Zero-memory non-linear (ZMNL) methods have long been a type of very useful tools in creating super-Gaussian random excitations for fatigue test. The major drawback of this method is that the magnitude distortion can be seen in both auto-power spectral density (ASD) and cross power-spectral density (CSD) of the excitation if the dynamic range of the target power spectral density (PSD) is large. To study the problem, we introduced Fourier series of a Gaussian signal into a cubic system, which is a common mathematical model shared by most of the ZMNL functions. We found that the cubic system produces a component leading to the distortion of both ASD and CSD. Meanwhile, if the shape of the reference ASD is flat in a frequency band, the distortion will not happen in the band. Based on this findings, a novel method is proposed in this article. It employs a pseudo reference PSD with flat ASDs to generate non-Gaussian signals in order to avoid the PSD distortions. Designed FIR filters are then applied to rescale the ASDs of the generated signals. After, iterative processes are introduced to recover the kurtoses of these filtered signals. The method is applied on a two-input and two-output numerical model, the feasibility and the availability of the method is verified. Finally, two control schemes based on the proposed pseudo reference PSD method are provided for a shaker table test. Test results show that both control schemes can eliminate the mismatch between the target PSD and the measured PSD of a shaker table.

零内存非线性（ZMNL）方法长期以来一直是一种非常有用的工具，可用于创建用于疲劳测试的超高斯随机激励。该方法的主要缺点是，如果目标功率谱密度（PSD）的动态范围为，则在激励的自功率谱密度（ASD）和交叉功率谱密度（CSD）中都可以看到幅度失真。大。为了研究该问题，我们将高斯信号的傅里叶级数引入了三次系统，这是大多数ZMNL函数共享的通用数学模型。我们发现立方系统产生了导致ASD和CSD失真的分量。同时，如果参考ASD的形状在频带中是平坦的，则在该频带中将不会发生失真。基于这一发现，本文提出了一种新颖的方法。它采用带有平面ASD的伪参考PSD来生成非高斯信号，以避免PSD失真。然后应用设计的FIR滤波器来重新缩放生成信号的ASD。之后，引入迭代过程以恢复这些滤波信号的kurtoses。将该方法应用于两进两出数值模型，验证了该方法的可行性和有效性。最后，针对振动台测试，提供了两种基于拟议的伪参考PSD方法的控制方案。测试结果表明，两种控制方案都可以消除振动台振动台的目标PSD与测得的PSD之间的不匹配。然后应用设计的FIR滤波器来重新缩放生成信号的ASD。之后，引入迭代过程以恢复这些滤波信号的kurtoses。将该方法应用于两进两出数值模型，验证了该方法的可行性和有效性。最后，针对振动台测试，提供了两种基于拟议的伪参考PSD方法的控制方案。测试结果表明，两种控制方案都可以消除振动台振动台的目标PSD与测得的PSD之间的不匹配。然后将设计的FIR滤波器应用于重新调整生成信号的ASD。之后，引入迭代过程以恢复这些滤波信号的kurtoses。将该方法应用于两进两出数值模型，验证了该方法的可行性和有效性。最后，针对振动台测试，提供了两种基于拟议的伪参考PSD方法的控制方案。测试结果表明，两种控制方案都可以消除振动台振动台的目标PSD与测得的PSD之间的不匹配。提供了两种基于拟议的伪参考PSD方法的控制方案用于振动台测试。测试结果表明，两种控制方案都可以消除振动台振动台的目标PSD与测得的PSD之间的不匹配。提供了两种基于拟议的伪参考PSD方法的控制方案用于振动台测试。测试结果表明，两种控制方案都可以消除振动台振动台的目标PSD与测得的PSD之间的不匹配。