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Fig. 11. Comparison of estimated results for the distribution output of the concentration of polystyrene at the last time point in Case Study 1.

Figure 11 Comparison of estimated results for the distribution output of the concentration of polystyrene at the last time point in Case Study 1.

Related Figures (19)

Fig. 1. The procedures of EKF recursion algorithm.
Fig. 1. The procedures of EKF recursion algorithm.
Fig. 2. Measured data with different types of gross errors, (a) outlier, (b) bias and (c) drift. G. Hu, Z. Zhang and A. Armaou et al./Journal of the Taiwan Institute of Chemical Engineers xxx (xxxx) Xxx
Fig. 2. Measured data with different types of gross errors, (a) outlier, (b) bias and (c) drift. G. Hu, Z. Zhang and A. Armaou et al./Journal of the Taiwan Institute of Chemical Engineers xxx (xxxx) Xxx
Fig. 3. Structure of the robust EKF state estimation system. estimation and data reconciliation are described in Section 2.1. The details of the other stages will be described in this section.
Fig. 3. Structure of the robust EKF state estimation system. estimation and data reconciliation are described in Section 2.1. The details of the other stages will be described in this section.
Fig. 4. Illustration of random and gross errors.
Fig. 4. Illustration of random and gross errors.
Fig. 5. Gross error identification in the moving window.
Fig. 5. Gross error identification in the moving window.
Information of process states for the free radical polymerization of styrene. Table 1 lease cite this article as: G. Hu, Z. Zhang and A. Armaou et al., Robust extended Kalman filter based state estimation for nonlinea lynamic processes with measurements corrupted by gross errors, Journal of the Taiwan Institute of Chemical Engineers, https://doi.org ee IW ey OS The measured’ variables were’ selected as y= V1 ke V2.ke¥3,k Val! = (Coke Gk Cue: Te], and the measurement In order to investigate the validity and effectiveness of the proposed MC-REKF, the reaction of the free radical polymerization of styrene was considered. The mathematical model presented by Schmidt and Ray was applied to describe the dynamics of polymerization in a jacketed continuous stirred tank reactor [32]. The reaction mechanism of polymerization consists of first (i) the decomposition of an initiator, and then (ii) the formation of a monomer radical, (iii) chain propagation, finally (iv) termination reactions. The output of interest in this process is the distribution of the polystyrene concentration as a function of its chain length at the outflow of the reactor. The estimation of the distribution output is crucial on account of its significance on the product
Information of process states for the free radical polymerization of styrene. Table 1 lease cite this article as: G. Hu, Z. Zhang and A. Armaou et al., Robust extended Kalman filter based state estimation for nonlinea lynamic processes with measurements corrupted by gross errors, Journal of the Taiwan Institute of Chemical Engineers, https://doi.org ee IW ey OS The measured’ variables were’ selected as y= V1 ke V2.ke¥3,k Val! = (Coke Gk Cue: Te], and the measurement In order to investigate the validity and effectiveness of the proposed MC-REKF, the reaction of the free radical polymerization of styrene was considered. The mathematical model presented by Schmidt and Ray was applied to describe the dynamics of polymerization in a jacketed continuous stirred tank reactor [32]. The reaction mechanism of polymerization consists of first (i) the decomposition of an initiator, and then (ii) the formation of a monomer radical, (iii) chain propagation, finally (iv) termination reactions. The output of interest in this process is the distribution of the polystyrene concentration as a function of its chain length at the outflow of the reactor. The estimation of the distribution output is crucial on account of its significance on the product
The concentration of polystyrene was selected as the pro- cess state and estimated based on the measurement data. Considering the number of the chain length, there are a total of 1003 process states, ie, Xp = [X1,X2,X3,X4,%5,---,X1003]) = [Cres Cres Tes Guy, k> C_y,k> +++» Cggo.kl’» The dynamic discretized equations in the nonlinear process model are given by where C,,and Cue are the concentrations of the initiator and the monomer respectively. k denotes the time point. 7, is the temperature of reactor. Cy, , represents the concentration of the polystyrene with chain length of n units of monomer. wy,_1, W2k-11-++» Wy4903,k-1 are the process noise added to state vari- ables. They follow a normal distribution with a constant standard deviation. The total information of the process states for the free radical polymerization of styrene is listed in Table 1. As pointed in [33], the state variables C,, Gy and T must be redefined using the dimensionless variables before simulation since they vary greatly in magnitude. At a steady state set-point reactor temperature T;; of 310K and the inlet initiator concentration Chi, ss = 0.5888 kmol m-3, the following values can be obtained.
The concentration of polystyrene was selected as the pro- cess state and estimated based on the measurement data. Considering the number of the chain length, there are a total of 1003 process states, ie, Xp = [X1,X2,X3,X4,%5,---,X1003]) = [Cres Cres Tes Guy, k> C_y,k> +++» Cggo.kl’» The dynamic discretized equations in the nonlinear process model are given by where C,,and Cue are the concentrations of the initiator and the monomer respectively. k denotes the time point. 7, is the temperature of reactor. Cy, , represents the concentration of the polystyrene with chain length of n units of monomer. wy,_1, W2k-11-++» Wy4903,k-1 are the process noise added to state vari- ables. They follow a normal distribution with a constant standard deviation. The total information of the process states for the free radical polymerization of styrene is listed in Table 1. As pointed in [33], the state variables C,, Gy and T must be redefined using the dimensionless variables before simulation since they vary greatly in magnitude. At a steady state set-point reactor temperature T;; of 310K and the inlet initiator concentration Chi, ss = 0.5888 kmol m-3, the following values can be obtained.
Fig. 6. Comparison of reconciled results for the concentration of live polymers in Case Study 1. Fig. 7. Comparison of reconciled results for the concentration of the initiator in Case Study 1.
Fig. 6. Comparison of reconciled results for the concentration of live polymers in Case Study 1. Fig. 7. Comparison of reconciled results for the concentration of the initiator in Case Study 1.
Fig. 8. Comparison of reconciled results for the temperature of reactor in Case Study 1. G. Hu, Z. Zhang and A. Armaou et al./Journal of the Taiwan Institute of Chemical Engineers xxx (xxxx) Xxx
Fig. 8. Comparison of reconciled results for the temperature of reactor in Case Study 1. G. Hu, Z. Zhang and A. Armaou et al./Journal of the Taiwan Institute of Chemical Engineers xxx (xxxx) Xxx
Fig. 9. Comparison of reconciled results for the concentration of the initiator in Case Study 1.
Fig. 9. Comparison of reconciled results for the concentration of the initiator in Case Study 1.
Fig. 10. Comparison of residuals between the estimated values and the true values of the concentration of polystyrene in Case Study 1.
Fig. 10. Comparison of residuals between the estimated values and the true values of the concentration of polystyrene in Case Study 1.
Fig. 12. Comparison of reconciled results for the concentration of live polymers in Case Study 2.
Fig. 12. Comparison of reconciled results for the concentration of live polymers in Case Study 2.
Fig. 13. Comparison of reconciled results for the concentration of the initiator in Case Study 2
Fig. 13. Comparison of reconciled results for the concentration of the initiator in Case Study 2
Fig. 14. Comparison of reconciled results for the temperature of reactor in Case Study 2. G. Hu, Z. Zhang and A. Armaou et al./Journal of the Taiwan Institute of Chemical Engineers xxx (xxxx) Xxx
Fig. 14. Comparison of reconciled results for the temperature of reactor in Case Study 2. G. Hu, Z. Zhang and A. Armaou et al./Journal of the Taiwan Institute of Chemical Engineers xxx (xxxx) Xxx
Fig. 15. Comparison of reconciled results for the concentration of the initiator in Case Study 2.
Fig. 15. Comparison of reconciled results for the concentration of the initiator in Case Study 2.
Fig. 16. Comparison of residuals between the estimated values and the true values of the concentration of polystyrene in Case Study 2.
Fig. 16. Comparison of residuals between the estimated values and the true values of the concentration of polystyrene in Case Study 2.
Fig. 17. Comparison of estimated results for the distribution output of the concentration of polystyrene at the last time point in Case Study 2.
Fig. 17. Comparison of estimated results for the distribution output of the concentration of polystyrene at the last time point in Case Study 2.
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Computer ScienceExtended Kalman FilterMoving Horizon Estimation
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