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首页> 外文期刊>Applied Mathematical Modelling >A new point estimation method for statistical moments based on dimension-reduction method and direct numerical integration
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A new point estimation method for statistical moments based on dimension-reduction method and direct numerical integration

机译：基于降维和直接数值积分的统计矩点估计新方法

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摘要

Estimation of statistical moments of structural response is one of the main topics for analysis of random systems. The balance between accuracy and efficiency remains a challenge. After investigating of the existing point estimation method (PEM), a new point estimate method based on the dimension-reduction method (DRM) is presented. By introducing transformations, a system with general variables is transformed into the one with independent variables. Then, the existing PEMs based on the DRMs are investigated. Based on the qualitative analysis of difference in the approximations for response function and moment function, a new PEM is proposed, in which the response function is decomposed directly and the moments are calculated by high dimensional integral directly. Compared with the existing PEM based on univariate DRM, the proposed method is more friendly and easier to implement without loss of accuracy and efficiency; as compared with the PEM based on the generalized DRM, the proposed method is of better precision at the cost of nearly the same efficiency and computational complexity, further, it does hold that the even-order moments are nonnegative. Finally, several examples are investigated to verify the performance of the new method.
机译：结构响应统计矩的估计是随机系统分析的主要主题之一。准确性和效率之间的平衡仍然是一个挑战。在研究了现有的点估计方法（PEM）之后，提出了一种基于降维方法（DRM）的新点估计方法。通过引入转换，将具有通用变量的系统转换为具有独立变量的系统。然后，研究了基于DRM的现有PEM。在对响应函数和矩函数的近似差异进行定性分析的基础上，提出了一种新的PEM方法，该函数直接分解响应函数，并通过高维积分直接计算矩。与现有的基于单变量DRM的PEM相比，该方法更友好，更易于实现，并且不会损失准确性和效率。与基于广义DRM的PEM相比，该方法具有更高的精度，但效率和计算复杂度几乎相同，而且它确实认为偶数阶矩是非负的。最后，研究了几个例子以验证新方法的性能。

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