Damage modeling and detection for a tree network using fractional-order calculus
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ORIGINAL PAPER
Damage modeling and detection for a tree network using fractional-order calculus Xiangyu Ni
· Bill Goodwine
Received: 4 April 2020 / Accepted: 25 July 2020 © Springer Nature B.V. 2020
Abstract Large networks are increasingly common in engineered systems, and therefore, monitoring their operating conditions is increasingly important. This paper proposes a model-based frequency-domain damage detection method for an infinitely large self-similar network. The first aim is to exactly model the overall frequency response for any specific damage case of that network, which we show has an explicit multiplicative relation to the undamaged transfer function. Then, leveraging that knowledge from modeling, this paper also proposes an algorithm to identify damaged components within that network as well as quantifies their respective damage amounts given a noisy measurement for that network’s overall frequency response. Keywords Mathematical modeling · Damage identification · Network systems · Fractional calculus
The support of the US National Science Foundation under Grant No. CMMI 1826079 is gratefully acknowledged. X. Ni (B) · B. Goodwine Aerospace and Mechanical Engineering, University of Notre Dame, 365 Fitzpatrick Hall, Notre Dame, IN 46556, USA e-mail: [email protected] B. Goodwine e-mail: [email protected]
1 Introduction Network systems exist everywhere in real life, for instance, ventilating systems, plumbing networks, natural and robotic swarms, and power grids. Controlling and monitoring the operational health of such large networks are research topics which have a long history. For examples of controlling networks, see the survey paper [27], the book [29] and the paper [31] for multivehicle cooperative control, and the papers [2,7,11,30] for formation control. The convergence speed of a consensus behavior within scale-free networks is studied in [35]. Health monitoring of large networks and structures is another crucial consideration in modern industry. Some related research can be seen in the survey paper [39]. Different types of health monitoring methods have been proposed in [20,32,34]. One class of approaches uses system identification to monitor a system’s health as illustrated in [6,8,18,28]. The damage detection method proposed in this paper belongs to that class. In addition to those real networks, many researches are also conducted on hypothetical networks which are infinitely large and perfectly self-similar. Those researches take advantage of the fact that those idealized networks have less computational burden to model as opposed to real large-scale yet finite networks [15]. Moreover, as stated in [21,26], infinitely large networks’ behavior is good approximations for them. In light of those considerations, we also choose those ide-
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alized networks as the starting point of our work. Other real networks which are modeled as infinite networks include bio-systems in human body. Fractal models of human blood vessels using tree-like structures are proposed in [14]. Fr
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