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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.

The polynomial dimensional decomposition (PDD) method is a popular tool to establish a surrogate model in several scientific areas and engineering disciplines. The selection of appropriate truncated polynomials is the main topic in the PDD. In this paper, an easy-to-implement adaptive PDD method with a better balance between precision and efficiency is proposed.

First, the original random variables are transformed into corresponding independent reference variables according to the statistical information of variables. Second, the performance function is decomposed as a summation of component functions that can be approximated through a series of orthogonal polynomials. Third, the truncated maximum order of the orthogonal polynomial functions is determined through the nonlinear judgment method. The corresponding expansion coefficients are calculated through the point estimation method. Subsequently, the performance function is reconstructed through appropriate orthogonal polynomials and known expansion coefficients.

Several examples are investigated to illustrate the accuracy and efficiency of the proposed method compared with the other methods in reliability analysis.

The number of unknown coefficients is significantly reduced, and the computational burden for reliability analysis is eased accordingly. The coefficient evaluation for the multivariate component function is decoupled with the order judgment of the variable. The proposed method achieves a good trade-off of efficiency and accuracy for reliability analysis.

The purpose of this paper is to analyze the perspectives of the People’s Republic of China (PRC) Belt and Road strategy. The challenge in terms of studying the New Silk Road concept comes from the fact of dramatic difference between the declared ambitions of the Chinese state and the elusive character of concrete Chinese involvement, in particular as far as the digital dimension of the strategy is concerned.

The goal will be achieved by comparing the Chinese expansion in the Post-Soviet Central Asia with nowadays declarations concerning the digital version of the New Silk Road. For China, the Post-Soviet Central Asia was the first frontier approached on the basis of genuinely own integration strategy: the New Silk Road Diplomacy, which later evolved into the New Silk Road concept. An overview of Chinese activity in the region tells a lot about its grand strategy of today.

To paraphrase T.S. Kuhn, what one sees depends on not only what one is looking at but also what one has learned to notice. The Post-Soviet Central Asia shows the way Beijing thinks about integration. PRC achieved the most by basing on the free rider effect: concentrating on economic expansion, while other Powers provided relative regional security and stability.

The comparison of the beginnings of the New Silk Diplomacy in the 1990s with the plans of the New Digital Road gives a unique angle to grasp the specific features of the Chinese approach to international integration.