S-IDAP Methodology - Dynamic Linear Modeling (4 Models explained)

S-IDAP uses Dynamic Linear Model (DLM) Corrosion Rate Calculations. Wall loss through corrosion by nature is a time dependent process. However, since the environmental and process conditions are usually varying over time, it is seldom a strictly linear process. DLMs reflect this (stochastic) behavior of the model parameters. Moreover, events may take place that have such a large impact on the wall thickness and/or the CR that explicit modelling is required.

Multi-Process DLM Methodology

Trending is an application of a so-called multi-process DLM where several models are updated simultaneously. Posterior probabilities are used to decide which model applies at a certain moment in time and a weighted average of the models is used for prediction. Trending does the following for each feature considered, given wall thickness measurements over time:

• It predicts the Wall Thickness (WT) at future moments in time.

• It predicts the Corrosion Rate (CR).

• It estimates the Remnant Life (RL).

• It indicates Anomalies in measurements and in corrosion behavior.

By looking at actual Wall Thickness readings over several years, it becomes clear that often:

• The experimental variation (scatter) is quite large.

• There are often many “outliers”.

• The CR is in general not constant over time.

• The number of measurements in a series is often limited.

This makes this type of data less suitable for forecasting using simple regression techniques. Therefore, we use a multi-process DLM. This is a special case of Bayesian forecasting and has several advantages:

• It is more flexible, i.e., model parameters (CR and WT level) may vary over time.

• Subjective knowledge, e.g., prior estimates, bounds on parameters, changes in the process, etc. can be incorporated.

• It is fully recurrent, i.e., at any point in time all past information is condensed into the posterior probability distributions.

The S-IDAP Four Models

In the S-IDAP Module four models have been implemented (that is why it is called a multi process model). In the main model (Model 1) the parameters of the model, the level and the slope, are allowed to vary slowly in time (linear). The other 3 models have been implemented to cope with discontinuities in the data trend:

• Model 2 representing a wrong measurement (outlier).

• Model 3 representing a sudden change in level. This could happen, e.g., when a piece of Equipment is changed, without notification in the database.

• Model 4 representing a sudden change in CR (change in slope). This could happen, e.g., when operating conditions are changed at some point in time.

The four models are illustrated in the below image.

Each time a new measurement is available the likelihoods of all four models are updated and a new prediction, which is a weighted average of the individual forecasts, is generated. Based on the posterior probabilities (if the probability of (one of) the alternative models (model 2, 3 or 4) is high), an “Anomaly” warning signal is generated (see S-IDAP Results Tab).

For more information on Dynamic Linear Modeling see Appendix: Analysis of a Dynamic Linear Model (DLM)