Tham khảo tài liệu 'computational mechanics of composite materials part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Reliability Analysis 315 Var Di x rn tk Ễ Di j x O h - E d x O h 2 M -1 j 1 standard deviation of the th SDP component in the moment t ơ dì x O tk 4Var Di x tk coefficient of variation of the th SDP component in the moment t a Di x rn tk Var Di x rn tk E 2 d x o tk covariance matrix estimator of the ith SDP component in the moment t Cov Di x 1 rn tk Di x 2 O tk 77 7 s d j x 1 o tk - i d j x 1 o tk M -1 j 1 x d j x 2 o tk - e d j x 2 o tk Next on the basis of all statistical estimators of the SDP components Dị x O t computed for the moments t1 t2 . tm let us introduce the polynomial approximation of the respective probabilistic moments. This approximation is shown for the example of the expected values and the variances e D x o t Y Ap tp p k i 1 q Var Di x tk ẺBq tq q k i 1 where the coefficients Ap Bq depend on estimated values of the probabilistic moments approximated in the moments t1 t2 . tm. Thus on the basis of discrete values of these moments their continuous time functions are obtained. It should be underlined that and enable us generally to provide an extrapolation of the expected values and variances which is the basis of the approach proposed. Finally let us introduce the following time continuous functions being stochastic upper U i x T and lower L i x T bounds for every SDP components Dị x O t in the form 316 Random Composites V 3 p Dì x o t ew Dt x o t U i 1 Di x o t U i x t L xt To obtain these bounds for some Tt 0 rc the well-known following bounds for Gaussian variables are used U i x T e dì x o t 3 y Var Di x o t E i x t e dì x o t -3 y Var Dị x o t It should be noted that the interval x t U i x t can be contracted by decreasing the coefficient multiplied by the standard deviations of Di x o t in and . However the probability value specified in will decrease respectively as a result. As was stated above the main purpose of our analysis is to make a prognosis of the stochastic .
