Predictive model for pit growth on underground pipes

It is difficult to understand the process of underground corrosion, but the progress of pitting depth can be predicted after finding out a statistical law describing many samples of pitting depth. Several statistical models for pitting depth have been proposed recently. These models were applied to data sets of pitting depth on cast iron pipes and their fitness and contents of the data sets were examined. The corrosion rate of a cast iron pipe depends on the corrosiveness of soils. Thus, the corrosion rate was explained by establishing the relationship between pitting depth and environmental factors. The relationship was explored through regression analysis with pitting depth as a dependent variable and environmental factors as independent variables. Pitting depth is expressed as a power of time t: eta = gammat(alpha) (gamma and alpha are constants). The following statistical model has been proposed based on the above relationship. It is supposed that the observed value gamma of pitting depth eta is expressed as a log-normal linear model with environmental factors x(1), x(2),..., x(p) and error: y = etaexp(epsilon)[epsilon similar to N(0,sigma(2))], eta = t(alpha) exp(beta(0) + Sigma(f=1)(p)beta(j)x(j)) The model was, applied to five data sets, which were composed of similar to1,000 samples extracted from five areas in Japan. For each data set, environmental factors that have large influences on pitting depth were examined, and a common prediction formula of pitting depth was proposed with respect to the proposed statistical model.