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

www.infosys.com

1

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

• Overview

• Composite Skin Engineering - Overview.

• Optimization of Aircraft Composite Skins

Assumptions

Decision variables, Objective, constraints

• Genetic Algorithms Based Composite

Stacking Sequence Generation Approach

Encoding and Decoding, Initial solutions generation

Improving the solutions :Genetic Algorithm Operators

Convergence Criteria

• Speedup using GPU

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 )

Part1

Part2

Part3

2

Part1 : Composite Skin Engineering

3

Composite Laminate Skins- Overview

• Composites relevance to Aircraft industry.

• Plies, fiber orientations, laminate, zones

1

1

2 3 4 5 6

7

8

9

10

11

12

13

14

15

16

17

18

4

90o ply

45o ply

0o ply

-45o ply

Laminate Stacking (45o/-45o/0o/90o)

Fiber Orientation

Zones

Plan view of Aircraft Wing Skin

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

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 450

6 At the top of the laminate 00 ply should be placed such that there are at least 3 plies between 00 ply and outer

surface of the laminate.

The stacking sequence generation is subjected to the following “stacking rules “.

Assumptions

Problem Formulation

first level composite skin optimization is already performed.

Constraints

6

Mathematical formulation Cond….

Minimize Violation of stacking rules, i.e.: Minimize Penalty P = P1 + P2 +… + Pn

Where P1, P2, …..Pn are penalties for non-compliance of 1, 2,… nth stacking sequence rule

Objective function

Decision Variables For each layer of laminate , assign one of the orientations: (00, 900, +450, -450)

7

Part2 : Genetic Algorithms Based Composite

Stacking Sequence Generation Approach

8

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 00, 450, 900 and -450 randomly to design variables.

• The fitness (reciprocal of number of rule violations) for this solution is computed.

9

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.

GA Steps

10

Step1: Encoding, decoding

and initial solution

Step2: Improving Initial solutions

using Selection, Cross Over, Mutation Step3 : Convergence

1001011010011001

0101010010010101

1001001010101011

0100101010101011

1100110110001010

1001001001010101

1101001001001001

1001001000100101

15.0

23.0

124.0

0.0

23.0

89..0

21.0

10.0

0100011010011001

0101001010010101

0101001010101011

1010101011000011

1100110110001010

1001001001010101

1101001000101001

1101001011001011

15.0

0 00

204.0

10.0

21.0

81.0

2.0

10.0

1100110110001010

1100110110001010

1100110110001010

1100110110001010

1100110110001010

1001001001010101

1100110110001010

1001001000100101

100.0 100.0

100.0

100.0

100.0

2.0

5.0

18.0

First Generation Second Generation Last Generation

Solution1

Solution2

Solution3

Solution4

Solution N

…..

…..

Selection,

Cross Over,

Mutation

Selection,

Cross Over,

Mutation

Fitness

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

• The Objective function in the current problem, i.e. number of stacking rule violations, is translated into the ‘fitness’ of an individual solution.

Ply Orientation Encoded Bits

0o 00

45o 01

-45o 10

90o 11

Encoding

Decoding

Problem Space Laminate Stacking

Sequence

(90/45/90/0/-45/0)

Solution Space Encoded Laminate Stacking Sequence:

Sol 1: 110111001000

Sol 2: 011111001000

………………………….. Sol n: …….………………..

Evaluate Solution

11

Fittest solution

occupies more

area on the wheel

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.

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. 0.001.

Selection

Point Wheel

rotation

Least Fit solution

occupies smallest

segment on the wheel

40%

35%

12%

8%

5%

Mutation

Cross Over

Parent1

Parent2

Offspring1

Offspring2

Cross Sites

12

• Maximum number of iterations reaches a prefixed number.

• 85-90% of similarity in solutions in the current generation is reached.

GA Step3: Convergence Criteria

13

Scope for Parallelization

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

Computations across generations are

dependent : can’t be parallel.

Computations

within a

generation are

independent of

each other:

Can be parallel.

14

Step1: Encoding, decoding

and initial solution

Step2: Improving Initial solutions

using Selection, Cross Over, Mutation

Step3 :

Convergence

1001011010011001

0101010010010101

1001001010101011

0100101010101011

1100110110001010

1001001001010101

1101001001001001

1001001000100101

15.0

23.0

124.0

0.0

23.0

89..0

21.0

10.0

0100011010011001

0101001010010101

0101001010101011

1010101011000011

1100110110001010

1001001001010101

1101001000101001

1101001011001011

15.0

0 00

204.0

10.0

21.0

81.0

2.0

10.0

1100110110001010

1100110110001010

1100110110001010

1100110110001010

1100110110001010

1001001001010101

1100110110001010

1001001000100101

First Generation Second Generation Last Generation

Solution1

Solution2

Solution3

Solution4

Solution N

…..

…..

Selection,

Cross Over,

Mutation

Selection,

Cross Over,

Mutation

Fitness

100.0 100.0

100.0

100.0

100.0

2.0

5.0

18.0

Part3 : Utilizing GPU power

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• 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).

GPUs Introduction

16

Steps in Programming Using a GPU

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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.

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.

Selection

Cross Over

Mutation

Converged

?

• Copy computed results

from Device to Host,

using CUDAMemcpy

(with argument

DeviceToHost)

• Write solution to an

output file.

Stop

Yes

No

Routines that run on GPU

Positions of calls to

__syncthreads ().

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Stacking Sequence Generation Problems and

Results

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Problem Number of

Zones

CPU Alone

(Seconds)

CPU + GPU

(Seconds)

Performance benefit

Composite Skin Problem 1 5 2.25 0.5 4.5 times

Composite Skin Problem 2 6 3.2 0.52 6.15 times

Composite Skin Problem 3 40 300 37 8.1 times

CPU Used GPGPU Used

Intel Xeon Processor with 2GB RAM, 2.53GHz

clock rate

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

Comparison of Execution time with CPU alone and with GPU

Programming.

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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.

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.

Composite Skin Problem1

150mm

300mm

2

3

4

1

Zone

Number

Number of

Plies

Initial Stacking Sequence

(un-optimized)

1 40 (010/4510/9010/-4510)

2 30 (012/456/906/-456)

3 24 (08/456/904/-456)

4 10 (04/452/902/-452)

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Generated Stacking Sequence

Zone Stacking Sequence

1 [-452/ 90/ 45/ 0/ 45/ 0/ 90/ 0/ 45/-45/ 452/-45/ 0/ 90/ 0/

902/-45]s

2 [45/ 90/ 45/-45/ 45/-45/ 0/ 90/ 02/ 02/ 90/ 0/-45]s

3 [90/ 45/ 90/-45/ 02/ 45/-45/ 0/ 45/ 0/-45]s

4 [-45/ 45/ 90/ 02]s

Initial Stacking

Best

Solution

Zone 1 Stacking Sequence Rule

violated

1 [-452/ 90/ 45/ 0/ 45/ 0/ 90/ 0/ 45/-45/

452/-45/ 0/ 90/ 0/ 902/-45]s

None

2 [903/-45/ 0/ 45/ 02/ 45/ 0/ 90/ 45/ 0/

45/-45/ 90/-45/ 45/-452]s

4

3 [90/ 45/ 90/ 45/-45/0/ 45/0/ 45/0/ 90/

45/-45/90/02/90/-453]s

3

CPU Alone

(Seconds)

CPU+GPU

(Seconds)

Performance

benefit

2.25 0.5 4.5 times

Performance benefit

500mm 75mm

1700mm

2 3 4 5 6

1

1

Zone

Number

Number

of Plies

Thickness Law & Initial

Stacking Sequence (un-

optimized)

1 40 (010/4510/9010/-4510)

2 30 (012/456/906/-456)

3 24 (08/456/904/-456)

4 20 (08/454/904/-454)

5 16 (06/454/902/-454)

6 8 (02/452/902/-452)

Composite Skin Problem2

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.

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Generated Stacking Sequence

Zone Stacking Sequence

1 [-452/ 90/ 45/ 0/ 45/ 0/ 90/ 0/ 45/-45/ 452/-

45/ 0/ 90/ 0/ 902/-45]s

2 [45/ 90/ 45/-45/ 45/-45/ 0/ 90/ 02/ 02/ 90/ 0/-

45]s

3 [90/ 45/ 90/-45/ 02/ 45/-45/ 0/ 45/ 0/-45]s

4 [90/-45/ 45/-45/ 0/ 90/ 0/ 45/ 02]s

5 [45/ 90/-45/ 45/ 02/-45/ 0]s

6 [-45/ 45/ 90/ 0]s

Initial Stacking

CPU Alone

(Seconds)

CPU+GPU

(Seconds)

Performance

benefit

3.2 0.52 6.15 times

Performance benefit

Zone

Number

Number of

Plies

Thickness Law & Initial Stacking

Sequence (un-optimized)

1 200 (050/4550/9050/-4550)

2 190 (076/4538/9038/-4538)

3 176 (062/4544/9026/-4544)

4 166 (084/4524/9034/-4524)

5 216 (054/4554/9054/-4554)

6 202 (082/4540/9040/-4540)

7 188 (066/4546/9030/-4546)

8 184 (092/4528/9036/-4528)

9 216 (054/4554/9054/-4554)

10 200 (080/4540/9040/-4540)

11 194 (068/4548/9030/-4548)

12 178 (090/4526/9036/-4526)

13 160 (040/4540/9040/-4540)

14 182 (074/4536/9036/-4536)

15 192 (078/4538/9038/-4538)

16 196 (044/4544/9044/-4544)

17 168 (042/4542/9042/-4542)

18 144 (036/4536/9036/-4536)

19 136 (068/4520/9028/-4520)

20 142 (070/4520/9028/-4524)

21 96 (024/4524/9024/-4524)

22 96 (048/4514/9020/-4514)

22 104 (052/4516/9020/-4516)

23 102 (042/4520/9020/-4520)

24 104 (052/4516/9020/-4516)

25 100 (040/4520/9020/-4520)

26 80 (020/4520/9020/-4520)

27 90 (046/4512/9020/-4512)

28 90 (036/4518/9018/-4518)

29 96 (048/4514/9020/-4514)

30 82 (034/4516/9016/-4516)

31 16 (04/454/904/-454)

32 28 (014/454/906/-454)

33 30 (012/456/906/-456)

34 36 (018/454/908/-456)

35 32 (014/456/906/-456)

36 14 (06/452/904/-452)

37 10 (04/452/902/-452)

38 12 (06/452/902/-452)

39 16 (08/452/904/-452)

40 8 (02/452/902/-452)

Composite Skin Problem3

• 40 zones skin

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Composite Skin Problem 3-Results

Zone Stacking Sequence

1 [45/ 90/-452/ 0/ 90/ 04/ 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/-452/ 904/-45/-45/ 90/-453/ 90/-453/ 902/-45/ 90/-45/ 902]s

2 [902/-45/ 452/0/ 45/-45/ 45/-45/ 45/-45/ 0/ 90/ 0/ 90/ 0/ 90/ 45/-45/ 0/ 45/-45/ 0/ 90/ 02/ 90/ 45/ 0/ 45/-45/ 45/-

45/ 454/ 0/ 45/-45/ 45/ 0/ 90/ 02/ 45/-45/ 45/-45/ 0/-452/ 0/ 90/ 02/ 90/-45/-45/ 02/ 90/ 04/ 90/ 04/ 90/ 0/-45/ 0/

90/ 0/ 90/ 0/ 90/ 0/ 90/ 04/ 90/ 0/-453/ 90]s

3 [90/-45/ 90/ 90/-45/ 0/ 45/ 0/ 90/ 45/-45/ 452/-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/ 452/ 0/ 90/ 45/ 0/ 45/-45/ 45/ 0/ 90/ 0/ 45/-45/ 453/-45/ 90/ 03/-

45/ 0/ 90/ 03/ 0/-45/ 0/-45/ 03/-45/ 0/-453/ 0/-452/ 02]s

6 [-452/ 45/ 0/ 90/ 45/-45/ 0/ 902/-45/ 454/ 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/ 453/-45/ 45/-45/ 45/-45/ 90/ 0/ 90/-45/ 0/ 90/ 0/ 90/ 0/-452/ 03/ 90/ 0/ 90/ 0/ 90/ 0/-45/ 0/

90/-45/ 0/ 90/ 0/ 90/ 03/ 90/ 0/ 90/ 0/-45/ 0/ 90/ 02/ 90/-45/ 02/-452/ 04/-45/ 02]s

The final stacking sequence obtained for few zones are shown in below Table.

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CPU Alone

(Seconds)

CPU+GPU

(Seconds)

Performance benefit

300 37 8.1 times

Performance benefit

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.

• 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.

Future work

25

Discussions

26

THANK YOU

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