Entropy algorithms for detecting incipient damage in high-rise buildings subjected to dynamic vibrations

Abstract

Civil structures are considered vital elements to the society and economy, but they are susceptible to different kinds of damage during their lifetime. Hence, the development of methodologies capable of assessing the condition of civil structures is of paramount importance. In this work, a new entropy-based methodology for detecting incipient damage in a high-rise building subjected to dynamic vibrations is presented. As different entropy methods have been introduced in the literature, the most representative entropy methods, Shannon entropy, Renyi entropy, approximate entropy, sample entropy, permutation entropy, and dispersion entropy, are investigated for evaluating their performance for damage detection. For performing this task, the vibrational responses measured in the high-rise building to different levels of damage are analyzed.

A precise bare simulation approach to the minimization of some distances. Foundations

“…pure enumeration, gradient or steepest descent methods, etc. 13 ) may be problematic or intractable. For instance, (7) covers kind of "K−dimensional (not necessarily regular) polka dot (leopard skin) pattern type" relaxations…”

“…In the following, we compute/approximate (27) -and some variants thereof -by our bare simulation (BS) method, by "mimicking" the deterministic minimization problem (8) respectively (13). Let us first remark that, as usual, each probability distribution (probability measure) P on Y = {d 1 , .…”

“…The above considerations open the gate to our desired "mimicking" of ( 8) and (13) to achieve (27) (and some variants thereof) by our bare simulation (BS) method. To proceed, we employ a family of random variables (W i ) i∈N of independent and identically distributed R−valued random variables with probability distribution…”

“…. , δ Xn , and independent random synaptic weights With the above-mentioned ingredients, we are now in the position to tackle a variant of the distance minimization problem (27), by our bare simulation method through "mimicking" the deterministic minimization problem (8) respectively (13). For this, we also employ the conditional distributions…”

“…Some exemplary (mostly recent) studies and applications appear e.g. in Nath [270] -as well as in Arikan [15], Sundaresan [353], Bunte & Lapidoth [67], Sason & Verdu [321], Kumar et al [205] -for coding and guessing, in Bennett et al [39] in connection with unconditionally secure secret-key agreement protocols and quantum cryptography, in Mayoral [257] for cluster sampling, in Aviyente et al [21] for information extraction in certain neurophysiological signals (so-called event-related potentials), in Tao et al [355] as well as in Jiao et al [171] for early defect/fault detection of rolling element bearings, in Pham et al: [292] for blind source separation, in Liu et al [226] as well as in Rong et al [311] to electron density functional theory (DFT) for quantum chemical reactivity, in Sason [319] for data compression, in Carravilla et al [73] for the recognition of HIV-1 antibodies through STED microscopy and the corresponding design of therapeutic interventions, in Joshi et al [175] for the identification and tracking of relevant T cell receptors for adoptive immunotherapy, in Erguzel et al [121] for the investigation of Electroencephalography (EEG) signals of subjects suffering from some psychiatric disorders, in German-Sallo [133] for fault-characteristics extraction from discrete signals in manufacturing systems, in Schober et al [323] for investigations of some evolutions of the T cell antigen receptor (TCR) repertoire, in Seweryn et al [326] for the assessment of similarity and diversity of expression profiles in single cell systems, in Amezquita-Sanchez [13] for the detection of incipient damage in high-rise buildings subjected to dynamic vibrations, in Barennes et al [32] for comparing the accuracy of current T cell receptor sequencing methods employed for the understanding of adaptive immune responses, in Kumar et al [201] for the segmentation of digital images through multilevel iterative variational mode decomposition (VMD), and in Pandey [280] for the quantification of cosmic homogeneity.…”