16 Using a Machine Learning Approach for Computational Substructure in Real-Time Hybrid Simulation 165 Fig. 16.1 Model and substructuring of CBFs for HS testing (RNN) with different hidden layers and time step delays is modeled and tested for performance. Both algorithms are compared with the pure analytical models first. Then, following the assessment of their performance in the pure analytical model predictions, the metamodels are further tested in the HS loop with real feedback from the actuator that is free to move without specimen attached as explained later. In general, an LR model predicts by simply computing a weighted sum of the input features, plus a constant called bias term [14], shown in Eq. (16.1). Here ˆy is the predicted value, nis the number of features. xi is the ith feature value, andθj is the jth model parameter (including the bias termθ0 and the feature weights term). ˆy =θ0 +θ1x1 +θ2x2 +· · ·+θnxn (16.1) The LR model is trained by using a pure analytical solution of the CBF. For the training, five features are selected to be the input of this metamodel to predict the output as a command displacement of the experimental substructure of the HS system. The features for training are selected as: ground motion acceleration, displacement feedback value of the brace, force feedback value of the brace, one step behind the value of the predicted displacement, and two steps behind the value of the predicted displacement. First, the pure analytical solution is used as training data, generated by using the pure analytical solution responses and assuming that there is a 28-time step time delay for the feedback values. Moreover, since it is hard to explore the exact delay from the actuator feedback, this model is run first in the HS loop without including the displacement feedback from the actuator. However, the displacement feedback of the actuator is recorded to be used in the next training phase. Then, a more refined model is generated by using the “real” displacement and force feedback, and the other three features that are used for the training phase. For the RNN model, three different models are trained and generated. An RNN is an artificial neural network that allows exhibiting temporal dynamic behavior since the model uses its memory to process the sequence of inputs [21]. For the RNN models, the inputs are ground motion acceleration and force feedback. Basic RNN models are generated by using different hidden layers to find the optimum hidden layer number for an accurate response. Once the models are trained, each method is evaluated, and the results are shown. Root mean square error (RMSE) is calculated to evaluate the performance of the model predictions. The first verification is done for a pure analytical machine learning algorithm to see the model capabilities offline. Here, the prediction is made for each step while running the simulation. Once all the models are compared for the pure analytical solution, the one with the least RMSE error will be put in the HS loop. The first validation for the HS system is where the metamodel is compiled in the xPC and is tried with “fake” feedback with actuators on the system (online) to see the actuator performance. After this, the “real” feedback is fed into the metamodel, and the system response is evaluated against the pure analytical system response. The RMSE values are calculated for these cases as well as discussed next. 16.4 Model Parameters for HS The analytical substructure for the HS model consists of two columns (W14x311) with fixed end conditions and a beam (W36x150), which also has moment connections to the columns. Both columns and the beam are considered linear elastic elements, wherein braced frames the nonlinearity is commonly limited only to the braces. The mass and the damping of the system are considered to be part of the analytical substructure. The one-bay one-story braced frame is simplified as single degree of freedom (SDOF) for validation and modeling purposes. The dynamic properties of the SDOF model is as defined
RkJQdWJsaXNoZXIy MTMzNzEzMQ==