Dynamic mode decomposition (DMD) has emerged as a popular data-driven modeling approach to identifying spatio-temporal coherent structures in dynamical systems, owing to its strong relation with the Koopman operator. For dynamical systems with external forcing, the identified model should not only be suitable for a specific forcing function but should generally approximate the input–output behavior of the underlying dynamics. A novel methodology for modeling those classes of dynamical systems is proposed in the present work, using wavelets in conjunction with the input–output dynamic mode decomposition (ioDMD). The wavelet-based dynamic mode decomposition (WDMD) builds on the ioDMD framework without the restrictive assumption of full state measurements. Our non-intrusive approach constructs numerical models directly from trajectories of the full model’s inputs and outputs, without requiring the full-model operators. These trajectories are generated by running a simulation of the full model or observing the original dynamical systems’ response to inputs in an experimental framework. Hence, the present methodology is applicable for dynamical systems whose internal state vector measurements are not available. Instead, data from only a few output locations are only accessible, as often the case in practice. The present methodology’s applicability is explained by modeling the input–output response of an Euler–Bernoulli finite element beam model. The WDMD provides a linear state-space representation of the dynamical system using the response measurements and the corresponding input forcing functions. The developed state-space model can then be used to simulate the beam’s response towards different types of forcing functions. The method is further validated on a real (experimental) data set using modal analysis on a simple free–free beam, demonstrating the efficacy of the proposed methodology as an appropriate candidate for modeling practical dynamical systems despite having no access to internal state measurements and treating the full model as a black-box.

动态模式分解 (DMD) 已成为一种流行的数据驱动建模方法，用于识别动力系统中的时空相干结构，因为它与库普曼算子有很强的关系。对于具有外力的动力系统，识别出的模型不仅应该适用于特定的力函数，而且应该大致近似于基础动力学的输入-输出行为。目前的工作提出了一种对这些类别的动力系统进行建模的新方法，将小波与输入-输出动态模式分解 (ioDMD) 结合使用。基于小波的动态模式分解 (WDMD) 建立在 ioDMD 框架之上，没有全状态测量的限制性假设。我们的非侵入式方法直接根据完整模型输入和输出的轨迹构建数值模型，不需要完整模型操作员。这些轨迹是通过运行完整模型的模拟或观察原始动力系统对实验框架中输入的响应而生成的。因此，本方法适用于内部状态向量测量不可用的动态系统。相反，只有少数几个输出位置的数据是可访问的，这在实践中经常发生。通过对欧拉-伯努利有限元梁模型的输入-输出响应建模来解释本方法的适用性。WDMD 使用响应测量和相应的输入强制函数提供动态系统的线性状态空间表示。然后可以使用开发的状态空间模型来模拟光束对不同类型的力函数的响应。该方法在真实（实验）数据集上进一步验证，使用简单自由梁的模态分析，证明了所提出的方法作为实用动力系统建模的合适候选者的有效性，尽管无法访问内部状态测量和处理完整模型作为黑盒。