基于三点拉格朗日数字滤波器的响应谱优化分析

Optimization Analysis of Response Spectra Based on Three-Point Lagrange Digital Filter

响应谱被广泛用于评估振动环境下武器装备系统(如火炮、战车)的可靠性和耐久性,其计算精度主要取决于所采用的数字滤波器模型。构建了任意激励下基于数字滤波器的响应谱计算模型,基于卷积核对比了斜阶跃响应不变法和三点拉格朗日法引入的偏置误差和相位误差,基于三点拉格朗日数字滤波器对疲劳损伤谱和极值响应谱进行了优化分析。分析结果表明,在给定采样率下,三点拉格朗日法引入的偏置误差小于斜阶跃响应不变法,且相位误差接近0。该方法用于响应谱计算时可进一步提高计算精度,进而提高振动环境下武器装备系统的可靠性和耐久性评估精度。

Response spectra are widely used to evaluate the reliability and durability of armament systems(e.g.,guns and fighting vehicles)in an vibration environment.Its accuracy mainly depends on the digital filter model.A mathematical model for calculating response spectra under arbitrary excitation based on digital filters was built.The bias and phase errors introduced by using the ramp invariant and three-point Lagrange methods were then compared based on the convolution kernel.An optimization analysis was also made of the fatigue damage spectrum and extreme response spectrum based on three-point Lagrange digital filters.The result shows that,with a given sampling frequency,the three-point Lagrange method introduces a smaller bias error and nearly zero phase error,compared with the ramp invariant method.It also shows that the three-point Lagrange method can be used to increase the accuracy for calculating response spectra,thus making it more accurate when the reliability and durability of armament systems in an vibration environment is evaluated.