It is a challenging task to effectively estimate the upper bound as well as the lower bound of failure probability under epistemic and aleatory uncertainties in a dynamic environment. This paper proposes a novel approach to estimating both the lower and upper bounds of the time-variant hybrid failure probability by combining the proposed box moments and improved maximum entropy methods. The sparse grid sampling technique is first employed to simplify the time-variant hybrid performance function for the integration. A new continuous maximin algorithm based on the improved particle swarm optimization is then proposed for estimating the box moments. The probability density function and the time-variant hybrid failure probability can be finally estimated with the improved maximum entropy method by introducing the nonlinear transformation with an adjustable parameter. Two engineering examples are employed to testify the effectiveness of the proposed method.

在动态环境中的认知和偶然不确定性下有效地估计故障概率的上限和下限是一项具有挑战性的任务。本文提出了一种新方法，通过结合所提出的盒矩和改进的最大熵方法来估计时变混合故障概率的下限和上限。首先采用稀疏网格采样技术来简化积分的时变混合性能函数。然后提出了一种新的基于改进粒子群优化的连续最大化算法来估计框矩。通过引入参数可调的非线性变换，采用改进的最大熵方法最终可以估计概率密度函数和时变混合失效概率。两个工程实例被用来证明所提出方法的有效性。