Dynamic behavior of an unconstrained smart device under seismic shaking

Chapter 2 presented a study of the dynamic behavior of a smart device placed on the underlying surface of subjected to seismic motion. The smart device was modeled as a rigid block and its frictional interactions with the underlying base was represented using an existing model (sticking-spring-damper friction model), which was modified for the purposes of this research. The first modification used an interpolation technique to enhance detection of transition points, which must be accurately detected because of the frequency of their occurrence during seismic

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motion. The second modification entailed extending the model to handle vertical accelerations. In this process, the assumption that the normal load is a constant value was relaxed.

To demonstrate the feasibility of the modified friction model, experiments were conducted with a custom-built shaking table. The shaking table consisted of stepper motor and linear actuator and was controlled by Labview and an Arduino microprocessor chipset. The shake table could produce precise, repetitive motions for a given ground motion. Placed on the table were smart devices that recorded multiple rounds of acceleration measurements, which were then combined to reduce the noise. Due to minor surface imperfections, the measured acceleration during sliding motions were not a perfect plateau as computed in the numerical analysis. Nevertheless, the overall response computed by the modified friction model showed good agreement with the acceleration responses measured by an independent and accurate non-contact measurement system.

After validation, the modified friction model was used to investigate the possibility that a device would slide on a flat surface. The aim of this study was to define from a practical perspective the conditions under which the smart device would stick to the surface for a given earthquake intensity. To study the sliding response spectra, a 4-story steel special moment frame (SMF) model designed by NIST was used. The SMF was designed with deep columns and reduced beam sections (RBS) using ASTM A992 steel. Seven scale factors were computed by following the scaling method in FEMA P-695 to generate new records, specifically for three hazard levels: 2%, 10%, and 50% chances of occurrence in 50 years. It was shown that vertical accelerations have a small effect on the sliding behavior of smart devices. The concept of a ‘probability of exceeding the slip limit curve’ was introduced and used to relate the probability of exceeding a given slip limit versus first period spectral acceleration for a given structure and location. This

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curve suggested that the smart device with a static coefficient of friction of 0.4 and 0.5 can read the movement of the underlying surfaces with a maximum slip of less than 2cm for events with a magnitude corresponding to a 10% and 50% chance of occurrence in 50 years. Once generalized by taking into account other structures and locations, this information could be of value in future crowd-sourced, post-disaster reconnaissance efforts.

6.1.2 Identifying stick-slip characteristics of a smart device

Chapter 3 highlighted two key challenges utilizing smart devices to characterize seismic damage of buildings in a quantitative manner. For one, accelerometers in a smart device produce noisy data and are sampled at a relatively slow rate. For another, sliding can contaminate the acceleration record. To address these issues, first, the error equation for MEMS-based accelerometers in smart devices was presented. The deterministic errors were estimated experimentally by using the static multi-position method. It was shown that the optimal sampling rate to minimize error for a specific smart device must be in excess of 1000Hz to ensure accuracy. Although current devices cannot achieve this sampling rate, it is highly likely that future devcies will because a new generation of high‐resolution, low‐noise accelerometers, such as Nano‐g or nanoelectromechanical system (NEMS) accelerometers, appears poised to enable smart devices.

After development of the error equation, a stick-slip identification method was introduced to determine whether the motion of the smart device is representative of the motion of the floor underneath. This crucial step uses the acceleration measurements, taking into account that acceleration measurements contaminated by excessive sliding action cannot represent the motion of the underlying surface. In a simulated acceleration response, it was shown that the theoretical

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sliding motions are step shaped with a clear plateau. However, in the measured acceleration response, the sliding motions were observed to have rounded shapes and chattering, which hinders the differentiation of sliding and sticking motions. For the first step of stick-slip identification method, the noise associated with a smart device’s measurement of acceleration is established and noise reduction methods are compared. After considering multiple methods, it was shown that the maximal overlap discrete wavelet packet transforms (MODWPT) method out-performs other wavelet transform methods in noise reduction for measurement of acceleration by a smart device, while still maintaining the shape of transitions between sticking and sliding. Then, a kinetic coefficient of friction (KCOF) estimation method was proposed based on the observation that a plateau occurs during sliding. To address the occurrence of chattering during sliding due to imperfections in the frictional surfaces, configurable thresholds were applied. From the shake table experiments, it was shown that the results of the estimated KCOF are in good agreement with the true KCOFs. The estimated KCOF was used to compute slipping accelerations and corresponding sliding motions. It was shown that a 93.9% correct detection rate could be achieved using the proposed method.

6.1.3 Stick-slip classification based on machine learning techniques

Chapter 4 presented an accurate and robust accelerometer-based stick-slip motion classification framework based on two different machine learning methods, supervised learning algorithms and deep learning algorithms. For the former, three methods were investigated: 1) the ReliefF algorithm was used to select highly correlated features among the potential features; 2) the zero- crossing window was selected as the best performing segmentation method for raw acceleration data; and 3) linear discriminant analysis (LDA) and kernel discriminant analysis (KDA) were used to improve the class separability and showed a modest improvement in classification

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accuracy. For the latter, a detailed examination of a combination of three hyperparameters of the proposed recurrent neural networks (RNN) and its performance were considered important to further improve the accuracy of the network. Two internal layers, 40 units for each internal layer and c=6 gradient clipping parameter were selected. The RNN for the deep learning algorithm showed somewhat better classification accuracy (93.2%) than two other supervised learning techniques, 89.0% for multilayer perception (MLP), and 86.1% for support vector machines (SVM).