330 370 410 450 Time (s)
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-Y(t)
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Figure 4.15: Local RRE plots for floors of UCLA building
in post damage RRE and pre damage RRE (i.e. ∆hεRR−Yii) for each floor as shown in bardiagram (Fig. 4.16) which indicates the appearance of damage not only at a single floor but the system as a whole which corroborates to the previously mentioned results on modal identification [63].
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0
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Floor number Percentage Change in local RRE (ε rr)
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Figure 4.16: Bar diagram indicating percentage change in local RRE for EW and NS direction that the proposed algorithm is well equipped to detect damage when the number of sensors used to acquire data is reduced (i.e., for underdetermined systems), which is clearly an advantage while dealing with practical economics of health monitoring of real full-scale structures. The results show efficacy of the current framework to detect damage for underdetermined cases up to 20% change in the level of nonlinearity. The superiority of the RPCA based damage detection framework is clearly evident through the comparison with the traditional windowed batch PCA based framework, which is promising from a real time damage detection standpoint. Presented case studies show that the proposed approach results in successful damage detection and works well even when used with both experimentally acquired data as well as large scale field data closely emulating practical scenarios.
Although the proposed methodology provides successful detection results even for underdeter- mined systems, it is expected that the method will not function if the input is provided only from a single sensor. An essential prerequisite of the RPCA based processes is the requirement of multi- channel input data, a luxury that sometimes cannot be afforded due to cost, unavailability of good quality sensors and other factors. This issue is addressed in detail in the next chapter where the theoretical development of a newer real time damage detection strategy is discussed in detail that functions using a single-channel input data.
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Chapter 5
Online damage detection using recursive singular spectrum analysis and its hybrid extension
One of the main limitations of the RPCA based methods reviewed in the previous chapter is their inability to operate in situations where the input to the algorithm is obtained from a single sensor.
Such instances occur, for example, in tall structures where instrumentation in each DOF is practi- cally not feasible, embedding a dense array of sensors is economically not viable and positioning of these sensors into strategic locations for continuous monitoring is inaccessible. For such instances, algorithms solely premised on detecting spatio-temporal real time damage from single sensor input is clearly advantageous over the traditional identification schemes as well as some recent trends in the associated area. Towards this, a new algorithm known as recursive singular spectrum analysis (RSSA) is newly proposed in this chapter that takes into consideration the input from a single sensor in order to determine the spatio-temporal patterns of damage to the structure. To the best of the knowledge of the author, concepts utilizing RSSA in the purview of real time structural damage detection has so far not been explored in the literature.
In this chapter, a novel framework has been introduced using RSSA as a structural damage detection tool that works in real time as the data streams in. The motivation to identifying dam- TH-1989_156104031
age patterns using single sensor vibration data as input is provided first, followed by the detailed description of the methodology. The key DSFs used to address the detection problem is presented next. Subsequently, the applications of the proposed method on numerically simulated systems, experimental verification and practical case studies are also presented. En route, a novel framework has been proposed using an improvised variation of the FOEP approach through the association of RPCA-RSSA methods as online damage detection tool that works in real time. The key idea is todetect finer levels damage in real time, an attempt that has not been established in the literature so far. In this context, a new hybrid approach is proposed where the output vibration response is first transformed utilizing the RPCA algorithm to be subsequently utilized by the RSSA algorithm for providing eigenspace updates in real time. In order to provide an easy understanding of the terminologies used in this chapter, the important acronyms are provided in Table 5.1.
Table 5.1: Important acronyms RSSA Recursive Singular Spectrum Analysis PC Principal Components
ERD Eigen Ratio Difference
RMSSA Recursive Multi-channel Singular Spectrum Analysis
5.1 Motivation
The development of online damage detection techniques based on processing of response streaming in real time, still remains a challenge. The primary motivation behind the present work is to develop a unified damage detection framework using single and multiple sensors that can process data online and detect damage in a structure in real time. Applications involving aging and wearing out of components, processes dealing with seismic signals, are generally time-varying where the signals evolve in real time and the process becomes too complex to be analyzed via a simple offline method [1, 2]. In practical SHM scenarios, data streams continuously in real time, which further necessitates that the algorithm should be amenable towards online implementation, independent of any baseline (reference) data. Traditional SSA requires a batch of data to elicit principal components (PCs) of the original time series, via eigen decomposition of the covariance matrix, that solely works offline. In this chapter, a baseline free approach has been proposed which facilitates the monitoring of TH-1989_156104031
structural systems directly using acceleration data, based on RSSA, as a tool for real time processing of data using single channel input data. The proposed method utilizes the FOEP approach for the Hankel covariance matrix estimate with every new sample obtained in real time. While the traditional SSA approach processes chunks of data acquired in batch mode, RSSA provides online processing of data based on rank one eigenvector updates in a recursive framework, as and when the data streams in real time. Once the eigen-space updates are obtained, an approximation of the original time series is carried out by reconstruction, where the framework then utilizes TVAR modeling in conjunction with DSFs for identifying the instant of damage [51].
Largely premised on the idea that damage is manifested through an alteration in the structural dynamical properties such as natural frequencies, mode shapes and damping, a significant number of damage detection algorithms and strategies have been proposed in recent times [1–5]. However, the evolution of real time damage detection schemes capable of conducting baseline-free damage identification, still poses a challenge, primarily, due to the underdevelopment of algorithms that are amenable towards real time implementation. The occurrence of damage is often a real time event [3]
that requires the DSFs to function online, in a recursive fashion, for a continuously streaming data. As the majority of the established damage detection algorithms function offline in batch mode process, the development of online algorithms becomes imperative in the context of real time structural damage identification [75, 96]. This can be carried out by extensively by a family of eigen value perturbation techniques known as the FOEP based implementations [133, 134] and tailoring it towards real time SHM. This chapter explores the family of the FOEP techniques that have been developed in the recent years (includes RPCA and RSSA based algorithms) and also demonstrates how new hybrid approaches can be proposed based on the requirement of a particular type of SHM problem. The key entitlement of any new proposed algorithm within the family of FOEP techniques is that it should exhibit finer levels of detectability compared to the other members of the FOEP family, in the backdrop of sparse and dense sensor economics and different types of nonlinearities inherently present or induced by the damage event.
There are two major issues that are overcome using the methods proposed here. The first one is the difficulty introduced in the damage detection process due to the requirement of multi- channel sensor data. The second difficulty is in the finer level of real time damage detection that TH-1989_156104031
is successfully addressed by the hybrid FOEP based RPCA-RSSA approach, which remains one of the major entitlements of this dissertation. Despite the amalgamation of the recursive approaches in the hybrid algorithm, the time complexity for providing eigenspace updates in real time is still a bare minimum, which is reported in the later stages of this chapter. The scope of the present work assesses the detection prowess of the proposed FOEP based real time SHM methods in general and a hybrid method in particular, to address simultaneous temporal and spatial damage of both linear and nonlinear systems in real time. Case studies aimed at detecting real time damage for weakly to strongly nonlinear family of structural systems have been explored in detail. The present work deals with damage detection on numerically simulated systems, complemented with experimental test beds involving the previously described setups and newer trials using vibro-impact systems, from which important conclusions are drawn. Both the methods are successfully applied on real life cases on the vibration data obtained from UCLAFB that concludes the chapter with an extensive comparison of the performance of the real time detection methods developed so far.