An Online Machine Learning Multi-resolution Optimization Framework for Energy System Design Limit of Performance Analysis
Authors: Oluwamayowa O. Amusat, Luka Grbcic, Remi Patureau, M. Jibran S. Zuberi, Dan Gunter, Michael Wetter
Organizations: Scientific Data Division, Computing Sciences, Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA 94720 · Applied Mathematics & Computational Research Division (AMCR), Computing Sciences, Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA 94720 · Building & Industrial Energy Systems (BIES) Division, Energy Technologies Area, Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA 94720 · Energy Analysis Division, Energy Technologies Area, Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA 94720
Designing reliable integrated energy systems for industrial processes requires optimization and verification models across multiple fidelities, from architecture-level sizing to high-fidelity dynamic operation. However, model mismatch across fidelities obscures the sources of performance loss and complicates the quantification of architecture-to-operation performance gaps. We propose an online, machine-learning-accelerated multi-resolution optimization framework that estimates an architecture-specific upper bound on achievable performance while minimizing expensive high-fidelity model evaluations. We demonstrate the approach on a pilot energy system supplying a 1 MW industrial heat load. First, we solve a multi-objective architecture optimization to select the system configuration and component capacities. We then develop an machine learning (ML)-accelerated multi-resolution, receding-horizon optimal control strategy that approaches the achievable-performance bound for the specified architecture, given the additional controls and dynamics not captured by the architectural optimization model. The ML-guided controller adaptively schedules the optimization resolution based on predictive uncertainty and warm-starts high-fidelity solves using elite low-fidelity solutions. Our results on the pilot case study show that the proposed multi-resolution strategy reduces the architecture-to-operation performance gap by up to 42% relative to a rule-based controller, while reducing required high-fidelity model evaluations by 34% relative to the same multi-fidelity approach without ML guidance, enabling faster and more reliable design verification. Together, these gains make high-fidelity verification tractable, providing a practical upper bound on achievable operational performance.
Figures & tables
Figure 1: Three platform layers used in the Platform-Based Design of the industrial plant and its controller.
Figure 3: Charging and discharging of the battery (green), and hot water tank charging (orange). The electricity price and the equivalent for gas are shown with dotted lines.
Figure 4: The flowchart of the ML-Accelerated multi-resolution control strategy.
Figure 5: Pareto front for multi-objective problem. The squares represent individual designs on the solution front. The shaded areas highlight the three distinct regimes observed. The red square represents the design to be considered in the limit of performance analysis.
Figure 6: Installed PV capacities for designs on Pareto front.
Component
Capacity
PV
306.2 kW
Heat pump
862.2 kW
Battery
1124.8 kWh
Hot water tank
1911 kWh
Table 2: Equipment sizes for design selected for the limit of performance analysis*
Figure 7: Mean total operating cost of the energy system over one year for all used methods. A lower operating cost at any point in the year indicates better performance.
Approach
Mean ($)
Median ($)
Min ($)
Max ($)
Std ($)
Std (%)
HR
97,482
97,498
97,019
97,913
317
0.33
MRws
74,157
73,845
72,723
76,216
1,275
1.72
MLRF1-MRws
73,807
74,024
72,660
74,520
695
0.95
MLRF2-MRws
73,054
73,250
72,039
73,677
659
0.91
MLGB-MRws
73,188
73,109
71,778
74,758
1,075
1.47
Rule-based ∗
80,194
–
–
–
–
–
Table 3: Total yearly cost statistics for different approaches over 4 runs. The standard deviation percentages are computed relative to the mean values.
Figure 8: A detailed analysis of each of the four runs of the ML-Accelerated variants is presented, where (a) displays the total number of exploratory evaluations (lower is better), and (b) shows a comparison of the total yearly operating costs ()ofeachrunagainstthe\text{MR}_{ws}$ method and the best-performing IDAES approach (lower is better).
MLRF1-MRws
MLRF2-MRws
MLGB-MRws
Statistic
Total
High UCB
Total
High UCB
Total
High UCB
Mean
1,107,000
643,000
1,118,000
654,000
962,000
498,000
Std
97,381
97,381
95,937
95,937
22,361
22,361
Min
1,008,000
544,000
1,020,000
556,000
924,000
460,000
Max
1,264,000
800,000
1,248,000
784,000
980,000
516,000
Table 4: Statistics of exploratory evaluations over four runs for each ML-Accelerated variant. The Total denotes the total exploratory evaluations, while the High UCB Only column denotes the exploratory evaluations triggered by the ML model uncertainty. The standard deviation is derived from the high UCB exploratory runs, while the remaining evaluations are fixed across all runs.
Total
SoC (%)
T median (%)
System
Run
Evals
Prec
PICP
NMIW
Prec
PICP
NMIW
Prec
1
115
2.6
81.7
0.07
20.0
85.2
47.19
21.7
2
126
5.6
87.3
0.50
31.7
83.3
43.23
31.7
3
129
4.7
89.1
0.36
31.8
80.6
48.54
31.8
4
128
6.2
83.6
1.08
25.8
89.1
48.20
28.1
Avg
124
4.8
85.4
0.51
27.5
84.6
46.79
28.5
Table 5: Uncertainty Exploration Analysis for GB. System column represents the union of violations. All metrics in %.
Total
SoC (%)
T median (%)
System
Run
Evals
Prec
PICP
NMIW
Prec
PICP
NMIW
Prec
1
139
4.3
84.2
1.06
30.2
79.9
40.27
32.4
2
142
7.7
87.3
3.39
27.5
81.7
37.13
30.3
3
196
5.6
89.3
4.75
21.9
85.7
33.04
24.0
4
177
5.1
91.0
5.20
29.4
82.5
34.76
32.2
Avg
163
5.7
87.9
3.60
26.9
82.4
36.30
29.4
Table 6: Uncertainty Exploration Analysis for RF1. System column represents the union of violations. All metrics in %.
Total
SoC (%)
T median (%)
System
Run
Evals
Prec
PICP
NMIW
Prec
PICP
NMIW
Prec
1
161
6.2
90.7
4.68
24.8
91.9
69.37
25.5
2
200
2.0
95.5
1.93
21.5
94.5
69.63
22.0
3
136
9.6
91.9
9.71
22.8
90.4
60.84
24.3
4
146
9.6
92.5
11.86
25.3
89.7
69.95
28.1
Avg
160
6.4
92.6
7.05
23.5
91.6
67.45
24.7
Table 7: Uncertainty Exploration Analysis for RF1. System column represents the union of violations. All metrics in %.
Figure 9: Mean total operating cost of the energy system over one week of all compared methods for ablation purposes. A lower operating cost at any point in the week indicates better performance.
Approach
Mean ($)
Median ($)
Min ($)
Max ($)
Std ($)
MR
3,864
3,856
3,808
4,034
46
MRws
3,760
3,752
3,715
3,823
29
HR
4,202
4,170
4,026
4,533
117
HRws
3,954
3,897
3,775
4,308
150
Rule-based ∗
3,991
–
–
–
–
IDAES ∗
2,727
–
–
–
–
Table 8: Cost statistics for the methods in the ablation study.
Figure 10: SOC comparison from different control strategies across seasons.
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.
Appendix
Component
Sizing parameter Bk
Fixed cost C~fixed,k (USD)
Variable capital cost C~var,k
Ref.
PV
Capacity - power (kW)
0
3500 \nicefracUSDkW
[ 40 ]
Gas boiler
Capacity - power (kW)
79670
367 \nicefracUSDkW
[ 40 ]
Heat pump
Capacity - power (kW)
0
2055 \nicefracUSDkW
[ 40 ]
Battery
Capacity - energy (kWh)
0
757 \nicefracUSDkWh
[ 41 ]
Hot water tank
Capacity - volume (m 3 )
1520
4845 \nicefracUSDm3
[ 40 ]
Appendix
Table A.1 : Sizing and unit cost parameters for energy system
Figure C.1 : Hourly electricity prices per season.
Process Model
Parameter
Value
Photovoltaics
PV efficiency, ηPV
17.1%
Heat Pump
Coefficient of performance, ηCOP
3.0
Hot side outlet temperature
92oC
Gas boiler
Boiler efficiency, ηboiler
0.90
Natural gas heating value, HHV
35,396\nicefrackJm3
Outlet temperature
92oC
Appendix
Table C.1 : IDAES Model Parameters.
Figure D.1 : Installed capacities of generation and storage technologies for Pareto-optimal designs
Figure E.1 : Electricity purchase from grid: IDAES vs. ML-based approaches.
Department of Mechanical Engineering, University of Engineering and Technology Lahore, Kala Shah Kaku, Pakistan · The Sargent Centre for Process Systems Engineering, Department of Chemical Engineering, University College London, London, UK · Department of Chemical Engineering, College of Engineering, King Saud University, Riyadh, Saudi Arabia +3