Inverse optimization-based parameter reconstruction and dynamic behavior identification in industrial process models
Keywords:
Inverse optimization, minimax estimation, differential-algebraic equations, parameter reconstruction, adjoint sensitivity analysis, orthogonal collocation, interior-point methods.Abstract
Accurate reconstruction of unknown physical parameters in dynamic industrial processes remains challenging, particularly when measurements are affected by sudden impacts and bounded disturbances rather than ordinary random noise. Traditional least-squares techniques assume Gaussian errors and may therefore produce biased parameter estimates under the extreme disturbances commonly observed in reactors and separation systems. This study formulates parameter estimation as a minimax inverse optimization problem governed by nonlinear differential-algebraic equations. The outer problem minimizes estimation error with respect to unknown parameters, whereas the inner problem identifies the worst possible disturbance. Tikhonov regularization is included to manage uncertainty and stabilize parameter recovery. The resulting bi-level model is reformulated as a Mathematical Program with Equilibrium Constraints using variational inequality conditions. Solution existence is established through the Ky Fan minimax theorem under compactness assumptions, while Hadamard stability confirms the well-posedness of the inverse problem. Necessary optimality conditions are derived using an adjoint system. The continuous model is discretized through orthogonal collocation, and log-sum-exp smoothing is applied to the nonsmooth minimax terms. The final nonlinear problem is solved using a primal-dual interior-point method with progressive mesh refinement. Case studies involving a continuously stirred-tank reactor and a distillation process produce parameter error norms below 2.03% and a tray-efficiency RMS error of 0.0187. The method improves performance by 54.6% over nonlinear least squares and 47.5% over Kalman filtering, while converging in approximately 30 iterations. These findings demonstrate that minimax inverse optimization provides a rigorous and computationally practical alternative for parameter reconstruction in disturbed nonlinear industrial processes.
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