The rig integrates several subsystems whose outputs directly map to the variables later used in the regression dataset:

To ensure measurement reliability, all thermocouples were calibrated prior to experimentation using a temperature calibrator (Sika TP 37 450 E.2) as shown in Figure 4. The calibration was performed over a temperature range of 0 °C to 100 °C, with increments of 5 °C. At each step, the thermocouples were allowed to stabilize for 5 minutes before recording measurements.

The calibration results indicated that all thermocouples exhibited good agreement with the reference sensor. The maximum absolute error was ±0.27 °C, while the mean absolute error across all calibration points was ±0.18 °C (See Table 1). The measured deviations remained within the acceptable tolerance for the present study, demonstrating that the installed thermocouples were functioning properly and that the resulting temperature data were sufficiently accurate for system performance analysis. In addition, repeated calibration checks confirmed that the sensors exhibited stable responses without noticeable drift. Based on these results, the thermocouple measurements were considered reliable for subsequent experimental testing.

An uncertainty analysis was conducted to quantify the reliability of both measured and derived parameters. Uncertainties of direct measurements were estimated based on instrument specifications and calibration results, while uncertainties of derived quantities were calculated using standard root-sum-square (RSS) error propagation.

The uncertainties associated with air velocity, temperature, electrical measurements, and geometric dimensions were propagated to determine the uncertainty ranges of the calculated thermal and electrical performance parameters. The resulting uncertainty ranges are summarised in Table 2, indicating that the experimental errors were within an acceptable range for system performance evaluation.

The uncertainty analysis enhances the transparency and reproducibility of the experimental methodology and provides a quantitative basis for evaluating the reliability of the reported results. Total expanded uncertainties for and COP were estimated to be in the ranges of 4.5% - 7.2% and 5.0% - 8.5%, respectively.

The experimental dataset consisted of direct measurements and derived quantities, structured as follows:

represent the supplied voltage and current, respectively, cp is the specific heat capacity of air, indicates air mass flow rate, v is measured air velocity and subscripts indicate hot and cold lines and A is the cross section area of the duct.

The experimental dataset was obtained from six independent thermal energy system test runs and merged into a dataset containing 487 records. Each record includes input variables, the target output, and derived thermodynamic performance indicators. In addition to the raw inputs and outputs, two derived quantities were calculated. The derived values were not used as predictors but were retained for secondary analysis of system performance. A dataset sample is shown in Figure 6. For each experimental run, the initial 10–20 minutes of operation were excluded from the dataset to remove start-up transients. During this period, the system undergoes rapid thermal adjustments, including heat accumulation within the thermoelectric modules, heat sinks, and ducting, as well as stabilization of airflow and electrical input conditions.

The present study is explicitly focused on quasi-steady-state operation, where system variables vary within a relatively stable range. This focus enables the development of regression models that capture the steady thermal behaviour of the system without being influenced by strong time-dependent effects.

While transient dynamics are physically important and can significantly influence system performance, particularly COP during start-up and load changes, they require dedicated time-dependent modelling approaches and higher-resolution temporal data. Such analysis is beyond the scope of the current study but represents an important direction for future research.

In order to assess performance under different operating conditions, six independent tests were conducted in the University of Nottingham Buildings, Energy and Environment Laboratory. Figure 7 shows the measured room temperatures and hot side exit temperatures. For each test, the initial 10–20 min of operation was discarded to allow the duct unit to warm up. Although the warm-up period is not, by itself, a reliable indicator of performance, retaining it would introduce strong transients into the dataset. We therefore report quasi-steady segments to characterise the unit near steady operation. As a result, the reported performance is slightly higher than a full-cycle average, but it remains representative of sustained heating operation. Ambient temperature was imposed via the environmental chamber set-point. The supplied cold-air temperature increased slightly before entering the unit due to duct heat gains; in practice, similar effects can occur depending on installation location and should be considered in performance evaluation.

In Test 1, the chamber was set to 8 °C and 80% RH (winter conditions), as shown in Figure 7. The system received 425 W electrical input, and the hot-side fan speed was adjusted to maintain an air velocity of 3.5 m s−1. The hot-side outlet reached around 50 ◦C, not suitable for direct room supply, but viable for mixing with cold outdoor air, and the measured COP ≈ 1.8. In Test 2, the chamber temperature was 10 °C and the hot-side fan speed was slightly reduced to 3.0 m s−1. Consequently, the hot-air supply temperature increased to 55 °C, and COP improved to 2.1.

In Test 3, the chamber conditions were the same as in Test 2, but the hot-side air velocity was further reduced to probe the unit’s operating limits. The hot-air supply temperature rose to ≈ 58 °C, while COP declined to ≈ 1.9, indicating performance degradation as the hot-side temperature approached values that are sub-optimal, and close to the safe operating limits, for the TECs. In Tests 4–5, the electrical input was reduced to 170 W and the hot-side air velocity to 2.5 m s−1 to assess low-power operation. In Test 4, the hot supply temperature stabilised at around 35 °C, appropriate for direct space heating, with COP of 1.7. In Test 5, increasing the cold-side setpoint to 12 °C left the hot supply temperature essentially unchanged but yielded a slight COP improvement. In Test 6, the setup was returned to the Test 1 conditions to check repeatability; comparable results were obtained. Collectively, these six tests delineate a practical operating envelope for realistic building applications.

Data preprocessing followed several systematic steps to ensure consistency and model readiness. First, the datasets from six independent experimental runs were merged into a unified structure, removing redundant time-stamp metadata while retaining the key thermodynamic variables. Second, pre-computed and 𝐶𝑂𝑃 values were excluded during training to prevent data leakage, as they are deterministic functions of and other inputs. Third, all input variables were inspected for zero variance, and those with constant values across all samples were removed. Finally, the input features were normalized to have a zero mean and unit variance, a crucial step, particularly for artificial neural networks (ANNs) and support vector machines (SVMs), which are sensitive to feature scaling. The dataset was then split into training (80%) and testing (20%) subsets using stratified sampling based on the variable to preserve the distribution of the output variable.

To comprehensively evaluate predictive performance, a diverse set of regression models was implemented:

This ensemble of models was deliberately chosen to encompass both interpretable baselines and more flexible machine learning approaches, thereby enabling a robust performance comparison.

Model evaluation was performed on the held-out test set using three standard regression performance metrics: root mean squared error (RMSE), mean absolute error (MAE), and the coefficient of determination (). RMSE penalizes larger errors more heavily, thereby highlighting model robustness. MAE provides an easily interpretable measure of average prediction error, and quantifies the proportion of variance in explained by the model. Cross- validation was also conducted during training to assess model stability and mitigate overfitting.

The summary of model performances is presented in Table 3. Among all models tested, Linear Regression yielded the lowest RMSE on the test set, followed closely by Decision Trees and Random Forest, indicating that the relationship between inputs and was predominantly linear. More complex neural models (Neural Net and BRNN) underperformed, likely due to limited dataset size and convergence issues.

The superior performance of Linear Regression can be interpreted in light of the underlying thermodynamic behaviour of the thermoelectric system. Under quasi-steady operating conditions, the dominant physical relationships governing system performance are inherently linear or near linear. In particular, the heat transfer rate is defined as a linear function of mass flow rate and temperature difference and the experimental conditions are controlled within a relatively narrow operating range, the resulting system response exhibits approximately linear behaviour with respect to key input variables.

Furthermore, the thermoelectric modules operate within a quasi-steady regime, where input electrical power and temperature gradients vary smoothly without strong nonlinear transients. While thermoelectric materials can exhibit nonlinear characteristics under extreme conditions, these effects are limited within the operating envelope considered in this study.

As a result, the mapping between input variables and the hot-side outlet temperature can be effectively approximated using linear relationships. This explains why Linear Regression not only achieves the lowest prediction error but also generalizes better than more complex models, which may overfit the limited dataset without capturing additional meaningful structure.

To further evaluate the practical utility of the regression framework, the experimentally measured thermal performance indicators–namely, the heat transfer rate and the coefficient of performance (COP)–were compared against values recomputed using the predicted from the best-performing model (linear regression).

Table 4 summarizes the error metrics between measured and recomputed indicators. The recomputed Q ̇ achieved an RMSE of 87.2 𝑊 and an MAE of 37.8 𝑊, while COP achieved an RMSE of 0.213 and an MAE of 0.100. These low error magnitudes indicate that the regression-predicted can be reliably used to derive secondary performance quantities with minimal degradation in accuracy.

Figures 9 and 10 complement these numerical results by illustrating the temporal evolution of the measured and recomputed indicators. The line plots show that the recomputed and COP closely follow the experimental measurements across varying operating conditions, reinforcing the quantitative evidence from Table 4.

In Figure 9, the recomputed heat transfer rate tracks the experimental with high fidelity, accurately capturing steady-state regions and major operating transitions. Minor discrepancies appear during abrupt transients, where nonlinear system responses and measurement noise can lead to deviations. Despite these localized differences, the strong alignment confirms that the regression model preserves the thermodynamic integrity of the system.

A comparable trend is observed in Figure 10, where the recomputed COP mirrors the experimental profile. The predictions remain stable across most operating regimes, with only slight underestimations at peak performance intervals. This consistency is particularly significant, as it demonstrates that the regression approach provides both statistical accuracy and physically meaningful outcomes.

Taken together, the metrics in Table 4 and the visual trends in Figures 9 and 10 highlight the robustness of the linear regression model in supporting reliable thermal performance evaluation. This dual validation underscores the model’s suitability for deployment in real-time monitoring and decision-support applications in building energy systems.

While the recomputed heat transfer rate and COP closely follow the experimental trends, noticeable deviations are observed during transient periods. These discrepancies can be attributed to several factors. First, the regression models are trained on quasi-steady-state data and therefore do not explicitly capture transient thermal dynamics, such as short-term heat accumulation within the heat sinks, thermoelectric modules, and ducting system. During rapid changes in operating conditions, these effects can lead to temporary mismatches between predicted and measured responses. Second, variations in fan speed and airflow conditions can introduce fluctuations in convective heat transfer, particularly during transitions between operating points. These variations may not be fully reflected in the input variables used for regression, contributing to localized prediction errors. Third, measurement noise and sensor response time, especially for thermocouples, can introduce small temporal delays and uncertainties in recorded temperatures, further contributing to deviations.

In addition, the calculation of heat transfer rate and COP involves multiple measured variables, and therefore uncertainties propagate through these calculations. In particular, small errors in temperature difference and mass flow rate directly influence the estimated heat transfer rate , which in turn affects the COP.

Despite these localized deviations, the overall agreement between measured and recomputed values confirms that the regression model provides a reliable approximation of system performance under quasi-steady conditions.

The regression model was implemented within a Shiny-based graphical interface to enable interactive evaluation of thermoelectric HVAC performance. Rather than serving as a standalone visualization tool, the interface functions as a decision-support platform, allowing users to explore system behaviour under varying operating conditions.

The GUI integrates model predictions with physics-based recomputation of key performance indicators, including heat transfer rate and COP. This ensures that predicted outputs remain physically interpretable and directly relevant to engineering analysis.

By enabling real-time adjustment of input variables within experimentally validated ranges, the interface supports scenario-based exploration, allowing users to assess how variations in operating conditions influence system performance. This capability is particularly valuable for identifying optimal operating regimes and understanding system sensitivity to key parameters.

Furthermore, the integration of predictive modelling with dynamic visualization facilitates rapid interpretation of system behaviour, supporting applications in system monitoring, design evaluation, and operator training.

While previous studies have explored experimental thermoelectric systems, regression-based modelling, or user-oriented tools independently, the novelty of this work lies in their structured integration and validation within a single framework. The contributions of this study are not based on the introduction of fundamentally new algorithms, but rather on:

The proposed GUI demonstrates how data-driven models can be operationalized into system monitoring, operator training, and energy efficiency assessment tools by combining predictive analytics with interactive visualization. This dual emphasis on predictive accuracy and user-oriented design underscores the practical relevance of the work and its potential for adoption in building energy system management. The interface includes multiple visualization modes and logging functionality to support both instantaneous and temporal performance analysis (Figs. 11-13).

The Shiny-based implementation encompasses the entire research workflow, from rigorous regression modelling and validation to real-time prediction, physical precomputation, and interactive visualization. By embedding the best- performing model into an accessible GUI, this work demonstrates a practical pathway for translating advanced data-driven models into operational tools. Such integration is particularly valuable in energy system applications, where decision-makers often require interpretable, physics-grounded, and user-friendly platforms rather than abstract model outputs. The proposed framework, therefore, not only advances predictive accuracy but also enhances transparency, usability, and applicability — bridging the gap between academic modelling and real-world deployment.

This work demonstrates an integrated pathway from experimental data acquisition to model development and real-time deployment for thermoelectric HVAC systems. It should be noted that transient behaviour, including start-up dynamics and thermal inertia effects, is not captured in the present modelling framework and may contribute to additional variability in real-world operation. A key consideration in interpreting the modelling results is the size and structure of the experimental dataset. The dataset comprises 487 samples obtained from six steady-state test conditions, which represents a moderate-scale dataset in the context of machine learning applications. While sufficient for regression analysis and comparative benchmarking of interpretable models, this data volume is relatively limited for training more complex models such as deep neural networks. The observed underperformance of neural network-based models (NeuralNet and BRNN) can therefore be attributed to insufficient data to support parameter-rich architectures, as well as potential convergence and generalization challenges. In contrast, simpler models such as Linear Regression and tree-based methods demonstrated strong and stable performance, reflecting the structured nature of the dataset and the predominantly linear relationships between variables.

These results highlight the importance of aligning model complexity with dataset scale. For moderate-sized, experimentally derived datasets, simpler and more interpretable models may offer superior performance and robustness compared to more complex machine learning approaches. The discussion below highlights the methodological contributions, findings, and broader significance.