Taking into Account Uncertainties of Non-Destructive Tests in the Estimation of Stochastic Degradation Processes

Controlling the ageing of passive components and facilities implies a good knowledge of the various degradation phenomena and of their evolution. To achieve that goal, a mathematical model that describes degradation kinetics (such as a crack growth model) and enables the assessment of the component’s remaining lifetime and its uncertainties is obviously useful. Such a tool is for instance needed to optimize the maintenance policy while preserving safety. Stochastic processes may be used to describe the random evolution of a degradation indicator around an average trend. Their construction, that is to say the estimation of the trend and of the intrinsic variability around it, relies on the statistical treatment of degradation measures. Expert’s knowledge remains of course a part of the estimation process, for instance to choose a relevant trend type (e.g. a linear trend that depends on several physical variables). In most real applications, the available data is provided by non-destructive tests (NDT). Of course, this source of information is not perfect, since it is affected by measurement uncertainty. Previous studies of such data-sets suggest that this uncertainty can lead to a biased assessment of the degradation kinetics, at least if it is not properly taken into account in the construction of the stochastic degradation process. In this paper, we propose some statistical methods that explicitly make use of the available knowledge on NDT uncertainties to overcome this difficulty. The approach relies on variations of the Expectation-Maximization algorithm, which has been historically developed to process data-sets that include hidden information (in our situation, the hidden information is the difference between the measurement and the true value of the degradation indicator). The proposed statistical tools can be applied to several types of stochastic processes. The practical interest of this work is finally illustrated through a simulated application. 1. Context: Stochastic Degradation Models Improving the knowledge of degradation phenomenon is a key industrial issue for the control of ageing of a facility. In this paper, the focus is placed on degradation mechanisms that affect passive components (e.g. tubes, pipes), and that can be measured through a scalar indicator (such as crack length, corrosion loss of material, etc.). Let Xt denote the value of the degradation indicator at time t; in the following we assume that the higher Xt, the more critical the degradation. In a decision process, it may be useful at time t0 to forecast a future value Xt of this indicator (t>t0). Suppose for instance that a company has to plan a preventive maintenance act on a critical component or structure, affected by an identified degradation phenomenon. The underlying goal here is to optimize maintenance costs (i.e. to avoid over-frequent maintenance) while preserving safety (i.e. planning the intervention soon enough to avoid failure). Roughly speaking, the “optimal” moment T is the time at which the degradation indicator comes too close to a safety/failure threshold sT . In mathematical terms, this means that: ECNDT 2006 Tu.3. 7.2