[ Paper Review ] Strategically switching metaheuristics for effective parameter estimation

Strategically switching metaheuristics for effective parameter estimation of electrochemical lithium-ion battery models

• Journal : Energy Storage ’23 (IF 8.9)
• 10 citations

 

[ summary ]

• SIA의 23개 baseline function 중 10개 선택 (특정 metaheuristic에 효과적인 모양) (table 2)
• 10개의 baselie function 학습한 FuncNet(CNN)을 사용해 object function와 가장 유사한 baseline function 식별 ⇒ FuncNet으로 objective function identify함
• CNN에서 식별된 가장 유사한 baseline function을 기반으로 적절한 metaheuristic recommend
• local optima에서 벗어나기 위해 metaheuristic suitability tests, particle resampling 수행
• 실험 : ISC-free P2D 및 ISC embedded P2D(ISC-P2D) 모델을 사용하여 성능 비교

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1. Problem Statement

• Beneficial P2D models must estimate relatively many parameters
  • existing method : gradient-based optimization algorithms & various metaheuristics
• Swarm intelligence-based algorithms (SIAs) is recently developed as data-efficient metaheuristics
  • problem :
    • SIA perform differently according to a given objective function
    • There is no guideline that specifies the SIA suitable for the objective function

⇒ For accurate P2D model parameter estimation, propose a systematic method for applying a proper SIA at the right iteration

 

 

2. Contribution

• A systematic guide is proposed to strategically switch numerous metaheuristics(SSM)
• The best metaheuristic is recommended by the identified objective function
• The outstanding parameter estimation performance of SSM is demonstrated

 

3. Methodology

Propose strategically switching metaheuristics (SSM)

 

 

1️⃣ Select 10 baseline functions as labeled classes among 23 baselines → two baseline functions for each metaheuristic

• 23 baselines are well used in metaheuristics approach
• effectively optimized for certain metaheuristics
• provide a fair chance to each metaheuristic

 

 

2️⃣ Identify baseline function, metaheuristic

• Train FuncNet using 10,000 data sets for each class
• FuncNet is based on CNN (FuncNet work as metaheuristic algorithm selector)
  • Find the most similar baseline function with object function → based on current particle distribution
  • Recommend the corresponding effective metaheuristic
  • +) Select baseline function in the direction that objective function gradually optimizes in the parameter space

 

 

• Switching criterion
  • Set criteria for evaluating the performance of currently used baseline function
  • Whenever the inequality is met, have a chance to improve the metaheuristic

 

 

 

3️⃣ Overall, SSM (strategically switching metaheuristics )

• At each iteration, SSM
  1. evaluates the objective function values for all particles (3)
  2. updates SSM metaheuristic according to the objective function (3) and criterion (4)

• Currently employed metaheuristic can change to a new one for the better → proper convergence

 

 

 

[ SSM workflow ]

Iteration이 지날 수록 objective function과 유사한 baseline (metaheuristic) 선택

• violet box : algorithm selector (FuncNet)
• red box : parameter estimation

 

4️⃣ Get global optimal solution → Particle resampling

• If solutions are likely to be in a local optimal solution (if there is too little variation)
  • All particles are reinitialized in the exploratory search space outside the current particle distribution
  • Particle Resampling = Select 22 parameter combinations

 

4. Experiment Result Analysis

• Cell : lithium cobalt oxide (LCO)/graphite batteries at the beginning-of-life (BOL)
• Profile : CCCV (constant current constant voltage) with reference input current of 0.5 C-rate
• Model : ISC-free P2D, ISC embedded P2D(ISC-P2D)
  • In ISC-P2D model, terminal voltage difference between ESC and ISC was negligible → ESC can use as alternative of ISC

 

 

4.1 Experiments with ISC-free battery cell

• (a) : SSM outperforms other SIAs
  • RMSE of SSM decreases steadily → adaptively switching metaheuristics and particle resampling
• (b) : Escape local optima
  • Mainly selected GWO for fast convergence
  • To escape from local optima through particle resampling\

 

• SSM has the lowest standard deviations in both voltage RMSE and estimated parameter
  • Implies that the SSM produces more reliable results

 

4.2 Experiments with ISC-affected battery cells

• Use actual battery with an ESC resistance of 50 Ω

• (a)-(b) : Simulated and actual voltage response
  • (a) : CCCV profile / (b) : dynamic profile → RMSE : 16.xx mV
• (c)-(f) : Simulated and actual voltage response error in CCCV, Dynamic profile

⇒ estimated P2D model parameters well describe real physical lithium-ion battery cells

 

 

4.3 Experiments for various operation conditions

• 8 experiments on ISC, profile, and temperature
  • parameter estimation method : GWO, SSM
  • estimate 22 parameters in the ISC-P2D model

• Estimation accuracy : the SSM surpasses the GWO by 3.51 mV

 

 

• In most cases, the SSM has the outstanding voltage response on the rest region
• In case 4, SSM’s RMSE is higher than GWO’s but the SSM better captures the subtle effects of an ISC

 

5. Conclusion

• Proposed SSM to fully exploit the shape of an objective function around sample points
• By estimating the ISC resistance and other electrochemical parameters, the proposed SSM has effective parameter estimation performance.
• further study
  • Test (1) other commercial batteries and (2) severe low and high temperature conditions

 

 

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Background Knowledge

• ISC-P2D model
  • ISC resostamcd amd current flowing relationship

 

• Fig 1 - (a)에서 ISC resistance가 포함된 P2D 모델
  • separator domain에 effective conductivity (𝜎 eff 𝑠)추가 →internal short circuit 생성
• Fig 1 - (b)(c)는 ESC resistance가 포함된 P2D 모델

 

• ISC resistance은 ESC와 동일하게 구현 (가정 : electrode와 electrolye resistance 무시할 수 있음)
• 연구에서는 ESC를 통해 ISC resistance 구현 → parameter estimation 성능 실험
  • ISC resistance 측정 어려움 → ESC resistance를 대안으로 사용

 

 

• Swarm intelligence-based algorithms (SIAs)
  • One of metaheuristics, provide sufficiently good optimal solutions with tolerable computational effort
  • 동작 방법
    • start with particles (or entities) randomly located in a search space.
    • update particle positions using their own unique strategies each tim
  • 논문에서는 5가지 SIA 방법 사용됨 → 23개의 baseline function 사용해서 계산됨
    • bald eagle search (BES), grey wolf optimizer (GWO), honey badger algorithm (HBA), particle swarm optimizer (PSO), and salp swarm algorithm (SSA)
    • 각 SIA have their own optimizing strategies (baseline functions) favorable to certain