Damage detection of mechanical structures such as bridges is an important research problem in civil engineering. Using spatially distributed sensor time series data collected from a recent experiment on a local bridge in Upper State New York, we study noninvasive damage detection using information-theoretical methods. Several findings are in order. First, the time series data, which represent accelerations measured at the sensors, more closely follow Laplace distribution than normal distribution, allowing us to develop parameter estimators for various information-theoretic measures such as entropy and mutual information. Second, as damage is introduced by the removal of bolts of the first diaphragm connection, the interaction between spatially nearby sensors as measured by mutual information becomes weaker, suggesting that the bridge is "loosened." Finally, using a proposed optimal mutual information interaction procedure to prune away indirect interactions, we found that the primary direction of interaction or influence aligns with the traffic direction on the bridge even after damaging the bridge.

Learning Geometry emphasizes exploring different representations such as virtual manipulatives, written math formulas, and verbal explanations, which help students build mathematical concepts and develop critical thinking. Student’s performance in G.C.E (O/L) examination in Sri Lanka for the Geometry component is at a very low level. This study aims to identify the difficulties of learning Geometry at Grade 11 and provide some suggestions for overcoming these issues using active based learning. This study uses a quantitative survey, a diagnostic test, and a teaching experiment conducted with randomly selected three hundred students from grade 11students and 35 mathematics teachers from 42 schools in Vadamarachchi education zone Sri Lanka. Questionnaires were used to collect data from the teachers and the students. The diagnostic test was also used to collect data from the students. Forty students were selected for the teaching experiment based on diagnostic test results and divided into two equally talented groups using a rubric. The teaching experiment was done to test the effectiveness of activity-based teaching methods in teaching Geometry. Findings from the study revealed that students had greater difficulties in learning Geometry such as drawing diagrams for a given geometric problem and applying more than one theorem to solve a given Geometry problem. Furthermore, Students’ disinterest in the Geometry component and their family background affects their Geometry learning. Additionally, results from the teaching experiment indicate that the student-based learning approaches are more effective than conventional methods for teaching Geometry.

Understanding the causes of sinkholes and determining the earth's subsurface properties will help Engineering Geologists in designing and constructing different kinds of structures. Also, determining of subsurface properties will increase possibilities of preventing expensive structural damages as well as a loss of life. Among the available health monitoring techniques, non-destructive methods play an important role. Full-waveform inversion together with the Gauss-Newton method, which we called as the regular method, able to determine the properties of the subsurface data from seismic data. However, one of the drawbacks of the Gauss-Newton method is a large memory requirement to store the Jacobian matrix. In this work, we use a different cell size approach to address the above issue. Results are validated for a synthetic model with an embedded air-filled void and compared with the regular method. HIGHLIGHTS• Full seismic waveform method based on Gauss-Newton method was used to detect embedded sinkholes in Earth's subsurface.• The difference cell size method is proposed to address the computational and memory requirements in Regular Full-wave inversion method.• Results are compared with regular full waveform inversion method• Less computational time is required for sinkhole detection with the proposed method.

Full-waveform inversion (FWI) is a non-destructive health monitoring technique that can be used to identify and quantify the embedded anomalies. The forward modeling of the FWI consists of a simulation of elastic wave equation to generate synthetic data. Thus the accuracy of the FWI method highly depends on the simulation method used in the forward modeling. Simulation of a 3-D seismic survey with small-scale heterogeneities is impossible with the classic finite difference approach even on modern super computers. In this work, we adopted a mesh refinement approach for simulation of the wave equation in the presence of small-scale heterogeneities. This approach uses cubic smoothing spline interpolation for spatial mesh refinement step in solving the wave equation. The simulation results for the 2-D elastic wave equation are presented and compared with the classic finite difference approach.

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