The document describes a study that used genetic algorithms and finite element analysis to optimize the design of a hospital bed structure to minimize mass while ensuring it can independently support the left or right leg. The study developed a 54-beam bed structure model and defined optimization parameters and constraints for a genetic algorithm in MATLAB to identify the minimum mass design. The optimized design reduced cross-sectional sizes and had a total mass of 49.25kg while meeting stress, displacement and other constraints.

1. The Optimization Design of Hospital Bed Structure
for Independently Supporting Left and or Right Leg
Using Genetic Algorithms
Atthaphon Ariyarit
Supervisor: Rung Kittipichai
Department of Mechanical Engineering
Mahidol University, Thailand
2nd International Conference on Mechanical,
Industrial, and Manufacturing Technologies
Singapore, Feb 26-28, 2011

2. Content
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Introduction
Objective
Related Works
Hospital Bed Structure
Finite Element Analysis
Genetic Algorithms
Optimization Problem
Result and Discussion
Conclusion
MIMT 2011, Singapore, Feb 26-28, 2011
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3. Introduction
• Many types of the hospital bed
• Lift the head and/or leg section of bed
MIMT 2011, Singapore, Feb 26-28, 2011
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4. Causes & Problems
• Structure of the hospital bed is typically
complicate and heavy
• Hard to move because of heavy weight
• Bed cannot support independently either left
or right broken-leg
• Today, either left or right leg side of bed
structure can be lifted
MIMT 2011, Singapore, Feb 26-28, 2011
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5. Objective
• Design the hospital bed structure for
supporting left and/or right Leg
• Minimize structural mass of a base of
bed subject to structural constraints
MIMT 2011, Singapore, Feb 26-28, 2011
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6. Related Works
• Jenkins (1997)
Multistory frame with truss-supported
hangers for optimization study
MIMT 2011, Singapore, Feb 26-28, 2011
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7. Related Works
• Annicchaiarico and Cerrolaza (1998)
• Coello and Christiansen (2000)
• Deb and Gulati (2001)
25-bar truss tower
MIMT 2011, Singapore, Feb 26-28, 2011
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8. Hospital Bed Structure
• Size of bed structure: width x length is 0.8 x 2 m
• Analyze only a base of bed structure
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9. Hospital Bed Structure
• Material of structure is Steel Alloy 4140
• Down and side force were assumed as
distributed force
MIMT 2011, Singapore, Feb 26-28, 2011
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10. Finite Element Analysis
FEA is applied to bed structure to find
Structural deformation, stress and buckling
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11. Genetic Algorithms
• GAs is an optimization method
• GAs is a stochastic search method based on
the theory of natural selection
• GAs is an unconstrained optimization method
• Technique of penalty function is used to solve
constrained optimization problem
MIMT 2011, Singapore, Feb 26-28, 2011
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12. Genetic Algorithms
• The search procedure start with an initial population as
parents
• Initial population of individual is randomly created
• Real-number design parameters is in binary string
• Genetic operator are applied to the parent to create
offspring
• Probability of a gene used for breeding in terms of
fitness
• Procedure is repeated until an optimum is achieved
MIMT 2011, Singapore, Feb 26-28, 2011

13. Operator of Genetic Algorithm
• Selection
• Crossover
– Parent1 =
– Parent2 =
– Offspring1 =
– Offspring2 =
1010|1101
1100|1010
1010|1010
1100|1101
• Mutation
– Parent =
– Offspring =
1001001
1011000
MIMT 2011, Singapore, Feb 26-28, 2011
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14. Genetic Algorithms
MIMT 2011, Singapore, Feb 26-28, 2011
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15. Optimization Problem
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GAs parameter
Each design variable contained 10 binary bits
The number of population in each generation was 500
The number of generation was set to 1500
The probability of crossover on each generation was 0.8
The probability of mutation on each generation was 0.2
Bound Constraints
Search limits of the width and height in each cross-section
area of the element was defined between 1 to 5 cm
• Displacement Constraints
• Displacement of structure is allowed <= 1 cm
MIMT 2011, Singapore, Feb 26-28, 2011
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16. Optimization Problem
The optimization problem can be written as
Minimize f(x) = the mass of 54-beam structure
Subject to 1 – Ri
0; i = 1, …, 54
λi – 1
0;
i = 1, …, 54
ν
- (1 - 0 .0 1 ) 0;
j = 1, …, 34
and 0.01 xk 0.05; k = 1, 2, …, 108
• All are done in MATLAB with
developing FE code
j
MIMT 2011, Singapore, Feb 26-28, 2011
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17. Result of Optimization Problem

18. Result of the best fitness on each generation
49.25 kg

19. Results at Minimum Mass
Element No.
1,6
2,7
3,5
4
8,9
10
11,16
12,15
13,14
17,42
18,41
19,40
20,39
21,38
Width
0.0296
0.0210
0.0101
0.0141
0.0120
0.0132
0.0256
0.0182
0.0156
0.0292
0.0102
0.0268
0.0403
0.0150
Height
0.0170
0.0126
0.0267
0.0110
0.0258
0.0150
0.0116
0.0175
0.0231
0.0157
0.0288
0.0101
0.0114
0.0382
Element No.
22,37
23,36
24,43
25,48
26,47
27,46
28,45
29,44
30,50
31,49
32,51
33,53
34,52
35,54
MIMT 2011, Singapore, Feb 26-28, 2011
Width
0.0222
0.0108
0.0140
0.0278
0.0279
0.0125
0.0152
0.0202
0.0165
0.0140
0.0171
0.0107
0.0102
0.0108
Height
0.0460
0.0288
0.0110
0.0167
0.0203
0.0209
0.0376
0.0218
0.0100
0.0180
0.0143
0.0179
0.0211
0.0237
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20. Result and Discussion
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21. Conclusion
• Mass of bed structure was successfully minimized
• Size of cress-section area in each beam was
reduced
• Displacement of each node or structure was
accepted
• Stress in each element was accepted
• Therefore, it is possible to design the hospital bed
for independently supporting left and or right leg
using GAs including FEA
MIMT 2011, Singapore, Feb 26-28, 2011
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22. Conclusion
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23. Thank you very much
for your attention
MIMT 2011, Singapore, Feb 26-28, 2011

24. MIMT 2011, Singapore, Feb 26-28, 2011