Modeling method for non-stationary road irregularity based on modulated white noise and lookup table method
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摘要: 针对实测道路功率谱密度频率结构不同与汽车行驶速度变化引起的非平稳问题, 分析了现有路面不平度模型的准确性, 提出了一种基于调制白噪声与查表法的非平稳路面不平度建模方法; 结合白噪声生成方法和离散功率谱密度的计算公式, 推导出了能够确保路面不平度计算功率谱与设计功率谱完全吻合的Band-Limited White Noise模块参数设定方法; 通过不同设定值组合的白噪声功率谱密度与路面不平度功率谱密度计算结果对比, 验证了所提出的Band-Limited White Noise模块参数设定值的准确性; 为解决频率指数不等于2的空间域内非平稳路面不平度建模问题, 提出了由1个基准项和若干个精度校正项组成, 且调制传递函数模的平方逼近具有任意频率指数的道路功率谱表达式; 为获取考虑车速变化影响的频率时变的时域内非平稳路面不平度输入模型, 基于空间路面不平度固定不变的原理, 提出了利用查表法, 获得变车速工况下时域内非平稳路面不平度; 通过空间域内非平稳路面不平度建模及考虑车速变化的非平稳路面不平度建模应用, 验证了所提建模方法的优越性。研究结果表明: 使用基于调制白噪声的非平稳路面不平度建模方法构建的空间域路面不平度功率谱曲线, 与应用实例中的设计目标曲线吻合良好, 且结合查表法可以有效地解决时变车速带来的时域内非平稳路面不平度建模问题。Abstract: To solve non-stationary problems caused by different power spectrum density(PSD) frequency structures of measured roads and vehicle speeds, a modulated white noise and lookup table based modeling methods were proposed based on an analysis of the accuracy of existing road roughness models. Combining the white noise generation method with the calculation formula of discrete PSD, a parameter setting method of Band-Limited White Noise module was developed to ensure the calculated power spectrum of road irregularity is fully consistent with the designed power spectrum.The accuracy of the proposed Band-Limited White Noise module parameter setting value was verified by comparing calculation results of white noise power spectrum density and road roughness power spectrum density according to different combinations of setting values. To solve the modeling problem of non-stationary road in spatial domain whose frequency index is not equal to 2, a road power spectrum expression was proposed, which consists of a reference item and several precision corrected items, and modulus square of modulation transfer function approximates arbitrary frequency exponent. To obtaining a frequency-time-varying input model of non-stationary road considering the influence effects of vehicle speed change in time domain, a lookup table operation was used to obtain time-domain non-stationary road irregularity derived from time-varying vehicle speed based on a fixed spatial road irregularity. The superiority of the proposed modeling methods was verified by applications of spatial-domain non-stationary road irregularity modeling and non-stationary road irregularity modeling considering time-varying vehicle speed. Research result shows that the power spectrum density curves of road irregularity in spatial domain constructed by modulated white noise based non-stationary road irregularity modeling method agree well with the designed objective curves in the application examples. The non-stationary problem of road irregularity caused by time-varying vehicle speed is effectively solved by using the lookup table method.
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图 3 过大采样频率设计值对路面不平度、路面白噪声功率谱密度的影响
Figure 3. Influences on road irregularity and white noise PSD of excessive sampling frequency setting
图 4 W为0.8、2.0时的路面不平度与功率谱密度曲线
Figure 4. Road irregularity and PSD curves when W are 0.8 and 2.0
图 5 W为1.4、2.0时的路面不平度与功率谱密度曲线
Figure 5. Road irregularity and PSD curves when W are 1.4 and 2.0
图 6 W为2.6、2.0时的路面不平度与功率谱密度曲线
Figure 6. Road irregularity and PSD curves when W are 2.6 and 2.0
图 7 W为3.2、2.0时的路面不平度与功率谱密度曲线
Figure 7. Road irregularity and PSD curves when W are 3.2 and 2.0
图 8 等速与变速工况下的路面不平度对比
Figure 8. Comparison of road irregularity under constant and variable speed conditions
图 9 等速与变速工况下的路面白噪声对比
Figure 9. Comparison of road white noise under constant and variable speed conditions
表 1 不同频率指数的建模参数拟合值
Table 1. Fitting values of modeling parameters under different frequency indices
W 0.8 1.4 2.6 3.2 α0 0.244 8 0.417 0 0.946 8 1.612 0 α1 0.273 0 0.193 5 0.097 1 0.062 2 α2 4.056 7 2.261 7 1.007 4 0.724 0 β1 0.062 2 0.097 1 0.193 5 0.272 9 β2 0.724 3 1.007 3 2.261 8 4.055 0 
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