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Weibull polynomial model for probabilistic load analysis
Published in H. Furuta, M. Dogaki, M. Sakano, Reliability and Optimization of Structural Systems, 2018
Firstly, bias of skewness and the corresponding third-order PWM are compared in Figure 3 for four of the six cases given in Table 1. It is remarkable to note from Figure 1 that bias of PWM is almost zero for all sample sizes (N) ranging from 40 to 200. In contrast, the bias of skewness is fairly significant for small sample sizes (N < 60), which gradually diminishes with increasing values of N (Figure 3). The negative bias or underestimation of skewness is large in Case 2 of exponential polynomial. In a relative sense, bias decreases with decrease in skewness of parent polynomial. Unbiased nature of PWM estimates, irrespective of the sample size, is an attractive property, and it has been confirmed using samples simulated from other heavy-tail distributions [4]. The variability of skewness and PWM estimates is reported in terms of RMSE in Figures 4(a) and 4(b), respectively. RMSE values for skewness are much greater than that of corresponding PWM estimates. It is interesting that RMSE in Case 6 is the largest (40–80%), though the associated bias is the smallest among six cases analyzed here. In Case 6, RMSE of PWM estimates is comparatively small that ranges from 10–20%. RMSE of standard deviation is compared with corresponding PWM in Figure 5. Although standard deviation exhibits higher variability than PWM, the difference is not as significant as in the case of skewness.
Ceramics and the Mechanical Properties of Ceramic Coating Materials
Published in Yichun Zhou, Li Yang, Yongli Huang, Micro- and MacroMechanical Properties of Materials, 2013
Yichun Zhou, Li Yang, Yongli Huang
For four-point bending, L1 and L2 represent the span of the lateral and medial, respectively. Y represents a dimensionless coefficient, and is related to a/W and the loading rate. In the range 0≤a/W≤ 0.6, it can be represented by the following a/W exponential polynomial [2]: () Y=A0+A1×aW+A2aW2+A3aW3+A4aW4
A NEW APPROACH FOR APPROXIMATION SOLUTIONS OF FPK EQUATIONS
Published in W. Q. Zhu, G.Q. Cai, R.C. Zhang, Advances in Stochastic Structural Dynamics, 2003
Haiwu Rong, Xiangdong Wang, Guang Meng, Wei Xu, Tong Fang
Recently, Er (13] proposed an exponential polynomial function method, in which the PDF of the stationary responses of a nonlinear stochastic system is assumed to be an exponential function of polynomials in state variables with unknown parameters. A special measure is taken to satisfy FPK equation in the weak sense of integration with the assumed PDF. The parameters in the approximate PDF" could be solved from a set of quadratic algebraic equations. However, the quadratic algebraic equations are difficult to solve.
Application of Mean-covariance Regression Methods for Estimation of EDP|IM Distributions for Small Record Sets
Published in Journal of Earthquake Engineering, 2022
The MVR accounts for information on the dispersion of in the determination of the mean parameter. As it is shown in Spady and Stouli (2018) the MVR estimated parameters cannot be interpreted as maximum likelihood estimates in general but, they can be interpreted as estimates of a penalized weighted least-squares loss function. Based on the criteria for the MVR (Spady and Stouli 2018), two types of scale functions are proposed in Spady and Stouli (2018). The polynomial models, with and the exponential-polynomial models, for . In this study, an exponential-polynomial model is used for mean-variance regression with . This is done because the domain of exponential-polynomial model is , which leads to unconstraint minimization in Equation (7) ( is always larger than 0). The parameter estimation of MVR could be done by first, concentrating out for each and estimating by solving the following equations (Spady and Stouli 2018):
Detection of defects in fabrics using information set features in comparison with deep learning approaches
Published in The Journal of The Textile Institute, 2022
For the detection of defects in fabrics, it is very essential to represent the texture of a fabric. Self similarity and randomness are the basic properties of a texture. The orderliness, i.e. arrangement of pixel intensities plays a major role in the formation of any type of texture. The main fact is that the fabric texture is more orderly but this orderliness is disturbed in the face of defects of different kinds. We are motivated to investigate the possibilistic entropy function that gives both order (certainty) and disorder (uncertainty) of pixel intensities in a sub-image. The defective free fabrics are more orderly. So fabric with defects can be easily identified by measuring the entropy values that are high when they represent uncertainty and less when they represent the certainty. In this paper, we are bent upon using the Hanman-Anirban entropy function with exponential polynomial gain function having free parameters.
Identification of dynamical systems with structured uncertainty
Published in Inverse Problems in Science and Engineering, 2018
John A. Burns, Eugene M. Cliff, Terry L. Herdman
Although the estimated parameters are similar, the predictive capability of these models can vary dramatically. Figure 10 contains plots of the predictions of each model for the time interval . Observe that the prediction using the SMD model begins to diverge from the true solution. However, using the PMF method produces a model that is essential the true solution on this interval. Figure 11 illustrates that eventually all models converge to a steady state solution. This is the correct qualitative behaviour of the system and this is captured using the special exponential polynomial expansion of the discrepancy function . However, the SMD method still does not produce the correct quantitative steady-state value. Finally, it is interesting to note that even the logistics model is better at predicting the correct steady state value than the model based on the SMD method.