Calculation of the Residual Sum of Squares for all Possible Regressions

When the number of independent variables for a regression analysis is not too large, calculation of all possible regressions is an alternative to the various stepwise procedures available. However, the amount of information available from all possible regressions is quite large even for a moderate number of variables. And screening out most of the regressions can be done simply on the basis of information contained in the residual sum of squares.

This paper presents an efficient procedure for the calculation of the residual sum of squares for each regression and some suggestions for screening procedures.     

Efficient robust design via Monte Carlo sample reweighting

A novel probabilistic method for the optimization of robust design problems is presented. The approach is based on an efficient variation of the Monte Carlo simulation method. By shifting most of the computational burden to outside of the optimization loop, optimum designs can be achieved efficiently and accurately. Furthermore by reweighting an initial set of samples the objective function and constraints become smooth functions of changes in the probability distribution of the parameters, rather than the stochastic functions obtained using a standard Monte Carlo method. The approach is demonstrated on a beam truss example, and the optimum designs are verified with regular Monte Carlo simulation. Copyright © 2006 John Wiley & Sons, Ltd.     

Gradient and parameter sensitivity estimation for systems evaluated using Monte Carlo analysis

The performance evaluation of many practical systems can be handled only through computationally intensive Monte Carlo simulation. Although a number of specialist techniques have been proposed, in general, estimation of the sensitivity of the outcome to changes in parameters involves duplicate simulations and finite differences for each parameter of interest. An approximate technique for gradient sensitivity estimation was outlined previously. It is appropriate when the performance function is uni-modal and relatively smooth in the region of interest. It generates all gradients simultaneously by converting Monte Carlo simulation run outcomes to an approximate analytic problem defined by a simplified response surface. The gradients then follow immediately. No extra simulation runs are required. Herein that approach is extended to non-Normal random variables and to the estimation of parameter sensitivities for random variable means and standard deviations. Some illustrative examples are given with comparisons to sensitivities computed by conventional Monte Carlo. The influence of constraint function(s) defining the admissible solution region is also considered.     

略论商品包装的动态流程和系统组合

探讨商品包的动态流程,以商品包装的多元功能为起点,从设计定位的角度解构商品包装的动态整合,试图探讨商品馐谣主体因素和生成程序。     

Calculation of shape factors by means of the equal energy partitioning method and its modification

Abstract

The present study develops a method called the energy equal partitioning method. This method divides all the solid angles of a radiating source properly so that the energy carried by the beams within each small range of the solid angle are equal. The fraction of energy beams arriving at the wall surface is then examined to obtain the shape factor. This method can be efficiently applied to complex geometries. Comparing the rate of convergence and the cost of computing time shows that the shape factor obtained by the present method is better than that obtained by the Monte Carlo method. The influence of the geometric configuration on the accuracy of the shape factor is also investigated. The shape factor obtained by this method is modified by using the original shape factor as a weighting factor. An iteration procedure is developed. The resulting shape factors satisfy the reciprocity law and energy conservation law and the degree of closeness to the exact shape factors is found to be better.     

Efficient estimation of first passage probability of high-dimensional nonlinear systems

An efficient method for estimating low first passage probabilities of high-dimensional nonlinear systems based on asymptotic estimation of low probabilities is presented. The method does not require any a priori knowledge of the system, i.e. it is a black-box method, and has very low requirements on the system memory. Consequently, high-dimensional problems can be handled, and nonlinearities in the model neither bring any difficulty in applying it nor lead to considerable reduction of its efficiency. These characteristics suggest that the method is a powerful candidate for complicated problems. First, the failure probabilities of three well-known nonlinear systems are estimated. Next, a reduced degree-of-freedom model of a wind turbine is developed and is exposed to a turbulent wind field. The model incorporates very high dimensions and strong nonlinearities simultaneously. The failure probability of the wind turbine model is estimated down to very low values; this demonstrates the efficiency and power of the method on a realistic high-dimensional highly nonlinear system.     

Probability matching priors for linear calibration

Summary In the linear calibration problem, a model is fit to paired observations arising from two measurement techniques, one known to be far more accurate (but also more expensive) than the other. The fitted model is then used with univariate observations from the less accurate technique to impute values from the more accurate one. The Bayesian paradigm emerges as attractive in this context, but the choice of an appropriate noninformative prior distribution has been controversial. In this paper we derive a class of such distributions, and provide sufficient conditions under which they lead to proper posterior densities. These priors, which we refer to asprobability matching priors, are designed to produce posterior credible intervals which are asymptotically identical to their frequentist counterparts. We provide details on the implementation of our procedure using sampling-based methods, and obtain significant simplifications over previous Bayesian approaches in this area. We compare the performance of several members of our prior class in the context of two illustrative examples.     

Efficient Technique for Assessing Actual Non‐normal Quality Loss: Markov Chain Monte Carlo

Markov chain Monte Carlo (MCMC) techniques have been extensively developed and are accepted for solving various real‐world problems. However, process capabilities are rarely analyzed with the means of MCMC. This study integrates the MCMC technique into Bayesian models for assessing the well‐known quality loss index C_pm for gamma and Weibull process distributions. After the MCMC iterations are completed, the quality manager can make reliable decisions via the proposed credible intervals. Furthermore, this study provides performance comparisons of the estimators of C_pm obtained by the MCMC and bootstrap techniques. Simulations show that the MCMC technique performs better than the bootstrap technique in most of the cases that were considered. Copyright © 2016 John Wiley & Sons, Ltd.     

Selection function in breakage processes: PBM and Monte Carlo modeling

Breakage, i.e., formation of smaller fragments from larger initial particles, is an important phenomenon – wanted or unwanted – in many particulate processes. In this work, the volume and time dependent selection function for pure breakage process is modeled based on the population balance modeling approach. It is found that the selection function is directly correlated with the stressing frequency, probability of successful events, and some integral properties of the number density function. A discrete population balance equation is applied to compute the total number of particles and particle size distribution numerically. Moreover, an event-driven constant number Monte Carlo simulation algorithm is presented, and the simulation results are used as an alternative to experimental results. The volume dependency of the selection function is incorporated successfully in the Monte Carlo simulation while selecting particles for stressing event. Some important properties of any particulate process, such as the total number of particles and the size distribution of particles are validated successfully using the Monte Carlo results. This offers new insights into the estimation and interpretation of breakage kinetics.     

Efficient stationary multivariate non-Gaussian simulation based on a Hermite PDF model

An efficient stationary multivariate non-Gaussian simulation method is developed using spectral representation and third order Hermite polynomial translation. An approximate closed form relationship is employed to identify the Hermite translation parameters based on target skewness and kurtosis. This preserves a high degree of accuracy over the entire admissible range of the Hermite translation, and eliminates the need for iterative solution of the translation parameters. The Hermite PDF model is suitable for a wide range of strongly non-Gaussian stochastic process. In addition, an explicit bidirectional relationship between the target non-Gaussian and Gaussian correlation is developed to eliminate the need for iteration or numerical integration to identify the underlying Gaussian correlation. Examples apply the simulation method to both theoretical targets and experimental wind pressure data.     

Mono-sized sphere packing algorithm development using optimized Monte Carlo technique

In this paper, fuel cell catalyst layer was developed using the optimized sphere packing algorithm. An optimization technique named adaptive random search technique (ARSET) was employed in this packing algorithm. The ARSET algorithm will generate the initial location of spheres and allow them to move in the random direction with the variable moving distance, randomly selected from the sampling range (α), based on the Lennard–Jones potential and Morse potential of the current and new configuration. The solid fraction values obtained from this developed algorithm are in the range of 0.610–0.624 while the actual processing time can significantly be reduced by 5.58–34% based on the number of spheres. The initial random number sampling range (α) was investigated and the appropriate α value is equal to 0.5.     

Estimation under the Burr type XII failure model based on censored data: a comparative study

Summary Based on type-2 censored samples, the maximum likelihood, uniformly minimum variance unbiased, Bayes and empirical Bayes estimators of one of the two shape parameters (k) and reliability functionR(t) of the Burr type XII failure model are computed and compared. Computations show that when the censoring sizer=10, the EBE’s of κ andR(t),t=0.9, are better than the corresponding UMVUE’s for as few asm ^*=7 past samples fork andm ^*=11 past samples forR(0.9), in the sense of having smaller estimated risks, when the gamma conjugate prior is used.     

Calculation of the mutual diffusion coefficient by equilibrium and nonequilibrium molecular dynamics

A nonequilibrium molecular dynamics method for the calculation of the mutual diffusion coefficient for a mixture of hard spheres is described. The method is applied to a 50-50 mixture of equidiameter particles having a mass ratio of 0.1 for the two species, at a volume of three times close-packing. By extrapolating the results to the limit of vanishing concentration gradient and infinite system size, we obtain a value in statistical agreement with the result obtained using a Green-Kubo molecular dynamics procedure, which is also described. The non-equilibrium calculation yields a mutual diffusion coefficient which decreases slightly with increasing concentration gradient. The Green-Kubo timecorrelation function for mutual diffusion displays a slow decay with time, qualitatively similar to the long-time tail which has been predicted by the hydrodynamic theory of Pomeau.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

铯喷泉钟C场的测量与计算

在铯原子喷泉钟实验中,C场均匀度决定了二阶塞曼频移的不确定度评定。使用微波激励法可以测量C场各个高度经时间加权的磁感应强度的平均值。为了得到C场的实际磁场分布,需要对微波激励法的测量结果进行去时间加权计算。介绍了两种去时间加权的算法,并利用仿真数据对算法进行了验证。最后使用微波激励法和两种去时间加权算法,结合蒙特卡洛不确定度评定方法对NIM6铯喷泉钟C场进行了测量与计算。     

An Efficient Sampling Technique for Bayesian Inference With Computationally Demanding Models

In the environmental sciences, a large knowledge base is typically available on an investigated system or at least on similar systems. This makes the application of Bayesian inference techniques in environmental modeling very promising. However, environmental systems are often described by complex, computationally demanding simulation models. This strongly limits the application of Bayesian inference techniques, because numerical implementation of these techniques requires a very large number of simulation runs. The development of efficient sampling techniques that attempt to approximate the posterior distribution with a relatively small parameter sample can extend the range of applicability of Bayesian inference techniques to such models. In this article a sampling technique is presented that tries to achieve this goal. The proposed technique combines numerical techniques typically applied in Bayesian inference, including posterior maximization, local normal approximation, and importance sampling, with copula techniques for the construction of a multivariate distribution with given marginals and correlation structure and with low-discrepancy sampling. This combination improves the approximation of the posterior distribution by the sampling distribution and improves the accuracy of results for small sample sizes. The usefulness of the proposed technique is demonstrated for a simple model that contains the major elements of models used in the environmental sciences. The results indicate that the proposed technique outperforms conventional techniques (random sampling from simpler distributions or Markov chain Monte Carlo techniques) in cases in which the analysis can be limited to a relatively small number of parameters.     

Efficient adaptive CUSUM control charts based on generalized likelihood ratio test to monitor process dispersion shift

In practice, a shift in the process parameters (location and/or dispersion) is unknown in prior and cannot be diagnosed precisely with the classical cumulative sum (CUSUM) control chart. To overcome this issue, this study proposed two adaptive CUSUM (ACUSUM) control charts. The proposed control charts utilized linear weighted function that is inspired by generalized likelihood ration test (GLRT) to monitor small and certain range of shift in the process dispersion. In more details, the proposed control charts methodologies are based on GLRT, exponentially weight moving average statistic, and score functions. To obtain the run length of the proposed control charts for performance assessment, algorithms are designed in MATLAB based on Monte Carlo simulation technique. Further, average run length (ARL) is used as a performance measure tool to compare the control charts performance for a single shift. For certain range of shift, extra quadratic loss function, relative ARL, and performance comparison index performance measures based on ARL are calculated. Some existing control charts are used for comparison purpose. The proposed control charts show outstanding capability to detect out-of-control signal against these control charts. Moreover, real-life data of inside diameter of cylinder bore in an engine block are used to reveal the practicality and worth of the proposed control charts relative to other control charts.     

Trackless ring identification and pattern recognition in Ring Imaging Cherenkov (RICH) detectors

An algorithm for identifying rings in Ring Imaging Cherenkov (RICH) detectors is described. The algorithm does not make use of tracking information to seed ring centres. The algorithm is necessarily Bayesian and makes use of a Metropolis-Hastings Markov chain Monte Carlo sampler to locate the rings. In particular, the sampler employs a novel proposal function whose form is responsible for significant speed improvements over earlier trackless methods. The method is optimised for finding multiple overlapping rings in detectors similar to the LHCb experiment's “RICH2” detector.     

Is High TC Possible in (Ga,Mn)N?: Monte Carlo Simulation vs. Mean Field Approximation

The magnetic properties of diluted magnetic semiconductors (DMSs) are calculated from first-principles by mapping the ab initio results on a classical Heisenberg model. By using the Korringa–Kohn–Rostoker coherent potential approximation method within the local density approximation, the electronic structure of (Ga,Mn)N and (Ga,Mn)As is calculated. Effective exchange coupling constants J_ijs are calculated by using the formula of Liechtenstein et al. (A.~I. Liechtenstein, M. I. Katsnelson, V. P. Antropov, and V. A. Gubanov, 1987, J.~Magn. Magn. Mater. Vol. 67, p. 65). It is found that the range of the exchange interaction in (Ga,Mn)N is very short due to the exponential decay of the impurity wave function in the gap. On the other hand, in (Ga,Mn)As, the interaction is weaker but long ranged because the extended valence hole states mediate the ferromagnetic interaction. Monte Carlo simulations show that the T_C values of (Ga,Mn)N are very low since percolation is difficult to achieve for small concentrations and the mean field approximation strongly overestimates T_C. Even in (Ga,Mn)As the percolation effect is still important.