The synthesis of data from instrumented structures and physics-based models via Gaussian processes

Abstract

At the heart of structural engineering research is the use of data obtained from physical structures such as bridges, viaducts and buildings. These data can represent how the structure responds to various stimuli over time when in operation. Many models have been proposed in literature to represent such data, such as linear statistical models. Based upon these models, the health of the structure is reasoned about, e.g. through damage indices, changes in likelihood and statistical parameter estimates. On the other hand, physicsbased models are typically used when designing structures to predict how the structure will respond to operational stimuli. These models represent how the structure responds to stimuli under idealised conditions. What remains unclear in the literature is how to combine the observed data with information from the idealised physics-based model into a model that describes the responses of the operational structure. This paper introduces a new approach which fuses together observed data from a physical structure during operation and information from a mathematical model. The observed data are combined with data simulated from the physics-based model using a multi-output Gaussian process formulation. The novelty of this method is how the information from observed data and the physics-based model is balanced to obtain a representative model of the structures response to stimuli. We present our method using data obtained from a fibre-optic sensor network installed on experimental railway sleepers. The curvature of the sleeper at sensor and also non-sensor locations is modelled, guided by the mathematical representation. We discuss how this approach can be used to reason about changes in the structures behaviour over time using simulations and experimental data. The results show that the methodology can accurately detect such changes. They also indicate that the methodology can infer information about changes in the parameters within the physics-based model, including those governing components of the structure not measured directly by sensors such as the ballast foundation.

Dynamic testing and analysis of the world's first metal 3D printed bridge

“…Data-driven design, where in-situ structural monitoring is used to refine design assumptions, has the potential to reduce i) the uncertainty in the structural design process, ii) material usage, and iii) costs, while increasing the user comfort and lifetime of the structure [1]. The key to this approach is the blending of in-situ observations of similar structural forms with predictions of behaviour made through engineering models, such as finite element (FE) modelling [2,3]. While there is a wide range of available methods for: a) in-situ structural sensing [4][5][6], b) updating of numerical structural models [7][8][9][10], and c) fusing in-situ measurements with numerical models [11][12][13][14], little attention has been given to date in how in-situ structural monitoring may provide the greatest benefit for improving structural design [15].…”

Spatial Statistical Models: An Overview under the Bayesian Approach

“…Moreover, spatial statistics has been increasingly applied in physical and environmental sciences. It has been used to provide estimates for the curvature of a railway sleeper supported on compacted ballast, through the multiple output Gaussian process to guide inference in unobserved regions [56]; to quantify the uncertainty, in spatially varying material parameters, such as polycrystalline, through a Gaussian random field [57,58]; to study material properties and spatial variability in elastostatics [59]. In environmental science, it has been used in extreme value analysis to quantify the uncertainty associated with an increased risk of flooding in Great Britain [60]; to determine the spatial pattern of the association of socioeconomic factors to Japanese encephalitis; to understand the seasonal effect and spatial variability in yield maps in farm precision in Southeastern Australia [61]; to determine the expected number of scores in a golf game [62].…”

A Digital Twin of Bridges for Structural Health Monitoring

“…For example, a Gaussian process (GP) based DCE method has been developed by integrating GPs with physics-based models (e.g. FE models) [10]. This work used the experimentally tested and field monitored railway sleepers as a case study, with the goal of predicting their operational performance over time.…”

“…The case study considered two railway bridges in Staffordshire, UK which have pervasive sensor networks installed at the time of construction. The study involves an interdisciplinary collaboration between the Cambridge Centre for Smart Infrastructure and Construction (CSIC) and the Alan Turing Institute (ATI), combining the expertise of bridge monitoring [4], finite element modeling [5], [6], building information modeling (BIM) [7], [8] and statistical modeling [9], [10], with the end objective of creating a working digital twin for the instrumented Staffordshire bridges.…”