A grid reconstruction strategy based on pseudo Wigner-Ville analysis for dynamic optimization problem

Weifeng XU; Aipeng JIANG; Haokun WANG; Enhui JIANG; Qiang DING; Hanhan GAO

doi:10.11949/j.issn.0438-1157.20180805

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A grid reconstruction strategy based on pseudo Wigner-Ville analysis for dynamic optimization problem

更新时间：2020-06-24

- A grid reconstruction strategy based on pseudo Wigner-Ville analysis for dynamic optimization problem
- CIESC Journal Issue S1, Pages: 158-167(2019)
- 作者机构：
  
  杭州电子科技大学自动化学院，浙江杭州 310018
- 作者简介：
- 基金信息：
- DOI：10.11949/j.issn.0438-1157.20180805
  CLC： TP 273.1
- Received：10 July 2018，
  
  Revised：2018-09-25，
- 稿件说明：
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徐炜峰, 江爱朋, 王浩坤, 蒋恩辉, 丁强, 高寒寒. 一种基于伪Wigner-Ville分析的动态优化问题网格重构策略[J]. 化工学报, 2019, 70(S1): 158-167

XU Weifeng, JIANG Aipeng, WANG Haokun, JIANG Enhui, DING Qiang, GAO Hanhan. A grid reconstruction strategy based on pseudo Wigner-Ville analysis for dynamic optimization problem[J]. CIESC Journal, 2019, 70(S1): 158-167
徐炜峰, 江爱朋, 王浩坤, 蒋恩辉, 丁强, 高寒寒. 一种基于伪Wigner-Ville分析的动态优化问题网格重构策略[J]. 化工学报, 2019, 70(S1): 158-167 DOI： 10.11949/j.issn.0438-1157.20180805.

XU Weifeng, JIANG Aipeng, WANG Haokun, JIANG Enhui, DING Qiang, GAO Hanhan. A grid reconstruction strategy based on pseudo Wigner-Ville analysis for dynamic optimization problem[J]. CIESC Journal, 2019, 70(S1): 158-167 DOI： 10.11949/j.issn.0438-1157.20180805.

摘要

为了解决控制向量参数化方法逼近精度和计算时间之间的矛盾，提出了一种基于伪Wigner-Ville时频分析的控制向量参数化方法。该方法首先给定较少的网格进行第一次优化迭代，快速获得控制变量的大致轨迹。然后通过伪Wigner-Ville分析得出不同时间网格节点瞬时频率变化对性能指标的影响，籍此对原有网格节点进行重构，包括对时间节点的消除、细化。并且结合变时间节点控制向量参数化方法的思想，将瞬时频率为极大值时对应的时间节点作为待优化参数，与控制变量一同进行求解优化，从而找到准确的最优时间切换点。三个经典的化工反应实例用于验证所提方法，计算结果表明：与传统的控制向量参数化方法和文献结果相比，所提方法可以更有效地重构时间网格，找到准确的时间切换点，不仅计算成本低，而且计算精度更出色。

Abstract

In order to solve the contradiction between approximation accuracy and computation time of control vector parameterization (CVP) method

a control vector parameterization method based on pseudo Wigner-Ville time-frequency analysis is proposed. The method first gives a small number of meshes for the first optimization iteration

and quickly obtains the approximate trajectory of the control variables. Then

through the pseudo Wigner-Ville analysis

the influence of the instantaneous frequency change of the mesh nodes on the performance index is obtained

and the original mesh nodes are reconstructed based on above analysis

including the elimination and refinement of the time nodes. And then combined with the variable time node CVP method

the corresponding time nodes with the maximum instantaneous frequency are used as parameters

which are optimized together with the control variables to find accurate time switching points. Three classical chemical reaction examples are used to verify the proposed method. The calculation results show that compared with the traditional CVP method and literature results

the proposed method can reconstruct the time grid more effectively and find more accurate time switching points

leading to lower calculation cost and more accurate solution.

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references

彭鑫 , 祁荣宾 , 杜文莉 , 等 . 一种改进的知识进化算法及其在化工动态优化中的应用 [J]. 化工学报 , 2012 , 63 ( 3 ): 841 - 850 .

Peng X , Qi R B , Du W L , et al . An improved knowledge evolution algorithm and its application to chemical process dynamic optimization [J]. CIESC Journal , 2012 , 63 ( 3 ): 841 - 850 .

罗雄麟 , 夏车奎 , 孙琳 . 有旁路换热网络全周期节能的动态优化控制实现方法 [J]. 化工学报 , 2013 , 64 ( 4 ): 1340 - 1350 .

Luo X L , Xia C K , Sun L . A dynamic optimization control approach of life cycle energy saving for heat exchanger network with bypasses [J]. CIESC Journal , 2013 , 64 ( 4 ): 1340 - 1350

Zhang B , Chen D , Wu X . Graded optimization strategy and its application to chemical dynamic optimization with fixed boundary [J]. Journal of Chemical Industry & Engineering , 2005 , 56 ( 7 ): 1276 - 1280 .

Rein L . Optimal control by dynamic programming using systematic reduction in grid size [J]. International Journal of Control , 1990 , 51 ( 5 ): 995 - 1013 .

Kirk D E . Optimal control theory: an introduction [J]. Positively Aware the Monthly Journal of the Test Positive Aware Network , 2004 , 23 ( 2 ): 13 - 5 .

Srinivasan B , Palanki S , Bonvin D . Erratum to “Dynamic optimization of batch processes I. Characterization of the nominal solution”: [Computers and Chemical Engineering 27 (2003) 1-26] [J]. Computers & Chemical Engineering , 2003 , 27 ( 5 ): 759 - 760 .

Szymkat M , Korytowski A . Method of monotone structural evolution for control and state constrained optimal control problems [C] // European Control Conference . IEEE , 2015 : 294 - 299 .

Liu P , Li G , Liu X , et al . Novel non-uniform adaptive grid refinement control parameterization approach for biochemical processes optimization [J]. Biochemical Engineering Journal , 2016 , 111 : 63 - 74 .

Binder T , Cruse A , Villar C A C , et al . Dynamic optimization using a wavelet based adaptive control vector parameterization strategy [J]. Computers & Chemical Engineering , 2000 , 24 ( 2 ): 1201 - 1207 .

Schlegel M , Stockmann K , Binder T , et al . Dynamic optimization using adaptive control vector parameterization [J]. Computers & Chemical Engineering , 2005 , 29 ( 8 ): 1731 - 1751 .

Liu P , Liu X . Empirical mode decomposition-based time grid refinement optimization approach for optimal control problems [J]. Optimization Letters , 2017 , 11 ( 7 ): 1243 - 1256 .

Liu P , Li G , Liu X , et al . A novel non-uniform control vector parameterization approach with time grid refinement for flight level tracking optimal control problems [J]. ISA Transactions , 2018 , 73 : 66 - 78 .

Li G , Liu P , Liu X . A control parameterization approach with variable time nodes for optimal control problems [J]. Asian Journal of Control , 2016 , 18 ( 3 ): 976 - 984 .

Teo K L , Jennings L S , Lee H W J , et al . The control parameterization enhancing transform for constrained optimal control problems [J]. Journal of the Australian Mathematical Society , 1999 , 40 ( 3 ): 314 - 335 .

Loxton R C , Teo K L , Rehbock V , et al . Optimal control problems with a continuous inequality constraint on the state and the control ☆ [J]. Automatica , 2009 , 45 ( 10 ): 2250 - 2257 .

Loxton R C , Teo K L , Rehbock V . Optimal control problems with multiple characteristic time points in the objective and constraints ☆ [J]. Automatica , 2008 , 44 ( 11 ): 2923 - 2929 .

Daniel Y C K , Stevens W F . Studies of singular solutions in dynamic optimization (Ⅱ): Optimal singular design of a plug-flow tubular reactor [J]. AIChE Journal , 1971 , 17 ( 1 ): 160 - 166 .

Reddy K V , Husain A . Computation of optimal control policy with singular subarc [J]. Canadian Journal of Chemical Engineering , 1981 , 59 ( 4 ): 557 - 559 .

Luus R . Iterative Dynamic Programming [M]. New York : Chapman & Hall/CRC , 2000 : 767 - 767 .

Gunn D J , Thomas W J . Mass transport and chemical reaction in multifunctional catalyst systems [J]. Chemical Engineering Science , 1965 , 20 ( 2 ): 89 - 100 .

Dadebo S A , Mcauley K B . Dynamic optimization of constrained chemical engineering problems using dynamic programming [J]. Computers & Chemical Engineering , 1995 , 19 ( 5 ): 513 - 525 .

Angira R , Santosh A . Optimization of dynamic systems: a trigonometric differential evolution approach [J]. Computers & Chemical Engineering , 2007 , 31 ( 9 ): 1055 - 1063 .

Li G , Liu X . Comments on “optimal use of mixed catalysts for two successive chemical reactions” [J]. Journal of Optimization Theory & Applications , 2015 , 165 ( 2 ): 678 - 692 .

Lee J , Ramirez W F . Optimal fed‐batch control of induced foreign protein production by recombinant bacteria [J]. Chemical Engineering Science , 1994 , 40 ( 5 ): 899 - 907 .

Tholudur A , Fredramirez W . Obtaining smoother singular arc policies using a modified iterative dynamic programming algorithm [J]. International Journal of Control , 1997 , 68 ( 5 ): 1115 - 1128 .

Sarkar D , Modak J M . Optimization of fed-batch bioreactors using genetic algorithms: two control variables [J]. Chemical Engineering Science , 2003 , 14 ( 11 ): 1127 - 1132 .

Balsa C E , Banga J R , Alonso A A , et al . Dynamic optimization of chemical and biochemical processes using restricted second-order information [J]. Computers & Chemical Engineering , 2001 , 25 ( 4 / 5 / 6 ): 539 - 546 .

Shelokar P S , Jayaraman V K . Multicanonical jump walk annealing assisted by tabu for dynamic optimization of chemical engineering processes [J]. European Journal of Operational Research , 2008 , 185 ( 3 ): 1213 - 1229 .

Zhou Y , Liu X . Control parameterization-based adaptive particle swarm approach for solving chemical dynamic optimization problems [J]. Chemical Engineering & Technology , 2014 , 37 ( 4 ): 692 - 702 .

Zhang P , Liu X , Ma L . Optimal control vector parameterization approach with a hybrid intelligent algorithm for nonlinear chemical dynamic optimization problems [J]. Chemical Engineering & Technology , 2015 , 38 ( 11 ): 2067 - 2078 .

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