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Conversion of the correlated random variables into independent variables, especially into independent standard normal variables, is the common technology for estimating the statistical moments of response and evaluating reliability of random system, in which calculating the equivalent correlation coefficient is an important component. The purpose of this paper is to investigate an accurate, efficient and easy to implement estimation method for the equivalent correlation coefficient of various incomplete probability systems.

First, an approach based on the Mehler’s formula for evaluating the equivalent correlation coefficient is introduced, then, by combining with polynomial normal transformations, this approach is improved to be valid for various incomplete probability systems, which is named as the direct method. Next, with the convenient linear reference variables for eight frequently used random variables and the approximation of the Rosenblatt transformation introduced, a further improved implementation without iteration process is developed, which is named as the simplified method. Finally, several examples are investigated to verify the characteristics of the proposed methods.

The results of the examples in this paper show that both the proposed two methods are of high accuracy, by comparison, the proposed simplified method is more effective and convenient.

Based on the Mehler’s formula, two practical implementations for evaluating the equivalent correlation coefficient are proposed, which are accurate, efficient, easy to implement and valid for various incomplete probability systems.

A local equivalent linearization methodology is proposed to simulate non‐linear shock absorbers and dual‐phase dampers in the convenient frequency domain. The methodology based on principle of energy similarity, characterizes the non‐linear dual‐phase dampers via an array of local damping constants as function of local excitation frequency and amplitude, response, and type of non‐linearity. The non‐linear behaviour of the dual‐phase dampers can thus be predicted quite accurately in the entire frequency range. The frequency response characteristics of a vehicle model employing non‐linear dual‐phase dampers, evaluated using local linearization algorithm, are compared to those of the non‐linear system, established via numerical integration, to demonstrate the effectiveness of the algorithm. An error analysis is performed to quantify the maximum error between the damping forces generated by non‐linear and locally linear simulations. The influence of damper parameters on the ride improvement potentials of dual‐phase dampers is further evaluated using the proposed methodology and discussed.

This paper deals with structural shape and thickness optimization of axisymmetric shell structures loaded symmetrically. In the finite element stress analysis use is made of newly developed linear, quadratic, and cubic, variable thickness, C(0) elements based on axisymmetric Mindlin‐Reissner shell theory. An integrated approach is used to carry out the whole shape optimization process in a fully automatic manner. A robust, versatile and flexible mesh generator is incorporated with facilities for generating either uniform or graded meshes, with constant, linear, or cubic variation of thickness, pressure etc. The midsurface geometry and thickness variations of the axisymmetric shell structure are defined using cubic splines passing through certain key points. The design variables are chosen as the coordinates and/or the thickness at the key points. Variable linking procedures are also included. Sensitivity analysis is carried out using either a semi‐analytical method or a global finite difference method. The objective of the optimization is the weight minimization of the structure. Several examples are presented illustrating optimal shapes and thickness distributions for various shells. The changes in the bending, membrane and shear strain energies during the optimization process are also monitored.

The purpose of this paper is to find an accurate, efficient and easy-to-implement point estimate method (PEM) for the statistical moments of random systems.

First, by the theoretical and numerical analysis, the approximate reference variables for the frequently used nine types of random variables are obtained; then by combining with the dimension-reduction method (DRM), a new method which consists of four sub-methods is proposed; and finally, several examples are investigated to verify the characteristics of the proposed method.

Two types of reference variables for the frequently used nine types of variables are proposed, and four sub-methods for estimating the moments of responses are presented by combining with the univariate and bivariate DRM.

In this paper, the number of nodes of one-dimensional integrals is determined subjectively and empirically; therefore, determining the number of nodes rationally is still a challenge.

Through the linear transformation, the optimal reference variables of random variables are presented, and a PEM based on the linear transformation is proposed which is efficient and easy to implement. By the numerical method, the quasi-optimal reference variables are given, which is the basis of the proposed PEM based on the quasi-optimal reference variables, together with high efficiency and ease of implementation.

The purpose of this paper is to design a numerical model to calculate the individual evacuation time among secondary students based on Knowledge, Attitude and Practice (KAP), human characteristics and travel distances.

Validated KAP questionnaires were distributed among 290 respondents. The KAP level was obtained based on the assigned scores. During a fire drill, the individual evacuation time was calculated by using personal digital watch while the travel distances were recorded and measured. A linear numerical model was derived by using multiple linear regression to identify the significant variables and the coefficients.

The CVI, CVR and Cronbach’s α value (0.75, 0.59 and 0.7, respectively) which are greater than minimum accepted level proved the reliability and consistency of the instrument. The evacuation time prediction by the developed numerical model showed strong correlation with the actual time (R=0.95). The regression analysis found that 89 per cent proportion of variance in the evacuation time are determined by the predictors. Based on the linear equation, it found that the decrease in weight, knowledge level and walking speed while increase in BMI, flat and stair travel distances could increase evacuation time. From the six significant variables, weight, walking speed, flat and stair distances showed significant correlation in the model with p<0.001, while BMI and knowledge showed p<0.05. The integration with mobility factors expand the formula which applicable within dynamic fire scenario.

The involvement of examination students in the study is restricted by the Ministry of Education Malaysia to avoid interruption of learning session which limited the data representation.

Instead of using the traditional direct measurement of the evacuation time, the developed numerical model is an alternative convenient approach which could be used as one of the pre-assessment tool to identify the level of safety among students. The low cost and shorter time application of this model become one of the greatest advantages compared to other available approaches. The calculated individual evacuation time could be used directly to develop a better fire safety policy.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

Over the last decade, latent growth modeling (LGM) utilizing hierarchical linear models or structural equation models has become a widely applied approach in the analysis of change. By analyzing two or more variables simultaneously, the current method provides a straightforward generalization of this idea. From a theory of change perspective, this chapter demonstrates ways to prescreen the covariance matrix in repeated measurement, which allows for the identification of major trends in the data prior to running the multivariate LGM. A three-step approach is suggested and explained using an empirical study published in the Journal of Applied Psychology.

The issue of export instability exerts an enduring fascination for economists with an interest in the area of economic development. Over several decades a voluminous literature has emerged embracing debates on the domestic consequences and on the causes of export instability. The purpose here is to examine these debates and an attempt is made to set out different theoretical stances, to classify and examine empirical findings, and to indicate the directions in which the debates have moved. Such a statement of a review article's purpose is, of course, incomplete without more specific delineation of the boundaries within which the general objectives are pursued. Here that delineation has three facets.

Sufficient conditions for bounded input‐bounded output (BIBO) stability are established for a class of time‐variable linear semi‐state systems. These conditions are expressed directly in terms of system parameters and reduce to testing of negative semi‐definiteness of a time‐varying matrix. Simple algebraic conditions convenient for the computer applications are derived for this purpose. It is shown how the results obtained can be applied in the analysis of linear time‐variable RLC electrical networks.