Validation of vibration-based structural health monitoring on retrofitted railway bridge KW51

Highlights

• Railway bridge KW51 is monitored before, during, and after retrofitting.

• Natural frequency data are used to validate vibration-based SHM.

• The results obtained from linear regression and robust PCA are compared.

• Finite element simulations are adopted to introduce more subtle structural changes.

Abstract

In this paper, the feasibility of structural health monitoring based on natural frequencies is investigated for a steel bowstring railway bridge in Leuven, Belgium. The data used in the study are obtained from an ongoing long-term monitoring campaign on the railway bridge and include acceleration measurements on the bridge deck and the arches. During the monitoring period, the railway bridge has been retrofitted, resulting in data for two distinct states of the structure. Particular attention is paid to removing the effects of environmental conditions, such as temperature, which affect the modal characteristics of the structure and therefore may lead to false-positive or false-negative damage detection. A comparison is made between standard linear regression and robust principal component analysis (PCA), two black-box modeling techniques which are adopted to remove natural frequency variations resulting from changes in the environmental conditions. In order to assess the success rate of these techniques, a receiver operating characteristic (ROC) curve analysis is performed, considering the actual retrofit as well as a number of more subtle structural changes, which are modeled using a detailed finite element model of the structure. The state transition can be observed for the actual retrofit as well as for smaller structural modifications that result in relatively small natural frequency shifts.

Introduction

Structural health monitoring (SHM) relies on the observation that structural changes, for example due to damage, affect the behavior of a structure, i.e. its deflection, vibrations, etc. Monitoring the response of a structure during its lifetime has therefore been proposed as a tool to detect damage at the earliest possible stage. According to Rytter [1], SHM is composed of the following four identification stages:

• Detection – Is there any damage present in the structure?

• Localization – What is the location of the damage?

• Assessment – What is the type and severity of the damage?

• Prediction – What is the remaining service life of the structure?

Damage detection (stage 1) very often makes use of dynamic response data, for example accelerations, to extract damage-sensitive features, for example natural frequencies. Those features are used to detect novelties that could possibly be attributed to damage. Once damage has been detected, the data are adopted to localize and assess the damage (stages 2 and 3). This step often involves the use of a model, for example when model updating is applied [2]. In the last and most challenging stage, damage progression models are adopted to predict the remaining lifetime of the structure. This paper focuses on damage detection (stage 1).

Many damage-sensitive features proposed in the literature, including natural frequencies, are influenced by environmental and operational conditions. Environmental conditions include for example temperature, relative humidity, and wind speed. Operational conditions involve altering of loading conditions, for example the traffic crossing a bridge, or control operations for the case of a wind turbine. The changes in damage-sensitive features due to variations in environmental and operational conditions are often of the same order of magnitude as those resulting from damage, which may lead to false-positive or false-negative damage detection. It is the differentiation between damage and the conditions determined by the environment and operation of the structure which poses a big challenge for damage detection [3], [4].

The use of physical models to predict and remove the influence of environmental and operational conditions on the dynamic response of the structure is in most cases very difficult. This is mainly due to the complex and often non-linear relation between the environmental and operational parameters and the mechanical properties of the building materials and the support conditions [5], [6]. As such, black-box models are commonly used in damage detection as a valuable alternative for physical models. Black-box models are purely data-driven and are obtained by means of system identification, also referred to as machine learning. The structure of the model and its parameters are not based on physical laws. Two types of data-driven models exist, which are referred to as input–output models and output-only models. Inputs consist of the environmental and operational variables that drive the so-called natural variation in the structural behavior (temperature, relative humidity, …). Outputs consist of the damage-sensitive features (e.g. natural frequencies). In this contribution, it is assumed that only data obtained in the original (undamaged) state of the structure can be used in the training of the model. This situation is in particular relevant for civil engineering structures which are mostly characterized by a unique design and a large variety of possible damage scenarios.

The simplest approach to determine an input–output model that allows removing the environmental and operational conditions is linear regression [3], [7]. Alternative approaches that do not assume a linear relation between the inputs and the outputs but allow identifying a global non-linear input–output mapping are based on neural networks [8] and support vector machines [4], [9]. Input–output modeling requires that all relevant environmental and operational variables are measured. This is rarely the case. As indicated by Rainieri et al. in [6], the identification of an input–output model becomes very challenging when multiple environmental and operational variables act simultaneously and are potentially correlated. This is why many approaches in the literature aim at compensating the damage-sensitive features by means of so-called output-only modeling, where measurements of the environmental and operational variables are not required. The most popular approach for output-only modeling relies on linear principal component analysis (PCA) [10], [11], where a linear relationship between the measured features is identified. When the variation of the features does no longer match the identified relationship, this may point towards damage. As an alternative to PCA, Rainieri et al. have recently proposed the use of second-order blind identification (SOBI) [6]. This technique has the advantage over linear PCA that it can provide fundamental insight in the causes of the natural variability. The relationship between damage-sensitive features is often non-linear [4], which poses another challenge for damage detection. In this case, linear PCA and SOBI can no longer be applied. A very promising approach that allows identifying a non-linear output-only model is kernel PCA, that was proposed for application in SHM by Reynders et al. in [4]. Kernel PCA consists of a computationally efficient non-linear version of linear PCA, for which the structure of the non-linear model does not need to be explicitly defined. A recent application of kernel PCA can be found in [12].

The previously discussed and commonly adopted linear PCA technique is characterized by a large sensitivity to outliers in the training data [13]. Robust PCA, a recently developed technique which is widely adopted in the field of image processing, serves as an extension of linear PCA and aims at removing outliers in the training data prior to the actual determination of the principal components describing the variation in the data [13], [14]. The use of robust PCA was introduced into the field of structural health monitoring by Gharibnezhad et al. in [15], where different types of robust PCA algorithms are compared and discussed. This paper explores one specific type of robust PCA, i.e. robust PCA via sparse plus low-rank (S+LR) [14].

The presence of actual damage in a structure that is being monitored is rare. This complicates the validation of damage detection approaches. A common approach to investigate the detection capabilities of SHM methods in those cases where no actual damage is present is to generate frequency shifts that correspond to realistic damage scenarios, based on a numerical model of the structure [12], [16]. Many of the aforementioned black-box modeling approaches for damage detection have also been applied to experimental data from the Z24 benchmark problem, where long-term monitoring was performed on a highway bridge prior to progressive damage tests [3], [4], [17]. Several approaches, including kernel PCA, succeed in identifying the damage present in this case. The damage induced in some of the progressive damage tests is rather large, however. The detection of more subtle structural changes (in an early stage) remains a challenge. In addition, it is desirable to develop validation cases which consider different types of structures and other types of damage.

This paper investigates the use of natural frequencies to monitor the health of steel bowstring railway bridge KW51 in Leuven, Belgium, shown in Fig. 1. The data used in this study are obtained from an ongoing long-term monitoring campaign on the railway bridge, which includes acceleration measurements on the bridge deck and the arches. The acceleration data have been used to extract the evolution of the natural frequencies over a period of 15 months. In this period, the connections of the diagonals to the bridge deck and the arches were strengthened after the observation of damage. As such, the data set includes data for two different states of the structure, i.e. before and after retrofitting.

Using the aforementioned natural frequency data, a comparison is made between standard linear regression and robust PCA via sparse plus low-rank (S+LR). It is investigated to what extent these techniques enable removing variations in the natural frequency data that are due to changes in environmental conditions, and, as such detecting the actual changes in the structural behavior that are introduced by damage or, in this case, by the retrofit. Furthermore, a calibrated detailed finite element model of the structure is used to simulate a number of more subtle structural changes. This enables a more extensive comparison of damage detection methods.

The paper is organized as follows. First, Section 2 describes the vibration monitoring of railway bridge KW51 and presents the identified modal characteristics obtained from the monitoring campaign. Next, Section 3 presents the two damage detection methods and their application to the monitoring data. In Section 4, a detailed finite element model of the railway bridge is adopted to simulate structural modifications other than the actual retrofit. It is investigated to what extent the two damage detection methods succeed in detecting the state transition would these structural modifications occur. Finally, Section 5 concludes the work.

A detailed description of the data used in this paper can be found in [18]. The data are available for download at [19].