76 N. S. Gulgec et al. The authors propose a Long Short-Term Memory (LSTM) based framework to estimate the stress or strain responses from the acceleration information. The proposed technique aims to build a relationship between acceleration and strain for a few selected locations under the loading conditions included in the training dataset. In the testing phase, acceleration data from desired locations (i.e., the number of desired locations is greater than the selected ones) are fed into the architecture to predict strain responses. This approach is validated on ambient data collected from a bridge over 2 months. The rest of the paper is organized as follows. First, related work and background information on deep learning are provided in Sects. 2 and 3, respectively; then, the proposed approach is described in Sect. 4. In Sects. 5 and 6, the experimental setup and the proposed network architecture are introduced. The main findings of this study are discussed in Sect. 7. Conclusions and future work are presented in Sect. 8. 2 Related Work Several studies have investigated how expensive sensor measurements can be obtained by using inexpensively collected vibration data. Determining displacement responses from accelerometers has been commonly studied due to its challenges such as sensor and installation cost, and the inaccessibility of a reference point for full-scale structures [10–12]. The quantitative results showed that displacements could be obtained by utilizing acceleration responses. The acceleration data has also been utilized to estimate strain responses at unmeasured locations when direct measurement is not possible; this approach is called virtual sensing. It is possible to group the virtual response estimation techniques into three main groups, namely, Kalman filtering [13, 14], a joint input-state estimation [15], and modal expansion [16, 17]. It is also discussed that multi-sensor data has the potential to improve the performance of response estimation [14]. Among the combination of input variables measuring accelerations, strains, and tilts to see the effect on the performance of strain estimations, the highest performance is found to be in the fusion of acceleration and tilt. Previous research achieved promising results showing that strain response estimation is possible with acceleration data. Nevertheless, they suffer from several limitations. The mentioned techniques are dependent on the accuracy of the finite element models. Moreover, the majority of these approaches focus on zero-mean stationary processes and assume the unknown system input as zero-mean white noise which restricts the application domain. The objective of this study is to overcome these limitations by proposing a data-driven, deep learning-based approach which can be generalizable to different kind of vibrations and overcome the problem of learning long-time dependencies. 3 Background Creating entirely accurate and detailed structural models is a very challenging task due to the complexity of structures. Thus, data-driven approaches become prominent for SHM applications where a surrogate model, constructed using collected structural responses, is substituted for a real model [18]. With today’s advanced technology enabling crowdsourcing, the abundance of data is an opportunity to extract information about infrastructure condition throughout their entire life. Utilizing deep neural networks (DNNs) is an ideal solution for taking advantage of this massive data [19]. The output of DNNs is formed by nonlinear mapping of the input data; therefore, their performance improves when more data is available. DNNs consist of multiple linear layers and nonlinear transformations, where each layer is trained to extract some relevant information. After this training step, the learned DNN architecture provides informed decisions based on the data-driven predictions. The implementation of DNNs varies greatly depending on the application domain. LSTM networks proposed by Hochreiter and Schmidhuber [20] are widely used to exhibit temporal dynamic behavior for a time sequence. LSTMs are a type of recurrent neural networks (RNNs) where the present decisions (at time step t) are affected by the recent past (at time step t −1). LSTMs comprise a chain of recurrent nodes forming memory cells. These cells remember the information and provide control over which information to let through and which information to forget with the help of input gate, forget gate, and output gate. The Refs. [20, 21] provide more detailed information and equations about the architecture of LSTMs.
RkJQdWJsaXNoZXIy MTMzNzEzMQ==