Knowledge extraction from time series and its application to surface roughness simulation

Knowledge extracted from time series data influences decision-making in business, medicine, manufacturing, science and in other fields. Various knowledge extraction methods have so far been proposed wherein it is typically assumed that a piece of time series data possesses a set of trends that deterministically or stochastically repeat in time. However, for noisy time series data (data having no trend) the delay maps (return maps) (x(t) ,x (t + δ)) ,t =0 ,1 ,... , δ =1 ,2 ,... , N(N is a small integer), are more informative than the time series itself. This paper shows a knowledge extraction method that extracts a small set of "if ... then ... " rules from the return maps of a given set of time series data. A JAVA TM based tool is developed to automate the rule extraction process. This tool is also able to use the extracted rules recursively to simulate the qualitatively similar time series. The performance of the proposed knowledge extraction method (as well as the tool) is demonstrated by using an example time series (surface roughness profile of a machined surface). This exemplification demonstrates that the proposed knowledge extraction method can be used to enhance the performance of computer integrated manufacturing systems by giving those systems a means to exchange the information of nonlinear behaviors among the subsystems (process planning, quality control, and so on).