modern super-high-rise buildings and long-span bridges is an important design consideration [1]. Some extreme events have shown that wind loads can cause excessive vibration, static deflection, and even damage, which have a significant impact on the safety and reliability of structures. Therefore, it is important to monitor wind loads acting on structures accurately during their service life for evaluation of safety and for the purposes of structural control [2,3]. Monitoring wind loads thus becomes an important component of structural health monitoring [4] and an important supplement to the specifications [5].

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 mentioned above focus on establishing 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 [6–8] and lack of simulation methods for CFD based numerical wind tunnel studies [9–11], the accurate wind loads are difficult to acquire. On the contrary, field measurement, which is the most reliable, direct, and effective way, includes measurements of wind speed and direction and structural surface pressures.

Since sensors need to be attached to structural surfaces, it is difficult to obtain accurate measurements of wind speeds and directions [12]. In contrast, monitoring structural surfacepressures, which not only simplifies measuring procedures, but also overcomes the drawbacks during wind speed and direction measurements, is a very efficient field measuring approach [13–15].

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 structure surfaces. This method not only damages structure 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 [16,17]. 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 structure surface pressure directly so as to improve the quality of measurements [10,17].

Dan et al. [19] have proposed a kind of front-end deep thin spherical shell (DTSS) wind pressure sensor (WPS), which can measure the wind speed and attack angle at the same time. But the thin shell (0.1 mm) causes production difficulties and initial defects. In this paper we modified the fiber layout so that the structural parameters were changed as well, which means it’s easier to produce.

Optimal design of the sensor

Structure design of the sensor

This sensor is consisted of force bearing system, sensing system and limit system [20] as shown in Fig. 1.

The FBG based WPS is based on the principle of curved arch structures. 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.

The transition system and temperature compensation before modified is shown in Fig. 2(a): 3 FBGs at a length of the diameter of the shell, intersect at an angle of 60°, one end is hinged and the other is sliding supported. For the sake of improving sensitivity, we redesign the fiber path as shown in Fig. 2(b). We reduce the length of the FBGs and add three hinge bearings inside the shell. Taking the minimum bending radius into consideration, the length reduction of the FBGs simplified the layout.

Wind pressure-strain transition mathematical model of WPS

The transition of wind pressure to strain can be established according to mechanics analysis. According to the wind-bearing characteristics of the sensor, the spatial wind loadq, at any angle is decomposed into three orthogonal-direction loads q_{\mathrm{1}}, q_{\mathrm{2}} and q_{\mathrm{3}}. Wind load q_{\mathrm{1}} is perpendicular to the bottom of the spherical shell; q_{\mathrm{2}} and q_{\mathrm{3}}are parallel to the bottom of the spherical shell. Wind load q_{\mathrm{2}} is perpendicular to and q_{\mathrm{3}} is parallel to the FBG, as shown in Fig. 3.

We assume {\epsilon }_{ij} as the strain of G_i induced by q_j, so we can get:

(1){\epsilon }_i={\displaystyle \sum _{j=\mathrm{1}}^{\mathrm{3}}{\epsilon }_{ij}}

where{\epsilon }_iis the strain of G_i induced by q_{\mathrm{1}},q_{\mathrm{2}}and q_{\mathrm{3}}.

According to the symmetry of the structure, there are only 4 independent variables.

(2)\begin{array}{l}{\epsilon }_{\mathrm{11}}={\epsilon }_{\mathrm{21}}={\epsilon }_{\mathrm{31}}\\ {\epsilon }_{\mathrm{22}}=-{\epsilon }_{\mathrm{32}}\\ {\epsilon }_{\mathrm{12}}=\mathrm{0}\\ {\epsilon }_{\mathrm{23}}={\epsilon }_{\mathrm{33}}\end{array}\}

The effect of wind load in any direction can be determined from the individual loads in the above three directions. Furthermore, since the maximum wind load could not exceed 80 m/s in nature, wind pressures (q_{\mathrm{1}},q_{\mathrm{2}} and q_{\mathrm{3}}) are approximatively proportional to the four independent variables as follows:

(3)\begin{array}{l}{\epsilon }_{\mathrm{11}}=a\cdot q_{\mathrm{1}}\\ {\epsilon }_{\mathrm{22}}=b\cdot q_{\mathrm{2}}\\ {\epsilon }_{\mathrm{13}}=c\cdot q_{\mathrm{3}}\\ {\epsilon }_{\mathrm{23}}=d\cdot q_{\mathrm{3}}\end{array}\}

The strains and the corresponding components of wind pressures can be expressed as the following equation by substituting Eqs. (1–3).

(4)\left[\begin{array}{lll}a& \mathrm{0}& c\\ a& b& d\\ a& -b& d\end{array}\right]\left\{\begin{array}{l}{q}_{\mathrm{1}}\\ q_{\mathrm{2}}\\ q_{\mathrm{3}}\end{array}\right\}=\left\{\begin{array}{l}{\epsilon }_{\mathrm{1}}\\ {\epsilon }_{\mathrm{2}}\\ {\epsilon }_{\mathrm{3}}\end{array}\right\}

We can computed the wind pressure in three directions according to the equation above.

(5)q=\sqrt{q_{\mathrm{1}}^{\mathrm{2}}+q_{\mathrm{2}}^{\mathrm{2}}+q_{\mathrm{3}}^{\mathrm{2}}}

Thereby, the angle {\theta }_{\mathrm{1}} between any wind pressureq, and direction perpendicular to sensor base, and the angle {\theta }_{\mathrm{2}} between q and q_{\mathrm{3}} could be determined as follows.

(6)\{\begin{array}{l}\tan {\theta }_{\mathrm{1}}={\displaystyle \frac{\sqrt{q_{\mathrm{2}}^{\mathrm{2}}+q_{\mathrm{3}}^{\mathrm{2}}}}{q_{\mathrm{1}}}}\\ \tan {\theta }_{\mathrm{2}}={\displaystyle \frac{q_{\mathrm{2}}}{q_{\mathrm{3}}}}\end{array}

The Eqs. (4–6) are the transition mathematical model of wind pressure to strain.

Optimal model for parameters of WPS

The basic geometric parameters are shown in Fig. 4(a).We used ANSYS to optimize the geometric parameters of the model. The DTSS was modeled using the shell element SHELL63 and the FBGs were modeled using the link element LINK8 as shown in Fig. 4(b). We computed the strain{\epsilon }_{\mathrm{1}},{\epsilon }_{\mathrm{2}}and{\epsilon }_{\mathrm{3}}of G_{\mathrm{1}},G_{\mathrm{2}}andG_{\mathrm{3}}under the maximum wind speed of 60 m/s. We pre-stretch the FBGs to \mathrm{1300}\mathrm{\mu }\mathrm{\epsilon } to get the negative strain.

The geometric parameters are L,\alpha ,tas shown in Fig. 4(a) and the material parameters are elastic modulus and Poisson’s ratio of the spherical shell. The objective function of this optimal problem could be shown as Eq. (7):

(7)max f=f(\theta ,q)=\sqrt{{\epsilon }_{\mathrm{1}}^{\mathrm{2}}+{\epsilon }_{\mathrm{2}}^{\mathrm{2}}+{\epsilon }_{\mathrm{3}}^{\mathrm{2}}}

whereq={[q_{\mathrm{1}},q_{\mathrm{2}},q_{\mathrm{3}}]}^{\mathrm{T}} is the wind pressure vector; \theta ={[L,\alpha ,t,E,\mu ]}^{\mathrm{T}},\theta \in \Theta,\Thetais the feasible engineering region.

This optimal problem is to find {\theta }_{\mathrm{o}\mathrm{p}\mathrm{t}} which can make f({\theta }_{\mathrm{o}\mathrm{p}\mathrm{t}},q) reach its maximum value and not exceed the ultimate strain \pm \mathrm{1300}\mathrm{\mu }\mathrm{\epsilon }.

The optimal result

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, the feasible region of\Theta is given in Table 1. 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 Table 1.

We studied the transition relationship of wind pressure to strain about the model given in Fig. 5, using finite element method. The result showed that the WPS works in its linear range and the coefficient a, b, c, d we mentioned above is 0.5567, 0.4809, –0.6224 and 0.2706\mathrm{\mu }\mathrm{\epsilon }/\mathrm{P}\mathrm{a}.

The mechanics behavior of the wind bearing component

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.

Comparison of the model before and after modified

After modified, the WPS didn’t lose its sensitivity and had better linearity compared with the sensor before modified. The maximum strain of the FBGs before and after modified is shown in Fig. 6.

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 3920 Pa), the pressures in three directions, that isq_{\mathrm{1}},q_{\mathrm{2}}and q_{\mathrm{3}}, are classified into different levels, respectively, which are then applied to the numerical model to analyze the corresponding maximum stress of the DTSS.

Figure 7 shows Von Mises stresses of the spherical shell under the maximum levels of wind pressures in three directions. It is clear from Fig. 7 that, under the action ofq_{\mathrm{1}}, 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 ofq_{\mathrm{2}}, greater stresses appear at the edge of the spherical shell except for some areas between endpoints ofG_{\mathrm{2}} and G_{\mathrm{3}}, and the maximum stress appears near the base. Under the action of q_{\mathrm{3}}, greater stresses appear at the edge of the spherical shell except for some areas on both sides of endpoints ofG_{\mathrm{1}}, 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.

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 3920 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 Table 2 and Fig. 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.

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 Table 3 and Fig. 9, respectively. It shows 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.

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, we modified a WPS based on the work by Dan et al. [21]. 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. 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 because of increasing thickness, it can be manufactured in large volumes.

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