Stochastic process deterioration modelling for adaptive inspections

Abstract

In this paper we have considered an option to model deterioration process for infrastructure components using stochastic process representation as an alternative to random variable modelling that is prevalent approach when uncertainty is taken into account. In particular, we have identified that Gamma process represents very simple and effective method to establish consistent deterioration models for structures that are subject to inspection. As a result of such approach we see an opportunity to establish adaptive inspection regime that would account much better for structure specific deterioration path, site specific environment, in service inspection outcomes, inspection technique effectiveness, etc. An example is presented to demonstrate deterioration modelling and further work identified.

fib Bulletin 109. Existing concrete structures life management, testing and structural health monitoring

“…Graphical representationof a gamma process can be used to illustrate that successive gamma PDF or CDF functions are independent of each other. Consequently, the conditional distribution of variable X can only be formulated based on the current observation [243] . This property is very well suited for capturing typical deterioration processes in structural engineering.…”

“…Both, expected value and CoV, are solely functions of the gamma process parameters and only indirectly dependent on time [243] .…”

“…The other parameters, however, are unknown quantities and need to be adapted by drawing on expert knowledge and/or statistical analyses such as the Maximum Likelihood Method, the Method of Moments or Bayesian Statistics. Another study [243] have used the Method of Moments for determining both values. Regarding special cases, the gamma process is called stationary if the deterioration is linear in time, i.e., when b = 1 in the power-law Eq.…”

Comparison of stochastic prediction models based on visual inspections of bridge decks

“…A random variable X that follows gamma distribution can be described using the shape parameter a > 0, the rate parameter ß > 0 and the following probability density function (PDF): When modelling deterioration in terms of a gamma process, the question that arises is how expected deterioration increases over time. Empirical studies show that the expected deterioration at time t is often proportional to a power law (Ohadi, Micic 2011):…”

Stochastic process model for timber-concrete composite beam deterioration

“…Rather slowly, but since the late nineties, continuous stochastic processess have emerged as an alternative approach to random variable models to provide predicted profiles for componental deterioration. As an alternative to continuous stochastic processes discrete stochastic process have also been in use where management of infrastructure was of concern but these models can sometimes result in udully conservative estimates, Ohadi and Micic (2011).…”