Linear Steady-state Observability and Redundancy Analysis

You are given a process network consisting of process units and mass flows between units (see thumbnail image, taken from [1]) at steady-state. Some of these flows are measured, while some are unmeasured. In any case, you know that all flows must balance: all flows going in a unit must equal all flows going out of that unit. Thus, we can use the measured values to solve for the unmeasured values. But, is the measurement information enough?

This MATLAB code answers the following questions:

1. Among the unmeasured flows, is there a flow that CANNOT be solved from the values of the measured flows using balance calculations?

2. Among the measured flows, is there a flow that CAN STILL be solved by balance calculations even if we might decide NOT to measure that flow anymore?

These are issues of observability and redundancy in flows, defined by Narasimhan and Jordache in [2]. The example process network in the code is the one found as Example 4.4 in [1]. You can input your own process network as an incidence matrix, and then define which of the flows are measured.

The code outputs a list of unobservable unmeasured flows (the answer to question 1) and a list of redundant measured flows (the answer to question 2). It also outputs a minimum list of unobservable flows that needs to be measured so as to make the network fully observable. The QR factorization method for linear observability and redundancy analysis is described in the references below. Observability and redundancy analysis is important for data reconciliation, i.e. if you are uncertain about the measured values, you can reconcile the data at hand using statistical techniques. However, only redundant flows can be reconciled.

References:
[1] Romagnoli & Sanchez, "Data Processing and Reconciliation for Chemical Process Operations", 2000
[2] Narasimhan & Jordache, "Data Reconciliation & Gross Error Detection - An Intelligent Use of Process Data", 2000