(460f) Integrated Multiscenario Sensor Network Design for Data Reconciliation and Process Optimization

The design of sensor networks for chemical plants is an important and complex task with several desiderata. First, a sensor network should enable all variables of interest to be observable, that is, to be measured directly or to be inferred from other measured variables through a given process model. In addition, a certain degree of redundancy is required in order to conduct effective data reconciliation, where the reconciled values of the variables should be as close to the real values as possible. As such, observability, redundancy, and estimation precision are three key requirements for a sensor network, which have been widely studied in the literature. For example, Kelly and Zyngier (2008) propose a mixed-integer linear programming (MILP) formulation for the joint optimization of these three properties of a sensor network. However, like most other existing works, their method regards the capital cost of the sensor network as the main objective function of the design problem. To further quantify the loss of operational profit caused by measurement uncertainty, Nabil and Narasimhan (2012) introduce an “average loss,” which is defined as the weighted sum of error variances (and covariances) of individual measurements. The weights reflect the economic importance of each individual measurement and their interactions. However, in their proposed mixed-integer conic programming (MICP) formulation, a minimum observable network is established a priori in order to generate the corresponding matrix parameters and inequalities, and observability relies on the positive definiteness of a kernel matrix. Also, hardware redundancy is not considered in the MICP model. In addition, a chemical plant always has to operate under varying conditions, which lead to different operational decisions but may also impact the availability of measurements. The sensor network design that accounts for multiple operating scenarios and minimizes the expected loss across all scenarios, to the best of our knowledge, also has not been considered in the literature.

In this work, we formulate a sensor network design problem that optimizes the plant performance over multiple operating scenarios while considering observability, redundancy, and precision. An integrated mixed-integer nonlinear programming (MINLP) model is developed where no preset network is required and no matrix inequalities are included. Compared with the work of Kelly and Zyngier (2008), not only the error variances but also the covariances are calculated in the MINLP in order to compute the estimation precision and the expected average loss over all scenarios. Given a capital cost budget, the proposed MINLP yields a globally optimal redundant (including hardware redundancy) sensor network that guarantees observability and minimizes overall average loss. A base-2 normalized multiparametric disaggregation technique is applied to solve instances of the MINLP of relevant sizes. We apply the proposed framework to a set of benchmark sensor network design problems. The computational results indicate that sensor networks obtained from our multiscenario design exhibit significantly improved expected plant performance compared to sensor networks obtained using a single nominal scenario or by maximizing estimation precision rather than economic performance.

References

1. Kelly, Jeffrey D. , and D. Zyngier . "A new and improved MILP formulation to optimize observability, redundancy and precision for sensor network problems." Aiche Journal5(2010):1282-1291.
2. Nabil, M. , and S. Narasimhan . "Sensor Network Design for Optimal Process Operation Based on Data Reconciliation." Sustainable Building Systems19(2012):6789–6797.