Performance prediction of electronic fan and water pump of engine cooling system based on joint simulation and machine learning

Abstract

The performance of fans and pumps is pivotal to the efficiency and responsiveness of the engine cooling system. In this study, a joint simulation model incorporating a detailed engine cooling system was developed and calibrated using vehicle road cycle tests, and the predictive capabilities of four different machine learning models for water pump and fan speeds were systematically evaluated. Calibration results indicate that the simulated speeds deviate from experimental values by less than 2%, accurately reflecting real-world driving conditions. Moreover, the instantaneous fuel consumption closely mirrors the experimental data, and the error in cumulative fuel consumption under the NEDC is limited to 1.4%. The simulation outcomes for the cooling system remain within a 5% error margin, thus meeting the designated calibration criteria. Among the water pump speed prediction models, the SVR model demonstrates the highest accuracy and reliability, achieving a test mean square error (MSE) of 0.03986. In contrast, for fan speed prediction, the RF model delivers superior performance with a test MSE of 0.00052, aligning closely with experimental observations without overfitting. Consequently, the RF model proves to be the most accurate and reliable approach for fan speed prediction. These findings provide a solid theoretical basis and a robust modeling foundation for intelligent management of engine cooling systems.

Introduction

In the face of escalating concerns over environmental pollution and energy shortages, the sustainable development of human society is encountering significant obstacles¹. Consequently, the pursuit of highly efficient, energy-saving automotive technologies has become a top priority. As the principal power source in automobiles, engine energy-saving techniques (including turbocharging and lean combustion) have progressed rapidly^2,3. These innovations have dramatically elevated engine thermal efficiency from under 5% to nearly 50%, marking a considerable leap in performance⁴. However, the increased heat load on internal engine components has intensified the need for effective heat dissipation, thereby placing greater demands on the cooling system. During combustion, around 20–30% of the released heat is transferred to the coolant through the combustion chamber wall and eventually dispersed into the atmosphere⁵. Furthermore, subsystems such as the intercooler and lubricating oil circuit depend on the same coolant for heat removal, significantly broadening the functional scope of the cooling system^6,7.

Most traditional cooling systems rely on mechanically driven components, where the water pump and fan are belt-driven from the crankshaft, causing their speeds to fluctuate with engine rotation⁸. This configuration substantially restricts the system flexibility and responsiveness. Moreover, to ensure engine safety under extreme conditions, these systems are typically designed to handle maximum loads, resulting in excessive heat dissipation in most real-world scenarios⁹. Studies indicate that only 3–5% of the operational duration of conventional cooling systems precisely aligns with the engine actual heat rejection requirements. For the remainder of the time, they either overcool or respond inadequately to changing heat loads¹⁰. In practice, vehicle operating conditions vary extensively, and the associated cooling needs differ substantially among these scenarios. Conventional systems cannot dynamically adjust coolant temperature to maintain it within the optimal range¹¹. This limitation not only leads to energy inefficiencies but also risks overcooling, ultimately compromising engine performance. When coolant temperature drops excessively, the resultant lower cylinder wall temperature reduces combustion efficiency and increases frictional losses, thereby elevating fuel consumption¹². Consequently, the inability of traditional cooling systems to ensure precise temperature regulation has become increasingly problematic (particularly in high-efficiency modern engines), and underscores the urgent need for more intelligent, adaptive solutions¹³.

Electronic water pumps present notable advantages over traditional mechanical pumps, primarily due to their capacity to independently regulate speed in response to real-time vehicle operating conditions¹⁴. This capability facilitates precise management of coolant flow, thereby optimizing engine cooling. Furthermore, electronic water pumps are generally more compact, simpler to install and better suited to the limited space often available in modern vehicles¹⁵. In contrast, mechanical water pumps, directly driven by engine speed, cease functioning once the engine is turned off. However, even after shutdown, the cylinder temperature can remain high, causing continued heat transfer to the coolant and potentially leading to localized boiling or engine damage¹⁶. By virtue of their electrical drive, electronic water pumps can continue operating post-shutdown, preserving normal coolant flow and preventing thermal harm. Although these pumps draw electrical energy from the engine output (which typically has a conversion efficiency of around 60%), they nevertheless provide substantial energy-saving benefits¹⁷. For instance, Cortona et al.¹⁸ designed an electronically driven cooling system and optimized it using a prior control strategy, and the experimental results showed that the electronic water pump consumed only 16% of the power required by its mechanical counterpart while satisfying cooling demands. Even after accounting for conversion losses, the electronic pump remained more efficient. Likewise, Cho et al.¹⁹ replaced a conventional mechanical water pump with an electronic alternative, combining experimental and simulation analyses. Their findings demonstrated that this solution reduced coolant flow, saved 87% of energy consumption and decreased radiator size by 27%, all without sacrificing cooling performance.

Electronic fans likewise exceed traditional mechanical fans in both flexibility and efficiency. Conventional mechanical fans are belt-driven from the engine, causing fan speed to vary proportionally with engine rpm²⁰. Such an arrangement restricts their ability to meet the engine’s diverse cooling demands, especially under low-load or low-speed conditions, where fan efficiency tends to be suboptimal²¹. In contrast, electronic fans are powered electrically, enabling them to regulate speed independently in response to real-time engine and vehicle requirements. This ensures precise airflow control and enhances overall cooling efficiency. Electronic fans not only reduce energy consumption under low engine loads but also provide sufficient cooling capacity during high-load scenarios²². Their smaller size and lower weight compared to mechanical fans further contribute to reduced vehicle weight and improved fuel economy. Additionally, because they rely on an electrical power source, electronic fans can continue functioning even after the engine shuts down²³. This operation prevents coolant from remaining at elevated temperatures for prolonged periods, thereby mitigating thermal damage and preserving engine integrity. Although electronic fans do consume electrical energy, their capacity to modulate power usage based on real-time demand typically results in lower overall energy consumption than conventional fans²⁴. Accordingly, they deliver significant advantages in terms of energy savings and cooling performance. Reflecting this, an increasing number of automotive manufacturers have adopted electronic fans across various vehicle segments, making them a key component in modern automotive cooling systems, particularly in the context of energy conservation and powertrain optimization²⁵.

Despite marked advances in electronic water pumps and fans, several research gaps persist. First, much of the existing literature concentrates on individual components rather than examining the cooling system as a cohesive entity, thereby limiting insights into the intricate interplay among the water pump, fan and engine operating parameters. Furthermore, most studies focus predominantly on experimental approaches or steady-state simulations, lacking the robust predictive capacity required to optimize performance across a broad spectrum of dynamic driving scenarios. While some investigations do consider the potential energy savings that electronic components can provide, they often rely on simplified models or isolated performance indices, offering only a partial perspective on balancing thermal management, energy efficiency and component reliability. Moreover, relatively few studies explore advanced techniques (such as combining machine learning with joint simulation) to accurately forecast the performance of electronic water pumps and fans under real-world operating conditions. To address these gaps, the present research aims to enhance the predictive modeling of electronic water pumps and fans using a joint simulation and machine learning framework. First, a detailed multi-physics simulation model was established based on empirical data, capturing complex interactions among engine combustion, coolant flow and fan airflow. This simulation platform was then integrated with machine learning algorithms trained on both simulation outputs and experimental observations, resulting in four predictive models capable of providing real-time performance estimates across a wide range of operational scenarios. By systematically merging simulation and machine learning, this study tackles a critical gap in existing research and lays a foundation for more adaptive, energy-efficient approaches to engine cooling.

Methods

Experimental setup

The prototype vehicle used in this study is a passenger car equipped with a conventional cooling system and a six-speed automatic transmission. Table 1 summarizes its key technical parameters. The test engine, a commercially available supercharged gasoline engine with intake manifold fuel injection, incorporates advanced features such as turbocharging and intake variable valve timing (VVT) to enhance both performance and fuel efficiency, and its main technical specifications are listed in Table 2. To ensure the accuracy of the test data, rigorous attention must be paid to various factors, including experimental equipment, methods, standards and conditions. It is crucial that the test equipment is operated correctly, and that the corresponding specifications and requirements are strictly followed so as to keep measurements within the specified error range. The tests are conducted under national standards to evaluate engine performance, and the experimental setup comprises an AVL bench test system as well as several measurement and control instruments, such as an AVL electric dynamometer, a Lambda analyzer and an emissions analyzer. This setup is characterized by excellent stability and high measurement precision, ensuring reliable data collection and analysis throughout the testing process. Figure 1 presents the prototype vehicle and a schematic of the experimental setup.

Table 1.

Main technical parameters of the prototype vehicle.

Item	Content
Mass (kg)	1620
Length × Width × Height (mm)	4567 × 1786 × 1454
Wheelbase (mm)	2750
Tire radius (mm)	353
Drive type (-)	Front drive
Rolling resistance coefficient (-)	0.0086
Maximum speed (km/h)	200
Wind resistance coefficient (-)	0.39
Windward area (m2)	2.4

Fig. 1.

Prototype vehicle and schematic diagram of the test.

Table 2.

Principal technical parameters of the tested engine.

Item	Content
Type (-)	Four-stroke, intake VVT
Stroke (mm)	84.8
Bore (mm)	75
Displacement (L)	1.4
Compression ratio (-)	9
Intake form (-)	Turbocharge
Connecting rod length (mm)	133
Rated torque (N·m)/speed (r/min)	220/2500
Rated power (kW)/speed (r/min)	92/5500

Joint simulation model

A joint simulation model was developed based on road-cycle testing of a best-selling production vehicle. The recorded data from these tests were used to calibrate the simulation model, which is primarily built in GT-Cool. With the engine and vehicle parameters described in the preceding section, the relevant model configurations were established in GT-Suite, and the cooling system model was calibrated using the test data. Final simulation outputs were visualized in GT-Post, following standard modeling procedures. The comprehensive cooling system model encompasses several primary subsystems, namely the engine model, the cooling system, the water pump model, the radiator model and the fan model. These subsystems are tightly interconnected and collectively form an integrated simulation framework for the cooling system. Figure 2 illustrates the overall model architecture, highlighting the key interactions and operational principles necessary for an in-depth analysis of cooling system behavior.

Fig. 2.

Complete model of the prototype vehicle.

Because engine performance directly affects critical metrics such as emissions and fuel consumption²⁶, the fidelity of the cooling system simulation hinges on an accurate and robust engine model. In this study, the engine model was developed in the GT-Power module of GT-Suite. By combining the various engine components (intake and exhaust piping, the crankcase, cylinders and throttle), the complete engine model was assembled, as depicted in Fig. 3. These modules provide essential coverage of the entire engine operating cycle, from intake and combustion to exhaust. This modeling approach enables detailed simulation and analysis of combustion processes, heat transfer characteristics and related parameters. Additionally, to enhance the precision of coolant heat transfer predictions, the thermal properties of the coolant are configured based on factors such as temperature, dynamic viscosity and thermal conductivity.

Fig. 3.

Engine model of the prototype vehicle.

The cooling system moderates engine temperature through heat dissipation, ensuring that engine components remain within safe operating ranges²⁷. Excessive temperature can cause increased component wear, diminished efficiency and unacceptable emissions. Conversely, overcooling can result in higher pollutant emissions, elevated wear and wasted energy. In this study, the cooling system is simulated in the GT-Cool module, and appropriate operating parameters are specified for each key component, ensuring realistic behavior within the simulated environment. As shown in Fig. 4, the cooling system model comprises modules for the radiator, water pump, fan and thermostat. These elements interact to manage temperature and thermal loads under diverse operating conditions, thereby safeguarding efficient and reliable engine operation.

Fig. 4.

Overall model structure of the cooling system.

The water pump circulates coolant through the engine to regulate its temperature and preserve thermal balance. By continuously circulating fluid, the pump removes excessive heat generated by the engine, preventing potentially damaging temperature extremes. The water pump analyzed here is a centrifugal type, known for its high flow efficiency and operational stability. The shaft power (P_b) of the water pump can be calculated by the Eq. (1):

1

where H, Q and ε are the pump head, volume flow rate and isentropic efficiency, respectively. The pump head map is demonstrated in Fig. 5, which was obtained experimentally to characterize the pump head under different operating conditions.

Fig. 5.

Pump head map of the prototype vehicle.

The automotive radiator’s principal role is to lower coolant temperature so that heat can be effectively transferred away from the engine, maintaining its optimal thermal state. As a key part of the cooling system, the radiator’s performance significantly influences the overall thermal management of the engine. In GT-Cool, accurate radiator simulation depends on providing specific parameters that mirror real-world conditions. Table 3 presents the radiator parameters employed in this study, reflecting the actual structural attributes of the test vehicle’s radiator to ensure that simulation results are consistent with experimental observations.

Table 3.

Structural parameters of the radiator.

Item	Value
Hight (mm)	44
Width (mm)	645.5
Thickness (mm)	15
Radiator core rows (-)	1
Number of pipes per row for radiator cores (-)	70
Radiator core diameter (mm)	23.5

Finally, the fan supplies supplementary cooling airflow to the radiator, preventing overheating and maintaining effective heat exchange. By boosting the airflow, the fan bolsters the radiator’s heat-dissipating capacity and stabilizes coolant temperature, thereby further enhancing the engine’s thermal management. In GT-Cool, capturing the fan’s operation accurately necessitates input of parameters including power, rotational speed and airflow rate. These inputs allow the simulation to reflect the fan’s performance under varying conditions. Figure 6 illustrates the fan’s pressure-rise map derived from experimental data, providing key insights into its dynamic behavior and integration within the cooling process.

Fig. 6.

Fan pressure rise MAP.

Machine learning model

KNN is a classical supervised learning algorithm extensively used for both classification and regression, and its fundamental principle is to predict the label or value of an unknown sample by measuring distances between observations. In practice, KNN identifies the K closest labeled samples in the feature space and then employs either a majority vote or a weighted average of these neighbors to determine the final output. A critical aspect of KNN lies in the choice of distance metric: Euclidean distance is commonly adopted for continuous variables, whereas Manhattan distance is often used for categorical attributes. Moreover, KNN is notably sensitive to noise and outliers, and data preprocessing and normalization are typically performed to mitigate the impact of varying feature scales. The number of neighbors (K) also substantially influences model performance. A very small K may lead to overfitting by rendering the model too sensitive to noise in the training data, while an excessively large K can lead to underfitting by obscuring fine-grained data patterns. The optimal K is usually determined via cross-validation or other model evaluation techniques.

SVR is a regression-oriented method derived from the theoretical framework of Support Vector Machines (SVM), and its core concept is to construct a regression hyperplane in a high-dimensional feature space that optimally fits the data by maximizing the separation margin, in line with the maximum margin optimization criterion. Unlike conventional regression models, SVR does not solely target minimizing the training error. Instead, it tolerates deviations within a specified range, thereby achieving enhanced robustness against noise and outliers. Conceptually, SVR identifies a function in the feature space such that most data points lie within a defined ε-tube around the regression curve, where ε represents the permissible error threshold. Points outside this boundary are regarded as support vectors, and only these vectors contribute to determining the final model output. This design limits overfitting and boosts generalization, and training an SVR involves solving a quadratic programming problem that locates the optimal regression hyperplane and support vectors. Through kernel methods, SVR can transform inputs into a higher-dimensional space, thereby effectively managing nonlinear regression problems.

RF is an ensemble learning technique widely used for classification and regression, and it comprises multiple decision trees whose outputs are aggregated (via Bootstrap Aggregating or Bagging) to enhance predictive accuracy and reliability. As a non-parametric algorithm, RF exhibits high fault tolerance and handles high-dimensional, noisy or incomplete datasets effectively. During its construction, multiple sub-datasets are generated through random sampling from the original dataset, meaning that some samples may be repeated within each sub-dataset. A distinct decision tree is trained on each sub-dataset, and a random subset of features is considered instead of the full feature set at each node split. This randomness fosters diversity among the trees, thus improving the model generalization performance. Typically, the Classification and Regression Tree (CART) algorithm is used to form each decision tree, relying on metrics such as Gini impurity (for classification) or mean squared error (for regression) to select split nodes. Often, these trees are grown to their maximum depth without pruning to preserve diversity. In the prediction phase, classification results are integrated by voting, whereas regression outputs are combined by averaging the predictions of all individual trees.

AdaBoost is a popular ensemble algorithm aimed at bolstering classification performance by sequentially assembling multiple weak classifiers, frequently simple decision trees. Its core mechanism is to iteratively adjust sample weights, ensuring that the subsequent weak classifiers focus more intensively on those samples misclassified by earlier classifiers, thereby progressively enhancing accuracy and robustness. Conceptually, AdaBoost is an additive model whereby each iteration yields a new weak classifier, and the weights of training samples are updated based on the previous classifier’s performance. Specifically, AdaBoost begins by assigning uniform weights to all samples. At each iteration, a weak classifier (often a decision tree stump) is trained, its error rate ε_t is computed and the sample weights are updated accordingly. Classifiers with lower error rates receive greater emphasis, whereas those with higher error rates have reduced influence in subsequent rounds. This process amplifies the weights of misclassified samples while reducing those of correctly classified ones, prompting new classifiers to focus on the previously misclassified instances and thereby boosting overall accuracy. Ultimately, the strong classifier is formed by a weighted combination of all the weak classifiers. The weight α_t of each classifier is related to its error rate ε_t, which is calculated by the Eq. (2):

2

The final predictions are generated through weighted voting or weighted averaging, where the contribution of each weak classifier is adjusted according to its weight α_t.

Results and discussions

Joint simulation model validation

Vehicle performance calibration is essential for evaluating the agreement between a simulation model and real-world vehicle behavior. As illustrated in Fig. 7, this process involves comparing several critical parameters, including vehicle speed, engine speed, engine torque, instantaneous fuel consumption, and cumulative fuel consumption. Figure 7(a) compares simulated and measured vehicle speeds. The results demonstrate close alignment, with a maximum relative error below 2%, indicating that the simulation model accurately captures the vehicle’s operating status under various conditions. In Fig. 7(b), simulated engine speed generally matches the test data. However, in the second half of the cycle (shaded region), a sharper increase in the simulated engine speed is observed during rapid vehicle speed changes. This discrepancy stems from GT-Suite’s immediate response to varying vehicle speed, whereas actual drivetrain components (e.g., clutch and transmission) introduce a delay, resulting in a slight lag in measured engine speed. Despite this, the overall simulation accuracy remains within acceptable limits. Figure 7(c) shows the comparison of engine torque. Torque evolution tracks changes in engine speed, yielding high consistency between simulation and experiment in the first half. Under high-speed, heavy-load conditions in the second half, the simulated torque exhibits a sharp rise, owing to the model’s rapid adjustment of fuel injection based on throttle changes, while an effect that the physical vehicle replicates more gradually. Figure 7(d) presents instantaneous fuel consumption, which mostly aligns with the test data, especially in later stages where simulated and experimental values overlap almost entirely. During the initial 200 s, however, simulated consumption is slightly lower, a discrepancy primarily attributable to the model’s simplified representation of the cold-start process. As the test proceeds, simulated and measured fuel consumption converge, indicating that the model increasingly reflects real-world combustion processes. During rapid speed changes, surge phenomena can also be detected in the simulation, as computational calculations respond more promptly than mechanical systems in the actual engine. Finally, Fig. 7(e) compares simulated and measured cumulative fuel consumption. The two curves remain close, although a minor gap gradually widens over time due to the accumulation of small errors. In the NEDC cycle test, the measured cumulative fuel consumption is 845.8 g, compared to 833.6 g in the simulation, corresponding to a relative error of only 1.4%. These results confirm that the simulation model can accurately represent the vehicle’s overall fuel economy. In summary, calibration of these diverse performance indicators reveals strong consistency between the simulation model and experimental data, thereby validating the model’s accuracy and reliability for both vehicle performance and fuel economy studies.

Fig. 7.

Comparison of experimental and simulation values for key parameters.

Performance validation for the cooling system primarily involves assessing key parameters such as flow rates in the primary and secondary coolant loops, along with system temperatures. Specifically, the large-loop flow rate is predominantly determined by radiator parameters, whereas the small-loop flow rate is regulated by the HVAC system. Figure 8 illustrates the radiator’s major performance indicators, including coolant flow rate, inlet temperature, and outlet temperature. From Fig. 8(a), the simulated large-loop flow rates closely match the experimental data, albeit with slightly higher early-stage values. This discrepancy occurs because the thermostat in the simulation responds immediately upon reaching its opening temperature, whereas the wax-type thermostat in practice exhibits a lag, thus slowing the coolant flow increase. Figure 8(b) compares radiator inlet temperatures, revealing that the simulated values generally align with the experimental results, although between 300 and 500 s the simulated inlet temperature is marginally higher. This behavior arises from the simulation’s quicker thermostat response, which admits high-temperature coolant to the radiator more rapidly, thereby increasing the inlet temperature. In Fig. 8(c), from 300 to 500 s, the simulated radiator outlet temperature also exceeds the measured values. As before, this discrepancy reflects the thermostat’s swifter response in the simulation, directing hot coolant to the radiator sooner and thereby raising its outlet temperature. Beyond approximately 1100 s, the simulated large-loop flow rates drop below the experimental values because of a slightly smaller thermostat opening in the model, reducing the flow of high-temperature coolant to the radiator even though heat dissipation demands remain unchanged. Consequently, the simulated radiator outlet temperature becomes lower than the measured temperature at this stage. Figure 9 displays the corresponding parameters for the HVAC system: coolant flow rate, inlet temperature, and outlet temperature. The simulation results closely agree with the experimental values, although the simulated HVAC outlet temperature is slightly lower during the initial phase. This minor discrepancy occurs because the simulation’s HVAC subsystem absorbs a portion of coolant heat early on. During the high-speed segment of the NEDC cycle, the small-loop coolant flow rate shows pronounced fluctuations, driven by the rapid increase in engine speed and the associated variations in heat rejection demands. Moreover, the actual thermostat reacts relatively slowly to temperature changes, resulting in heightened temperature oscillations. Overall, most cooling system simulation outcomes show strong consistency with experimental observations. Although minor deviations arise during the initial thermostat opening and under high-speed, heavy-load conditions, the maximum relative error remains within 5%. This level of accuracy satisfies the calibration requirements for cooling system performance.

Fig. 8.

Experimental and simulation values of the key performance parameters of the radiator.

Fig. 9.

Experimental and simulation values of the key performance parameters of the HVAC.

Model prediction comparison

Data preprocessing is pivotal to model training, as data quality directly impacts predictive performance. In this study, normalization was used to map all sample features to the interval [0,1]. The primary aim of normalization is to mitigate the influence of disparate feature magnitudes on model training. Large discrepancies in feature values can cause those with higher magnitudes to dominate the training process, biasing the model and can also reduce the speed of convergence. Notably, the data employed herein originate from the joint simulation model. After normalization, the dataset was randomly divided into a training set (80% of the total data) and a test set (20%). Out of 1180 total observations, 944 were allocated to the training set and 236 to the test set. Because fan and water pump speeds strongly affect their performance, these speeds were designated as the model outputs, whereas vehicle speed, brake mean effective pressure (BMEP), engine speed, coolant temperature and thermostat opening served as model inputs. This study adopts the mean squared error (MSE) metric to evaluate model accuracy, and Table 4 presents the pertinent parameters for the KNN, SVR, RF and AdaBoost models.

Table 4.

Pertinent parameters for the four comparative ML models.

Model	Parameter	Value
KNN	N_neighbors	5
	Algorithm	kd_tree
	Leaf_size	30
SVR	Kernel	rbf
	Degree	3
	epsilon	0.1
RF	N_estimators	100
	Max_depth	3
	Min_samples_split	2
AdaBoost	N_estimators	100
	Learning_rate	0.1
	Loss	square

The predicted results for water pump speed are presented in Figs. 10 and 11; Table 5. Figure 10(a) illustrates that the KNN model predicted values for the test set generally align with the experimental data. However, significant deviations are observed in certain data points, particularly within the speed range of 3500 r/min to 4500 r/min, as highlighted in scatter plot 11(a). According to Table 5, the MSE for the KNN model on the test set is 0.04943, indicating a satisfactory prediction performance without evidence of overfitting. Further analysis of Fig. 10(b) reveals that the SVR model predictions closely match the experimental values, with only a few outliers exhibiting large deviations. Figure 11(b) shows that most SVR-predicted values are centrally distributed along the regression line, demonstrating superior overall performance compared to the KNN model. Specifically, the SVR model achieves an MSE of 0.03986 on the test set, significantly outperforming the KNN model. The RF model predicted values for the test set are depicted in Fig. 10(c) and show a strong overlap with the experimental data, with only minor deviations in individual predictions. These deviations, also observed in other models, are primarily attributable to inherent noise in the dataset rather than differences in model architecture. Figure 11(c) indicates that the RF model’s predictions are evenly distributed around the regression line. Although the RF model exhibits a lower MSE on the training set (0.00367) compared to the SVR model (0.02548), its MSE on the test set (0.04302) is slightly higher than that of the SVR model (0.03986). This suggests a minor degree of overfitting in the RF model. Figure 10(d) shows that the AdaBoost model’s predicted values for the test set generally agree with the experimental data, with minor deviations in most data points and larger deviations in a few instances. In Fig. 11(d), the predicted points predominantly lie above the regression line. Table 5 indicates that while the AdaBoost model has a lower MSE on the training set (0.02224) compared to the SVR model (0.02548), its MSE on the test set (0.07165) is higher than that of the SVR model (0.03986). This disparity also points to an overfitting issue within the AdaBoost model. In summary, the SVR model provides the most accurate and reliable predictions for water pump speed. It achieves a low MSE on the test set, exhibits high consistency with experimental values, and does not demonstrate significant overfitting. These characteristics confirm the SVR model’s effectiveness for predicting water pump speed with a high degree of accuracy and reliability.

Fig. 10.

Predicted results of the water pump speed on the test set.

Fig. 11.

Predicted results of the water pump speed on the test set.

Table 5.

Predicted results of the water pump speed.

Item	MSE of KNN	MSE of SVR	MSE of RF	MSE of AdaBoost
Training set	0.02109	0.02548	0.00367	0.02224
Test set	0.04943	0.03986	0.04302	0.07165
Total set	0.02959	0.02979	0.01547	0.03706

The prediction results for fan speed are presented in Figs. 12 and 13; Table 6. Figure 12(a) shows that the KNN model’s predicted values for the test set closely match the experimental values, with only slight deviations in a few data points. This is further illustrated in Fig. 13(a), where most predicted points are near the regression line, with noticeable deviations occurring between speeds of 3500 r/min and 4500 r/min. While this phenomenon is visible in both the line and scatter plots, it is more pronounced in the latter. Overall, the KNN model demonstrates good performance, achieving a MSE of 0.01426 on the test set. The MSE for the training set is slightly higher but very close to that of the test set, indicating that the KNN model has high accuracy and does not exhibit overfitting or underfitting. Figure 12(b) reveals that the predicted values of fan speed from the SVR model show a reasonable fit with the experimental data, but significant deviations remain in many data points, particularly in the higher speed ranges. As shown in Fig. 13(b), most predicted points deviate from the regression line, with only a few points falling on it. The MSE for the SVR model on the training set is 0.03317, significantly higher than that of the KNN model, while the test set MSE is 0.14572, much higher than the training set value. This disparity indicates clear overfitting in the SVR model. The RF model demonstrates outstanding performance in predicting fan speed. As shown in Fig. 12(c), the predicted values on the test set almost entirely overlap with the experimental data, which is further confirmed in Fig. 13(c), where the predicted points are evenly distributed on both sides of the regression line. The MSE for the RF model on the test set is only 0.00052, demonstrating exceptional prediction accuracy and excellent overall performance. The AdaBoost model presents more moderate performance. As shown in Fig. 12(d), the predicted values on the test set exhibit moderate overlap with the experimental data, though predictions near zero are particularly inaccurate. However, Fig. 13(d) shows that the majority of the predicted points are near the regression line, with an MSE of 0.00410 on the test set. Despite some inaccuracies in predicting values close to zero, the AdaBoost model generally provides predictions that are close to the actual values, with small deviations. However, its performance is not as strong as the RF model. In conclusion, the RF model performs the best in fan speed prediction. With an exceptionally low MSE on the test set, the predicted values align closely with the experimental data, and there are no significant overfitting issues. These characteristics demonstrate the RF model’s high accuracy and reliability for fan speed prediction. Therefore, the Random Forest-based prediction model was selected as the optimal model for fan speed prediction.

Fig. 12.

Predicted results of the fan speed on the test set.

Fig. 13.

Predicted results of the fan speed on the test set.

Table 6.

Predicted results of the fan speed.

Item	MSE of KNN	MSE of SVR	MSE of RF	MSE of AdaBoost
Training set	0.01013	0.03317	0.00006	0.00344
Test set	0.01426	0.14572	0.00052	0.00410
Total set	0.01137	0.03396	0.00019	0.00364

Conclusions

In this study, a joint simulation model and its detailed engine cooling system were developed and calibrated based on vehicle road cycle tests. On this basis, the prediction performance of four different machine learning models for water pump and fan speeds was comparatively analyzed. The main conclusions are shown below:

(1) The simulation model exhibits strong agreement with experimental data, thereby confirming its accuracy and reliability. Discrepancies in vehicle speed remain below 2%, closely capturing real-world driving conditions. Instantaneous fuel consumption aligns with test results following the initial cold start, and cumulative fuel consumption under the NEDC exhibits a minimal 1.4% error.

(2) After 1100 s, simulated flow rates fall slightly behind experimental values because of smaller thermostat openings. Similarly, HVAC system parameters display strong consistency with measured data, aside from minor early-stage temperature offsets. Overall, cooling system simulations maintain errors within 5%, satisfying calibration accuracy requirements.

(3) Of the four machine learning models evaluated, the SVR model achieves the highest accuracy (test-set MSE = 0.03986), making it the most precise and reliable choice for water pump speed prediction. In contrast, the KNN model exhibits marked deviations in the 3500–4500 r/min range, while the RF model shows slight overfitting (test-set MSE = 0.04302). The AdaBoost model has the largest test-set MSE (0.07165), indicating pronounced overfitting.

(4) For fan speed, KNN demonstrates good accuracy (test-set MSE = 0.01426) without overfitting, whereas the SVR model clearly overfits (test-set MSE = 0.14572). Although AdaBoost performs moderately (test-set MSE = 0.00410), it struggles at low-speed prediction. The RF model excels (test-set MSE = 0.00052), showing strong alignment with experimental data and no evident overfitting, thereby constituting the optimal choice for fan speed prediction.

These findings not only provide theoretical basis for intelligent management of engine cooling system, but also offer modeling foundation for the comprehensive performance improvement of the vehicle. In the future, machine learning models and joint simulation models will be further combined to optimize the comprehensive performance of the vehicle.

Author contributions

Yujin Zou: Investigation, Data analysis and Writing this manuscript; Renwang Li: Supervision and Conceptualization; Honghua Pan: Supervision, Conceptualization, Methodology and Reviewing; Xiao Sun: Conceptualization and Reviewing; Jun Fu: Methodology and Reviewing;

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.