Detection of linearly dependent and inconsistent equations in process system models

doi:10.3969/j.issn.0438-1157.2013.12.023

›› 2013, Vol. 64 ›› Issue (12): 4422-4426.DOI: 10.3969/j.issn.0438-1157.2013.12.023

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Detection of linearly dependent and inconsistent equations in process system models

WANG Kexin¹, SHAO Zhijiang¹, Lorenz T.Biegler²

1. Department of Control Science and Engineering, Zhejiang University, Hangzhou 310027, Zhejiang, China;
2. Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA

Received:2013-05-31 Revised:2013-08-20 Online:2013-12-05 Published:2013-12-05
Supported by:
supported by the National Basic Research Program of China (2012CB720503)，the High-tech Research and Development Program of China (2012AA040305)，the National Natural Science Foundation of China (61104134，61273085) and the Natural Science Foundation of Zhejiang Province (Y1110243).

系统模型中线性相关矛盾方程的检测方法

王可心¹, 邵之江¹, Lorenz T.Biegler²

1. 浙江大学控制科学与工程学系, 浙江杭州 310027;
2. Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA

通讯作者: 邵之江
作者简介:王可心（1974- ），女，博士。
基金资助:
国家重点基础研究发展计划项目（2012CB720503）；国家高技术研究发展计划项目（2012AA040305）；国家自然科学基金项目（61104134，61273085）；浙江省自然科学基金项目（Y1110243）。

Abstract

Abstract: Simulation and optimization based on equation-oriented models benefit the most from advanced modeling and optimization methods.However,linearly dependent and inconsistent constraints that arise from poor models or nonlinear programming (NLP) algorithms result in failure in practice.A method to detect the inconsistent constraints in this case is proposed.The detection is based on the infeasible system identification of NLP solvers and takes advantage of the structure of linearly dependent systems.Efficiency of the detection process can be improved significantly through proper linear solver invocations.Numerical experiments on examples derived from CUTE and COPS test sets demonstrate the effectiveness of the proposed method.

Key words: linearly dependent system, inconsistency detection, feasibility restoration

摘要： 基于开放方程的模拟与优化能够充分体现先进的建模与优化技术在过程系统工程中的应用优势。但是由于建模错误或者优化算法本身导致的线性相关的系统模型，可能构成不相容的约束集合最终使求解失败。对这种情况提出了矛盾约束集合的检测方法。该方法与非线性规划（NLP）算法对不可行系统的识别相结合，利用线性相关系统的结构特征，对不可行驻点处的线性系统进行分析和检测。在此过程中通过合理利用线性求解器能够显著提高矛盾约束检测的效率。基于CUTE/COPS算例构造基于线性相关不相容模型的优化问题并进行矛盾约束检测，数值结果验证了本文提出方法的有效性。

关键词: 线性相关系统, 矛盾检测, 可行性恢复

CLC Number:

TQ021.8

WANG Kexin, SHAO Zhijiang, Lorenz T.Biegler. Detection of linearly dependent and inconsistent equations in process system models[J]. , 2013, 64(12): 4422-4426.

王可心, 邵之江, Lorenz T.Biegler. 系统模型中线性相关矛盾方程的检测方法[J]. CIESC Journal, 2013, 64(12): 4422-4426.

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Detection of linearly dependent and inconsistent equations in process system models

系统模型中线性相关矛盾方程的检测方法

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