Research On Parallelization Of Simulation And Computing Of Complex Mechatronics Systems

With the aid of computer simulation,engineers can optimize design parameters of an industrial product at an early stage of its development cycle,and obtain a reduction in the overall cost and time of the development cycle.It is highly beneficial to accelerate simulation programs,because even simplified models of physical systems can impose a considerable computational load on the processors at hand,and commonly a large number of simulations with different system designs have to be conducted during the development.However,the maximum speed for processors seems to have reached its peak due to issues regarding power dissipation.Manufacturers have begun to build multi-core processors consisting of several cores working in parallel.Therefore,parallelization becomes even more important for accelerating computer programs.A simulation program of a system is essentially a program of solving governing equations of the system.Governing equations of a mechatronics system(i.e.,a mechanism coupled with systems from other domains,e.g.,electronics,hydraulics,pneumatics,and magnetic)are commonly represented by a set of Differential Algebraic Equations(DAEs).Solving the algebraic part of equations often takes up a lion's share of simulation time of an entire simulation program,and therefore parallelization of the algebraic part plays a key role in achieving effective parallelization of the entire simulation program.This thesis investigates methods for parallelizing algebraic-equation-solving-tasks of mechatronics system simulation programs.The research problem is decomposed into three sub-problems described as follows:1)A mechanical system is commonly represented by a set of DAEs of index-3,where position constraint equations are often nonlinear algebraic equations,which are solved using iteration methods.The number of iterations for achieving a certain level of precision of solution for nonlinear algebraic equations is inconstant and unpredictable.That leads to an uncertain amount of computation of solving a set of nonlinear equations.Even worse,the coefficient matrix of unknown variables(namely the Jacobian)of a nonlinear equations is usually time-varying,and can be singular.Therefore,extra computation is required to deal with the singularity problem.In this paper,we present a linearization method to avoid solving nonlinear constraint equations.In the linearization method,direction cosine coordinates are used to substitute a part of relative angle coordinates.Then,with a coordinates partitioning method for solving the governing equations,angle coordinates are eliminated from being made the unknowns of the position constraint equations.Thus,the nonlinearity derived from transcendental functions are removed.However,the orthogonal constraint equations that constrain the direction cosine coordinates are also nonlinear,but are eliminated by being converted into penalty terms added to velocity constraint equations.The constraint equations derived from the new method are all linear,but the same in size(i.e.,number of unknowns)with those generated by the conventional relative coordinate method.The computation amount of linear algebraic equations is relatively constant and can be evaluated.Thus,a static task graph can be obtained for further parallelization.Moreover,by properly selecting unknown variables for position constraint equations,the coefficient matrix of unknowns can be constant and nonsingular.The computation amount of this kind of position constraint equations can be further reduced by converting them to right-hand-side expressions.Numerical experiments are conducted,which show that the new method is good in speed,precision,and stability.2)With coordinate partitioning method,the index of DAEs representing mechanisms is reduced.Thus,simulation of mechatronics systems can be parallelized in a unified method.Most of the algebraic equations of governing equations of a mechatronics system can be transformed into assignment statements through symbolic manipulations,while the rest are coupled forming equation blocks,each of which should be solved as a unit.Each assignment statement or the routine of solving an equation block can seem as a task.Since some of the tasks depend on the results of others,these equation-solving-tasks can be parallelized follow the method for scheduling constrained tasks,which has been extensively studied.However,the fact that most of the tasks are assignment statements and an assignment statement usually has very low computation amount leads to two main difficulties:It is in general difficult to extract parallelism of a large number of constrained tasks;and a high CCR(Communication to Computation Ratio)is introduced due to large run-time overhead(using to launch,track and synchronize tasks),which will further deteriorate the performance.To handle this situation,clustering methods are often employed to merge tasks together,so as to reduce the number and increase the average computation amount of tasks.However,following the clustering methods proposed in current references,tasks that fulfill some certain precedence relationship are merged,without taking the feature of computation amount into consideration.Parallelism among tasks tends to be significantly reduced because the parallel relationship between high computation amount tasks can be changed.To address this problem,a new strategy for clustering algebraic-equation-solving tasks derived from simulation programs of mechatronics systems is developed in this thesis.In the new clustering method,tasks with small computation amount are merged to those of high computation amount,so that the precedence relationship amount "large" tasks remains unchanged and there is no sharp decrease in parallelism.A method for estimating the parallelization performance before clustering is also devised to avoid ineffective parallelization attempts.A large number of numerical experiments(including experiments on benchmark systems in literature)are conducted to demonstrate the effectiveness of the clustering and the estimation methods.3)Even with the clustering method proposed above,a typical mechatronics system might generate a large number of algebraic-equation-solving-tasks.For large size instance of constrained task scheduling problem,experimental results given in literature have shown that advanced searching algorithm(e.g.,Guided-random-search-based algorithms)do not provide significant better solutions than heuristic algorithms do.Therefore,we conjecture that the scheduling methods adopted in current research work do not exploit parallelism effectively in large number of constrained tasks.To prove the conjecture,Cellular Genetic Algorithm(CGA)is firstly extended to the scheduling of constrained tasks.Experiments are performed out.Results show that solutions provided by CGA are significant better than those of methods employed in previous work,and CGA is more robust than BGA.A genetic algorithm has a drawback that it is very time-consuming in solving large instance of scheduling problem.However,to reduce the drawback,GPU based cellular genetic algorithms are presented in this paper.At the end of the text of the thesis,prototype implementations of the proposed methods are introduced,and the effectiveness and value of the methods are demonstrated by an application of a relatively complex mechatronics system.