In a traditional time-series analysis one assumes a model for the system. This model has a specified form that is consistent over time. However, in most continuous processes changing tank levels, system upsets (events), and transient process behaviors impact the accuracy of forecasts based on these global models. System behavior is often more closely related to local (short-term) process conditions and events that are repeated at random over time. The global model can predict average behavior, but it often does not accurately predict the local behavior of such a system. The traditional purpose of dynamic time warping was to detect predetermined patterns in speech recognition (time-series data). The technique depends on the development of templates, which represent known patterns or behavior. In this paper we extend the dynamic time warping technique to forecast process measurements using recent process data to define a (dynamic) template. This new dynamic template, dynamic-time-warping approach is compared to traditional methods of predicting process measurements when behavior typical of a continuous process is present. The key properties of such processes are described. The dynamic time warping approach is shown to be an effective method of prediction under these process assumptions.
Key Words: Forecasting Techniques, Time-Series Analysis.
By BENJAMIN J. NELSON Weyerhaeuser Company, Tacoma, WA 98477-2999 GEORGE C. RUNGER Arizona State University, Tempe, AZ 85287-5906
THE ability to reliably forecast future events is important for many types of decision-making and quality improvement projects. To forecast events that will occur in the future, the forecaster relies on past information of process data. The historical data is analyzed to determine a pattern that can be used to predict future system responses. Therefore, the ability to forecast is impacted by the accuracy of the pattern recognition process and the assumption that the same pattern of system behavior will continue in the future. If the system behavior changes, the predictions from the model will be less accurate. To develop a reliable forecasting model, the underlying system behavior should be understood and the model should be capable of adapting to changes in the system behavior.
With many of the current methods of forecasting, such as those based on exponential smoothing and Box-Jenkins models, one assumes a single global model when forecasting future behavior. Other methods rely on a global concept, in that the format of the model is specified, but allow for parameter adjustments based on current information. However, the underlying assumptions for these methods do not always reflect the true system behavior. The global model or the appropriate adaptive weights can change in processes with numerous transient events. Rather than weighting the most recent data, it might be more appropriate to put higher weight on past system behavior that most closely matches the current data.
When forecasting process data, there are more issues. Events which impact the system behavior may be occurring upstream in the process. The impact of these events on the model is dependent on the operations between the actual event and the data collection point. Global models can work poorly when transient events occur. In addition, the current operating conditions can distort the effect (signature) of an event. It would be useful to develop a forecasting method that properly accounts for all of these possible system behaviors, events, and operating conditions (i.e., a method that is robust to different operating conditions and can still be used to identify events).
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