Study Of Parallel Optimization Algorithms With Engineering Application For Large-scale Structure

As engineering structures become more and more sophisticated with the development ofscience and technology, structural optimization design has gradually replaced the traditionalstructural design methods, and has been used more and more widely in the field ofengineering. Structural optimization design builds structural optimization model according tothe object of structural design, and transforms the structural design process into the solving ofstructural optimization problem. Currently, many structural optimization methods have beendeveloped for solving small-scale and medium-scale structural optimization problems, ofwhich the Augmented Lagrange Multiplier (ALM) method and the Sequential QuadraticProgramming (SQP) method have the best numerical results and have been used most widely.However, when solving the structural optimization problems for large-scale and complexstructures in the field of aviation and aerospace using the ALM method and the SQP method,the amount of computation and storage in optimization iteration would increase dramatically,seriously affecting the computational efficiency. To solve large-scale structural optimizationproblems more efficiently, it’s necessary to improve the ALM method and the SQP method, toreduce the amount of computation and storage greatly and improve computational efficiency,as ensuring global convergence, numerical stability and high accuracy at the same time.In order to develop large-scale structural optimization methods based on gradient, BFGSmethod was studied and improved. First of all, in order to improve the utilization degree ofavailable information and improve the accuracy of approximate Hessian matrix (approximateinverse Hessian matrix), the thesis deduced a new quasi-Newton equation and a new BFGScorrection formula, and thus developed a new BFGS method. Secondly, in order to reduce theamount of computation and storage of BFGS method for solving large-scale unconstrainedoptimization problems, the thesis improved the block diagonal quasi-Newton method, anddeveloped a new block diagonal BFGS method, combining with the new BFGS method.Thirdly, in order to improve the computational efficiency of optimization iteration, the thesisapplied parallel method to the new block diagonal BFGS method and Armijo linear searchmethod, and developed a parallel new block diagonal BFGS method for large-scaleunconstrained optimization problems. The new BFGS method, the new block diagonal BFGSmethod and the parallel new block diagonal BFGS method were validated using25international standard benchmark numerical problems respectively.The thesis applied the parallel new block diagonal BFGS method to the ALM method,and developed an Augmented Lagrange Multiplier method based on parallel new block diagonal BFGS method for large-scale structural optimization problems. First of all, the thesisimproved the commonly used PHR-type Augmented Lagrangian function and the method tobuild sequential unconstrained optimization sub-problems, and built sequential optimizationsub-problems using improved PHR-type Augmented Lagrangian function as objective, andusing design variable limits as constraints. Secondly, the thesis built the approximate inverseHessian matrixes of optimization sub-problems using the new BFGS correction formula, andsolved the optimization sub-problems using modified parallel new block diagonal BFGSmethod and parallel Armijo linear search method. At the same time, in order to improve thecomputational efficiency of optimization iteration, the thesis developed a secondary linearsearch technology for structural optimization problems using weight as design objective, tofurther reduce the value of original objective function after Armijo linear search. Numericalexamples show that the Augmented Lagrange Multiplier method based on parallel new blockdiagonal BFGS method has good convergence and good computational accuracy, and couldimprove computational efficiency significantly.In the research to improve SQP method, the thesis developed a parallel predictorcorrector primal dual interior point sequential convex constraints quadratic programming(SCCQP) method for large-scale structural optimization problems. First of all, in order toimprove the accuracy of approximate sub-problems, the thesis built a convex constraintsquadratic programming (CCQP) sub-problem, using a quadratic function as objective andconvex functions based on mixed variables as constraints. Secondly, in order to reduce theamount of computation and storage in optimization iteration, the thesis developed a parallelpredictor corrector primal dual interior point method to solve the CCQP sub-problem. Thismethod transforms CCQP sub-problem into primal dual equations using primal dual interiorpoint method, and solves primal dual equations using parallel predictor corrector method. Insolving the primal dual equations, the method reduces the dimension of modified Newtonequations using dimensionality reduction technology, and transforms the modified Newtonequations with dimension reduction into almost block diagonal form combining with theparallel new block diagonal BFGS method, and then solves the modified Newton equationswith almost block diagonal form using parallel method. The search direction is achievedaccording to the solution of the CCQP sub-problem, and then parallel Armijo linear searchmethod is used to compute the step factor using Augmented Lagrange function as meritfunction. Numerical examples show that the parallel predictor corrector primal dual interiorpoint SCCQP method has good numerical results, and could improve computationalefficiency greatly. In order to reduce the design variables and constraints which participate in theoptimization iterative computation actually and improve computational efficiency, the thesismade a summary and analysis on the dimensionality reduction techniques for design variablesand constraints screening technology commonly used in structural optimization design, andproposed a technology of regional design variable chain for reducing the number of designvariables.In order to apply the Augmented Lagrange Multiplier method based on parallel newblock diagonal BFGS method and the parallel predictor corrector primal dual interior pointSCCQP method to engineering practice, the thesis developed a set of parallel optimizationsoftware system for large-scale structure. The optimization software system builds structuralfinite element model by CAD/CAE software, inputs the optimization initial information andcontrol parameters through the man-machine interface, and stores the data in finite elementmodel file and optimization file. The parallel optimization program of this optimizationsoftware system is wrote using FORTRAN language and MPI parallel programming model,and could achieve data fetch and management, analytic of equation expression, informationexchange and computation coordination between different computing nodes of parallelcomputer, structural response analysis and sensitivity analysis, constraints screening,optimization iterative computation and output of optimization results.By the optimization software system, on parallel computer including four computers andunder five load cases, the thesis made structural optimization design to T-tail structure, takingthe minimum structural weight as design goal, using the configuration parameters ofstructural components as design variables, using the wingtip deflection and torsion angle ofhorizontal tail, and the stress and strain of the structure as constraints. First of all, the thesisanalyzed the form of structural layout and the force transmission route of the T tail, and builtthe finite element model of the structure. Then, the thesis made design variable partition to thefinite element model, and set constraints. Finally, the thesis implemented optimizationcomputation calling two optimization algorithm modules of the optimization software systemrespectively, and the optimization results were checked and analyzed. The optimization resultsshow that the two structural optimization methods for large-scale structure developed by thethesis have good convergence, high accuracy and high computational efficiency.