A fast sparsity-free compressive sensing approach for vibration data reconstruction using deep convolutional GAN

Vibration data from physical systems, such as civil structures and machinery, often carries important information about the dynamic characteristics, but streaming acquisition of higher-frequency vibration often accrue large volumes of data, resulting in data transmission and storage challenges. Compressive sensing (CS) is a relatively newly-developed technique for efficient data representation, capable of reconstructing the target signal using only a few random measurements through sparse optimization. However, the real-world application of CS is hindered by the strong assumption of signal sparsity and a costly reconstruction process. In this work, we propose a novel deep learning method for vibration data reconstruction by using deep convolutional generative adversarial networks (DCGAN), which is composed of a generator G and a discriminator D. A modified 1D symmetric U-net architecture with shortcuts is presented for G to flexibly deal with different inputs, while a typical 1D classifier is used as D. A composite adversarial loss function is proposed considering errors in both time and frequency domains. The proposed DCGAN approach has several appealing properties. First, it directly learns the end-to-end mapping between the compressed and original signals without employing the sparsity assumption or random sampling, which fundamentally differs from existing sparsity-based CS methods. Second, the reconstruction process is highly computationally efficient as the network is fully feed-forward and no optimization is needed during data reconstruction. The proposed DCGAN approach is evaluated using the simulation data from a numerical 9-floor frame as well as experimental data collected from a large test steel grandstand. The results demonstrate the superiority of the proposed DCGAN in computational accuracy and efficiency compared to the tested sparsity-based algorithms. Furthermore, the influences of network configurations (network depth, down-sampling strategy, and shortcuts) are comprehensively explored.