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为了提高可靠性灵敏度求解数字模拟法的效率,提出了一种变量空间确定性低偏差均匀抽样与样本点处联合概率密度函数构造权重相结合的方法,来估计可靠性灵敏度。该方法通过均匀样本点处联合概率密度函数的权重保证了可靠性灵敏度的估计值收敛于真值,而由低偏差抽样代替原问题中的联合概率密度抽样则可以保证更低的误差阶以及在小失效概率条件下抽得的样本有更高的可能性落入失效域,从而保证了所提方法具有更高的收敛速度。另外,所提方法可以采用与独立变量相同的步骤来估计相关变量情况下的可靠性灵敏度,计算简便,适用范围广。算例充分证明了所提方法的优越性。
In order to improve the reliability and sensitivity of the digital simulation method, a method of combining the deterministic low-variance uniform sampling space with the construction weight of the joint probability density function at the sample point is proposed to estimate the reliability sensitivity. This method ensures that the reliability sensitivity estimates converge to true values by weighting the joint probability density function at uniform sample points, whereas substituting low-deviation sampling instead of joint probability density sampling in the original problem guarantees a lower error order, There is a higher probability that the samples drawn under the condition of small failure probability will fall into the failure field, thus ensuring a higher convergence speed of the proposed method. In addition, the proposed method can use the same steps as the independent variables to estimate the reliability sensitivity under the condition of related variables, and the calculation is simple and the application scope is wide. The example fully proves the superiority of the proposed method.