模态分析的快速计算方法及在重卡中的应用
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摘要
模态分析是依据动力学方程和输入输出数据为基础求解基于模态坐标下的结构动力学参数的一门科学。以保持计算精度的条件下降低实验成本、节约计算时间、实现结构动力学状态监控为目标，本文提出一整套针对大规模问题和复杂结构的模态分析的快速计算方法和系统。创新性的提出模型降阶与参数优化相结合的方法实现实验和工作模态分析的快速计算。依据适应性分析的要求，对重型卡车的驾驶室和车架等主要部分进行模态分析快速计算，并对结构改进提出相应建议和新的观点，文章应用先进软件和硬件技术，提出模态分析新的发展方向和技术实现手段，建立了完整的在线模态分析系统，主要包含以下几方面的工作：
（1）在系统软件中提出模型降阶与参数优化相结合的方法实现模态参数快速识别。在实验模态参数快速识别方法研究中将间接模型降阶方法与最小二乘复频域法相结合实现系统特征矩阵的正规化缩减；将表征计算效率的特征矩阵特征量进行参数化，建立优化设计模型，应用遗传算法对参数进行进一步全局优化。在时域工作模态参数快速识别方法研究中，将平衡截断方法应用于协方差驱动的随机子空间法中，结合最小信息准则在保持系统特征不变的情况下对特征矩阵进行降阶处理，采用遗传算法对随机子空间特征矩阵进行进一步优化。通过计算效率比较和具体算例说明模态参数快速识别方法的有效性和实用性。
（2）在硬件与系统实现上提出应用FPGA技术和实时系统相结合实现同步精确动态数据采集和快速高效计算。应用改进的FFT算法分别进行软件和硬件、实时和非实时计算效率和计算稳定性的比较研究，证明硬件和系统组成符合快速模态分析的要求，为在线模态分析打下良好的基础。
（3）根据适应性分析的思想，依据重卡各部分的实际特点采用不同的方法进行模态分析。根据重卡驾驶室白车身重量较轻、处于半独立状态且行驶时环境激励无法达到要求的特点，对某基础车型和某高端车型改进前后的驾驶室白车身进行基于最小二乘复指数法（LSCE）与最小二乘复频域法（LSCF）的实验模态分析，并结合有限元模态分析结果对各种方法进行比较研究并验证了结果的有效性。同时提出具体的修改意见并进行实际应用，对车型改进起了关键作用。提出第一阶模态频率质量比的概念，依据轻量化的发展方向修正过度提高第一阶模态频率的认知。应用间接模型降阶和参数优化的方法相结合对改进后的驾驶室白车身进行实验模态参数快速识别，在保证计算精度的条件下使计算效率得到很大提高。
（4）以重卡一体化车架和货箱为主要研究对象，根据满载时质量大、不便进行力锤或激振器激励的实际情况，提出利用环境激励对行驶中的车辆进行工作模态分析的方法。对环境激励下的样本进行时间序列分析得出其概率特征为类似维纳分布的平稳随机特征，结合功率谱密度分析结果认为其符合随机子空间工作模态分析的要求。根据误差模型建立协方差驱动随机子空间特征矩阵，采用平衡截断方法与参数优化相结合的方法对表征特征矩阵的参数进行缩减。采用最小信息准则确定系统阶数，对不同参数对计算效率和精度的影响进行分析和总结，在保证模态参数识别精度的条件下提高了计算效率。将工作模态分析快速计算结果与有限元模态分析结果进行比较，认为所得结论是可信的。
Modal analysis is a important subject in which the system’s dynamic parameters in themodal coordinate are estimated based on kinetic equation and input-output datas obtained frommodal experiments. In order to reduce the cost of experimentation and save computing time, thispaper proposed a set of methods and systems to realize modal analysis' fast calculation methodsfor large-scale problems and complex structures. Model order reduction and parameteroptimization combined methods is proposed to achieve modal parameters' fast calculation methodand used in heavy-duty truck’s cab and chassis respectively. Advanced software and hardwaretechnology are used to build complete fast modal analysis system and new direction is propose inthis paper. The main tasks are as follows.
(1) A model order reduction and parameter optimization combined method is proposed torealize fast modal analysis in system’s software. In accordance with experimental modal analysissystem model, the paper achieve the system characteristic matrix reduction in least squarescomplex frequency domain experimental modal analysis useing indirect model order reductionmethod. With the parameterization of the characteristic matrix’s component which determine theparameter identification efficiency, the optimal design model is established and the parameters areglobally optimized and reduced using improved genetic algorithm. In the study of the fast timedomain operational modal analysis method, combined with minimum information criterionbalanced truncation method is used in stochastic subspace identification method driven by thecovariance to reduce system characteristic matrix order and keep system’s characteristic. Andgenetic algorithm optimization is also used to realize optimization and reduction of characteristicmatrix. At last, through comparison of computational efficiency and specific example application,modal analysis' fast calculation methods is proved to be effective.
(2) A FPGA technology and real-time system combined method is proposed to achieve fast,synchronized and accurate dynamic data acquisition in system’s hardware. Through computationalefficiency and stability comparation using improved FFT algorithm between software andhardware in realtime and unrealtime system, the hardware and system structure are proved to beeffective to realize fast modal analysis and establish solid foundation to online modal analysis.
(3) Different approaches are proposed to do modal analysis to the heavy-duty truck’sdifferent parts according to the adaptive analysis method. Compare to whole vehicle, the cab’sbody-in-white was light and semi-independent, and also be not well excited in round environmentexcitation. So it is appropriate for experimenttal modal analysis. Comparative study betweenLeast-Squares Complex Exponential (LSCE) methd and Least Squares Complex Frequency (LSCF) method were done, and the result between each method and finite element modal analysis areproved to be similar and effective. The amendments based on the specific suggestions forimprovement was proved to be successful by practical application in markets. The concept of theratio between the first order modal frequency and the quality is put forward. And the originalcognition of over-improve the first order modal frequency through improving local quality iscorrected according to the lightweight trendency. Simultaneously, the fast modal analysis of theimproved cab body-in-white is done and the computational efficiency has a substantial increasingin conditions of ensuring the accuracy based on indirect model order reduction and parameteroptimazation combined method.
(4) Operational modal analysis method on running vehicles using environmental excitationin heavy truck road testing is proposed for the mass is too large and inconvenience to be artificiallyimposed external excitation. It was proved that the probabilistic characteristics of time seriescomposed of acceleration samples under uneven stone road environment excitation were similar tothe Wiener distribution through time series analysis. Combined the power spectrum analysis result,time series properties was regards as meeting the requirements of stochastic space modal analysis.Balanced truncation method and genetic optimization algorithms was combined to used in theframe’s stochastic subspace modal identification method driven by the covariance to reduces thecomputation. Minimum Information Standards was used to determine the key parameters’ value topromote optimization algorithms’ efficiency. It met the requirements of the online modal analysisand guarantee the accuracy of modal parameter identification. Compared with the finite elementmodal analysis result of the frame under different operating conditions, it believed that the fastmodal analysis results were reliable.
（1）在系统软件中提出模型降阶与参数优化相结合的方法实现模态参数快速识别。在实验模态参数快速识别方法研究中将间接模型降阶方法与最小二乘复频域法相结合实现系统特征矩阵的正规化缩减；将表征计算效率的特征矩阵特征量进行参数化，建立优化设计模型，应用遗传算法对参数进行进一步全局优化。在时域工作模态参数快速识别方法研究中，将平衡截断方法应用于协方差驱动的随机子空间法中，结合最小信息准则在保持系统特征不变的情况下对特征矩阵进行降阶处理，采用遗传算法对随机子空间特征矩阵进行进一步优化。通过计算效率比较和具体算例说明模态参数快速识别方法的有效性和实用性。
（2）在硬件与系统实现上提出应用FPGA技术和实时系统相结合实现同步精确动态数据采集和快速高效计算。应用改进的FFT算法分别进行软件和硬件、实时和非实时计算效率和计算稳定性的比较研究，证明硬件和系统组成符合快速模态分析的要求，为在线模态分析打下良好的基础。
（3）根据适应性分析的思想，依据重卡各部分的实际特点采用不同的方法进行模态分析。根据重卡驾驶室白车身重量较轻、处于半独立状态且行驶时环境激励无法达到要求的特点，对某基础车型和某高端车型改进前后的驾驶室白车身进行基于最小二乘复指数法（LSCE）与最小二乘复频域法（LSCF）的实验模态分析，并结合有限元模态分析结果对各种方法进行比较研究并验证了结果的有效性。同时提出具体的修改意见并进行实际应用，对车型改进起了关键作用。提出第一阶模态频率质量比的概念，依据轻量化的发展方向修正过度提高第一阶模态频率的认知。应用间接模型降阶和参数优化的方法相结合对改进后的驾驶室白车身进行实验模态参数快速识别，在保证计算精度的条件下使计算效率得到很大提高。
（4）以重卡一体化车架和货箱为主要研究对象，根据满载时质量大、不便进行力锤或激振器激励的实际情况，提出利用环境激励对行驶中的车辆进行工作模态分析的方法。对环境激励下的样本进行时间序列分析得出其概率特征为类似维纳分布的平稳随机特征，结合功率谱密度分析结果认为其符合随机子空间工作模态分析的要求。根据误差模型建立协方差驱动随机子空间特征矩阵，采用平衡截断方法与参数优化相结合的方法对表征特征矩阵的参数进行缩减。采用最小信息准则确定系统阶数，对不同参数对计算效率和精度的影响进行分析和总结，在保证模态参数识别精度的条件下提高了计算效率。将工作模态分析快速计算结果与有限元模态分析结果进行比较，认为所得结论是可信的。
Modal analysis is a important subject in which the system’s dynamic parameters in themodal coordinate are estimated based on kinetic equation and input-output datas obtained frommodal experiments. In order to reduce the cost of experimentation and save computing time, thispaper proposed a set of methods and systems to realize modal analysis' fast calculation methodsfor large-scale problems and complex structures. Model order reduction and parameteroptimization combined methods is proposed to achieve modal parameters' fast calculation methodand used in heavy-duty truck’s cab and chassis respectively. Advanced software and hardwaretechnology are used to build complete fast modal analysis system and new direction is propose inthis paper. The main tasks are as follows.
(1) A model order reduction and parameter optimization combined method is proposed torealize fast modal analysis in system’s software. In accordance with experimental modal analysissystem model, the paper achieve the system characteristic matrix reduction in least squarescomplex frequency domain experimental modal analysis useing indirect model order reductionmethod. With the parameterization of the characteristic matrix’s component which determine theparameter identification efficiency, the optimal design model is established and the parameters areglobally optimized and reduced using improved genetic algorithm. In the study of the fast timedomain operational modal analysis method, combined with minimum information criterionbalanced truncation method is used in stochastic subspace identification method driven by thecovariance to reduce system characteristic matrix order and keep system’s characteristic. Andgenetic algorithm optimization is also used to realize optimization and reduction of characteristicmatrix. At last, through comparison of computational efficiency and specific example application,modal analysis' fast calculation methods is proved to be effective.
(2) A FPGA technology and real-time system combined method is proposed to achieve fast,synchronized and accurate dynamic data acquisition in system’s hardware. Through computationalefficiency and stability comparation using improved FFT algorithm between software andhardware in realtime and unrealtime system, the hardware and system structure are proved to beeffective to realize fast modal analysis and establish solid foundation to online modal analysis.
(3) Different approaches are proposed to do modal analysis to the heavy-duty truck’sdifferent parts according to the adaptive analysis method. Compare to whole vehicle, the cab’sbody-in-white was light and semi-independent, and also be not well excited in round environmentexcitation. So it is appropriate for experimenttal modal analysis. Comparative study betweenLeast-Squares Complex Exponential (LSCE) methd and Least Squares Complex Frequency (LSCF) method were done, and the result between each method and finite element modal analysis areproved to be similar and effective. The amendments based on the specific suggestions forimprovement was proved to be successful by practical application in markets. The concept of theratio between the first order modal frequency and the quality is put forward. And the originalcognition of over-improve the first order modal frequency through improving local quality iscorrected according to the lightweight trendency. Simultaneously, the fast modal analysis of theimproved cab body-in-white is done and the computational efficiency has a substantial increasingin conditions of ensuring the accuracy based on indirect model order reduction and parameteroptimazation combined method.
(4) Operational modal analysis method on running vehicles using environmental excitationin heavy truck road testing is proposed for the mass is too large and inconvenience to be artificiallyimposed external excitation. It was proved that the probabilistic characteristics of time seriescomposed of acceleration samples under uneven stone road environment excitation were similar tothe Wiener distribution through time series analysis. Combined the power spectrum analysis result,time series properties was regards as meeting the requirements of stochastic space modal analysis.Balanced truncation method and genetic optimization algorithms was combined to used in theframe’s stochastic subspace modal identification method driven by the covariance to reduces thecomputation. Minimum Information Standards was used to determine the key parameters’ value topromote optimization algorithms’ efficiency. It met the requirements of the online modal analysisand guarantee the accuracy of modal parameter identification. Compared with the finite elementmodal analysis result of the frame under different operating conditions, it believed that the fastmodal analysis results were reliable.
引文
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