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Reliability analysis in the presence of Aleatory uncertainty
Published in Stein Haugen, Anne Barros, Coen van Gulijk, Trond Kongsvik, Jan Erik Vinnem, Safety and Reliability – Safe Societies in a Changing World, 2018
L.G. Crespo, S.P. Kenny, D.P. Giesy
Figure 3 shows the moment-matching RPM as well as moment-bounded RPMs of maximal entropy. Note that the most prominent features of the process, such as the peaks at the boundaries of the support set and the patterns of the lines in its interior, have faded in the latter predictor. Furthermore, note that the derivative discontinuities in the moment functions of Figure 4 yield derivative discontinuities in the percentile lines. Such discontinuities can be eliminated by using a Kernel smoother or by using another cost function. Alternatively, we can calculate a moment-bounded RPM having the cost function in Equation (13). The corresponding moment functions are shown as dotted lines in Figure 4. In contrast to the moments for the maximal entropy formulation, the new moments have continuous derivatives throughout X. The resulting RPM, shown at the bottom of Figure 3, exhibits smooth percentile lines. This is achieved at the expense of a minor entropy reduction to Ex[E]=0.73. As ne increases, the width of the confidence intervals reduces making moment- bounded RPMs converge to the moment-matching RPM. The PDF-matching or the maximum-likelihood staircase formulations are preferable when ne is sufficiently large.
Permutation Tests and Nonparametric Combination Methodology
Published in Corain Livio, Arboretti Rosa, Bonnini Stefano, Ranking of Multivariate Populations, 2017
Corain Livio, Arboretti Rosa, Bonnini Stefano
Alternative nonparametric solutions are proposed in the literature within the nonparametric regression framework. In this connection Cardot et al. (2007) suggested a permutation approach to check if a real covariate has a significant effect on a functional response in a regression setting using two test statistics, that is, an adapted F-statistic and a statistic based on the kernel smoother applied to the residuals. Zhang and Lin (2003) proposed a solution for testing the equivalence of two nonparametric functions in semi-parametric additive mixed models for correlated non-Gaussian data. This test extends the previous work of Zhang et al. (2000). Neumeyer and Dette (2003) proposed a new test for the comparison of two regression curves that is based on a difference of two marked empirical processes based on residuals that is applicable in the case of different design points and heteroscedas-ticity. Finally, from a functional data analysis and nonparametric regression perspective Hall and Van Keilegom (2007) suggested a Cramer-von Mises type test and took up the issue of studying how the data preprocessing interferes with the performance of two-sample statistical tests.
Local Methods for Dimension Reduction
Published in Yangsheng Xu, Ka Keung C. Lee, Human Behavior Learning and Transfer, 2005
From (11.1), it might at first appear that a spline smoother is a global parametric model rather than a local model. The model is indeed defined as the minimum of a global error function, and the resulting curve may be parameterized as a spline function. However, the number of parameters defining the spline is actually greater than the number of values in the training data, and the error term of the cost function is balanced against a smoothness measure based upon derivatives, which are by definition local. In fact, Silverman [220] shows that a spline smoother is equivalent to a kernel smoother with a variable-sized kernel.
Dynamics of fabric and dryer sheet motion in domestic clothes dryers
Published in Drying Technology, 2022
C. R. Jones, A. Corona, C. Amador, P. J. Fryer
Time averaged velocity, acceleration, and occupancy profiles are useful to understand the bulk behavior of fabrics and delivery articles. However, they give little insight into the degree of mixing in the dryer. Effective mixing is required to ensure the delivery article deposits SFE uniformly over the full surface area of the fabric load. Insight into this behavior can be gained by considering the change in axial and radial position of the tracer during each rotation. The location of the tracer was recorded each time the particle passed upwards across the horizontal center line of the drum, i.e., a full rotation was completed. For each pass the average axial coordinate and radius were calculated and subtracted from the average values of the previous pass, and data fitted to a probability density function using a kernel density estimation. The MATLAB R2019b ‘ksdensity’ function with a normal kernel smoother was used to calculate estimates, with the optimal bandwidth for a normal density estimation calculated, as described by Bowman and Azzalini.[25] As a continuous tracer trajectory could not be recorded for the large dryer, this analysis was only possible for the smaller dryer.