PCAGA: Principal component analysis based genetic algorithm for solving conditional nonlinear optimal perturbation

Conditional nonlinear optimal perturbation (CNOP) is an extension of linear singular vector(LSV) to nonlinear optimization. Generally, CNOP is solved with such adjoint based algorithms as SPG2, SQP. Unfortunately, it is often difficult to obtain the corresponding adjoint models for some nonlinear models. In addition, for nonlinear models containing discontinuous “on-off” switches, the adjoint based methods can hardly find the correct gradient direction for solving the CNOP. These two factors restrict the application of CNOP. Intelligence algorithms are utilized to handle these problems and has made some improvements. Nevertheless, the intelligent method cannot be applied to solve CNOP of complex models due to its dimensional limitation. Therefore, the principal component analysis based genetic algorithm (PCAGA) is proposed to solve the CNOP of complex models. The PCAGA is composed of two key processes: dimension reduction and genetic optimization. To demonstrate the validity, PCAGA is applied to solve the CNOP of the Zebiak-Cane (ZC) model for studying ENSO predictability and compared with the adjoint based method. Experimental results show that PCAGA can achieve similar results to the adjoint based method in the high-dimensional space of a medium- complexity model without the adjoint models. The proposed method also can future be applied to solve variational data assimilation (VDA).

[1]  Mu Mu,et al.  Influence of conditional nonlinear optimal perturbations sensitivity on typhoon track forecasts , 2012 .

[2]  B. Moore.  Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

[3]  Fevrier Valdez,et al.  Modular Neural Networks architecture optimization with a new nature inspired method using a fuzzy combination of Particle Swarm Optimization and Genetic Algorithms , 2014, Information Sciences.

[4]  Bin Wang,et al.  Conditional nonlinear optimal perturbations as the optimal precursors for El Nino–Southern Oscillation events , 2004 .

[5]  M. Mu.  Nonlinear singular vectors and nonlinear singular values , 2000 .

[6]  Bin Wang,et al.  Conditional Nonlinear Optimal Perturbations: Adjoint-Free Calculation Method and Preliminary Test , 2010 .

[7]  方昌銮,et al.  THE EFFECTIVENESS OF GENETIC ALGORITHM IN CAPTURING CONDITIONAL NONLINEAR OPTIMAL PERTURBATION WITH PARAMETERIZATION “ON-OFF” SWITCHES INCLUDED BY A MODEL , 2009 .

[8]  The effects of the model errors generated by discretization of , 2006 .

[9]  Wang Hong.  A Preliminary Application of Conditional Nonlinear Optimal Perturbation to Adaptive Observation , 2007 .

[10]  F. Jin,et al.  The Pacific Cold Tongue and the ENSO mode: a unified theory within the Zebiak-Cane model , 2000 .

[11]  Hui Xu,et al.  The Tangent Linear Model and Adjoint of a Coupled Ocean-Atmosphere Model and Its Application to the Predictability of ENSO , 2006, IGARSS.

[12]  Zhou Fei-fan.  The Study of Conditional Nonlinear Optimal Perturbation's Application in Typhoon Over the South China Sea , 2010 .

[13]  Oscar Castillo,et al.  Fuzzy System Optimization Using a Hierarchical Genetic Algorithm Applied to Pattern Recognition , 2014, IEEE Conf. on Intelligent Systems.

[14]  M. Mu.  Applications of Conditional Nonlinear Optimal Perturbation to the Studies of Predictability Problems , 2013 .

[15]  Hui Xu,et al.  Dynamics of nonlinear error growth and season‐dependent predictability of El Niño events in the Zebiak–Cane model , 2009 .

[16]  Jidong Gao,et al.  Generalized Adjoint for Physical Processes with Parameterized Discontinuities. Part V: Coarse-Grain Adjoint and Problems in Gradient Check , 1998 .

[17]  Fang Chang-luan.  THE EFFECTIVENESS OF GENETIC ALGORITHM IN CAPTURING CONDITIONAL NONLINEAR OPTIMAL PERTURBATION WHEN PARAMETERIZATION "ON-OFF" SWITCHES ARE INCLUDED BY MODEL , 2009 .

[18]  W. Duan,et al.  Contribution of the location and spatial pattern of initial error to uncertainties in El Niño predictions , 2012 .

[19]  Mu Mu,et al.  Investigating a nonlinear characteristic of El Niño events by conditional nonlinear optimal perturbation , 2009 .

[20]  M. Mu,et al.  Zigzag Oscillations in Variational Data Assimilation with Physical “On–Off” Processes , 2005 .

[21]  Hui Xu,et al.  Decisive role of nonlinear temperature advection in El Nino and La Nina amplitude asymmetry , 2008 .

[22]  Hui Xu,et al.  A SVD-based ensemble projection algorithm for calculating the conditional nonlinear optimal perturbation , 2015, Science China Earth Sciences.

[23]  Donghai Wang,et al.  A study on precursors to blocking anomalies in climatological flows by using conditional nonlinear optimal perturbations , 2010 .

[24]  Mu Mu,et al.  A new approach to studying ENSO predictability: Conditional nonlinear optimal perturbation , 2003 .

[25]  Tan Xiaowei.  A fast algorithm to obtain CNOP and its preliminary tests in a target observation experiment of typhoon , 2009 .

[26]  Zheng Qin.  Improved Particle Swarm Optimization Algorithms for Conditional Nonlinear Optimal Perturbation , 2011 .

[27]  Hui Xu,et al.  Behaviors of nonlinearities modulating the El Niño events induced by optimal precursory disturbances , 2013, Climate Dynamics.

[28]  Bin Wang,et al.  Conditional nonlinear optimal perturbation and its applications , 2003 .

[29]  Xiaoqing Lu,et al.  A variant constrained genetic algorithm for solving conditional nonlinear optimal perturbations , 2014, Advances in Atmospheric Sciences.

[30]  Fernando Paganini,et al.  IEEE Transactions on Automatic Control , 2006 .

[31]  Mu Mu,et al.  Conditions under which CNOP sensitivity is valid for tropical cyclone adaptive observations , 2013 .

[32]  W. Duan,et al.  Exploring the initial errors that cause a significant “spring predictability barrier” for El Niño events , 2009 .

[33]  Hongyu Li,et al.  PPSO: PCA based particle swarm optimization for solving conditional nonlinear optimal perturbation , 2015, Comput. Geosci..

[34]  Lü Xiao-Qing.  The feasibility of genetic algorithm for solving maximum prediction errors , 2011 .

[35]  Qiang Wang,et al.  An extension of conditional nonlinear optimal perturbation approach and its applications , 2010 .

[36]  Lei Chen,et al.  SAEP: Simulated Annealing Based Ensemble Projecting Method for Solving Conditional Nonlinear Optimal Perturbation , 2014, ICA3PP.