A new computationally efficient error adaptive first-order eigen-perturbation technique for real-time modal identification of linear vibrating systems is proposed. The existence of error terms in the approximation of the eigenvalue problem of response covariance matrix in a perturbative framework often hinders the convergence of response-only modal identification. In the proposed method, the error in first-order eigen-perturbation is incorporated using a feedback, formulated by exploiting the generalized eigenvalue decomposition of the real-time covariance matrix of streaming response data. Since the incorporation of the higher-order perturbation terms in the total perturbation is mathematically challenging, the proposed feedback approach provides a computationally efficient framework yet in a more elegant manner. A new criterion for the quality of updated eigenspace is proposed in the present work utilizing the concept of diagonal dominance. Numerical case studies and validation using a standard ASCE benchmark problem have shown applicability of the proposed approach in faster estimation of real-time modal properties and anomaly identification with minimal number of initially required batch data. The applicability of the proposed approach toward real-time under-determined modal identification problems is demonstrated using a real-time decentralized framework. The advantage of rapidly converging online mode-shapes is demonstrated using a passive vibration control problem, where a multi-tuned-mass-damper (MTMD) for a multi-degrees-of-freedom system is tuned online. An extension for online retuning of the detuned MTMD system further demonstrates the fidelity of the proposed algorithm in online passive control.
A robust real-time damage detection technique of earthquake-excited structures based on a new demodulation technique for nonlinear and non-stationary vibration signals through the identification of signal envelopes in real time is presented. In the present work, the need for the detection of envelope in a vibration signal in real time is addressed by reformulating the concept of Hermitian interpolation functions to a recursive Hermitian polynomial, which is a key entitlement of the present work. Once, the near real-time demodulation is achieved, the proposed framework proceeds to the newly developed error-adapted framework by addressing the errors accrued between the standard and generalized eigen perturbation formulation in the context of real-time estimation of proper orthogonal modes and linear normal modes. In the adaptive framework, the error is modeled as a feedback, which is constructed to account for the truncation in the order of eigen perturbation. In addition to the improved accuracy due to the envelope extraction, the proposed error-adapted eigen perturbation further improves the detectability over the currently available eigen perturbation–based real-time algorithms. To ensure robustness of the proposed algorithm, a new real-time damage indicator based on the maximum of principal eigenvector of the evolving transformed covariance matrix is proposed. The proposed modules together not only improve the detectability of the damage detection in real-time but also enhance the overall performance in presence of non-stationary excitation, that often mask the damage information in the higher energy zones of the amplitude and frequency-modulated response. Simulations for the proposed framework is performed by considering a 5 degrees-of-freedom linear and base-isolated nonlinear structural system driven by non-stationary stochastic excitations with damage simulated at intermediate floor at a particular time instant. Evidence of the near real-time demodulation and/or envelope removal from the signal and improved damage identification is also provided. An examination of the proposed framework using experimental data further validates the robustness of the proposed scheme.
<p>Numerous studies have been conducted on the connection between music and the brain, and it has been established that listening to music directly affects brain activity and stimulation. The potential benefits of music therapy, which uses music as a tool for healing and fostering well-being, have come to light in a number of circumstances. However, there is a gap in understanding the effects of Indian classical music (ICM) on the brain and its therapeutic applications. In this work, the authors propose a systematic approach for identifying brain regions evoked to live ICM stimuli, considering input and output uncertainties. The brain responses are captured through 24 channel Electroencephalogram (EEG) cap, which is utilized to allocate electrodes to different regions of the brain. The proposed region specific near-automated framework based on eigen perturbation framework provides a measure to capture the time evolution of brain activity for the melodic transition or transition from a raga to relaxation triggered by Indian classical music. This identification is relevant in understanding dynamic changes in brain responses during musical experiences providing a more comprehensive perception and processing of ICM in the human brain. This automated approach can help integrate it into evidence-based music therapy for cognitive, emotional, and psychological conditions. Probabilistic analysis based on extensive experimental studies with live Indian classical vocal stimuli brings forth many interesting results that are worth delving into for future directions in music therapy. The findings of this study provides evidence indicating ragas activate different brain regions based on listener's musical knowledge.</p>
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