时域内多源动态载荷的一种计算反求技术

A COMPUTATIONAL INVERSE TECHNIQUE FOR RECONSTRUCTION OF MULTISOURCE LOADS IN TIME DOMAIN

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.

The knowledge of the dynamic load acting on the structure is always required and important in many practical engineering problems, such as structural strength analysis, health monitoring and fault diagnosis, and vibration isolation. However, it is difficult to directly measure the dynamic load on a structure in some situations, such as the wind load on the tall building, the exciting force from road on the vehicle, etc. Meanwhile, the dynamic response measurement is correspondingly easy and accurate on a structure. Therefore, it is necessary to develop some inverse analysis techniques for load identification based on the measured dynamic responses. With the linearity and time-invariant suppositions, the loads are firstly expressed as a series of kernels of impulse functions or step functions in time domain and the total response of the system can be obtained using the product of the convolution integral of the kernel response and the loads. Through the discretization of convolution integral, the forward model for load identification is established. In fact, the inverse analysis for the load identification is to solve a deconvolution problem, but the deconvolution is an ill-conditioned problem in which the noisy responses and high condition numbers of the kernel matrix will induce the amplified errors in the identified load. Therefore, it is difficult to obtain a stable and accurate solution for such inverse problems. To deal with ill-condition of load reconstruction from the noisy responses, zero-phase digital filter, several regularization methods and optimized strategy for stable load identification are discussed. Through general filter, the noisy response signal will be smooth. But, it has a phase delaying compared with the original signal, and the errors will also be amplified in the identified load. The zero-phase digital filter, whose phase error is zero in the curve of phase-frequency characteristic, is realized through reversing the time serials of the signal. Moreover, a new extension algorithm is applied to improve the performance of the filter. Comparing with the common difference filter, this zero phase digital filter can not only avoid phase delaying, but also improve the wave aberration of the start and end section. After the investigation the ill-posedness arising from the inverse problem of load reconstruction, Tikhonov regularization, truncated singular value decomposition and total least squares method are adopted to provide efficient and numerically stable solution of the desired unknown load, and the L-curve method is proposed to determine the optimal regularization parameter. In order to avoid the inverse operation of the matrix, many optimized methods can be available and here the conjugate gradient method is adopted. In the numerical example, the reconstruction of dynamic loads from two sources with the noisy responses in the hood structure is investigated. The result indicates that the presented computational inverse technique is effective and stable for the load identification with the noisy response in time domain.