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An interval uncertainty analysis method for structural response bounds using feedforward neural network differentiation

机译：基于前馈神经网络微分的结构响应边界的区间不确定性分析方法

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摘要

This paper proposes a new interval uncertainty analysis method for structural response bounds with uncertain-but-bounded parameters by using feedforward neural network (FNN) differentiation. The information of partial derivative may be unavailable analytically for some complicated engineering problems. To overcome this drawback, the FNNs of real structural responses with respect to structure parameters are first constructed in this work. The first-order and second-order partial derivative formulas of FNN are derived via the backward chain rule of partial differentiation, thus the partial derivatives could be determined directly. Especially, the influences of structures of multilayer FNNs on the accuracy of the first-order and second-order partial derivatives are analyzed. A numerical example shows that an FNN with the appropriate structure parameters is capable of approximating the first-order and second-order partial derivatives of an arbitrary function. Based on the parameter perturbation method using these partial derivatives, the extrema of the FNN can be approximated without requiring much computational time. Moreover, the subinterval method is introduced to obtain more accurate and reliable results of structural response with relatively large interval uncertain parameters. Three specific examples, a cantilever tube, a Belleville spring, and a rigid-flexible coupling dynamic model, are employed to show the effectiveness and feasibility of the proposed interval uncertainty analysis method compared with other methods.
机译：通过前馈神经网络（FNN）的微分，提出了一种具有不确定但有界参数的结构响应边界的区间不确定性分析方法。对于某些复杂的工程问题，偏导数信息可能在分析上不可用。为了克服这个缺点，在这项工作中首先构造了关于结构参数的实际结构响应的FNN。 FNN的一阶和二阶偏导数公式是通过偏微分的后向链规则导出的，因此可以直接确定偏导数。特别地，分析了多层FNN的结构对一阶和二阶偏导数精度的影响。数值示例表明，具有适当结构参数的FNN能够近似任意函数的一阶和二阶偏导数。基于使用这些偏导数的参数摄动方法，可以在不花费大量计算时间的情况下近似FNN的极值。此外，引入了子区间法以相对较大的区间不确定参数获得更准确，可靠的结构响应结果。通过三个具体示例，悬臂管，贝氏弹簧和刚柔耦合动力学模型，证明了所提出的区间不确定性分析方法与其他方法相比的有效性和可行性。

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