Use of Genetic Algorithms with Multiple Metrics Aimed at the Optimization of Automotive Suspension Systems

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Use of Genetic Algorithms with Multiple Metrics
Aimed at the Optimization of Automotive
Suspension Systems

• Scott A. Mitchell, Joel Durgavich, Steve Smith,
  Alberto Damiano, Rosalyn MacCrackenSchool of
  Computational SciencesGeorge Mason University

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Presentation Outline

• Model Description
• Design Evaluation
• Optimization Algorithms
• Genetic Algorithm
• Optimization Testing
• Results
• Conclusions Future Work

04MSEC-59
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Suspen Model

• Reducing 3D system to 2D Front View
• Rigid Members
• Kinematic geometry analysis
• Analysis of Track, Camber, and the Roll Center

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Model Parameters

• Upper Chassis Width - the distance between the
  point where the right and left upper A-arm
  connects to the chassis.
• Lower Chassis Width - the distance between the
  point where the right and left lower A-arm
  connects to the chassis
• Chassis Height the vertical distance between
  the points where the upper and lower A-arms
  connect to the chassis.
• Static Height the vertical distance from the
  ground plane to the lower A-arm chassis
  connection point at static ride height.

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Model Parameters

• Upper A-arm Length the 2D length of the upper
  A-arm.
• Lower A-arm Length the 2D length of the lower
  A-arm

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Model Parameters

• Upright Length the 2D distance from where the
  lower A-arm attaches to the upright to the point
  where the upper A-arm attaches.
• Upper Upright Offset the distance from the
  point where the upper A-arm attaches to the
  upright and the tire centerline.
• Lower Upright Offset the distance from the
  point where the lower A-arm attaches to the
  upright and the tire centerline.
• Lower Offset Height the vertical distance from
  the point defined in the Lower Upright Offset and
  the bottom of the tire.
• Tire Rolling Radius the radius of the tire as
  loaded.

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Design Evaluation

• Multiple parameters of differing scales and units
• For example
• Camber (angle)
• Track (length)
• A Unitless scoring function was created.

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Scoring Function
Symmetric
Asymmetric
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Example Scoring Metrics

• Static Camber- The Static Camber test measures
  the tire camber when the vehicle is at the static
  location. (C -1.0 degrees, BoundL -2.0,
  BoundR 0.0 )
• Laden Camber This measurement extends the
  static camber test into the extremes of roll
  travel. The test analyzes camber angle of the
  tire that gains weight transfer due to cornering
  forces.( C 1.0 degrees, BoundL 0.5, BoundR
  -2.0 )
• Track - The Track test measures a vehicle track
  width at the static location. ( C 1.22 meters,
  BoundL 1.14, BoundR 1.24 )
• Scrub - The Scrub test measures the change in a
  vehicle track width as it moves through the
  defined path.( C 0.0 mm, BoundL 0.0, BoundR
  25.0 )
• Lateral RC Movement This test measures the
  lateral component of the roll center as it moves.
  The difference between the extremes is measured
  and scored. ( C 0.0 mm, BoundL 0, BoundR
  610.0 )
• Jacking This metric estimates the effects of
  jacking force. It uses the roll center height,
  track, and the roll (as a representation of
  lateral force). The largest jacking estimate is
  scored. ( C 0.0, BoundL 0.0, BoundR 25.0
  203 mm of RC height at 3.0 of roll ).

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Combined Scoring Function

• Individual Score values combined through
  weighting function.
• The weight, Wi, is the importance of the metric.

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Finding an Optimal Design

• Grid Algorithm
• Guaranteed coverage
• Requires GD tests, where there are G divisions on
  each of D degrees of freedom.
• Genetic Algorithm
• Faster
• May find a local optima instead of the global
  optimum.

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Genetic Algorithms

• First developed in the 1970s by John Holland and
  later expanded by De Jong in the 1980s 
• Attempts to encode "survival of the fittest"
  logic
• Pairs of solutions in a current solution
  population are mated to produce new results with
  fitter solutions more likely to be chosen for
  mating
• Fitter solutions are defined as solutions closer
  to the desired solution criteria (i.e. minimum,
  maximum, zero)

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Genetic Algorithm

• 1) Produce an initial population with random
  solutions generated at random and calculate the
  fitness of each solution
• 2) Repeat until a solution meets the exit
  criteria
• a. Determine the probability of selecting any
  given solution for mating
• i. Solutions with a higher fitness have a
  greater probability of being selected
• b. Produce a new generation using two operations
• i. Duplication/Reproduction, the direct copy of
  a solution
• ii. Crossover/Mating two solutions with the
  possibility of mutation
• c. Calculate the fitness of each new solution

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Real Value Mating

• Many different types of crossover operations can
  be chosen
• The following crossover operation has the benefit
  that the resulting gene values will be in the
  solution set
• For each gene in the chromosome
• new g1 a g1 (1 a) g2
• new g2 (1 a) g1 a g2
• where a is the crossover proportion.

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Mutations

• During reproduction there is a random chance
  that a mutation occurs.
• Mutations help the algorithm break free of local
  minima.
• The mutation operation is randomly selected
• New random value
• Boundary Value
• Crossover with the Boundary Value

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Optimization testing

• 2 Degree of Freedom Example
• Using a known model
• Upper Upright Offset
• Lower Upright Offset
• Testing Metrics
• Track ( C 1220 mm, BoundL 1140 mm, BoundR
  1240 mm)
• Static Camber (C -1.0, BoundL -2.0, BoundR
  0.0 )

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Parallel Equal Length Model

• Optimization of Camber Change in Bump Population
  1000 with 50 generations

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Swing Axle Model

• Optimization of Camber Change in Roll Population
  1000 with 50 generations

without Mutations
with 1 Mutation Rate
0.08 Camber change over 3.0 to -3.0 of roll
0.02 Camber change over 3.0 to -3.0 of roll
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Optimization Speeds

• 2D Model 3D Model
• Full 11D Model
• 45 minutes with Genetic Algorithm (1500x50)
• 34,400 years (est.) with 25 element Grid

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Optimal Rear Suspension Test
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Optimal Suspension Bounds
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Optimized Model
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Optimized Model Results
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Conclusions

• Scoring function is an effective way of combining
  multiple metrics of different types.
• Grid search algorithm is infeasible for high
  dimensionality problems.
• Genetic Algorithm is effective in finding optimum
  solution.
• Future Work
• Non-Darwinian guided optimization
• Parallelize optimization
• Asymmetric model (extends to 18D)
• Expand to combined front rear models