外文翻譯--重力壩功能可靠性的研究（節(jié)選）

1、Energy and Power Engineering, 2012, 4, 59-66 http://dx.doi.org/10.4236/epe.2012.42009 Published Online March 2012 (http://www.SciRP.org/journal/epe) A Study on the Functional Reliability of Gravity Dam Qiang Xu1, Jianyu

2、n Chen1,2*, Jing Li1 1School of Civil and Hydraulic Engineering, Dalian University of Technology, Dalian, China 2State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, China

3、 Email: xuqiang528826@163.com, {*eerd001, lijing}@dlut.edu.cn Received December 24, 2011; revised January 20, 2012; accepted February 8, 2012 ABSTRACT The research objective is to design and construct a method for functi

4、onal reliability analysis of concrete gravity dam. Firstly, the pseudo excitation method was utilized to analyze to calculate the probabilistic characteristics of concrete gravity dam excited by random seismic loading.

5、 Meanwhile, the response surface method based on weighted regression was associated to that method to analyze functional reliability of concrete gravity dam. Eventually, a test example was given to verify and analyze t

6、he convergence and stability of this method. Keywords: Concrete Gravity Dam; Random Load; Functional Reliability; Pseudo Excitation Method 1. Introduction The basic purpose of structural reliability analysis is to obtai

7、n the probabilistic responses of structural systems with uncertain design parameters, such as loadings, ma- terial parameters (strength, elastic modulus, Poisson’s ratio, etc.), and shape dimensions. Among the methods

8、 avail- able for these problems, the response surface method (RSM) is a powerful tool [1]. The theory and methods of RSM have been developed significantly during the last twenty years and have been documented in an i

9、ncreasing num- ber of publications. Although, from a theoretical point of view, the field has reached a stage where the developed methodologies are becoming widespread, RSM used to analyze large structures is still a

10、 complex and difficult task. In order to solve this problem, a rigorous series of tests has to be carried out. Linda and Ping (1999) [2] constructed confidence intervals about the difference in mean responses at the

11、stationary point and alternate points based on the proposed delta method and F-projection method and compared coverage probabilities and interval widths. Zheng and Das (2000) [3] proposed an improved response surface

12、 method and applied that to the reliabil- ity analysis of a stiffened plate structure. Guan and Melchers (2001) [4] evaluated the effect of response sur- face parameter variation on structural reliability. Byeng and Ky

13、ung (2004) [5] proposed the hybrid mean value (HMV) method for highly efficient and stable RBDO by evaluating the probabilistic constraint effectively. Gupta and Manohar (2004) [6] used the response surface method to

14、 study the extremes of Von Mises stress in nonlinear structures under Gaussian excitations. Herbert and Ar-mando (2004) [7] compared RSM and the artificial neu- ral network (ANN) techniques. Irfan and Chris (2005) [8]

15、proposed a new response surface called ADAPRES, in which a weighted regression method was applied in place of normal regression. Wong et al. (2005) [9] proposed an adaptive design approach to overcome the problem, whi

16、ch was that the solution of the reliability analysis initially diverged when the loading was applied in sequence in the NLFE analysis, and made several suggestions to improve the robustness of RSM. Jiang et al. (2006

17、) [10] improved the method to fit the indeterminate coefficients of re- sponse surface. Jin Weilian and Yuan (2007) [11] pre- sented a response surface method based on least squares support vector machines (LS-SLM) aim

18、ing at the reli- ability analysis problems with implicit performance func- tion. Chebbah (2007) [12] dealt with the optimization of tube hydro forming parameters in order to reduce defects which might occur at the end

19、of forming process such as necking and wrinkling by RSM. Jin et al. (2008) [13] pre- sented a new artificial neural net work-(ANN) based re- sponse surface method in conjunction with the uniform design method for predi

20、cting failure probability of struc- tures. Henri and Siu (2008) [14] described the use of higher order polynomials in order to approximate the true limit state more accurately in contrast to recently proposed algorith

21、ms which focused on the positions of sample points to improve the accuracy of the quadratic the sto- chastic response surface method (SRSM). TongZou et al. (2008) [15] presented an accurate and efficient Monte Carlo s

22、imulation method for limit-state- based reliability analysis at both component and system levels, using a re- sponse surface approximation of the failure indicator func- tion. Xuan et al. (2009) [16] proposed an adaptiv

23、e con- *Corresponding author. Copyright © 2012 SciRes. EPE Q. XU ET AL. 61where E(#) denotes the expected value of variable #. Fou

24、rier transform pairs are consisted of auto-spectral density function xxand Autocorrelation function ? ? S fxx R ? ? ? , it can be written as ? ? xx S f ? ? 2 d j f xx R e ? ? ? ? ?? ? 2 d j f xx f e f ? ?? ? 0 d xx S

25、f f ??? ? ???? ? ?(2) ? ? xx R S ? ??? ? ?(3) From Equations (1)-(3), it can be seen that ? ? 2 2 xx xx xx E D R ? ?(4) where xx E 2and xx D? ?denote the expected value and vari-ance of x t . when xx E 2= 0, xx D ca

26、n be determined from ? ? S f? ? S f? ?xx Pseudo excitation method is the numerical methods for xxand the basic principle of the pseudo excitation method is depicted as Figure 1. . Linear system under single-point and s

27、tationary ran- dom excitation x t , the response power spectrum of that is written as 2yy xx S H S ?i t e(5) This relationship is depicted as Figure 1(a), the meaning of frequency response function H is depicted as Fi

28、gure 1(b). When the harmonic excitation ? of sin- glepoint is applied in the linear system, the corresponding response i t y He ? ? i t e . It is worth noting that pseudo exci- tation is constructed by excitation, wh

29、ich was ? mul- tiplied by constant xx S? ?. The pseudo excitation is given by i xx t x t S e ? ? ?(6) The response can also be multiplied by the same con- stant. It is depicted as Figure 1(c). Still using ? ? # ?? ?

30、#to represent the corresponding pseudo response of variable , it should be noted from Figure 1(c) that 2 2 *xx yy H S S ? y y y ? ? ? ? ?(7) * i t i txx xx xx xy x y S e S He ? ? ? ? ? ? ? S H S ? ?(8) * * * i t i txx

31、x y x S H e S e ? ? ? ? x xx yx H S S ? ? ? ? ?? ? * # ? ? #1 y ? 2 y ?(9) where denotes the conjugate of . If considering two pseudo responses and de- pict as Figure 1(d), it could be seen that 1 2* * * 1 2 i t i t 1

32、2 1 2 xx xx y y H S e H S e H ? ? ? ? xx y y S H S ? ? ? ? ?2 1* * 2 1(10) 2 1 xx y y y y H S H S ? ? ? ?? ? ? ? * T S y y ? ? ? ?? ? ? ? * Txy S x y ? ? ? ?(11) From aforementioned analysis, it should be noted that yy(1

33、2) (13) ? ? ? ? * Tyx S y x ? ? ? ?(14) Thus it can be obtained that 2 2 , ff VV S f S V ? ? ? ?(15) where f and V denote internal force and displacement, respectively. 2.2. The Method to Calculate the Probabilistic Ch

34、aracteristics Here, all random variables are assumed to obey Gaussian distribution. Because other distribution form can be translate into Gaussian distribution easily, and Gaussian distribution is extensively applied

35、in the analysis of ran- dom variables. When dam is excited by static and random seismic load, the element’s displacement of dam is random vari- able. From static analysis of the dam, the expected value ? ? k of displ

36、acement of element k is obtained. And the variance E V? ? D V? ? t ? ? ? ?? ? MV CV KV F?? V ? Vk of displacement of element k can be derived as follow. The vibration equation of gravity dam is determined as (16) wh

37、ere , and V denote acceleration, velocity and displacement of nodes in dam model, respectively; K , and denote stiffness matrix, damping matrix and mass matrix of dam model, respectively; denotes random seismic load

38、. C M ( ) t FFrom Equation (16), it should be noted that gravity dam under random seismic load is a linear system. Ac- cordingly, the pseudo excitation method can be utilized in aforementioned system. The pseudo exci

39、tation is constructed as ( ) ( ) i f t F t S e ? ? ? ?( )(17) ? ? f F t ?and S where ? denote pseudo excitation and the power spectrum density of random seismic load, re- spectively. 2yy xx S H S ? ? ? H ? (a) Sxx

40、 (b) x = i t e ? (c) x ? = i t xx S e ? (d) x ? = i t xx S e ? ? ? H i t y He ? ??i t xx y S He ? ? ?? ? H ?1 1 i t xx y S H e ? ? ?? ? H ?2 2 i t xx y S H e ? ? ?Figure 1. The basic principle of the pseudo e