基于小波变换的线性及弱非线性结构动力学系统辨识方法
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摘要
需要建立描述结构性能的模型时,对系统的辨识就显得尤为重要。近几年来,在应用数学、理论物理和信号处理领域的研究者发展了一种能够对信号进行多分辨率分析的有效工具,这种工具就是小波变换。对结构动力学系统的自由衰减响应信号进行连续小波变换能将信号中包含的大量信息集中到一系列脊中,这些脊与信号中每一个频率成分的幅度和相位直接相关。通过提取脊并根据脊上的连续小波变换系数可以辨识系统的参数。
为了辨识密集模态,本文改进了传统的从线性系统的自由衰减响应中应用连续小波变换估计模态参数的方法。研究了特别是当需要辨识密集模态时自由衰减响应信号的连续小波变换。提出用一种鲁棒的重新加权迭代最小二乘法来拟合小波的幅度和相位曲线。为了识别密集模态的参数,提出选择最优分析尺度的方法,这种方法通过搜索拟合误差函数局部极小值的位置来实现。为了实现模态分离并抑制边界效应,通过使拟合误差函数局部极小值的和达到最小值实现了小波函数参数的选择。在两个三自由度有阻尼系统上的数值仿真结果表明本文提出的改进方法能够更加准确地估计包含密集模态的线性系统的自然频率和阻尼比。
利用脊上连续小波变换系数的幅度和相位,从结构动力学系统的自由衰减响应中辨识了弱非线性阻尼和刚度。为了消除连续小波变换幅度极值的频移,小波脊是通过在每一个时刻搜索规范化量图局部极大值的尺度位置来提取的。指出在单自由度系统的辨识过程中没有必要选择小波参数。辨识方法的有效性在两个包含非线性阻尼和刚度的单自由度仿真算例中得到了证明。
为了高效地估计渐进信号的瞬时频率和幅度,提出一种提取小波脊的方法。推导了尺度间隔和采样频率应当满足的不等式。任意给定一个小波脊提取的精度,通过解这些不等式并考虑到使连续小波变换计算的复杂性达到最小能够得到尺度间隔和采样频率的一对最优值。在使用这对最优参数计算连续小波变换之后,仅用传统方法提取的脊上的间断点就可形成一个更加可靠的新脊。提出的脊提取方法在一个弱非线性系统辨识的仿真算例上得到了验证,测试结果表明提出方法的计算量与传统方法相比有了明显降低。
最后,对研制的高精度转动惯量测量仪的相关技术参数进行了辨识。辨识结果表明:采用了提出的非线性系统辨识方法以后,仪器测量转动惯量的精度得到有效提高。
The identification of structural systems is very important when models for theprediction of systems performance are developed. In recent years, researchers inapplied mathematics, theoretical physics and signal processing have developed apowerful time-frequency signal-analysis tool, called wavelet transform, for themultiresolution analysis of signals. The continuous wavelet transform (CWT) of freedecay response signal of structural dynamic system concentrates the maximumamount of information contained in data near a series of ridges, which are directlylinked to the amplitude and phase of each component within the signal. From theextraction of the ridge and from the values of the CWT coefficients along the ridges,systemparameters can beidentified.
In order to identify closely spaced modes, the traditional method for theestimation of modal parameters from free decay response of a linear system usingCWT isimproved. The CWT of free decay response is investigated especially for thecase when closely spaced modes need to be analyzed. Arobust iteratively reweightedleast-squares (IRLS) linear regression method is introduced to fit wavelet amplitudeand phase curves. The selection of the appropriate analyzing scale is proposed toimprove the modal parameter estimation of the system with poorly separated modes,which is performed by searching the locations of the local minima of fitting errorfunctions. The parameter selection of wavelet function achieved by minimizing thesum of the local minimum values of fitting error function is also presented forachieving modal separation and minimizing edge-effect. The results of a numericalsimulation on two 3dof damped systems shown that the improved method canprovide a more accurate estimation of the natural frequencies and damping ratios forthelinear system withcloselyspaced modes.
Utilizing the amplitude and phase of CWT coefficients on ridge, weaknonlinearities on damping and stiffness are identified from the freedecay response ofa structural dynamic system. In order to eliminate the frequency-shift of CWTamplitude extreme, wavelet ridge is determined for each time by finding the scalewhere the normalized scalogram is a local maximum. The choice of the waveletfunction is not useful for the improvement of the sdof system identification accuracy.Theeffectiveness of the proposed method is demonstrated using numerical results for twosdof systems with nonlinearities on damping and stiffness.
A wavelet ridge extraction method is proposed for efficient estimation ofinstantaneous frequency and amplitude of the asymptotic signal. Inequalities arederived to provide limitations on scale interval and sampling frequency. The optimalscale interval and sampling frequency at any given accuracy can be evaluated bysolving these inequalities and minimizing the computational complexity of CWT.After the CWT of the signal is completed with these optimal parameters, a morereliable ridge can be formed using only the discontinuity points on the ridgeextracted using the conventional method. The results of a weak nonlinear systemidentification simulation test performed to verify the efficiency of the proposedmethod indicate that the computational load of the proposed method is much lowerthanthat ofthe conventional method.
At last, the technical parameters of self-developed high accuracy instrument formeasuring moment of inertia (MOI) are measured. The results show that theinstrument adopting the proposed technique for nonlinear system identification canimprove the measurement precision of MOI.
为了辨识密集模态,本文改进了传统的从线性系统的自由衰减响应中应用连续小波变换估计模态参数的方法。研究了特别是当需要辨识密集模态时自由衰减响应信号的连续小波变换。提出用一种鲁棒的重新加权迭代最小二乘法来拟合小波的幅度和相位曲线。为了识别密集模态的参数,提出选择最优分析尺度的方法,这种方法通过搜索拟合误差函数局部极小值的位置来实现。为了实现模态分离并抑制边界效应,通过使拟合误差函数局部极小值的和达到最小值实现了小波函数参数的选择。在两个三自由度有阻尼系统上的数值仿真结果表明本文提出的改进方法能够更加准确地估计包含密集模态的线性系统的自然频率和阻尼比。
利用脊上连续小波变换系数的幅度和相位,从结构动力学系统的自由衰减响应中辨识了弱非线性阻尼和刚度。为了消除连续小波变换幅度极值的频移,小波脊是通过在每一个时刻搜索规范化量图局部极大值的尺度位置来提取的。指出在单自由度系统的辨识过程中没有必要选择小波参数。辨识方法的有效性在两个包含非线性阻尼和刚度的单自由度仿真算例中得到了证明。
为了高效地估计渐进信号的瞬时频率和幅度,提出一种提取小波脊的方法。推导了尺度间隔和采样频率应当满足的不等式。任意给定一个小波脊提取的精度,通过解这些不等式并考虑到使连续小波变换计算的复杂性达到最小能够得到尺度间隔和采样频率的一对最优值。在使用这对最优参数计算连续小波变换之后,仅用传统方法提取的脊上的间断点就可形成一个更加可靠的新脊。提出的脊提取方法在一个弱非线性系统辨识的仿真算例上得到了验证,测试结果表明提出方法的计算量与传统方法相比有了明显降低。
最后,对研制的高精度转动惯量测量仪的相关技术参数进行了辨识。辨识结果表明:采用了提出的非线性系统辨识方法以后,仪器测量转动惯量的精度得到有效提高。
The identification of structural systems is very important when models for theprediction of systems performance are developed. In recent years, researchers inapplied mathematics, theoretical physics and signal processing have developed apowerful time-frequency signal-analysis tool, called wavelet transform, for themultiresolution analysis of signals. The continuous wavelet transform (CWT) of freedecay response signal of structural dynamic system concentrates the maximumamount of information contained in data near a series of ridges, which are directlylinked to the amplitude and phase of each component within the signal. From theextraction of the ridge and from the values of the CWT coefficients along the ridges,systemparameters can beidentified.
In order to identify closely spaced modes, the traditional method for theestimation of modal parameters from free decay response of a linear system usingCWT isimproved. The CWT of free decay response is investigated especially for thecase when closely spaced modes need to be analyzed. Arobust iteratively reweightedleast-squares (IRLS) linear regression method is introduced to fit wavelet amplitudeand phase curves. The selection of the appropriate analyzing scale is proposed toimprove the modal parameter estimation of the system with poorly separated modes,which is performed by searching the locations of the local minima of fitting errorfunctions. The parameter selection of wavelet function achieved by minimizing thesum of the local minimum values of fitting error function is also presented forachieving modal separation and minimizing edge-effect. The results of a numericalsimulation on two 3dof damped systems shown that the improved method canprovide a more accurate estimation of the natural frequencies and damping ratios forthelinear system withcloselyspaced modes.
Utilizing the amplitude and phase of CWT coefficients on ridge, weaknonlinearities on damping and stiffness are identified from the freedecay response ofa structural dynamic system. In order to eliminate the frequency-shift of CWTamplitude extreme, wavelet ridge is determined for each time by finding the scalewhere the normalized scalogram is a local maximum. The choice of the waveletfunction is not useful for the improvement of the sdof system identification accuracy.Theeffectiveness of the proposed method is demonstrated using numerical results for twosdof systems with nonlinearities on damping and stiffness.
A wavelet ridge extraction method is proposed for efficient estimation ofinstantaneous frequency and amplitude of the asymptotic signal. Inequalities arederived to provide limitations on scale interval and sampling frequency. The optimalscale interval and sampling frequency at any given accuracy can be evaluated bysolving these inequalities and minimizing the computational complexity of CWT.After the CWT of the signal is completed with these optimal parameters, a morereliable ridge can be formed using only the discontinuity points on the ridgeextracted using the conventional method. The results of a weak nonlinear systemidentification simulation test performed to verify the efficiency of the proposedmethod indicate that the computational load of the proposed method is much lowerthanthat ofthe conventional method.
At last, the technical parameters of self-developed high accuracy instrument formeasuring moment of inertia (MOI) are measured. The results show that theinstrument adopting the proposed technique for nonlinear system identification canimprove the measurement precision of MOI.
引文
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