Neutralization of temperature effects in damage diagnosis of MDOF systems by combinations of autoencoders and particle filters

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Highlights

  • Structural Health Monitoring in changing temperature conditions is here addressed.

  • We propound a time domain method for damage identification and localization.

  • An integrated framework combining Particle Filter and Auto-encoders is investigated.

  • Auto-encoders are exploited for neutralizing temperature effects on SHM outcomes.

  • A benchmark 6-DOF case-study demonstrates the capabilities of the proposed method.

Abstract

In the last years, scientific and industrial communities have put a lot of efforts into the development of a new framework for the assessment of structural integrity, generally known as Structural Health Monitoring (SHM), which should allow real-time, automatic evaluations of the state of the structures based on a network of permanently installed sensors. In the context of mechanical, aerospace and civil structures, several approaches have been proposed to address the SHM problem, yet, it remains often difficult to diagnose damages and estimate the structural health when dealing with varying operating and environmental conditions. Particle Filters have already been proposed as a time-domain-based method in the field of SHM, showing promising results as estimators of hidden, not directly observable states, such as those typically related to damages. At the same time, neural networks-based autoencoders have been proposed for structural damage detection, demonstrating to be capable of capturing damage-related features from vibration measurements. This work aims at exploiting the individual advantages offered by the two approaches by combining them in a novel algorithm for structural damage detection and localization, robust with respect to changing environmental conditions. The algorithm is further equipped with a fault indicator module stemming from the introduction of an automatic threshold and both deterministic and probabilistic fault indicators, thus offering a complete, valuable tool for supporting decision making with limited human intervention. The method is demonstrated with reference to a numerical MDOF system whose parameters are taken from a literature benchmark case study.

Introduction

Structural systems exposed to long service times, changing environmental and operating conditions and occasional loads may suffer from damage within their lifespan. For example, civil infrastructures, including buildings and bridges, crucial for a well-functioning society, face serious safety problems due to ageing [1]. In general, increasing the expected lifetime of a structure would be appealing, especially in case of very large infrastructures, because it can significantly increase the return on investment of the existing assets [2]. In this context, updating of maintenance policies plays a fundamental role for the economic and safe management of mechanical and structural systems. In fact, corrective and preventive maintenance strategies are gradually being replaced by condition-based and predictive maintenance techniques, relying on automatic evaluations of the state of the structures based on a network of permanently installed sensors, so-called Structural Health Monitoring (SHM), leading to large operative cost reductions and to the improvement of safety margins.

Several approaches have been proposed in the literature to correlate any deviation of suitably defined damage sensitive features (extracted from measured data) with the presence of a damage, possibly also identifying damage parameters, such as position, type, extent, and finally enabling damage prognosis. A typical categorization is made according to whether they operate in the frequency or time domain. As for the frequency domain feature extraction methods, it is worth mentioning the envelope spectrum [3], cepstrum [4], high-order spectrum and coherence function [5]. In particular, it has been thoroughly shown that damage detection may be successfully performed in the frequency domain by means of the transmissibility functions (TFs) [6], [7], [8], [9], [10], [11], [12], [13], defined as the ratio of two response spectra of like-variables at two different locations (or nodes of the structural model) for a given excitation [14]. Among time domain features, time-waveform indices, orbits, probability density functions and probability density moments are commonly used. Applying time domain methods, little to no data is lost before processing the signal, allowing for detailed analyses, yet with the possibiliy of incurring into the risk of making diagnosis more burdensome due to the often required accumulation of available data [5]. For the sake of completeness, it is worth mentioning that mixed time–frequency analysis may also be adopted. These hybrid approaches are particularly useful for revealing the inherent information of non-stationary signals, which may be contained in the measures taken from the damaged structure [15]. For a thorough discussion of such a class of analysis techniques, the reader is referred to [15], where the benefits and limitations of these methods are discussed.

However, a general problem of any feature extraction method is that they are sensitive to any change in the environmental and operating conditions, including temperature, pressure, humidity and operative loads, which act as confounding influences, thus hampering the damage identification process potentially increasing the false alarm rate, as widely discussed in [16], [17], [18], [19]. In this context, several approaches have been proposed to magnify the effect of damage over the monitored features and suppress the influence of confounding factors, usually referred to as data normalization [16]. Some methods rely on regression and interpolation techniques to “learn” the dependence of any measured feature from the varying boundary condition [20], [21], [22], [23]. Other methods leverage on a feature’s shift, induced by damage, “orthogonal” with respect to the reference normal condition space. These include, for example, singular-value decomposition [24], principal component analysis [25], factor analysis [26], cointegration [27], [28] and auto-associative neural networks [29]. However, most of these approaches can often only detect the presence of damages in structures, not being able to locate and quantify them. So far, no general method provides fault isolation for a wide range of systems while accounting for possible variations of operational and environmental conditions. In most cases, these methods appear to be, in fact, case-specific, hence no extension of such algorithms to generic problems seems to be able to provide reliable results. An exception seems the work in [30], where an approach is proposed based on the quantification of stiffness variation of all the elements in a structure due to temperature and damage effects, followed by suppression of temperature effects to estimate the actual damage location and extent. That method works in the frequency-domain, in fact the procedure needs a harmonic force to be applied to the structure under examination, in order to determine the actual frequency response function, which is further processed for detecting, localizing and quantifying the damage.

Recently, particle filters (PFs) and other Bayesian methods have been used as time-domain tools for structural parameters identification [31] and fault diagnosis [32], [33]. For example, some works used PFs for identifying the stiffnesses of a multiple-degree of freedom (MDOF) system subject to a seismic-like acceleration forcing function [34]. Moreover, the PF estimation capabilities in presence of non-linear dynamics for the spring components have also been investigated, albeit restricting the attention to the problem of system identification, without delving into the potentiality of the method as a damage diagnosis tool. To the best of the authors knowledge, the effects of environmental conditions have not been taken into account yet in damage diagnosis methods based on the use of PFs in the time domain.

Furthermore, machine learning approaches, specifically neural networks, have been widely implemented for damage diagnosis [35], [36], due to their performance in capturing the behavior of relevant damage features even in presence of very complex dynamics, whose detailed physics-based modeling would often require extraordinary computational efforts. In particular, neural network-based autoencoders have been quite extensively used for performing damage detection [35], [37], [38]. For example, some early work [39] proposed the use of autoencoders for extracting damage-related features from vibration measurements in the frequency domain, thus being able to perform novelty detection in MDOF-modeled systems. However, that procedure relied on the information extracted from the transmissibility function, which, as already mentioned, may not always provide reliable results in damage localization [14].

In this work, we propose an original time-domain approach to perform fault identification in structural components subject to degradation, under changing operating and environmental conditions. Exploiting the complementarity of PFs and autoencoders outlined above, in this paper it is proposed to combine them to derive a robust and flexible algorithm, offering the possibility to automatically perform damage detection and identification in a unique, coherent and simple framework. More specifically, the PF estimates some not directly observable structural parameters on the basis of commonly available vibration measurements (e.g., accelerations, positions, etc.). PF posterior estimation is then combined with temperature measurements using autoencoders, which suppress confounding influences over the estimated structural parameters. Finally, for an effective use of the algorithm as a decision support, a novel detection strategy is also proposed, based on the introduction of automatic thresholds, thus delivering a result less dependent from external, i.e., human, interpretation. The method is demonstrated with reference to a MDOF system whose parameters are taken from a literature benchmark case study [39].

The paper is organized as follows. In Section 2 the generic methodological approach is presented, focusing on the specific design of the PF and of the autoencoder, tailored to the specific application to the MDOF system model. Section 3 introduces a case study, which consists of a 6-DOF system affected by temperature variations. The Section first presents a brief sensitivity analysis aimed at tuning the performances of the PF algorithm, and then demonstrates the performances of the proposed methodology. In Section 4 the conclusions of this work are provided, along with a critical discussion of the main results achieved and possible future work.

Section snippets

Methodology

The methodology is proposed with reference to a modeling strategy commonly used to represent the dynamic behavior of many mechanical, aeronautical and civil structural systems, such as rotary machines, multi-storey buildings and multi-span bridges, i.e., the one-dimensional MDOF systems [40], [41], [42]. MDOF structural systems are also known as periodic structures, which basically consist of several structural components of the same type, i.e., springs, masses, dampers, joined together [43],

Case Study

The structure considered in this case study is modelled on the basis of the MDOF system shown in Fig. 1, considering six degrees of freedom. The structural parameter values characterizing the 6-DOF model are taken from the work in [39], i.e., mi=1kg i=1,,n,kj=104Nm and cj=20N·sm (i.e., β=2·10-3) j=1,,n+1. The process noises are described by normal distributions with zero mean and variances σw,position2=10-16m2,σw,speed2=10-16m2s2,σw,spring2=20N2m2 and σw,damping2=8·10-13 for position,

Discussion

The model-based framework presented in this work offers the advantage that, in real applications, most algorithm parameters can be set up by trial-and-error procedures during a preliminary, purely numerical phase, where the dynamic behavior of the system and the associated acceleration measurements are synthetically generated using the process and the measurement equations. The calibrated parameters are probably not “optimal” for the real application, due to the model errors, but would

Conclusions

This study proposes a novel combination of particle filter and neural network-based autoencoder to identify the structural parameters of mechanical and/or civil structures modelled as mono-dimensional MDOF systems, and to perform damage diagnosis (both detection and localization) in presence of changing environmental conditions. The case study reported in Section 3 demonstrates that the developed framework is capable of providing a real-time temporal estimation of the stiffness of each spring

CRediT authorship contribution statement

Francesco Cadini: Conceptualization, Methodology, Investigation, Formal analysis, Validation, Writing - review & editing. Luca Lomazzi: Investigation, Formal analysis, Software, Writing - review & editing. Marc Ferrater Roca: Formal analysis, Software, Writing - original draft. Claudio Sbarufatti: Validation, Writing - review & editing. Marco Giglio: Resources, Supervision.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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