Elsevier

Engineering Structures

Volume 209, 15 April 2020, 110301
Engineering Structures

A Dynamic Bayesian Network framework for spatial deterioration modelling and reliability updating of timber structures subjected to decay

https://doi.org/10.1016/j.engstruct.2020.110301Get rights and content

Highlights

  • A Dynamic Bayesian Network framework is used for reliability assessment and updating.

  • The Framework was applied to timber structures subjected to decay.

  • The Framework is able to take into account spatial and temporal variability of deterioration processes.

  • The Framework is useful for reliability updating when using spatially distributed data.

Abstract

Reliability assessment of existing timber structures subjected to deterioration processes is an important task to evaluate their serviceability and safety levels. Towards this aim, data collected after inspection campaigns are often used for updating structural reliability and planning future maintenance/inspection activities. Under natural conditions, timber decay involves a large number of uncertainties related to material properties and environmental exposure. These uncertainties are also affected by temporal and spatial variability of associated deterioration processes. In this context, the main objective of this study is to propose a Dynamic Bayesian Network approach for updating the structural reliability of deteriorating timber structures using inspection data. The proposed approach can account for the uncertainties in the decay process and the effect of spatial variability. It is also useful for reliability updating considering the uncertainties of inspection techniques. The proposed methodology is illustrated with the reliability updating of a timber beam subjected to decay deterioration. Results indicate that this approach is useful for evaluating and updating of structural reliability from spatially distributed inspection data. Reliability updating could also be carried out from partial observations at given areas, which is very useful for large-scale infrastructure.

Introduction

In civil construction, timber is a traditional material that is widely used for various types of structures. For example, there are about 27,000 timber bridges over a total of 40,000 bridges in Australia [1]. By observing historical buildings around the world, it can be seen that timber structures guarantee a long-term service life with high durability level. However, due to its sensitivity to environmental conditions and biological actions, various degradation processes could affect this material – e.g. decay fungi, marine borers, termites etc. Among these phenomena, decay attack is frequently recognised as a main cause leading to unexpected structural failures in timber structures. Decay mechanisms generally reduce the cross section of structural members [2], [3], [4]. For example, Kalamees [5] found that a building failed after 10 years because of the damage produced by dry rot (Serpula lacrymans). Serviceability and safety levels of timber deteriorating structures are therefore affected significantly, being far from the design values. For example, Ranjith & Setunge [1] found that for some timber structures over 50 years old, the risk of structural failure is very important. Consequently, reliability assessment of the existing timber structures is necessary to evaluate its serviceability and safety levels.

Reliability assessment is often performed after maintenance campaigns in which inspections are carried out to collect actual information about the structural performance. In this stage, a realistic modelling of the deterioration processes is important to provide rational lifetime assessments. Leicester et al. [2], [6] proposed decay deterioration models for exposed timber and timber in-ground contact in Australia. Statistical data for parameters of decay deterioration models were collected in several climate zones and correspond to various timber qualities. These models have been adapted or simplified for others regions. For example, Freitas et al. [7] describe the decay process in Brazil by determining a climate index from regressions. These models could be used for reliability assessment of existing structures; however, this task is difficult because of the high variability of the material properties and their interaction with the decay processes under real environmental conditions.

Performing inspection and maintenance of timber structures are then necessary to provide information about the performance of existing structures under real exposure conditions [8]. Data collected after inspection campaigns could be integrated in reliability assessment to re-evaluate the performance and safety of structures. Based on these analyses, appropriate maintenance decisions (repair, replace or do nothing) could be afterwards provided. To account for uncertainty of deterioration processes, reliability assessment of timber structures should be performed in a probabilistic framework. Lourenço et al. [3], [9], [10] assessed the structural safety of timber structures by using Monte Carlo methods for probabilistic modelling. Ranjith & Setunge [1] used Markov models combined with inspection data for deterioration prediction of timber bridges. Sousa et al. [11] used a Bayesian approach for updating reliability assessment with Non Destructive Testing data. However, these studies did not account for some aspects that might lead to inaccurate assessments such as: the spatial-variability and uncertainties of material properties, the changes in biological activity or environmental conditions and the imperfection of inspection techniques.

A Bayesian-based approach is a suitable tool that could incorporate all these issues for reliability assessment. In the form of multi-events, it turns in the form of a Bayesian network (BN) for describing the relationship between random variables. This approach has been used for reliability updating in some previous studies related to timber, concrete or steel durability [12], [13], [14], [15], [16]. Dynamic Bayesian Networks (DBN) are extensions of BN to deal with interactions between the components of a system or time-dependencies [17], [18], [19]. DBN will be therefore useful to represent the kinetics of deterioration processes such a timber decay. Within this context, this study proposes a framework for reliability assessment that can be updated from inspection data. The proposed framework is able to deal with:

  • The time-dependency of structural performance by using DBN;

  • The spatial variability of model parameters, deterioration processes or loading that is modelled by random field theory; and

  • The quality of inspection techniques that is introduced in terms of Probability of Detection (PoD) and Probability of False Alarm (PFA).

This study focuses on timber decay; however, the proposed framework could be also applied for reliability assessment and updating of steel/concrete structures subjected to other deterioration processes. The methodology could also be used for reliability updating with partial observations, which is very useful for the inspection/monitoring of large structures (bridges, pipelines, etc.) where only some areas of the structural components could be inspected/monitored for practical or economic reasons.

An introduction about BN random fields modelling is provided in Section 2. Section 3 presents the decay deterioration model and the construction of DBN for computing structural reliability. Since the proposed approach based on DBN is time-consuming, Section 4 performs a sensitivity analysis to study the influence of some considered approximations for modelling spatial variability. The effect of spatial discretisation is also explored in Section 4. Finally, the whole methodology is illustrated in Section 5 with a numerical example where partial simulated inspection data is employed to update structural reliability.

Section snippets

Bayesian Network modelling of random fields

Stationary random fields Yx,θ are used to model the spatial variability of material properties or model parameters. Stationarity could be reasonably assumed to represent the spatial variability of a deterioration process for a horizontally positioned beam or wall – e.g., for a reinforced concrete beam [20], [21], [22]. Stationary random fields are characterised by three parameters: mean μY, standard deviation σY and auto-correlation function ρYY. The auto-correlation function describes the

Decay deterioration in timber structures

Decay deterioration appears when timber structures are subjected to an ideal environment (high moisture and mild temperature) for the development of fungi. Decay in timber occurs after an initial incubation period tlag, and the speed of decay propagation is measured through the decay rate r measured by decay depth per unit of time (mm/year) (Fig. 4). Wang et al. [6] proposed a simplified model of decay deterioration (Eq. (5)) in which decay rate is modelled as a function of two parameters

Sensitivity analysis when considering the spatial variability

Considering the spatial variability of model parameters is important to obtain a more realistic reliability assessment. However, to include this behaviour in DBN modelling of structure’s performance is a difficult task due to the large number of correlated random variables resulting from the discretisation. This will lead to a densely connected BN where the computation demand becomes intractable [17]. A solution for this issue was detailed in Section 2 and lies in approximating the correlation

Updating structural reliability with partial inspection data

The updating of structural reliability is an important issue for existing timber structures subjected to deterioration processes. This process requires collecting data about the condition of structures and integrating these data for updating structural reliability. The outputs are useful to plan cost-effective maintenance actions. Nevertheless, for economic or practical reasons (accessibility) it is not always possible to inspect along the beam. Then, this section explores how the proposed

Conclusions and perspectives

This paper presented a methodology for modelling and updating reliability of structures subjected to deterioration processes. Dynamic Bayesian Networks were used for modelling decay and updating the reliability assessment with inspection data. The spatial variability of model parameters was introduced in DBN through Common Source Random Variables (CSRVs). CSRVs allow approximating the correlation among elements, and therefore, are useful to reduce the complexity (and computational requirements)

Author contribution statement

EBA and YA acquired the funding and directed the study. All the authors contributed to the conceptual formulation of the proposed framework. TBT implemented the algorithm in Matlab®. EBA and YA verified the approach and results. All the authors contributed to the analysis of the results. TBT proposed a first draft of the paper that was completed and verified by EBA and YA.

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.

Acknowledgements

The authors would like to acknowledge the financial support of project CLIMBOIS ANR-13-JS09-0003-01 as well as the labelling of the ViaMéca French cluster.

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