EXPONENTIAL–POLYNOMIAL CLOSURE METHOD FOR SOLVING TRUNCATED KOLMOGOROV–FELLER EQUATION
EXPONENTIAL–POLYNOMIAL CLOSURE METHOD FOR SOLVING TRUNCATED KOLMOGOROV–FELLER EQUATION
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DOI：
10.1142/s021987621240018x
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发表时间：
2012-07
影响因子：
1.7
通讯作者：
H. Zhu;G. Er;V. Iu;K. Kou
中科院分区：
文献类型：
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作者：
H. Zhu;G. Er;V. Iu;K. Kou
针对离散泊松脉冲激励下的非线性系统，给出了响应的概率密度函数（PDF）解。PDF解由Kolmogorov-Feller（KF）方程控制，该方程由指数多项式闭合（EPC）方法近似求解。进一步研究了泊松脉冲幅值为高斯分布或非高斯分布的Duffing振子，以说明EPC方法在这两种情况下的有效性。数值分析表明，与仿真结果相比，多项式阶数为6的EPC方法具有良好的结果，即使在振荡器响应的PDF的尾部。
The probability density function (PDF) solution of the response is formulated for nonlinear systems under discrete Poisson impulse excitation. The PDF solution is governed by the Kolmogorov–Feller (KF) equation, which is approximately solved by the exponential–polynomial closure (EPC) method. A Duffing oscillator is further investigated in the case of either Gaussian or non-Gaussian distributed amplitude of Poisson impulse to show the effectiveness of the EPC method in these cases. The numerical analysis shows that the EPC method with the polynomial order being 6 presents a good result compared with the simulated result, even in the tails of the PDF of the oscillator response.