Inference of multi-variable trends in unmeasured process quantities

In many applications the trends of unmeasured process quantities are of high interest. Often, these trends can be inferred with high confidence from the trends of some measured process quantities. For example, steady-state detection addresses a trend in the unmeasured state variables, but is usually inferred from stationarity of the measurements. This paper provides a method to analyze the confidence with which trends in measurements imply trends in unmeasured quantities. Thus, trends of unmeasured quantities can be inferred from measured trends with known accuracy. The suggested method, for example, facilitates the selection of a trend error in the measurements to bound the loss of profit in real-time optimization due to deviations from steady-state. Furthermore, the method can also be employed to assess candidate measurement configurations in a plant with respect to the achievable accuracy of steady-state or more general trend detection.