The approaches to discrete approximation of Pareto front using multi-objective evolutionary algorithms have the problems of heavy computation burden, long running time and missing Pareto optimal points. In order to overcome these problems, an approach to continuous approximation of Pareto front using geometric support vector regression is presented. The regression model of the small size approximate discrete Pareto front is constructed by geometric support vector regression modeling and is described as the approximate continuous Pareto front. In the process of geometric support vector regression modeling, considering the distribution characteristic of Pareto optimal points, the separable augmented training sample sets are constructed by shifting original training sample points along multiple coordinated axes. Besides, an interactive decision-making(DM)procedure, in which the continuous approximation of Pareto front and decision-making is performed interactively, is designed for improving the accuracy of the preferred Pareto optimal point. The correctness of the continuous approximation of Pareto front is demonstrated with a typical multi-objective optimization problem. In addition,combined with the interactive decision-making procedure, the continuous approximation of Pareto front is applied in the multi-objective optimization for an industrial fed-batch yeast fermentation process. The experimental results show that the generated approximate continuous Pareto front has good accuracy and completeness. Compared with the multi-objective evolutionary algorithm with large size population, a more accurate preferred Pareto optimal point can be obtained from the approximate continuous Pareto front with less computation and shorter running time. The operation strategy corresponding to the final preferred Pareto optimal point generated by the interactive DM procedure can improve the production indexes of the fermentation process effectively.
The soft-sensor modeling for fermentation process based on standard support vector regression(SVR) needs to solve the quadratic programming problem(QPP) which will often lead to large computational burdens, slow convergence rate, low solving efficiency, and etc. In order to overcome these problems, a method of soft-sensor modeling for fermentation process based on geometric SVR is presented. In the method, the problem of solving the SVR soft-sensor model is converted into the problem of finding the nearest points between two convex hulls (CHs) or reduced convex hulls (RCHs) in geometry. Then a geometric algorithm is adopted to generate soft-sensor models of fermentation process efficiently. Furthermore, a swarm energy conservation particle swarm optimization (SEC-PSO) algorithm is proposed to seek the optimal parameters of the augmented training sample sets, the RCH size, and the kernel function which are involved in geometric SVR modeling. The method is applied to the soft-sensor modeling for a penicillin fermentation process. The experimental results show that, compared with the method based on the standard SVR, the proposed method of soft-sensor modeling based on geometric SVR for fermentation process can generate accurate soft-sensor models and has much less amount of computation, faster convergence rate, and higher efficiency.
State estimation is the precondition and foundation of a bioprocess monitoring and optimal control. However,there are many difficulties in dealing with a non-linear system,such as the instability of process, un-modeled dynamics,parameter sensitivity,etc.This paper discusses the principles and characteristics of three different approaches,extended Kalman filters,strong tracking filters and unscented transformation based Kalman filters.By introducing the unscented transformation method and a sub-optimal fading factor to correct the prediction error covariance,an improved Kalman filter,unscented transformation based robust Kalman filter,is proposed. The performance of the algorithm is compared with the strong tracking filter and unscented transformation based Kalman filter and illustrated in a typical case study for glutathione fermentation process.The results show that the proposed algorithm presents better accuracy and stability on the state estimation in numerical calculations.
An iterative optimization strategy for fed-batch fermentation process is presented by combining a run-to-run optimization with swarm energy conservation particle swarm optimization (SEC-PSO). SEC-PSO, which is designed with the concept of energy conservation, can solve the problem of premature convergence frequently appeared in standard PSO algorithm by partitioning its population into several sub-swarms according to the energy of the swarm and is used in the optimization strategy for parameter identification and operation condition optimization. The run-to-run optimization exploits the repetitive nature of fed-batch processes in order to deal with the optimal problems of fed-batch fermentation process with inaccurate process model and unsteady process state. The kinetic model parameters, used in the operation condition optimization of the next run, are adjusted by calculating time-series data obtained from real fed-batch process in the run-to-run optimization. The simulation results show that the strategy can adjust its kinetic model dynamically and overcome the instability of fed-batch process effectively. Run-to-run strategy with SEC-PSO provides an effective method for optimization of fed-batch fermentation process.
