摘要:
载荷在时域内可用一系列脉冲或阶跃的核函数来表示，系统的响应是载荷与核函数相对应响应的卷积分. 在线性时不变的假设下，对系统动力响应的卷积分进行离散，并在此基础上分析载荷识别反问题的不适定性. 针对测量的响应数据中存在噪声时载荷识别的困难，探讨了稳定近似识别载荷的一些方法，包括零相位滤波技术、几种正则化方法和优化策略. 数值仿真算例表明，所述的载荷识别方法能够在响应数据含有噪声的情况下，有效稳定地实现多源动态载荷的重构.
关键词:
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载荷识别
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反问题
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正则化
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不适定性
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优化
Abstract:
The knowledge of the dynamic load acting on the structure is always requiredand important in many practical engineering problems, such as structuralstrength analysis, health monitoring and fault diagnosis, and vibrationisolation. However, it is difficult to directly measure the dynamic load ona structure in some situations, such as the wind load on the tall building,the exciting force from road on the vehicle, etc. Meanwhile, the dynamicresponse measurement is correspondingly easy and accurate on a structure.Therefore, it is necessary to develop some inverse analysis techniques forload identification based on the measured dynamic responses.With the linearity and time-invariant suppositions, the loads are firstlyexpressed as a series of kernels of impulse functions or step functions intime domain and the total response of the system can be obtained using theproduct of the convolution integral of the kernel response and the loads.Through the discretization of convolution integral, the forward model forload identification is established. In fact, the inverse analysis for theload identification is to solve a deconvolution problem, but thedeconvolution is an ill-conditioned problem in which the noisy responses andhigh condition numbers of the kernel matrix will induce the amplified errorsin the identified load. Therefore, it is difficult to obtain a stable andaccurate solution for such inverse problems. To deal with ill-condition ofload reconstruction from the noisy responses, zero-phase digital filter,several regularization methods and optimized strategy for stable loadidentification are discussed. Through general filter, the noisy responsesignal will be smooth. But, it has a phase delaying compared with theoriginal signal, and the errors will also be amplified in the identifiedload. The zero-phase digital filter, whose phase error is zero in the curveof phase-frequency characteristic, is realized through reversing the timeserials of the signal. Moreover, a new extension algorithm is applied toimprove the performance of the filter. Comparing with the common differencefilter, this zero phase digital filter can not only avoid phase delaying,but also improve the wave aberration of the start and end section. After theinvestigation the ill-posedness arising from the inverse problem of loadreconstruction, Tikhonov regularization, truncated singular valuedecomposition and total least squares method are adopted to provideefficient and numerically stable solution of the desired unknown load, andthe $L$-curve method is proposed to determine the optimal regularizationparameter. In order to avoid the inverse operation of the matrix, manyoptimized methods can be available and here the conjugate gradient method isadopted. In the numerical example, the reconstruction of dynamic loads fromtwo sources with the noisy responses in the hood structure is investigated.The result indicates that the presented computational inverse technique iseffective and stable for the load identification with the noisy response intime domain.
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