Review of “Game Theoretic Approach to Multiobjective Designs: Focus on Inherent Safety”

1. Review of “Game Theoretic Approach to MultiobjectiveDesigns: Focus on Inherent Safety” Author :Anjana Meel,Warren D. Seider

2. Overview • Profitability, controllability, flexibility and Safety are important objectives in the design of chemical processes • A method for designing optimal processes that are • are inherently safer • ensure high quality

3. Main idea of this paper Steady state of process are classified on the basis of instability and nonminimum-phase behavior to segregate the operating regimes into distinct zones. Zone1 Zone 2 Zone 3 Zone 3 Get local optimum designs corresponding to each zone zone1 zone2 Game Matrix zone3 zone4 compared with other locally optimal designs at alternate operating conditions, and/or process reconfigurations, to obtain the globally optimal design using game theory.

4. Local optimal design

5. Zone segregation • Why? • To do controller design in unstable steady state or nonminimum-phase is very hard. -> process redesign or reconfiguration is needed! • To get the optimal design in mixed region (stable+unstable,minimum+nonminimum phase) is very challenging -> designing in separated zone is needed! • Zone is separated into 4 regions (zone matrix) • an unstable steady state; a right-half plane (RHP) eigenvalue of the process Jacobian evaluated at the steady state. • Nonminimum-phase behavior : a zero of the process transfer function lies in the RHP. Inherent safety and product quality of the designs decrease in the transitions from I to IV

6. Extended bifurcation diagram AUTO is used (software for continuation and bifurcation analysis of differential Equations) DoedelE 97 Damkohler number Zone is classified in the Extended bifurcation diagram

7. Local optimal design procedureElimination or reduction of instability and nonminimum-phase behavior • process operation changes, • inlet changes involving feed concentrations • cooling water temperatures • process redesign • changing the reactor volume • heat-transfer area. • process reconfiguration • adding or removing recycle streams • placing reactors in parallel or series, with or without recycle.

8. Quantitative indices t: total income tax rate S: annual sales C: annual cost i: annual interest rate CTCI: total capital investment • Profitability index (PI) • Controllability Index (CI) • Safety and/or Product Quality Index (S/Q) • Flexibility index Re{RHP process} : the sum of the real parts of the right-half plane (RHP) eigenvalues of the process Jacobian Re{RHP zero dynamics}:sum of the real parts of the RHP eigenvalues of the zero dynamics Jacobian; w=2 Maximum flexibility when a design is at the midpoint of the zone

9. Global optimization :Game theory • Two gamers (row gamer, column gamer) • Row gamer select i and column gamer selects j • After selecting row gamer win the value of aij and column player loses aij. Equilibrium point Max (row minimum)=min (column maximum)

10. Description of elements of the Game • Players: (1) profitability, (2) controllability, (3) safety and/or product quality, (4) flexibility. • Actions/Strategies: assigned to each player involving operating parameter moves among the feasible operating zones. • Payoff consequences: quantitative index measures formulated for each player.

11. Global design: Isothermal CSTR with van der Vussereactions CAf : feed concentration, Vd=volume GAMBIT selects (zone I, Vd 0.5,CAf 7 kmol/m3) as an equilibrium in dominant action solution when S/Qn is used.

12. Review of “Plant-specific dynamic failure assessment using Bayesian theory” Anjana Meel,Warren D. Seider

13. Overview • Abnormal events of varying magnitudes result in • incipient faults, near-misses, incidents, and accidents in chemical plants. • Their detection and diagnosis has been an active area of research, but has received little attention in the CPI. • Objective of this paper • methods for plant-specific, dynamic risk assessment are developed to predict the frequencies of abnormal events utilizing accident precursor data, helping to achieve inherently safer operations.

14. Main ideas: to do this Statistical analysis (Bayesian model) Prior distribution model Accident Sequence Precursor Data Posterior distribution model Monte carlro xA,xB,1,xB,2

15. Fault tree event and Accident Sequence Precursor Data (ASP) • Fault event tree • estimate the probabilities of all possible causes behind an abnormal event • ASP contains data of fault event tree

16. Bayesian theory • Statistical approach to reasoning under uncertainty • The principal steps in application of Bayesian theory (i) specifying a probability model for unknown parameter values that includes prior knowledge about the parameters (ii) updating the unknown parameters using observed data (iii) evaluating the goodness of the conditioned model with respect to the data

17. Bayesian theory • Prior distribution model (beta distribution) Gamma function

18. Bayesian theory • Posterior distribution g(Data|x) : Identically and independently distributed (i.i.d.) data conditional upon x f(x) :prior distribution η :no of data δ :no of failure

19. Bayesian theory-Sample • Case1 :You have a box with white and black balls, but no knowledge as to the quantities • Case 2:You have a box from which you have drawn n balls, half black and the rest white Total :N n/2 n/2 What is the probability of choosing black ball?

20. Bayesian theory • Case 1 (a,b=N=1 (non-informative) • Expected value • Variance • Case 2 (a,b=N) • Expected value • Variance

21. Bayesian approach • Used to model these conditional failure probabilities with the help of prior knowledge about the failure probabilities. • The data on the accident sequence precursors and accidents are • used to obtain posterior failure probabilities. • predictive distribution in Bayesian analysis • enables prediction of the accident frequencies in the future.

22. Algorithm A process unit in the chemical plant is selected Event Tree Prior model ASP Posterior model Monte carlo Mean the proximity of the abnormal events to incipient faults, near-misses, incidents, and accidents

23. Algorithm

24. Example (exothermic CSTR)

25. High temperature CO :continued operation SD : shut down RA: run away (accident)

26. Accident sequence data

27. Bayesian model • Prior (Beta distribution) From CCPS guide Line Distribution function

28. Bayesian model • Posterior K :number of fail L: number of success where Nbj :the number of branch points for safety system j Nb: the vector of Nbj, j = 1, . . . , Ns Ns :number of safety systems