Sustainable design and control of a multi-sourced radiant heating system: Non-linear optimization under thermal comfort constraints
Bibliographic record
Abstract
• A non-linear optimizer is developed for a tri-source radiant floor heating system. • Thermal comfort constraints are applied to the system with two forms of storage. • The system achieves lifecycle costs of 420.7 k CAD and an average PMV of −0.12. • The LCOH of the system (0.143 CAD/kWh) is below those of gas and coal systems. • Lifecycle emissions (330.2 tons) are 47% lower than those of the gas-only system. The demand for energy-efficient heating solutions in buildings is increasing consistently, necessitating tools to determine the system’s optimal design and operation, while ensuring occupant comfort. This study develops a novel thermal comfort-constrained capacity-operation optimization framework for a multi-source (solar collectors, a biomass boiler, and a gas boiler) radiant floor heating system, addressing the limitations of existing literature that typically focus on non-linear optimization of single-source systems. The system incorporates two forms of thermal storage, namely a water tank and a thermally active floor slab, which magnifies the system’s non-linearities. Hence, a non-linear interior-point optimization algorithm (Ipopt) is implemented in MATLAB® to minimize lifecycle costs (LCC). Unlike conventional approaches, the developed optimization framework has three novel features: i) it captures the dynamics and complex interactions between heat generation, storage, and consumption components, ii) it constrains temperature levels to ensure energy quality while simultaneously solving thermal comfort equations at each time step, accounting for the dynamic response of the building in subsequent steps, and iii) it balances various operational and sizing decision variables, capturing the bi-directional impacts of optimal system capacity and management. The results reveal that the tri-source system achieves an LCC of approximately 0.42 mil. CAD (Canadian dollars), equivalent to 0.3 mil. USD, and a competitive levelized cost of heat (LCOH) of 0.143 CAD kWh −1 (0.1 USD kWh −1 ), maintaining a stable operative temperature between 19 °C and 25 °C, with an average predictive mean vote (PMV) of −0.12, and total lifecycle CO 2 emissions of 330.15 tons. Comparative analyses with simpler design variations indicate that the gas-only system incurs the lowest LCC at 0.302 mil. CAD (0.21 mil. USD), yet its emissions are nearly twice those of the tri-source system. Among renewable options, the solar-biomass system offers the best balance of economic (LCC of 0.506 mil. CAD or 0.36 mil. USD), environmental (110.9 tons of CO 2 ), and comfort metrics (mean PMV of −0.12).
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".