Model-free real-time optimization of process systems using safe Bayesian optimization

Conventional real-time optimization (RTO) requires detailed process models, which may be challenging or expensive to obtain. Model-free RTO methods are an attractive alternative to circumvent the challenge of developing accurate models. Most model-free RTO methods are based on estimating the steady-state cost gradient with respect to the decision variables and driving the estimated gradient to zero using integral action. However, accurate gradient estimation requires clear time scale separation from the plant dynamics, such that the dynamic plant can be assumed to be a static map. For processes with long settling times, this can lead to prohibitively slow convergence to the optimum. To avoid the need to estimate the cost gradients from the measurement, this article uses Bayesian optimization, which is a zeroth order black-box optimization framework. In particular, this article uses a safe Bayesian optimization based on interior point methods to ensure that the setpoints computed by the model-free steady-state RTO layer are guaranteed to be feasible with high probability (i.e., the safety-critical constraints will not be violated at steady-state). The proposed method can thus be seen as a model-free variant of the conventional two-step steady-state RTO framework (with steady-state detection), which is demonstrated on a benchmark Williams-Otto reactor example.     

设计余量对运行优化和化学过程控制性能的影响简

Operation optimization is an effective method to explore potential economic benefits for existing plants. The m.aximum potential benefit from operationoptimization is determined by the distances between current operating point and process constraints, which is related to the margins of design variables. Because of various ciisturbances in chemical processes, some distances must be reserved for fluctuations of process variables and the optimum operating point is not on some process constraints. Thus the benefit of steady-state optimization can not be fully achied（ed while that of dynamic optimization can be really achieved. In this study, the steady-state optimizationand dynamic optimization are used, and the potential benefit-is divided into achievable benefit for profit and unachievable benefit for control. The fluid catalytic cracking unit （FCCU） is used for case study. With the analysis on how the margins of design variables influence the economic benefit and control performance, the bottlenecks of process design are found and appropriate control structure can be selected.     

A multi-priority hierarchical optimization method for double-layer model predictive control

Considering the demand for the sequential regulation of manipulated variables in actual industrial process control, the conventional solution of double-layer model predictive control faces the problem that the weight coefficients are difficult to tune. This paper proposes an improved hierarchical optimization method for manipulated variables in the steady-state optimization layer of double-layer model predictive control. The proposed method can adjust the manipulated variables sequentially without an accurate weight coefficient to avoid difficulty in tuning the weight coefficients. The relation between the optimal solution and the feasible region of the steady-state optimization layer is analysed to describe the reoptimization of the key manipulated variables. The impact of the economic cost coefficient on the optimal solution with the sensitivity analysis method is studied, and the complexity of using the weight coefficient to solve the priority optimization problem of the manipulated variables is assessed. The steady-state optimization solution procedure is improved based on the theory of the multiobjective complete hierarchical method. The hierarchical and sequential optimization of the manipulated variables results in expanding the space and freedom of the key manipulated variables, increasing efficiency, reducing consumption, and improving economic performance. The improved hierarchical optimization method is direct and simple in achieving optimization sequentially and satisfies the need for adjusting the manipulated variables according to human intentions.     

GAMS supported optimization and predictability study of a multi-objective adsorption process with conflicting regions of optimal operating conditions

In process systems engineering, it is critical to design an effective and optimized process in a short period with minimum experimental trials. However, improvement of some process variables may deteriorate some other criteria due to conflicting regions of factor interests for optimal solution in multi-objective optimization (MOO) processes. Here, the global optimization of an adsorption case study with conflicting optimal solutions based on multi-objective Response Surface Methodology (RSM) design is facilitated with the implementation of BARON solver based on General Algebraic Modeling System (GAMS) with identical factor variables, levels, and model equations. RSM suggested fifteen different optimum settings of which the validation is quite expensive and onerous, whereas GAMS suggested a single optimum setting which makes it more economically viable especially for large scale systems. In addition, the GAMS-based optimization provided more accurate and reliable results when experimentally validated as compared to the RSM-based solution.     

Generalized initialization for the dynamic simulation and optimization of grade transition processes using two-dimensional collocation

Optimization modeling tools are essential to determine optimal design specifications and operation conditions of polymerization processes, especially when quality indices based on molecular weight distributions (MWDs) must be enforced. This study proposes a generalized MWD-based optimization strategy using orthogonal collocation in two dimensions, which can capture the dynamic features of MWDs accurately. To enable the strategy, this study considers generalized initialization methods for large-scale simulation and optimization. Here, a homotopy method based on intermediate solutions is adopted to generate initial values for general steady-state simulation models, starting from an arbitrary known solution for any steady-state simulation model. For dynamic simulation models, the response of a first-order linear system is adopted to initialize the state variables. Case studies show the effectiveness of this procedure to enable systematic, reliable, and efficient solution of the optimization problem.     

Optimization of multistage recycle systems by direct search

Optimal operation of chemical systems with recycle is considered. An optimization procedure, whereby the control variables are obtained by direct search, is developed. Suitability of this method for optimizing chemical engineering systems with recycle is tested by considering three systems of different complexity. Results close to the optimum were obtained in each case. For complex systems, however, care must be taken to ensure that global and not local optimum is obtained. Due to the ease of formulation and of programming, the proposed method provides an attractive alternative to the combined use of the gradient method and Lagrange multipliers.     

Explicit model predictive control of hybrid systems and multiparametric mixed integer polynomial programming

Hybrid systems are dynamical systems characterized by the simultaneous presence of discrete and continuous variables. Model‐based control of such systems is computationally demanding. To this effect, explicit controllers which provide control inputs as a set of functions of the state variables have been derived, using multiparametric programming mainly for the linear systems. Hybrid polynomial systems are considered resulting in a Mixed Integer Polynomial Programming problem. Treating the initial state of the system as a set of bounded parameters, the problem is reformulated as a multiparametric Mixed Integer Polynomial optimization (mp‐MIPOPT) problem. A novel algorithm for mp‐MIPOPT problems is proposed and the exact explicit control law for polynomial hybrid systems is computed. The key idea is the computation of the analytical solution of the optimality conditions while the binary variables are treated as relaxed parameters. Finally, using symbolic calculations exact nonconvex critical regions are computed. © 2016 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 62: 3441–3460, 2016     

一种化工过程优化的稀疏SQP算法

根据开放式方程模型结构统一、所得优化命题普遍稀疏的特点 ,提出了一种稀疏SQP算法 .利用一阶 /二阶导数构造Hessian矩阵 ,保持了系统的稀疏结构 .通过一个预处理过程获得命题的稀疏结构信息 ,显著减少构造高维矩阵所需工作量 .计算示例表明 ,该算法优于传统SQP法 ,也表明该算法的有效性     

A fault magnitude based strategy for effective fault classification

A common approach in fault diagnosis is monitoring the deviations of measured variables from the values at normal operations to identify the root causes of faults. When the number of conceivable faults is larger than that of predictive variables, conventional approaches can yield ambiguous diagnosis results including multiple fault candidates. To address the issue, this work proposes a fault magnitude based strategy. Signed digraph is first used to identify qualitative relationships between process variables and faults. Empirical models for predicting process variables under assumed faults are then constructed with support vector regression (SVR). Fault magnitude data are projected onto principal components subspace, and the mapping from scores to fault magnitudes is learned via SVR. This model can estimate fault magnitudes and discriminate a true fault among multiple candidates when different fault magnitudes yield distinguishable responses in the monitored variables. The efficacy of the proposed approach is illustrated on an actuator benchmark problem.     

Continuous global optimization of structured process systems models

Nonconvex models for the optimization of process systems in chemical engineering give rise to multiple suboptimal solutions, and a number of complications that often cause failure of standard local optimization techniques. A deterministic branch and bound algorithm is presented in this paper for the global optimization of structured process systems models that include non-convexities introduced by concave univariate, bilinear and linear fractional terms. The proposed branch and contract algorithm relies on a bounds contraction operation, which consists of the solution of a finite sequence of convex bounds-contraction subproblems for the subset of nonconvex variables in a problem. The application of the proposed algorithm is illustrated with several numerical examples, which include heat exchanger networks, chemical reactors, simplified process flowsheets, and waste-water treatment systems. The results show that by executing the contraction operation at selected branch and bound nodes, large portions of the search region over which the objective function takes only values above a known upper bound are eliminated. It is shown that with the proposed approach the total number of nodes in the solution tree is kept relatively small, and for some problems, no branching is required at all.     

Global optimization based on subspaces elimination: Applications to generalized pooling and water management problems

A global optimization strategy based on the partition of the feasible region in boxed subspaces defined by the partition of specific variables into intervals is described. Using a valid lower bound model, we create a master problem that determines several subspaces where the global optimum may exist, disregarding the others. Each subspace is then explored using a global optimization methodology of choice. The purpose of the method is to speed up the search for a global solution by taking advantage of the fact that tighter lower bounds can be generated within each subspace. We illustrate the method using the generalized pooling problem and a water management problem, which is a bilinear problem that has proven to be difficult to solve using other methods. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2336–2345, 2012     

Aspen Plus模拟在氟化工中的应用研究

Aspen Plus是生产装置设计、稳态模拟和优化的大型通用流程模拟系统。全球各大化工、石化、炼油等过程工业制造企业及著名的工程公司都是Aspen Plus的用户。举例介绍了Aspen Plus模拟在氟化工中的应用,分析可能存在的困难,并展望Aspen Plus模拟在氟化工中的应用前景。     

基于信赖域算法的精馏塔优化

从结构优化角度建立精馏塔优化的混合整数非线性规划(MINLP)模型,为了消除整数变量,引入绕流效率将MINLP问题转化为非线性规划(NLP)问题。针对得到的NLP问题提出一种优化方法,在该方法中采用结构优化中常用的信赖域优化算法进行求解,并应用虚拟瞬态连续性方程辅助优化中的稳态模拟。采用提出的优化方法对3个精馏系统进行设计优化,以不同初始值开始,均可得到令人满意的优化结果,表明所提优化方法具有良好的稳健性,对于较复杂的部分热耦合精馏过程仍然可以有效优化求解;信赖域算法在精馏塔优化中也表现出良好的收敛性。     

A modified iterative IOM approach for optimization of biochemical systems

The presented previously indirect optimization method (IOM) developed within biochemical systems theory (BST) provides a versatile and mathematically tractable optimization strategy for biochemical systems. However, due to the local approximations nature of the BST formalism, the iterative version of this technique possibly does not yield the true optimum solution. In this work, an algorithm is proposed to obtain the correct and consistent optimum steady-state operating point of biochemical systems. The existing linear optimization problem of the direct IOM approach is modified by adding an equality constraint of describing the consistency of solutions between the S-system and the original model. Lagrangian analysis is employed to derive the first order necessary optimality conditions for the above modified optimization problem. This leads to a procedure that may be regarded as a modified iterative IOM approach in which the optimization objective function includes an extra linear term. The extra term contains a comparison of metabolite concentration derivatives with respect to the enzyme activities between the S-system and the original model and ensures that the new algorithm is still carried out within linear programming techniques. The presented framework is applied to several biochemical systems and shown to the tractability and effectiveness of the method. The simulation is also studied to investigate the convergence properties of the algorithm and to give a performance comparison of standard and modified iterative IOM approach.     

化工过程预测控制的在线优化实现机制

多层结构的预测控制已逐渐成为工业过程控制领域的主流控制方案。在此控制架构基础上,根据操作工或工艺优化所给定期望值的不同,将稳态优化问题具体化为两种基本情况,并对此提出基于复合目标函数的优化问题,可针对不同过程要求退化为线性、二次或二者兼有的优化问题形式。为保证最优目标的可行性并在一定程度上避免关键变量饱和,对不可行的期望值适当调整。将所得最优目标增量化处理后送入模型预测控制动态控制层,确保了上下层之间变量传递的一致性。包含约束的全混槽反应器系统仿真实例表明,流程的优化实现层可针对不同的过程要求有效给出最优目标以便动态控制,说明了该优化流程的可行性。     

Integrating process and controller models for the design of self-optimizing control

The steady-state behavior of an existing plant depends on the independent input variables, process equipment and process controllers. This paper presents a method for formulating models that represent the effects of controllers when they are included within a steady-state process flowsheet. The method replaces the controller equations with the equivalent stationarity conditions representing the relationship between the controlled variables and the implemented manipulated variables at steady state. The method is demonstrated for the centralized multivariable Dynamic Matrix Control algorithm applied to two processes, binary distillation and gasoline blending. The integrated process and control system simulation is used to design controllers that improve the profitability of processes without extensive real-time calculations; this is sometimes termed self-optimizing control. For both processes, controllers were designed that yielded higher profit than standard control methods and that approached the highest possible profit achieved by frequent real-time optimization.     

基于子系统关联变量轮换的大系统在线协调优化

化工过程复杂大系统的在线优化过程中,存在流程前后的关联导致优化时间过长或得不到优化解的问题,需要按子系统优化并协调的优化方法来解决,而协调优化方法存在关联变量寻优方向不一致的问题。提出了一种基于子系统间关联变量轮换思想的分解协调优化方法,对大系统分解得到的子系统以轮换的方式进行优化,子系统中包含的多个优化问题分别在固定关联变量优化独立变量和固定独立变量优化关联变量的条件下求解,此轮换过程迭代进行,直至满足优化终止条件。将提出的方法应用在催化裂化装置仿真实例中与整体优化方法的结果作比较,证明了方法的有效性。最后,将基于关联变量轮换的协调优化方法应用在化工过程的在线优化中,结果表明本方法在在线优化应用中是可行的。     

A time-averaged model for gas-solids flow in a one-dimensional vertical channel

In this study, we are interested in deriving time-smoothed governing and constitutive equations for gas-solids flow in moderately dense systems where particle-particle collision is the main energy dissipation mechanism. Results obtained from dynamic simulations of a gas-solids flow in a 1D channel are used to show that it is possible to obtain expressions for the time-averaged constitutive relations based on Taylor series expansion. We demonstrate, by comparing with time-averaged transient results, that the 1st term (or laminar) in the series expressions of most non-linear constitutive relations can yield inaccurate quantitative and qualitative results. This means that steady-state models derived by simply removing the partial time derivative from the governing equations are not suitable for gas-solids flows. This study shows that it was necessary to include many terms of the Taylor series expression of non-linear constitutive relations (such as the granular energy dissipation term) due to large-scale oscillations that were computed for all flow variables at all locations in the 1D domain. In some cases, the Taylor series expansion diverged and the Euler transformation was used to improve the convergence of these series. In this moderately dense flow system, turbulence in the gas-phase was found to be just a reaction to turbulence in the solids phase that resulted from the large-scale motion of solids clusters. This resulted in a negative turbulent gas viscosity computed due to the fact that gas (in the horizontal direction) flows only to occupy regions vacated by clusters of solids. The steady-state results obtained using the time-smoothed gas-solids flow model compared well with the time-averaged results obtained using the transient model for all flow variables.     

化工过程总体裕量与控制性能的权衡优化

化工过程的总体裕量可以用操作优化的经济效益进行评价,根据稳态优化和动态优化的经济效益可进一步划分为服务于操作控制的控制裕量和表征过程可实现经济效益的工艺裕量,二者都与化工过程的控制性能有关。针对具有一定裕量的化工过程进行多目标动态优化,优化目标分别为操作点的经济效益与动态过程中的控制性能指标,采用0-1变量描述控制结构,将控制结构和控制器参数也作为优化变量进行混合整数动态优化,采用Constrained NSGA-Ⅱ算法求解非劣解集,根据非劣解集分析总体工艺裕量、总体控制裕量与控制性能指标的关系。通过催化裂化装置的实例分析发现,对于具有一定裕量的化工过程,控制性能越高,所需的总体控制裕量越多,表征操作优化可实现经济效益的总体工艺裕量越少,只有通过对总体控制裕量和总体工艺裕量进行权衡,才能找到兼顾工艺要求和控制性能的工艺操作点和控制设计方案。     

Nonlinear variable selection algorithms for surrogate modeling

Having the ability to analyze, simulate, and optimize complex systems is becoming more important in all engineering disciplines. Decision-making using complex systems usually leads to nonlinear optimization problems, which rely on computationally expensive simulations. Therefore, it is often challenging to detect the actual structure of the optimization problem and formulate these problems with closed-form analytical expressions. Surrogate-based optimization of complex systems is a promising approach that is based on the concept of adaptively fitting and optimizing approximations of the input–output data. Standard surrogate-based optimization assumes the degrees of freedom are known a priori; however, in real applications the sparsity and the actual structure of the black-box formulation may not be known. In this work, we propose to select the correct variables contributing to each objective function and constraints of the black-box problem, by formulating the identification of the true sparsity of the formulation as a nonlinear feature selection problem. We compare three variable selection criteria based on Support Vector Regression and develop efficient algorithms to detect the sparsity of black-box formulations when only a limited amount of deterministic or noisy data is available.