Large-scale Nonlinear Processes Research Articles

Multi-level optimization strategies for large-scale nonlinear process systems

With growing needs to develop and improve climate-friendly processes, optimization strategies are essential at all levels of decision-making in chemical and energy processes, including process development, process synthesis and design, as well as process operations, control, scheduling, and planning. Challenges include the formulation of well-posed and well-conditioned process models, and development and application of efficient, reliable optimization algorithms. Here we describe a synthesis of optimization concepts and algorithms that enable large-scale nonlinear programming, nonintrusive decomposition strategies and the inclusion of a wide class of surrogate models. All of these are crucial to address challenging nonconvex, multi-scale problems in Computer Aided Process Engineering (CAPE). These elements are demonstrated through dynamic optimization strategies for novel energy generation, demand-based optimization for specialty chemicals, and optimization with integrated heterogeneous models for carbon capture processes.

Distributed incipient fault detection with causality-based multi-perspective subblock partitioning for large-scale nonlinear processes

Detecting incipient faults is a crucial task in complex large-scale nonlinear industrial processes. However, conventional distributed frameworks encounter challenges in identifying appropriate subblock partitioning methods. To address this problem, we propose a novel distributed incipient fault detection method, called CMPSP-MKPCA, based on causal relationship multi-perspective subblock partitioning (CMPSP) and modified kernel principal component analysis (MKPCA), facilitating incipient fault detection in large-scale nonlinear processes. Firstly, considering the property of incipient faults to undergo limited propagation among process flow connections, we obtain fine-grainehe direction of potential incipient fault information propagation. Secondly, the design of multi-perspective detection blocks provides real-time selection of sub-block delineation results to adapt to the different needs of incipient faults during latency and transition periods. Thirdly, local detection is realized by combining the Modified KPCA method and Kullback-Leibler divergence (KLD), while the global detection statistics is obtained by Bayesian inference fusion. Simulation experiments based on the continuous stirred tank reactor (CSTR) system and the Tennessee Eastman (TE) system verify the effectiveness and superiority of the method.

Zero-order moving horizon estimation for large-scale nonlinear processes

Moving Horizon Estimation (MHE) is an optimization-based approach to nonlinear state estimation where the state estimate is obtained as the solution of a nonlinear optimization problem. Especially for large-scale nonlinear systems, the computational burden associated with the numerical solution of nonlinear optimization problems poses a major challenge when applying MHE in practice. To alleviate the computational effort, we propose an inexact, but computationally less expensive variant of the Gauss–Newton algorithm tailored to the nonlinear least-squares problem arising from the MHE formulation. The proposed algorithm combines two ideas: On the one hand, it uses the fact that the arrival cost matrix appears naturally within the Gauss–Newton Hessian approximation in order to avoid any explicit arrival cost update. On the other hand, the method follows a zero-order optimization approach, where fixed sensitivity approximations are used in order to reduce the number of sensitivity evaluations, while accepting some loss of optimality. The combination of these two ideas allows one to reuse the factorizations of the Hessian blocks associated with each stage, when moving from one MHE problem to the next, therefore significantly reducing the computational complexity. Additionally, a tailored integration method for large-scale stiff systems is proposed that can efficiently propagate approximate forward sensitivities, which are used within the inexact MHE algorithm. Both estimation accuracy and computational efficiency of the proposed method are evaluated by applying it to two case studies: a small-scale batch reactor model and the large-scale dynamic process of acrylic acid production.

Performance-driven optimal design of distributed monitoring for large-scale nonlinear processes

Centralized monitoring generally involves all measured variables in one model. However, the existence of variables without beneficial information may cause redundancy in the monitoring and degrade monitoring performance. This paper proposes a performance-driven distributed monitoring scheme that incorporates kernel principal analysis (KPCA) and Bayesian diagnosis system for large-scale nonlinear processes. First, a stochastic optimization method is utilized to select a subset of variables that provide the best possible performance for each fault and to decompose the process into several sub-blocks. Second, a KPCA model is established in each block to deal with nonlinearity and generate fault signature evidence. Finally, a Bayesian fault diagnosis system is established to identify the fault status of the entire process. Considering the significant calculation amount in Bayesian diagnosis, optimal evidence source selection is performed to reduce the redundancy. Case studies on the Tennessee Eastman benchmark process and a continuous stirred tank reactor process demonstrate the efficiency of the proposed scheme.

Application of MHE to large-scale nonlinear processes with delayed lab measurements

The paper addresses nonlinear estimation problems on nonlinear processes containing several lab measurements sampled slowly and with long delay, which is the usual case in industrial polymerization applications. A moving horizon estimation algorithm is developed to compute the theoretical optimal solution given the multi-rate measurements. In this algorithm, the MHE window is recalculated as the new lab measurement becomes available. Simulation studies on a polymerization process with plant model mismatch are performed. Observability analysis and estimation results of MHE with and without lab measurements show that lab measurements help identify the disturbances and can improve the performance of both estimation and closed-loop control.

Modelling and identification for highly nonlinear processes

This paper is devoted to modelling and identification of nonlinear dynamic systems. At first, we propose a new input–output representation to describe highly and/or large-scale nonlinear processes. The proposed mathematical model is nonlinear in parameters and is written as a product of several polynomials which may be selected in a sequential approach. In the second part of this note, a simple and recursive identification technique is detailed. It is shown that, under strong persistently exciting condition, global convergence of the parameters estimation algorithm is guaranteed. One of the main results of this contribution is that parameters to be estimated are considerably reduced in comparison with the general Kolmogorov–Gabor structure.