Neutralization of temperature effects in damage diagnosis of MDOF systems by combinations of autoencoders and particle filters
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., and (i.e., ) . The process noises are described by normal distributions with zero mean and variances and 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.
References (65)
- et al.
Lifetime extension of onshore wind turbines: A review covering germany, spain, denmark, and the uk
Renew. Sustain. Energy Rev.
(2018) - et al.
Damage detection and quantification using transmissibility
Mech. Syst. Sig. Process.
(2011) - et al.
Experimental validation of a structural health monitoring methodology: Part iii. damage location on an aircraft wing
J. Sound Vib.
(2003) - et al.
Health monitoring and active control of composite structures using piezoceramic patches
Compos.: Part B
(1999) - et al.
Structural health monitoring using transmittance functions
Mech. Syst. Signal Process.
(1999) - et al.
Structural health monitoring techniques for wind turbine blades
J. Wind Eng. Ind. Aerodyn.
(2000) Detection of bolt load loss in hybrid composite/metal bolted connections
Eng. Struct.
(2004)- et al.
Damage localization using transmissibility functions: A critical review
Mech. Syst. Sig. Process.
(2013) - et al.
Application of the wavelet transform in machine condition monitoring and fault diagnostics: a review with bibliography
Mech. Syst. Sig. Process.
(2004) Frequency response function interpolation for damage detection under changing environment
Mech. Syst. Sig. Process.
(2010)
Novelty detection in a changing environment: regression and interpolation approaches
J. Sound Vib.
On switching response surface models, with applications to the structural health monitoring of bridges
Mech. Syst. Signal Process.
Structural damage diagnosis under varying environmental conditions - part ii: Local pca for non-linear cases
Mech. Syst. Signal Process.
A regime-switching cointegration approach for removing environmental and operational variations in structural health monitoring
Mech. Syst. Signal Process.
Structural damage identification based on autoencoder neural networks and deep learning
Eng. Struct.
Vibration-based damage detection for composite structures using wavelet transform and neural network identification
Compos. Struct.
Applications of neural network models for structural health monitoring based on derived modal properties
Measurement
Structural fault detection using a novelty measure
J. Sound Vib.
Stochastic output error vibration-based damage detection and assessment in structures under earthquake excitation
J. Sound Vib.
Dynamics of multi-span continuous straight bridges subject to multi-degrees of freedom moving vehicle excitation
J. Sound Vib.
Finite element method based monte carlo filters for structural system identification
Probab. Eng. Mech.
Finite element prediction of damping of composite gfrp and cfrp laminates - a hybrid formulation - vibration damping experiments and rayleigh damping
Compos. Sci. Technol.
Modeling of young’s modulus variations with temperature of ni and oxidized ni using a magneto-mechanical approach
Mater. Sci. Eng.: A
Vibration-based structural health monitoring using output-only measurements under changing environment
Mech. Syst. Sig. Process.
Optimization of nonlinear, non-gaussian bayesian filtering for diagnosis and prognosis of monotonic degradation processes
Mech. Syst. Sig. Process.
Maintenance and management of civil infrastructure based on condition, safety, optimization, and life-cycle cost
Struct. Infrastruct. Eng.
Damage identification based on response-only measurements using cepstrum analysis and artificial neural networks
Struct. Health Monit.
Machine condition monitoring and fault diagnostics
Transmissibility as a differential indicator of structural damage
J. Vib. Acoust.
Detecting structural damage using transmittance functions
Effects of environmental and operational variability on structural health monitoring
Philos. Trans. R. Soc. London A Math. Phys. Eng. Sci.
Cited by (15)
Multiple local particle filter for high-dimensional system identification
2024, Mechanical Systems and Signal ProcessingUnsupervised data-driven method for damage localization using guided waves
2024, Mechanical Systems and Signal ProcessingParticle filter-based damage prognosis using online feature fusion and selection
2023, Mechanical Systems and Signal ProcessingA novel double-hybrid learning method for modal frequency-based damage assessment of bridge structures under different environmental variation patterns
2023, Mechanical Systems and Signal ProcessingUnsupervised long-term damage detection in an uncontrolled environment through optimal autoencoder
2023, Mechanical Systems and Signal ProcessingA new regime-switching cointegration method for structural health monitoring under changing environmental and operational conditions
2023, Measurement: Journal of the International Measurement Confederation