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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 study is to improve the efficiency and accuracy of response surface method (RSM), as well as its robustness.

By introducing cut-high-dimensional representation model (HDMR), the delineation of cross terms and the constitution analysis of component function, a new adaptive RSM is presented for reliability calculation, where a sampling scheme is also proposed to help constructing response surface close to limit-state.

The proposed method has a more feasible process of evaluating undetermined coefficients of each component function than traditional RSM, and performs well in terms of balancing the efficiency and accuracy when compared to the traditional second-order polynomial RSM. Moreover, the proposed method is robust on the parameter in a wide range, indicating that it is able to obtain convergent result in a wide feasible domain of sample points.

This study constructed an adaptive bivariate cut-HDMR by introducing delineation of cross-terms and constitution of univariate component function; and a new sampling technique is proposed.

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.

Based on univariate dimension-reduction model, this study aims to propose an adaptive anisotropic response surface method (ARSM) and its high-order revision (HARSM) to balance the accuracy and efficiency for response surface method (RSM).

First, judgment criteria for the constitution of a univariate function are derived mathematically, together with the practical implementation. Second, by combining separate polynomial approximation of each component function of univariate dimension-reduction model with its constitution analysis, the anisotropic ARSM is proposed. Third, the high-order revision for component functions is introduced to improve the accuracy of ARSM, namely, HARSM, in which the revision is also anisotropic. Finally, several examples are investigated to verify the accuracy, efficiency and convergence of the proposed methods, and the influence of parameters on the proposed methods is also performed.

The criteria for constitution analysis are appropriate and practical. Obtaining the undetermined coefficients for every component functions is easier than the existing RSMs. The existence of special component functions is useful to improve the efficiency of the ARSM. HARSM is helpful for improving accuracy significantly and it is more robust than ARSM and the existing quadratic polynomial RSMs and linear RSM. ARSM and HARSM can achieve appropriate balance between precision and efficiency.

The constitution of univariate function can be determined adaptively and the nonlinearity of different variables in the response surface can be treated in an anisotropic way.

The purpose of this paper is to propose a method for selecting the position and attitude trajectory of error measurement to improve the kinematic calibration efficiency of a one translational and two rotational (1T2R) parallel power head and to improve the error compensation effect by improving the properties of the error identification matrix.

First, a general mapping model between the endpoint synthesis error is established and each geometric error source. Second, a model for optimizing the position and attitude trajectory of error measurement based on sensitivity analysis results is proposed, providing a basis for optimizing the error measurement trajectory of the mechanism in the working space. Finally, distance error measurement information and principal component analysis (PCA) ideas are used to construct an error identification matrix. The robustness and compensation effect of the identification algorithm were verified by simulation and through experiments.

Through sensitivity analysis, it is found that the distribution of the sensitivity coefficient of each error source in the plane of the workspace can approximately represent its distribution in the workspace, and when the end of the mechanism moves in a circle with a large nutation angle, the comprehensive influence coefficient of each sensitivity is the largest. Residual analysis shows that the robustness of the identification algorithm with the idea of PCA is improved. Through experiments, it is found that the compensation effect is improved.

A model for optimizing the position and attitude trajectory of error measurement is proposed, which can effectively improve the error measurement efficiency of the 1T2R parallel mechanism. In addition, the PCA idea is introduced. A least-squares PCA error identification algorithm that improves the robustness of the identification algorithm by improving the property of the identification matrix is proposed, and the compensation effect is improved. This method has been verified by experiments on 1T2R parallel mechanism and can be extended to other similar parallel mechanisms.

This paper aims to investigate the differences in hot corrosion behavior of the GTD222 superalloy and TiC/GTD222 composite in a mixed salt of 75% Na₂SO₄ and 25% K₂SO₄ at 900°C.

The GTD222 superalloy and TiC/GTD222 nickel-based composite were prepared using selective laser melting (SLM). Subsequently, the hot corrosion behavior of the two alloys was systematically investigated in a salt mixture consisting of 75% Na₂SO₄ and 25% K₂SO₄ (Wt.%) at 900°C.

The TiC/GTD222 composite exhibited better hot corrosion resistance compared to the GTD222 superalloy. First, the addition of alloying elements led to the formation of a protective oxide film on the TiC/GTD222 composites 20 h before hot corrosion. Second, TiC/GTD222 composite corrosion surface has a higher Ti content, after 100 h of hot corrosion, the composite corrosion surface Ti content of 10.8% is more than two times the GTD222 alloy 4% Ti. The Ti and Cr oxides are tightly bonded, effectively resisting the erosion of corrosive elements.

The hot corrosion behavior of GTD222 superalloy and TiC/GTD222 composites prepared by SLM in a mixed salt of 75% Na₂SO₄ and 25% K₂SO₄ was studied for the first time. This study provides insights into the design of high-temperature alloys resistant to hot corrosion.

This study expands the isomorphic logic on the participatory guarantee system (PGS) alternative certification method, which aims to level the supply chain sustainability field to determine how the alignment of disadvantaged agrifood stakeholders (e.g. small/applicant farmers, local organizations, consumers and volunteer auditors) might neutralize the negative effects of stakeholder heterogeneity (SH) on PGS recognition.

The sample comprised 113 multilateral matching questionnaires collected from disadvantaged agrifood stakeholders participating in the PGS activities of the Green Conservation Label managed by Taiwan's Tse-Xin Organic Agriculture Foundation (TOAF). This study adopted hierarchical regression to test the hypotheses.

Stakeholder alignment, external community (EC) constructs, similar backgrounds (SBs) and value congruence (VC) diminish the negative effects of SH on PGS recognition.

PGS is an agrifood supply chain social movement designed to allow underprivileged actors to enact solutions collectively to address social inequities and ecological problems through fair procedures, collective assignments and collaborative intentionality. PGS members who leverage VC, SB and EC will have a greater chance of successfully overcoming their institutional disadvantages.

Based on the PGS activities initiated by disadvantaged agrifood stakeholders, this study transformed isomorphic logics, including coercive, mimetic and normative isomorphisms, into a mechanism with which individuals can build a governance structure that helps disadvantaged agrifood stakeholders develop alternative institutions by pooling their resources.