Determination of State Changes for Distributed Parameter Systems Based on Quantitative POD Angle Analysis

Abstract

For distributed parameter systems, recognition of state change is crucial to process operation with a wide range of motivations, for example, sensitivity analysis of input condition, selection of operating point and abnormal situation diagnosis, etc. A key task therein is developing a criterion from which the extent of state change can quantitatively determinated. In this paper, a novel concept, namely the POD (proper orthogonal decomposition) angle is proposed to form such a criterion, which is developed from the POD technique. Based on this new concept, some of its theoretical properties are also described and proven along with the introduction of POD angle. As an illustrative example for the usage of POD angle, a cyclohexane process is studied where the POD angle is used to analyze the influence of feed temperature on the temperature distribution of whole system. It is demonstrated that when feed temperature is operated in the range of 100 to 120 °Ñ, the POD angle will experience a change of 17.8022°, corresponding to fluctuant amplitude of 82.0309 °Ñ for the system temperature. Therefore, temperature distribution of system is sensitive to feed temperature in this situation. On the other hand, when feed temperature is operated in the range of 120 to 200 °Ñ, the POD angle changes only 1.1595° on average whilst the temperature distribution of whole system average varies only 5.0486 °Ñ, hence we conclude that the feed temperature imposes a minor impact on the temperature of the system as compared with the former case.

Keywords

• Distributed parameter systems
• Eigenfunction
• Proper orthogonal decomposition
• Cyclohexane process
• Operating point.