(104f) Data-Driven Tight Underestimation: Application to Process Safety

Machine learning (ML) models are surrogates that can be used to efficiently approximate large and computationally expensive models. The current ML models cannot guarantee the type of approximation (underestimation or overestimation). Deterministic global optimization approaches, such as convexification, relaxation and convex hull, can provide guaranteed under/overestimation, but they are often inefficient and apply to simpler problems with special properties (e.g., twice-differentiability, explicit expressions and known functional forms) [1]. In reality, there are numerous complex problems that require ‘conservative’ approximators. In other words, they need models which are mathematically guaranteed to take smaller or equal values to the original model over the domain of interest. One such application is process safety that is critical to the chemical process industry (CPI). The consequences of erroneous approximation of process parameters and safety metrics could be severe. The 20 largest incidents between 1972 and 2011 in the hydrocarbon industry cost $14.6 billion in property damage, let alone the damages incurred due to hazards, personal injury, and even death [2]. Developing efficient surrogate models with guaranteed prediction capability is of significant importance for the design, synthesis, optimization and control of safe chemical process systems [3].

Many safety incidents begin with a process upset, a deviation from normal process behavior. These process upsets may be intentional (e.g., plant shutdown) or unintentional (e.g., power failure). One of the most common approaches in mitigating these upsets is via an effective process control system. For the case of a heat exchanger, a process upset may negatively impact a heat exchanger’s safety rating. This safety rating metric predicts the severity of a potential tube rupture [4,5]. In the event of a tube rupture, the tube side can quickly overpressure the shell side. Upon the shell side pressure increasing beyond the hydrotest pressure, the shell material is prone to fail, potentially resulting in a catastrophic outcome [6,7]. Thus, a prompt control response is required to return an exchanger to a safe operating level with minimal compromises to other plant processes. In approximating the safety rating of heat exchangers, we are interested in an approximation that lies within an error window which is conservative by nature i.e., the approximated value must not exceed the true value. Using data from a rigorous dynamic simulation model [4], we first develop a data-driven piecewise linear underestimation (DDPLU) of safety rating that can be readily incorporated in the synthesis of safe heat exchanger networks. Motivated by the work of Rebennack and Kallrath [8], the DDPLU formulation ensures an efficient and tight but, at the same time, a conservative underestimation (vs. approximation) of safety rating. If the approximated value exceeds the true safety rating, it renders the safety rating useless and may lead to exchanger failure in the event of a tube rupture. For this purpose, we extend the formulation by combining DDPWLU with a data-driven edge-concave underestimator [9,10] which guarantees that a true-model-based safety rating is always higher than the approximated rating. The edge-concave underestimator exploits the properties of the function itself in the form of information captured through its Hessian thereby guaranteeing that the approximation is always conservative. Even though the underestimator is nonlinear, the linear facets of its vertex polyhedral convex envelope lead to a linear programming based relaxation of the original nonconvex problem making it computationally more tractable to solve. The end result is an integrated control-safety strategy that leverages tight conservative safety ratings in order to economically respond to process upsets.

References:

[1] Floudas, C.A. Deterministic Global Optimization: Theory, Methods and Applications. Nonconvex Optimization and Its Applications. 2000, Dordrecht, Netherlands: Kluwer Academic Publishers.

[2] Marsh & McLennan Companies Inc., (2012). The 100 largest losses 1972-2011: Large property damage losses in the hydrocarbon industry.

[3] Albalawi, F., Durand, H.; Christofides, P. D. (2017). Process operational safety using model predictive control based on a process Safeness Index. Computers & Chemical Engineering, 104, 76-88.

[4] Harhara, A.; Hasan, M. M. F. (2020). Dynamic modeling of heat exchanger tube rupture. BMC Chemical Engineering, 2(1), 1-20.

[5] Harhara, A.; Hasan, M. M. F. (2019). Incorporating Process Safety into Heat Exchanger Network Synthesis and Operation. In Computer Aided Chemical Engineering (Vol. 47, pp. 221-226). Elsevier.

[6] API Standard 521. (2014). Pressure‐Relieving and Depressuring Systems.

[7] Hellemans, M. (2009). The safety relief valve handbook: design and use of process safety valves to ASME and International codes and standards. Elsevier.

[8] Rebennack, S., & Kallrath, J. (2015). Continuous piecewise linear delta-approximations for univariate functions: computing minimal breakpoint systems. Journal of Optimization Theory and Applications, 167(2), 617-643.

[9] Hasan, M. M. F. (2018). An edge-concave underestimator for the global optimization of twice-differentiable nonconvex problems. Journal of Global Optimization, 71(4), 735-752.

[10] Bajaj, I.; Hasan, M. M. F. (2019). Deterministic Global Derivative-free Optimization of Black-Box Problems with Bounded Hessian. Optimization Letters, DOI: 10.1007/s11590-019-01421-0.