Interval State Estimation in Signed Directed Graph Based on Sensitivity Matrix Method

Signed directed graph (SDG) is an important graphic model to describe the variables and their relationships in complex systems. The samples are composed of all the variable values to denote the system states. However, some physical quantities are unmeasured and thus the sample we get is incomplete. If we want to obtain the complete sample, we have to estimate the unmeasured variables by the measured variables and the knowledge of the model. Since the SDG uses "0" to denote the normal state by an interval, what we want to obtain is the two ends of the interval, viz. the thresholds. By linearization of the measurement model, the estimation problem of the state uncertainty set can be solved by sensitivity matrix method. The sensitivity matrix is correlated with the modeling of SDG, so this method is applicable to the variable threshold estimation in large-scale complex systems modeled as SDGs Finally an example of a boiler system is shown to illustrate the method.