Semi-supervised detection of structural damage using Variational Autoencoder and a One-Class Support Vector Machine

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Semi-supervised detection of structural damage

using Variational Autoencoder and a One-Class

Support Vector Machine⋆

Andrea Pollastro1,3, Giusiana Testa2, Antonio Bilotta2, and Roberto Prevete1,3

1Department of Electrical Engineering and Information Technology, University of

Naples Federico II, Naples, Italy

2Department of Structures for Engineering and Architecture, University of Naples

Federico II, Naples, Italy

3Laboratory of Augmented Reality for Health Monitoring (ARHeMLab)

Abstract. In recent years, Artiﬁcial Neural Networks (ANNs) have

been introduced in Structural Health Monitoring (SHM) systems. A

semi-supervised method with a data-driven approach allows the ANN

training on data acquired from an undamaged structural condition to de-

tect structural damages. In standard approaches, after the training stage,

a decision rule is manually deﬁned to detect anomalous data. However,

this process could be made automatic using machine learning methods.

This paper proposes a semi-supervised method with a data-driven ap-

proach to detect structural anomalies. The methodology consists of: (i)

a Variational Autoencoder (VAE) to approximate undamaged data dis-

tribution and (ii) a One-Class Support Vector Machine (OC-SVM) to

discriminate diﬀerent health conditions using damage-sensitive features

extracted from VAE’s signal reconstruction. The method is applied to a

scale steel structure that was tested in nine damage scenarios by IASC-

ASCE Structural Health Monitoring Task Group.

Keywords: Semi-supervised Damage Detection ·Structural Health Monitor-

ing ·Variational Autoencoder ·One-Class Support Vector Machines ·Machine

Learning

1 Introduction

Anomaly detection is a key research problem within many diverse research areas

and application domains (see, for example, [1–3]). Anomalies (also said abnor-

malities,deviants, or outliers) can be viewed as data instances which move away,

are dissimilar, from the large part of collected data. Errors in the data can be the

cause of anomalies, but sometimes they can be indicative of a new, previously

unknown, underlying process [4]. Anomaly detection tasks have been tackled by

⋆This article was published on IEEE Access (2023). Please refer to the published

version. DOI: 10.1109/ACCESS.2023.3291674

arXiv:2210.05674v4 [cs.LG] 14 Aug 2023

2 A. Pollastro, G. Testa, A. Bilotta, R. Prevete

several Machine Learning (ML), and in particular Deep Learning (DL), tech-

niques [5–7]. However, a substantial part of anomaly detection approaches is

based on Autoencoder (AE) architectures [4, 8–13]. AEs correspond to neural

networks composed of at least one hidden layer and logically divided into two

components, an encoder and a decoder. From a functional point of view, an AE

can be seen as the composition of two functions Eand D:Eis an encoding

function (the encoder) which maps the input space onto a feature space (or la-

tent encoding space), Dis a decoding function (the decoder) which inversely

maps the feature space on the input space. A meaningful aspect is that by AEs,

one can obtain data representations in terms of ﬁxed latent encodings ⃗

h. In a

nutshell, in anomaly detection tasks AEs are trained to minimize reconstruction

error only on normal data instances, thus involving high reconstruction error

on anomalous data. Then, the reconstruction error is considered as an anomaly

score to classify the input data as anomalous or not, using a user-deﬁned de-

cision rule [14]. AEs’ architectures have been presented with several variations

such as Denoising Autoencoders (DAE), [15] which were meant to remove addi-

tional noise from input data, Sparse Autoencoders (SAE) [16], where a sparsity

constraint is introduced on the hidden layer in order to emphasize meaningful

features, and Variational Autoencoders (VAE) [17], that are generative models

where the latent space is composed by a mixture of distributions instead of a

ﬁxed vector.

In recent decades, the attention to procedures for anomaly detection due

to damage phenomena in civil constructions and infrastructures is more and

more growing. Indeed, (i) safety standards for new constructions have increased

- and therefore existing constructions could not comply with these standards

for little degradation phenomena (ii) both new and existing structures are be-

coming increasingly smart with the use of several embedded sensors providing

real-time information. For this reason, the research aimed at ﬁnding procedures

that allow the set up of a Structural Health Monitoring (SHM) system for struc-

tures and infrastructures, i.e., for both buildings and bridges, are very numerous.

Bridges are strategic structures for which important and expensive management

and maintenance activities are foreseen because they are structural types par-

ticularly subject to environmental phenomena and variations in use conditions

(loading-unloading cycles, temperature, etc.). Moreover, they do not have re-

serves of resistance capacity, which are characteristic of other structural types

such as, for example, buildings. On the one hand, a proper model of the physics

behavior of this type of structures in operational condition is not easy. This

stimulates the use of automatic monitoring systems that can continuously and

rapidly detect anomalous conditions due to damage, to ensure a quick response

from the infrastructure manager. On the other hand, it is necessary to consider

that (i) the high variability of the boundary conditions in which the bridge struc-

ture functions can alter the estimate of the anomaly (e.g., variable vibrations

induced by wind actions, highly variable traﬃc load during the functioning of the

structure, highly non-linear mechanical behavior of the materials that constitute

the bridge) (ii) any algorithm implemented for a structural monitoring system

Published on IEEE Access (2023), DOI: 10.1109/ACCESS.2023.3291674 3

hardly detect damage conditions if trained on an extensive database of measure-

ments performed mainly in the operating conditions of the structure, namely

in the absence of structural damage. This second aspect is crucial because the

diﬃculties of measuring damage conditions are due to the intrinsic assumption

made in the structural design approach, which expects the use of high safety

factors to ensure that the operational conditions are well far from the structural

limit condition. Therefore it is evident that investigating the use of damage de-

tection algorithms that accurately provide warnings for structural monitoring is

particularly challenging and interesting, regardless the subsequent necessity of

damage quantiﬁcation and structural prognostics. The monitoring strategies are

mainly characterized by (i) types of monitoring (static or dynamic), (ii) anal-

ysis methodologies (i.e. input-output, with known forces, or output-only, with

unknown forces) and (iii) analysis approach (i.e. data-driven or model-based, de-

pending on whether the creation of a model to support the method is required).

Static monitoring techniques usually consist of discrete more than continuous

detection of gradual and slow variations of some parameters in rather long pe-

riods. By contrast, dynamic monitoring methodologies - which can use diﬀerent

techniques for identifying dynamic parameters, in the frequency domain [18]

(e.g. peak picking, frequency domain decomposition, enhanced frequency do-

main decomposition) and in the time domain [19] (e.g. auto-regressive moving

average models) - generally need to use a large amount of data. The records

of accelerations, speeds and displacements can be post-processed through tech-

niques operating in time or frequency domain, which aﬀects the damage-sensitive

feature. In the frequency domain, the features can be curvature, strain energy,

ﬂexibility and interpolation error [20, 21] while, in the time domain, the feature

is generally an error parameter [22].

In this work, we propose a semi-supervised data-driven DL-based frame-

work to detect damages in an SHM system. Our proposal consists in using a

VAE, trained on undamaged raw data, to represent input data through damage-

sensitive features (typically involved in structural damage detection [23–25]) and

a One-Class Support Vector Machines (OC-SVM) [26] to classify data as un-

damaged or not, thus avoiding any user-deﬁned decision rule. Damage-sensitive

features are extracted by input data and their reconstruction computed through

the VAE. Diﬀerently from other works based on standard AEs, our proposal

leverages on the probabilistic aspects of a VAEs for the extraction of damage-

sensitive features from input raw data, which implies the capturing of more data

variability in the latent encoding space than a standard AE, avoiding in this way

several weaknesses that may be found by using AEs for anomaly detection in-

stead [14]. Moreover, since the probabilistic encoder of a VAE approximates the

generative distribution of input data through their latent representation (diﬀer-

ently from an AEs, where a deterministic mapping from the input to the latent

representation is learnt [14]), we expect that learning the distribution of undam-

aged data lets the encoder to model damaged data with diﬀerent distributions,

thus improving the robustness of the damage detection system. Finally, to the

best of our knowledge, among various anomaly diagnosis studies in SHM based

4 A. Pollastro, G. Testa, A. Bilotta, R. Prevete

on machine learning methods, this paper aims to propose for the ﬁrst time an

analysis of the VAE latent representations in modeling damaged/undamaged

data distribution and its impact on the damage detection through KL diver-

gence analysis on the various damage cases.

This paper is organized as follows. Section 2 brieﬂy reviews the related liter-

ature; Section 3 describes the proposed architecture; Section 4 introduces the

experimental assessment together with the discussion about the results, while

in Section 5 an analysis on the VAE’s functioning is provided. The concluding

Section 8 is left to ﬁnal remarks.

2 Related works

During the last years, due to the great success achieved in solving several kinds

of problems and due to the increasing accessibility to computing hardware, the

interest in using DL-based approach in processing massive data coming from

SHM systems is raising, thus moving researchers to design SHM damage detec-

tion methodologies towards autonomous data-driven systems. One of the main

advantages of introducing DL methods in SHM systems consists in automating

the feature extraction process from raw input data through learnable non-linear

transformations modeled as layers of a Deep Neural Network (DNN), thus elimi-

nating the need for human-designed features, the requirement for speciﬁc feature

knowledge and resulting in a DL-based SHM system that is end-to-end. [27]. The

use of DNNs has introduced the possibility to process large datasets acquired

from diﬀerent types of sensors in data-driven SHM systems [28,29].

Yan et al. in [30] presented a multiscale cascading deep belief network named

MCDBN for automatic fault identiﬁcation of rotating machinery. The same au-

thors in [31] proposed a novel hybrid deep learning model for multistep fore-

casting of diurnal wind speed called ISSD-LSTM-GOASVM. In [32], Xu et al.

provided a summary of the state-of-the-art progress of AI applications in civil

engineering for the entire life cycle of civil infrastructures. Li et al. in [33] con-

ducted a comparison between the performance of a Convolutional Neural Net-

work (CNN) and other methods, such as Support Vector Machine, Random

Forest, k-Nearest Neighbor, and Decision Trees for damage detection in an ex-

perimental cable bridge model. The results demonstrated that the accuracy score

was improved by at least 15 % when using a CNN. In [34], Li et al. presented

an approach that integrates the electromechanical admittance (EMA) technique

with CNNs to quantify structural damage severity under varied temperatures.

Ai et al. in [35] proposed a novel approach based on CNNs integrated with EMA

to identify compressive stress and load-induced damages of concrete cubic struc-

tures subjected to loading. The same authors, in [36], presented an EMA-based

damage detection approach based on Principal Component Analysis (PCA) in-

corporated with ANNs. In [37], a new approach that utilizes a 1-D CNN has been

introduced for detecting the general condition of a structure. This approach only

requires two states of damage during the training stage, speciﬁcally undamaged

Published on IEEE Access (2023), DOI: 10.1109/ACCESS.2023.3291674 5

and fully-damaged cases. The advantages in using 1-D CNNs in detecting struc-

tural damages were already inspected by the same authors in [38, 39], where

real-time capabilities of CNNs in detecting damages emerged. Shao et al. in [40]

introduced a framework that utilizes Transfer Learning in a DL-based system

for fault diagnosis. This approach enables and speeds up the training process of

DNNs. Ai et al. in [41] proposed a novel approach based on 2D-CNNs for the raw

EMA-based rapid damage quantiﬁcation on structures. Tian et al. in [42] Bidi-

rectional Long Short-Term Memory (LSTM) models to correlate girder vertical

deﬂection and cable tension for condition assessment in SHM.

In [43], the authors proposed a DL framework that utilizes cloud comput-

ing to achieve eﬃcient real-time monitoring and proactive maintenance of civil

infrastructures. Cheng et al. in [11] introduced a data-driven method for perform-

ing health monitoring on machines, which is based on Adaptive Kernel Spectral

Clustering (AKSC) and LSTM. In [44], a supervised anomaly detection method

has been proposed by the authors, which utilizes a cluster of DNNs trained on

time series signals transformed as grayscale images using computer vision tech-

niques. In particular, in [44], clusters of DNNs are composed by stacked AEs

trained by and greedy layer-wise training [45]. In [46], the authors presented an

anomaly detection method that utilizes a Deep Coupling Autoencoder (DCAE)

for handling multimodal sensory signals. The proposed method also integrates

feature extraction of multimodal data into data fusion for fault diagnosis.

According to the growing interest in using AEs to solve general anomaly

detection problems, several methods based on AEs for SHM damage-detection

systems were proposed in literature. In [47], a monitoring method based on

Conditional Convolutional AEs for identifying wind turbine blade breakages is

proposed. Pathirage et al. in [48–50] proposed several AE-based frameworks to

learn the relationship between the physical properties of a structure and its vi-

bration characteristics. The frameworks considered modal properties as input

data and produced elemental stiﬀness reduction parameters of the structure as

output. This was done to enable the detection of damages. In [51], a method

based on DAE is proposed to extract damage features from data of undamaged

structures aﬀected by noise and temperature uncertainties. Mao et al. in [52]

combine Generative Adversarial Networks (GAN) with AE to perform unsuper-

vised damage classiﬁcation on time series data that is transformed into images

through Gramian Angular Field imaging. In [53], stacked AEs were used to ex-

tract damage-sensitive features from modal parameters of vibration raw data.

Rastin et al. in [54] proposed convolutional AE to perform unsupervised dam-

age detection on benchmark datasets leveraging on reconstruction error of AE.

In [23], an unsupervised method based on acceleration signals was proposed.

The method involved preprocessing the raw signals through Continuous Wavelet

Transformation (CWT) and Fast Fourier Transformation (FFT), before feeding

the data from each sensor into an AE to extract features. The extracted features

were then classiﬁed as damaged or undamaged using an OC-SVM. The same

authors in [55] proposed a novel method to detect, in an unsupervised manner,

structural damages directly from raw acceleration responses (thus avoiding the

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Semi-superviseddetectionofstructuraldamageusingVariationalAutoencoderandaOne-ClassSupportVectorMachine⋆AndreaPollastro1,3,GiusianaTesta2,AntonioBilotta2,andRobertoPrevete1,31DepartmentofElectricalEngineeringandInformationTechnology,UniversityofNaplesFedericoII,Naples,Italy2DepartmentofStructuresforE...

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Semi-supervised detection of structural damage using Variational Autoencoder and a One-Class Support Vector Machine

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