Roland Schöbi

Maintenance planning using continuous-state partially observable Markov decision processes and non-linear action models

The signs of deterioration in worldwide infrastructure and the associated socio-economic and environmental losses call for sustainable resource management and policy-making. To this end, this work presents an enhanced variant of partially observable Markov decision processes (POMDPs) for the life cycle assessment and maintenance planning of infrastructure. POMDPs comprise a method, commonly employed in the field of robotics, for decision-making on the basis of uncertain observations. In the work presented herein, a continuous-state POMDP formulation is presented which is adapted to the problem of decision-making for optimal management of civil structures. The aforementioned problem may comprise non-linear and non-deterministic action and observation models. The continuous-state POMDP is herein coupled with a normalised unscented transform (NUT) in order to deliver a framework able to tackle non-linearities that likely characterise action models. The capabilities of this enhanced framework and its applicability to the maintenance planning problem are presented via two applications. In a first illustrative example, the use of the NUT is demonstrated within the framework of the value iteration algorithm. Next, the proposed continuous-state framework is compared against a discrete-state formulation for implementation on a life cycle assessment problem.

Structural reliability analysis for p-boxes using multi-level meta-models

In modern engineering, computer simulations are a popular tool to analyse, design, and optimize systems. Furthermore, concepts of uncertainty and the related reliability analysis and robust design are of increasing importance. Hence, an efficient quantification of uncertainty is an important aspect of the engineers workflow. In this context, the characterization of uncertainty in the input variables is crucial. In this paper, input variables are modelled by probability-boxes, which account for both aleatory and epistemic uncertainty. Two types of probability-boxes are distinguished: free and parametric (also called distributional) p-boxes. The use of probability-boxes generally increases the complexity of structural reliability analyses compared to traditional probabilistic input models. In this paper, the complexity is handled by two-level approaches which use Kriging meta-models with adaptive experimental designs at different levels of the structural reliability analysis. For both types of probability-boxes, the extensive use of meta-models allows for an efficient estimation of the failure probability at a limited number of runs of the performance function. The capabilities of the proposed approaches are illustrated through a benchmark analytical function and two realistic engineering problems.

Comparing probabilistic and p-box input modelling in structural reliability analysis

Structural reliability analysis aims at estimating failure probabilities with respect to a limit-state function accounting for uncertainty in the system’s basic variables. Typically, the uncertainty is modelled by probability theory. However, when only scarce datasets are available and knowledge is incomplete, a more general framework, such as probability-boxes, is more appropriate to describe the uncertainty. In this paper, we examine the effect of p-boxes on structural reliability analysis. Probability-boxes generally increase the complexity of the analysis and hence augment the computational costs. Using meta-models at different stages of the analysis reduces the total computational costs. In particular, advanced Kriging meta-models with adaptive experimental designs are used to estimate failure probabilities based on a small number of calls to the limit-state function. The effects are illustrated on two applications: an analytical toy function and a realistic engineering structure. computational model with a meta-model, such as polynomial chaos expansions or Kriging (Sudret 2012, 2015). Hence, in this paper, Kriging meta-models are used at different stages of the imprecise structural reliability analysis to enhance the overall computational performance. 2 DESCRIPTION OF VARIABLES 2.1 Probability theory Consider a random variable X(ω) in the probability space (Ω, F, P), where ω is an elementary event in the event space Ω, equipped with the σ-algebra F and probability measure P. Typically, a random variable is characterized by its cumulative distribution function (CDF) FX, which describes the probability that X ≤ x, i.e. FX(x) = P(X ≤ x). Thus, the probability measure P provides a single measure for the variability of variable X. This indicates that the variability is known and quantifiable. 2.2 Parametric probability-boxes A parametric probability-box (p-box) is a more general framework accounting for aleatory and epistemic uncertainty. A parametric p-box is defined by a CDF the parameters of which are known within intervals:

Maintenance Planning Under Uncertainties Using a Continuous-State POMDP Framework

Planning under uncertainty is an area that has attracted significant attention in recent years. Partially Observable Markov Decision Process (POMDP) is a sequential decision making framework particularly suited for tackling this problem. POMDP has this far mainly been used in robotics for a discrete-state formulation. Only few authors have dealt with the solution of the continuous-state POMDPs. This paper introduces the concept of approximating the continuous state using a mixture of Gaussians in order to render this methodology suitable for the problem of optimal maintenance planning in civil structures. Presently, a large part of existing infrastructure is reaching the end of its expected lifespan. The POMDP framework is used herein in order to take deterioration processes into account and to accordingly plan the optimal maintenance strategy for the remaining lifespan. The capabilities of the method are demonstrated through an example application on a bridge structure.