S0214 : GPU Based Stacking Sequence Generation For Composite Skins Using GA

Transcription

1 S0214 : GPU Based Stacking Sequence Generation For Composite Skins Using GA Date: 16th May 2012 Wed, 3pm to 3.25pm(Adv. Session) Sathyanarayana K., Manish Banga, and Ravi Kumar G. V. V. Engineering Services, Infosys Limited, Electronic City, Hosur Road, Bangalore, India 1

2 Contents: GPU Based Stacking Sequence Generation For Composite Skins Using GA Overview Composite Skin Engineering - Overview. Optimization of Aircraft Composite Skins Part1 Assumptions Decision variables, Objective, constraints Genetic Algorithms Based Composite Part2 Stacking Sequence Generation Approach Encoding and Decoding, Initial solutions generation Improving the solutions :Genetic Algorithm Operators Convergence Criteria Speedup using GPU Part3 Graphics processing Unit(GPU) and data parallel applications Method of using CUDA based GPU and Flow chart Speed up achieved and Observations. Stacking Sequence Results for three typical examples. Future work and Conclusion ( Pictures in this page are for illustration only ) 2

3 Part1 : Composite Skin Engineering 3

4 Composite Laminate Skins- Overview Composites relevance to Aircraft industry. Plies, fiber orientations, laminate, zones Fiber Orientation 45 o ply -45 o ply Zones o ply 90 o ply Laminate Stacking (45 o /-45 o /0 o /90 o ) Plan view of Aircraft Wing Skin 18 4

5 Optimization of Aircraft Composite Skins Optimization of real life aircraft composite skins is performed in two stages. In First Stage- a gradient based optimization technique In Second Stage, stacking sequence generation - the scope of current study. Objectives of the current study are : demonstrate utility of genetic algorithms for the problem showcase performance benefits of parallel computing using GPUs. 5

6 Problem Formulation Assumptions first level composite skin optimization is already performed. Constraints The stacking sequence generation is subjected to the following stacking rules. S. No. Stacking Sequence Rule 1 Laminate should be symmetric. 2 Number of plies of each orientation should remain same. 3 Laminate stacking sequence should not contain more than 4 plies in the same orientation together. 4 Laminate stacking sequence should not have more than 2 plies in the same orientation together at the top of the laminate. 5 Maximum difference in angle orientations between two consecutive plies must be equal to At the top of the laminate 0 0 ply should be placed such that there are at least 3 plies between 0 0 ply and outer surface of the laminate. 6

7 Mathematical formulation Cond. Objective function Minimize Violation of stacking rules, i.e.: Minimize Penalty P = P 1 + P P n Where P 1, P 2,..P n are penalties for non-compliance of 1, 2, n th stacking sequence rule Decision Variables For each layer of laminate, assign one of the orientations: (0 0, 90 0, +45 0, ) 7

8 Part2 : Genetic Algorithms Based Composite Stacking Sequence Generation Approach 8

9 Genetic Algorithms Genetic algorithms are search techniques based on principles of natural selection. Methods are suitable for combinatorial problems like stacking sequence generation. Capable of generating good solutions by evaluating a fraction of solutions among all possible options No need of gradient information of the objective function, so oblivious to the domain of the problem. The genetic algorithm process starts by assigning allowable ply orientations 0 0, 45 0, 90 0 and randomly to design variables. The fitness (reciprocal of number of rule violations) for this solution is computed. 9

10 GA Steps A Simple Genetic algorithm has the below steps: Step1. Encoding, decoding and Initial solutions creation: random 1 s and 0 s Step2. Improving the initial solutions: Selection, Crossover, Mutation Step3. Convergence and Stopping criterion: 85-90% similarity in solutions, or reaching preset maximum number of iterations. First Generation Second Generation Last Generation Step1: Encoding, decoding and initial solution Solution1 Solution2 Solution3 Solution4.... Solution N Fitness Step2: Improving Initial solutions using Selection, Cross Over, Mutation Selection, Cross Over, Mutation Selection, Cross Over, Mutation Step3 : Convergence

11 GA Step1: Encoding, decoding and Initial solutions creation Design Variables are encoded into bits of 1 s and 0 s In the current problem Design variables are the ply orientations at each level of the laminate Each ply orientation is encoded with two bits as given below Ply Orientation Encoded Bits 0 o o o o 11 The Objective function in the current problem, i.e. number of stacking rule violations, is translated into the fitness of an individual solution. Problem Space Laminate Stacking Sequence (90/45/90/0/-45/0) Evaluate Solution Encoding Decoding Solution Space Encoded Laminate Stacking Sequence: Sol 1: Sol 2: Sol n:... 11

12 GA Step2 : Improving the initial solutions :GA Operators Three operators : 1. selection, 2. cross-over 3. mutation 1. Selection : Selection operator is based on the survival of the fittest i.e. each solution gets number of copies into new solution space, in proportion to its fitness. 2. Cross-Over Operator: Cross over operators picks up two solutions at random within a generation and, between these solutions does swapping of bits from one to another, to create two new solutions. Least Fit solution occupies smallest segment on the wheel 5% 35% Parent1 Cross Sites Selection Point Fittest solution occupies more area on the wheel 40% 12% 8% Wheel rotation Parent2 Offspring1 Offspring2 Cross Over 3. Mutation Operator: Mutation randomly flips bits in solution according to a preset probability. This operator increases the chances of avoiding local minimum by keeping the population diverse to a minimum extent. Usually the probability of mutation is low e.g Mutation 12

13 GA Step3: Convergence Criteria Maximum number of iterations reaches a prefixed number % of similarity in solutions in the current generation is reached. 13

14 Scope for Parallelization Computations across generations are dependent : can t be parallel. First Generation Second Generation Last Generation Computations within a generation are independent of each other: Can be parallel. Step1: Encoding, decoding and initial solution Solution1 Solution2 Solution3 Solution4.... Solution N Fitness Step2: Improving Initial solutions using Selection, Cross Over, Mutation Selection, Cross Over, Mutation Selection, Cross Over, Mutation Step3 : Convergence Parallelization can be achieved using: 1. Multiple CPUs : expensive, limited cores 2. GPGPUs : becoming less expensive, commonly used for graphics processing, considered in this study 14

15 Part3 : Utilizing GPU power 15

16 GPUs Introduction A GPU is an additional computational device for a computer, in addition to CPU to perform faster computations. GPUs are designed to perform thousands of massively parallel computations and are traditionally used for large scale matrix operations. The serial code needs to be parallelized using the GPU specific languages like CUDA(NVIDIA s GPU API) used in this study OPENCL(platform neutral). 16

17 Steps in Programming Using a GPU Step CPU task GPU related task 1 Declare pointers to host(which is another name for CPU) data Declare pointers to device(another name for GPU) data 2 Allocate host pointers with Malloc Allocate device pointers with CUDAMalloc 3 Populate input data pointers of host. Copy data from host to device using CUDAMemcpy(with parameter HostToDevice). 4 Specify number of blocks and number of threads (kernel configuration). 5 Specify the kernel code (code to be run on device for each thread) and make a call to kernel code. 6 Perform processing on device 7 Copy the result data from device to host using CUDAMemcpy (with parameter DeviceToHost). 8 If required post process the result on host and present the results to user. 17

18 Flow Chart Start Allocate host and device pointers. Populate the Population data and other host data. Copy data from host to device using CUDAMemcpy(with argument HostToDevice). Launch as many threads on Device as there are individuals in populations and number of blocks equal to by number of zones. Call kernel function with parameters such as pointers to matrices of initial population, pointers to output data, genetic parameters (like number if points of cross over), stiffness information of plies and their orientations. Each thread is meant to compute fitness of one typical solution of stacking sequence and performs Genetic algorithm iterations. Fitness computation: Penalized objective function is computed based on constraint violations. Routines that run on GPU Converged? No Selection Yes Copy computed results from Device to Host, using CUDAMemcpy (with argument DeviceToHost) Write solution to an output file. Stop Cross Over Mutation Positions of calls to syncthreads (). 18

19 Stacking Sequence Generation Problems and Results 19

20 Comparison of Execution time with CPU alone and with GPU Programming. CPU Used Intel Xeon Processor with 2GB RAM, 2.53GHz clock rate Problem Number of Zones GPGPU Used 1.3 NVIDIA Tesla T10 Processor with 4GB Global Memory 30 Multi-processors 240 Cores, 16K Shared Memory per block, 32 Size warps, 512 thread per block, 1.3GHz clock rate CPU Alone (Seconds) CPU + GPU (Seconds) Performance benefit Composite Skin Problem times Composite Skin Problem times Composite Skin Problem times Observations : 1. Speed-up of up to 8 times were observed if GPU computation is used. 2. As the size of problem increases the performance benefit is higher because the full power of GPU is utilized. 20

21 Composite Skin Problem1 150mm mm This composite skin as shown contains four zones with the number of plies, initial thickness law and initial stacking sequence as shown. Each of the ply thickness is considered as 0.125mm which is same for all the composite skins analyzed in the current work. Performance benefit CPU Alone (Seconds) CPU+GPU (Seconds) 4 3 Performance benefit times Initial Stacking Zone Number of Number Plies Initial Stacking Sequence (un-optimized) 1 40 (0 10 /45 10 /90 10 / ) 2 30 (0 12 /45 6 /90 6 /-45 6 ) 3 24 (0 8 /45 6 /90 4 /-45 6 ) 4 10 (0 4 /45 2 /90 2 /-45 2 ) Generated Stacking Sequence Zone Stacking Sequence 1 [-45 2 / 90/ 45/ 0/ 45/ 0/ 90/ 0/ 45/-45/ 45 2 /-45/ 0/ 90/ 0/ 90 2 /-45] s 2 [45/ 90/ 45/-45/ 45/-45/ 0/ 90/ 0 2 / 0 2 / 90/ 0/-45] s 3 [90/ 45/ 90/-45/ 0 2 / 45/-45/ 0/ 45/ 0/-45] s 4 [-45/ 45/ 90/ 0 2 ] s Best Zone 1 Stacking Sequence Solution 1 [-45 2 / 90/ 45/ 0/ 45/ 0/ 90/ 0/ 45/-45/ 45 2 /-45/ 0/ 90/ 0/ 90 2 /-45] s 2 [90 3 /-45/ 0/ 45/ 0 2 / 45/ 0/ 90/ 45/ 0/ 45/-45/ 90/-45/ 45/-45 2 ] s 3 [90/ 45/ 90/ 45/-45/0/ 45/0/ 45/0/ 90/ 45/-45/90/0 2 /90/-45 3 ] s Rule violated None

22 Composite Skin Problem2 500mm mm This tapered composite skin has 6 zones with 2 zones having the same thickness. The geometry and thickness law for this composite skin are shown. Performance benefit CPU Alone (Seconds) CPU+GPU (Seconds) Performance benefit times 75mm Initial Stacking Zone Number Number of Plies Thickness Law & Initial Stacking Sequence (unoptimized) 1 40 (0 10 /45 10 /90 10 / ) 2 30 (0 12 /45 6 /90 6 /-45 6 ) 3 24 (0 8 /45 6 /90 4 /-45 6 ) 4 20 (0 8 /45 4 /90 4 /-45 4 ) 5 16 (0 6 /45 4 /90 2 /-45 4 ) 6 8 (0 2 /45 2 /90 2 /-45 2 ) Generated Stacking Sequence Zone Stacking Sequence 1 [-45 2 / 90/ 45/ 0/ 45/ 0/ 90/ 0/ 45/-45/ 45 2 /- 45/ 0/ 90/ 0/ 90 2 /-45] s 2 [45/ 90/ 45/-45/ 45/-45/ 0/ 90/ 0 2 / 0 2 / 90/ 0/- 45] s 3 [90/ 45/ 90/-45/ 0 2 / 45/-45/ 0/ 45/ 0/-45] s 4 [90/-45/ 45/-45/ 0/ 90/ 0/ 45/ 0 2 ] s 5 [45/ 90/-45/ 45/ 0 2 /-45/ 0] s 6 [-45/ 45/ 90/ 0] s 22

23 Composite Skin Problem3 40 zones skin Zone Number Number of Plies Thickness Law & Initial Stacking Sequence (un-optimized) (0 50 /45 50 /90 50 / ) (0 76 /45 38 /90 38 / ) (0 62 /45 44 /90 26 / ) (0 84 /45 24 /90 34 / ) (0 54 /45 54 /90 54 / ) (0 82 /45 40 /90 40 / ) (0 66 /45 46 /90 30 / ) (0 92 /45 28 /90 36 / ) (0 54 /45 54 /90 54 / ) (0 80 /45 40 /90 40 / ) (0 68 /45 48 /90 30 / ) (0 90 /45 26 /90 36 / ) (0 40 /45 40 /90 40 / ) (0 74 /45 36 /90 36 / ) (0 78 /45 38 /90 38 / ) (0 44 /45 44 /90 44 / ) (0 42 /45 42 /90 42 / ) (0 36 /45 36 /90 36 / ) (0 68 /45 20 /90 28 / ) (0 70 /45 20 /90 28 / ) (0 24 /45 24 /90 24 / ) (0 48 /45 14 /90 20 / ) (0 52 /45 16 /90 20 / ) (0 42 /45 20 /90 20 / ) (0 52 /45 16 /90 20 / ) (0 40 /45 20 /90 20 / ) (0 20 /45 20 /90 20 / ) (0 46 /45 12 /90 20 / ) (0 36 /45 18 /90 18 / ) (0 48 /45 14 /90 20 / ) (0 34 /45 16 /90 16 / ) (0 4 /45 4 /90 4 /-45 4 ) (0 14 /45 4 /90 6 /-45 4 ) (0 12 /45 6 /90 6 /-45 6 ) (0 18 /45 4 /90 8 /-45 6 ) (0 14 /45 6 /90 6 /-45 6 ) (0 6 /45 2 /90 4 /-45 2 ) (0 4 /45 2 /90 2 /-45 2 ) (0 6 /45 2 /90 2 /-45 2 ) (0 8 /45 2 /90 4 /-45 2 ) 40 8 (0 2 /45 2 /90 2 /-45 2 ) 23

24 Composite Skin Problem 3-Results The final stacking sequence obtained for few zones are shown in below Table. Zone Stacking Sequence 1 [45/ 90/-45 2 / 0/ 90/ 0 4 / 90/ 45/ 0/ 45/ 0/ 45/ 0/ 90/ 0/ 90/ 45/-45/ 0/ 90/ 45/ 0/ 90/ 45/-45/ 0/ 45/ 0/ 45/ 0/ 45/ 0/ 45/-45/ 0/ 90/ 45/ 0/ 90/ 45/-45/ 45/ 0/ 90/ 0/ 45/-45/ 0/ 90/ 45/ 0/ 45/ 0/ 45/-45/ 45/ 0/ 90/ 0/ 90/ 45/-45/ 45/ 45/-45/ 0/ 45/-45/ 45/-45/ 45/-45/ 90/-45 2 / 90 4 /-45/-45/ 90/-45 3 / 90/-45 3 / 90 2 /-45/ 90/-45/ 90 2 ] s 2 [90 2 /-45/ 45 2 /0/ 45/-45/ 45/-45/ 45/-45/ 0/ 90/ 0/ 90/ 0/ 90/ 45/-45/ 0/ 45/-45/ 0/ 90/ 0 2 / 90/ 45/ 0/ 45/-45/ 45/- 45/ 45 4 / 0/ 45/-45/ 45/ 0/ 90/ 0 2 / 45/-45/ 45/-45/ 0/-45 2 / 0/ 90/ 0 2 / 90/-45/-45/ 0 2 / 90/ 0 4 / 90/ 0 4 / 90/ 0/-45/ 0/ 90/ 0/ 90/ 0/ 90/ 0/ 90/ 0 4 / 90/ 0/-45 3 / 90] s 3 [90/-45/ 90/ 90/-45/ 0/ 45/ 0/ 90/ 45/-45/ 45 2 /-45/ 0/ 90/ 0/ 90/ 45/-45/ 0/ 45/-45/ 0/ 45/-45/ 0/ 45/ 0/ 45/-45/ 0/ 45/ 0/ 90/ 45/ 0/ 90/ 45/-45/ 0/ 90/ 45/-45/ 45 2 / 0/ 90/ 45/ 0/ 45/-45/ 45/ 0/ 90/ 0/ 45/-45/ 45 3 /-45/ 90/ 0 3 /- 45/ 0/ 90/ 0 3 / 0/-45/ 0/-45/ 0 3 /-45/ 0/-45 3 / 0/-45 2 / 0 2 ] s 6 [-45 2 / 45/ 0/ 90/ 45/-45/ 0/ 90 2 /-45/ 45 4 / 0/ 45/ 0/ 45/ 0/ 45/ 0/ 90/ 45/-45/ 0/ 45/ 0/ 45/-45/ 0/ 45/ 0/ 90/ 0/ 90/ 45/ 0/ 45/-45/ 45 3 /-45/ 45/-45/ 45/-45/ 90/ 0/ 90/-45/ 0/ 90/ 0/ 90/ 0/-45 2 / 0 3 / 90/ 0/ 90/ 0/ 90/ 0/-45/ 0/ 90/-45/ 0/ 90/ 0/ 90/ 0 3 / 90/ 0/ 90/ 0/-45/ 0/ 90/ 0 2 / 90/-45/ 0 2 /-45 2 / 0 4 /-45/ 0 2 ] s Performance benefit CPU Alone CPU+GPU Performance benefit (Seconds) (Seconds) times 24

25 Conclusions A genetic algorithm based stacking sequence generation approach has been presented which can be used to solve large scale composite skin generation problems in commercial aircraft industry. The approach is scalable and has been successfully demonstrated to solve the large scale stacking sequence generation problems. Three important composite skin stacking sequence generation problems have been solved using the current approach. All the stacking sequence rules are satisfied in the final results. Results demonstrate that use of GPGPU results in speed-up of up to 8 times (in stacking sequence generation domain) compared to computation using only CPU. Future work Further investigation needs to be done on how the inter zonal harmonization can be brought into the genetic algorithm based generation framework. The ply materials can be more than one and the orientations can be more than four, which when formulated in to model will increase complexity. 25

26 Discussions 26

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