Reliability Analysis Deflector of Underwater Wall Detection Device Based on Finite Element and Response Surface Methodology

Before the diversion plugging in hydropower project, underwater wall detection device can complete the probe of visual detection and obstacle clearing in high-velocity flow. Deflector which can provide a stronger compress diversion tunnel sluice gate power is the most important part in underwater wall detection device, but the mechanical and uncertainty analysis aren’t enough. In this paper, Finite Element Method and Response Surface Methodology are used to analyze strength and deformation of the deflector, meanwhile, the limit state functions about the maximal bending stress and maximal deformation are developed. Then, though comparing the data with experimental data and the value computed by user formula, the error is less than 2% and the error is allowable in engineering design. Finally, reliability analysis the deflector is achieved with the First-Order Reliability Method. In a word, form the calculating results and engineering operation, we know that the propose method in this paper using finite element method and response surface methodology to develop the function related to the limit functions of deflector under uncertainty is practical and feasible.


Introduction
In the process of hydropower project construction, the diversion tunnel sluice gates (see in Fig. 1) are seriously damaged due to long term erosion by high velocity silt laden flows. Before the diversion plugging, it is necessary to detect and understand the situation that steel water erosion and warpage of the diversion tunnel sluice gates. The long way would be to trial test by simple gate frame or underwater detect by frogman, but these methods have merits as well as their limitations and demerits. For example, though trial test by simple gate frame can detect obstacles, and we can't get the enough information that the steel water erosion and warpage. And the same time, the flow in the diversion IOP Publishing doi:10.1088/1757-899X/1043/5/052047 2 tunnel of the hydropower station is very high, profound depth and poor visibility duo to water turbidity, frogman touch is unable to obtain the accurate data of diversion tunnel sluice gates and the frogman faces danger each time under turbulent flow conditions.

Figure 1. Diversion tunnel of hydropower project
With the demand of detecting and cleaning for diversion tunnel sluice gates, underwater wall detection device represents the direction of underwater vehicle has gained rapid development. Underwater wall detection device which can carry sonar detection instrument, underwater television and cleaning device, in order to complete the probe of visual detection and obstacle clearing in highvelocity flow with convenient use and highly reliable. This device is mainly used for corrosion detecting and checking shoal materials in sluice gates, to ensure that the gates can run reliability during the diversion plugging, and then successfully close sluice gates.
At the same time, uncertainties are ubiquitous in any stage of underwater wall detection device development, and they are considerable and cannot be controlled. Uncertainties impact the underwater wall detection performance significantly, and a small variation of system inputs may cause an extreme quality loss, even a catastrophic failure. They may come from many aspects, such as environment, manufacturing, incomplete knowledge and so on. Uncertainties can be classified in two general types: aleatory (stochastic or random) uncertainty and epistemic (subjective) uncertainty [1][2]. Aleatory uncertainty is related to inherent variability and is efficiently modeled using probability theory. Epistemic uncertainty describes subjectivity, ignorance or lack of information and it can be reduced with increased state of knowledge or collection of more data. They may be from many aspects, such as environment, manufacturing tolerance, or incomplete knowledge. Therefore, it is important to quantify and analyze the uncertainty during the design procedure of underwater wall detection device.
The rest of this paper is organized as follows. Section 2 provides the general layout of underwater wall detection device. The analyze strength and deformation of deflector use Finite Element Method in Section 3. The develop limit state functions of deflector use Response Surface Methodology in Section 4. Section 5 presents the reliability analysis of the deflector. Some conclusions are given in Section 6.

General layout of underwater wall detection device
Underwater wall detection device which is used for detecting and cleaning of diversion tunnel sluice gates hydropower project consists several independent parts, shown in Fig. 2.  Fig. 2, the major structure can carry powerful magnet, steel wheel, guide plate, seal motor, cleaning device, guide plate, main control unit, underwater camera and color sonar, etc. The powerful magnet and steel wheel enable the underwater wall detection close to the diversion tunnel sluice wall at a certain distance. The seal motor and cleaning device are used for cleaning shoal materials in sluice gates. The underwater camera and color sonar can detect in the underwater environment for hours on end. The underwater part is connected by wirerope and armour cable to the surface control part.
In underwater wall detection device, the most important part is deflector, which can provide a stronger drive power that can compress the underwater wall detection device to diversion tunnel sluice gate. So far, there is limited work related to mechanical analysis of the deflector. Uncertainties are ubiquitous in any stage of deflector development, and they are considerable and cannot be controlled. Uncertainties impact the deflector performance significantly, and a small variation of system inputs may cause an extreme quality loss, even a catastrophic failure. Therefore, it is important to quantify and analyze the uncertainty during the design procedure of deflector.
In this paper, Finite Element Method (FEM) and Response Surface Methodology (RSM) is used to analyze strength and deformation of deflector and the limit state functions related to the maximal bending stress and maximal deformation of deflector are developed [3]. Based on them, reliability analysis of the deflector is achieved with the First-Order Reliability Method [4][5].

Stress and strain analysis of deflector
This thesis regards deflector of the underwater wall detection device as the research object, and the underwater part inside in groove wall of diversion tunnel sluice gate is given in Fig. 3.  .7 In Eq. (3.1), Fx is horizontal component of the pressure of high-velocity folw on deflectors, Fy is vertical component of the pressure of high-velocity folw on deflectors, ρ is water density, s area of the deflectors, c is drag coefficient of water, θ is angle adjustment between deflector and major structure, v is flow velocity.
In this paper, we design the deflector that the material using Q235 (бs=225MPa, бb=225MPa) and the three basic sizes is 0.62m(b)×0.31m(a)×0.015m(h). In order to have sufficient strength and stiffness under the impact of the high-velocity folw, we used two stiffeners to enhance the structure on the back of deflector (see Fig. 7). Then, Finite Element Method is used to analyze the strength and deformation of deflector when x1=100mm, x2=60mm, x3=5mm (see Fig. 8 and Fig. 9).  Fig. 8 and Fig. 9, we can find that the maximal bending stress of the deflector (б=212.71MPa) appeared at the hinge and the maximal deformation of the deflector (δ=1.1434mm) appeared at the middle of the main structure. After several cycles of analysis, the calculation model and the actual structure will arrive at the basic line, and also the accuracy of relative theories are confirmed basically. Form Fig. 7, the dependent variable of the develop limit state function is б that is maximal bending stress or δ that is maximal deformation of deflector, and the vector of independent variables is X=  2  2  2  10  11  1  12  2  13  3  14  1  15  2  16  3  17  1  2  18  1  3  19  2  3   2  2  2  20  21  1  22  2  23  3  24  1  25  2  26  3  27  1  2  28  1  3  29  2  3 x

Develop limit state function of deflector
After vectoring the Eq. (4.1), the vector formula is given Finally, we will use the data that see in Table 2 to verify accuracy of the Eq. (4.4).  Table 2, the relative errors of б and δ are no more than 2%, the result showed that the limit state functions are given using RSM proves credibility.

Reliability analysis of the deflector
In this paper, we use the First Order Reliability Method (FORM) to calculate the reliability. The computation procedure is given as follows.
Step one: Transform the original random variables from X-space to U-space by Rosenblatt transformation.
Step three: Calculate reliability R=Φ(β). Then, we would analyse the reliability of the defector. And the information on the continuous random variables and parameters are provided in Table 3. At the last, the Rб and Rδ can be pursued by Eq. (5.2) when x1=100mm, x2=65mm and x3=3mm that the value of design results have been used, and the results Rб=0.9898 and Rδ=0.9202 that greater than the desired reliability (R=0.9). At the same time, form the calculating results and the engineering operation in hydropower station on the Jinsha River, we can find out that the deflector of underwater wall detection device design is practical and feasible.

Conclusions
In this paper, we used Finite Element and Response Surface Methodology to develop limit state functions of the deflector in underwater wall detection device, and then analysed the reliability of the deflector under uncertainty. According to the analysis results, we can research further on the deflector, and the use of the proposed model in this paper will dispense with the large number of repetitive works, to a large extent enhance the efficiency.
However, there exist some limitations. Firstly, when the number of variables in RSM is large, the proposed method of developing the limit state function will be in a very difficult position. Secondly, a lot of uncertainties should be refined in this limit state function. Finally, our future work will focus on optimal design of the deflector in underwater wall detection device.