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This paper presents a dynamic study of sandwich functionally graded beam with piezoelectric layers that are used as sensors and actuators. This study is exploited later in the formulation of the active control laws, while using the optimal control Linear Quadratic Gaussian (LQG), accompanied by the Kalman filter. The mathematical formulation is based on Timoshenko’s assumptions and the finite element method, which is applied to a flexible beam divided into a finite number of elements. By applying the Hamilton principle, the equations of motion are obtained. The vibration frequencies are found by solving the eigenvalue problem. The structure is analytically then numerically modeled and the results of the simulations are presented in order to visualize the states of their dynamics without and with active control.

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Throughout this study, we employed unsupervised machine learning clustering algorithms, namely K-Means [1] and hierarchical agglomerative clustering (HAC) [2], to explore human locomotion and wayfinding using a VR Magic Carpet (VMC) [3], a table test version known as the Corsi Block Tapping task (CBT) [4]. This variation was carried out in the context of a virtual reality experimental setup. The participants were required to memorize a sequence of target positions projected on the rug and walk to each target figuring in the displayed sequence. the participant’s trajectory was collected and analyzed from a kinematic perspective. An earlier study [5] identified three different categories, but the classification remained ambiguous, implying that they include both kinds of individuals (normal and patients with cognitive spatial impairments). On this basis, we utilized K-Means and HAC to distinguish the navigation behavior of patients from normal individuals, emphasizing the most important discrepancies and then delving deeper to gain more insights.

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