Toward Optimal Design of a Factory Air Conditioning System Based on Energy Consumption Prediction

Abstract

The Make-up Air Unit (MAU) is an air conditioning system which plays an important role in serving semiconductor cleanrooms. It provides constant temperature and humidity for fresh air through various sections, including fresh air filtration, preheating, precooling, humidification, recooling, reheating, air supply, and high-efficiency filtration. However, the commonly used PID control method of the MAU indicates a deficiency in energy consumption. Hence, this research introduces a proactive energy-saving optimization control method based on machine learning and intelligent optimization algorithms. Firstly, the machine learning methods are used to train historical data of the MAU, resulting in a data-driven prediction model of energy consumption for the system. Subsequently, the customized genetic algorithm (GA) is used to optimize energy in cold and hot water systems. It facilitates the dynamic adjustment of the regulating valve opening for the cold and hot water coil in the fresh air unit, responding to real-time variations in outdoor air conditions. Meanwhile, it ensures that the supply air temperature and humidification adhere to specified requirements, thereby reducing the energy consumption associated with cold and hot water usage in the MAU. The experimental results indicate that the proposed algorithm can provide significant energy conservation in the MAU.

1. Introduction

1.1. Background

Common industrial plants include the electronics, food, pharmaceutical and new energy sectors. The high-cleanness area used to manufacture and service production within these industrial facilities is called a clean room [1]. The cleanrooms share common characteristics of being structurally complex, having high technological requirements, and varying environmental requirements [2]. The characteristics of the product determine the need for cleaning in the production process. Compared to other industries, environmental impurities can damage product characteristics. As the complexity of the products increases, strict control of the production environment becomes essential to ensure product quality.

In addition, global warming, resulting from carbon emissions, has become one of the most severe and urgent climate problems. Today, the construction sector directly generates 8% of the global carbon emissions due to the use of fossil fuels, and another 19% is indirectly emitted, resulting from the electricity and heat/cooling supply. Therefore, decarbonization in the building sector is necessary and promising for the global carbon neutrality target [3]. Hence, research on energy savings techniques in the building sector, for example factory air conditioning systems, i.e., the Make-Up Air Unit (MAU) system, has gained increasing attention in this study [4].

For the MAU system, it is crucial to control various air conditioning parameters during production, such as temperature, humidity, cleanliness, flow organization, and pressure balance. Conventional cleanrooms have the following characteristics:

• High temperature and humidity requirements: $T\le \pm 2 °$C, $RH\le \pm 5\%$.
• High requirements in cleanliness level.
• High air exchange rates and large fresh air supply.
• The balance in the pressure gradient.

The fresh outdoor air for the electronics plant is subjected to treatment by the MAU to meet the temperature and humidity requirements before entering the supply air manifold. Subsequently, air is transported through air supply ducts to the various production areas within the cleanroom. Figure 1 shows the operational principle of the MAU. The goal of our research in this paper is to search for the optimal cooling and heating capacities required by each coil in the air handling process under ideal conditions, while satisfying the MAU air supply requirements, thus maximizing the reduction in the MAU’s energy cost.

1.2. A Brief Introduction to the MAU’s Configuration and Control Strategy

As displayed in Figure 2, an MAU unit consists of five sections: precooling, preheating, humidifying, recooling, and reheating. Outdoor air is processed through these five stages to meet certain set specifications, including temperature and dew temperature, before being fed into cleanrooms. The precooling and preheating stages are not switched on at the same time, and it is usually the temperature or specific enthalpy of the outside air that determines which of the stages is switched on to process the outside air. After pre-processing, the air is humidified to raise the relative humidity to 100%. It then enters the recooling section for cooling and dehumidification to meet the set dew temperature. Finally, it enters the reheating section for heating to meet the temperature target. In summary, this is the whole process of air treatment in the MAU.

The MAU cools or heats air through hot and cold water coils, respectively, and valves are used to control the flow of water in the coils and thus the cooling or heating effect to achieve a preset target. PID control of valve openings is a common practice; however, an unreasonable setting based on experience can lead to wasted resources. For example, in winter mode, a high set value results in excessive humidification in the humidification section and and increase in the workload of the recooling section. In addition, PID control is less flexible and cannot adaptively adjust the control parameters according to the indoor and outdoor environment changes to maintain the optimal control state.

In summary, the original intention of designing this algorithm is to reduce the waste of energy without relying on expert experience to set the preset values of the pre-processing section. Hence, the MAU system can achieve adaptive adjustment according to environmental changes.

2. Related Work and the Motivation

Global warming, resulting from carbon emissions, has become one of the most severe and urgent climate problems. Nowadays, the building sector directly generates 8% of the global carbon emissions due to fossil fuel usage, and another 19% is indirectly emitted, resulting from electricity and heat/cooling supply. Therefore, decarbonization in the building sector is necessary and promising for the global carbon neutrality target [3,5,6,7]. Hence, the research about energy-saving techniques in the building sector, for example, the factory air conditioning systems in this study, has gained increasing attention.

Recently, an energy-saving control method for air conditioning based on support vector regression (SVR) and particle swarm optimization (PSO) was proposed [8], to optimize energy consumption while maintaining thermal comfort. The method considered indoor temperature, humidity, outdoor conditions, and thermal comfort constraints. By adjusting air conditioning settings intelligently, the method improved thermal comfort prediction accuracy and reduced energy consumption. A very new study [9] has explored energy-saving optimization for variable-flow air conditioning systems. This research aimed to enhance energy efficiency by dynamically adjusting flow rates based on demand and conditions. In [10], the energy-saving strategies for frequency-variable heat pump air conditioning systems was investigated, which focused on improving efficiency and reducing energy consumption. It is worth mentioning that the energy-saving rate of air conditioning systems varies based on urban climate. For example, drier climates tend to yield higher energy savings [11]. Also, in [12], climate change models were developed to predict meteorological parameters in the Greater Bay Area (Guangzhou, Nansha, Shenzhen, and Hong Kong), which can facilitate the climate-adaptive resilience in district buildings and cross-regional energy sharing.

The literature review and rational analysis show that the interdisciplinary between the machine learning and district energy systems shows promising prospects for the promotions of resilient and smart district energy systems [13,14,15]. The machine learning technique can be used in the prediction of district energy demand, robust model development, surrogate model [16,17] development for uncertainty and optimization analyses, geometrical and operating parameters’ optimal design, and efficient and robust energy management and control strategy development.

In the MAU system, traditional PID control is a common strategy that does not require the energy consumption model. The effect of the PID control method depends on whether the process variables are reasonable. When the process variables are unreasonable, the MAU wastes energy in the operation process. Based on the above literature review and analysis of traditional PID control methods, research gaps can be noticed:

• The PID control parameters are manually set based on experience; however, the system (or the parameters of PID) without professional operators may result in energy wastage. For example, a common problem is excessive humidification by the humidifier of the MAU in winter mode, followed by dehumidification through the cooling coil.
• Following the above issue, the energy cost of the MAU has not been considered in the control criterion of traditional PID control. Moreover, the roles of the machine learning techniques in energy prediction have not been characterized well in the MAU system. Hence, there is significant room to optimize the energy consumption in the overall framework of the MAU, in addition to meeting the requirements of the supply air temperature and humidity.
• The effect of PID control could be poor when outdoor air conditions and supply air requirements are complex. Moreover, it cannot adaptively adjust the control parameters according to changes in indoor and outdoor environments and maintain an optimal control state at all times.

To fill the aforementioned gap, we develop the data-driven optimization algorithm (DDOA) for the MAU, which is partly inspired from the recent research work of surrogate-assisted evolutionary algorithms [16,17]. The data-driven model of the MAU system can help make the operational parameters of PID more transparent. It simultaneously considers the air supply requirements and the energy cost of the MAU, through the customized optimization algorithm. To be specific, it adopts historical data and machine learning algorithms to identify patterns and make predictions without prior knowledge of the system’s physical properties. The data-driven models have several advantages like automatic pattern recognition, high accuracy, and self-improvement. Hence, we can develop the optimization method of the fresh air unit system through a mechanism model and historical data [18]. This not only facilitates the energy conversion in the air treatment process of the fresh air unit, but also realizes the prediction of supply air temperature, supply air dew point, and energy cost according to the outdoor air conditions.

3. The Proposed MAU Energy-Saving Control Method

The overall process of the proposed energy conservation framework in the MAU system mainly consists of the following four steps:

• Establish the energy consumption model of the MAU system: Based on the historical operation data of the MAU, we apply a machine learning algorithm to establish the data model. This model will correlate the coil opening with the energy supply of the MAU. Then, we can predict the temperature and the dew point of the supply air through an operation mechanism model of the MAU. Finally, the model is established to predict the MAU’s energy consumption for cold or hot water.
• Intelligent optimization method: It searches for the optimal coil opening to minimize energy consumption and achieve active energy-saving optimization.
• Control the MAU according to the optimization results: The algorithm controls the MAU according to the optimized coil opening. It also calculates the deviation between the actual value and the set value and corrects the deviation with the PID algorithm.
• Monitor the outdoor air temperature and humidity conditions in real time: When the temperature or humidity changes, the algorithm re-optimizes the energy saving.

The MAU energy-saving control method is shown in Figure 3. We can see that it consists of two main parts: establish the prediction model based on historical data, and apply the intelligent optimization algorithm [17,19,20]. To predict the energy cost of the MAU more accurately, the mechanistic model and the machine learning model (data-driven model) are simultaneously used here. Then, the intelligent optimization algorithm, i.e., the customized genetic algorithm (GA) [21,22], is applied to minimize the objective function of the prediction model, so that the optimized coil opening is provided to reduce the energy costs. For convenience, the symbols used in the process of establishing the models of the MAU and their meanings are presented in

Table 1. The symbols used in the system modeling process and their meanings.

Symbol	Meaning
h	Air-specific enthalpy
Q	The actual amount of cooling or heating provided by the coil to the air per unit time
m	Air mass flow rate
T	Air temperature
d	Air moisture content, kg water/kg dry air
$C_i$	$C_8=-5800.2206$, $C_9=1.3914993$, $C_{10}=-0.04860239$, $C_{11}=-5800.2206$, $C_{12}=1.3914993$, $C_{13}=-0.04860239$
$\alpha$	Heat transfer efficiency
c	The specific heat capacity of water
$\rho$	The density of water
f(TCV)	The flow characteristic of the coil control valve

. The details of the proposed method shown in Figure 3 are presented in the subsequent sections.

Figure 3 shows a close relationship between machine learning models, mechanism models, and objective functions. The machine learning model obtains the energy values corresponding to the outdoor air conditions and valve openings by training historical data. The mechanism model uses these energy values to determine whether the solution searched by the intelligent optimization algorithm meets the final air supply temperature and dew point temperature requirements. The objective function calculates the energy consumption by optimizing the water output corresponding to the valve opening, such that the intelligent optimization algorithm searches for the lowest energy consumption solution by minimizing the objective function.

3.1. Mathematical Model of MAU

MAU system modeling aims to describe the energy conversion process during MAU operation in mathematical models and provide a mathematical basis for subsequent MAU energy optimization. Therefore, briefly introducing the mathematical model of the MAU is necessary before describing our algorithm. We will take the phase of precooling as an example.

Based on the different cooling capacities provided by the precooling coil, outdoor air treatment in the precooling stage can be divided into two types: cooling only and dehumidification. To determine whether the air in the precooling stage is being dehumidified, it is first necessary to calculate the cooling capacity $Q_{dh}$ required to cool the outdoor air from its initial temperature to its dew point temperature ($Td$) within a unit of time. This cooling capacity is designated as $Q_{dh}$. By comparing $Q_{dh}$ with the cooling capacity provided by the precooling coil, $Q_{precooling}$, we can determine whether the coil’s capacity is sufficient for dehumidifying the air. The temperature at which air reaches saturation while maintaining moisture content is known as the dew point temperature. Given the outdoor air temperature ($T_{oa}$) and the outdoor air humidity ($R{H}_{oa}$), the energy conversion process involved in cooling the outdoor air to its dew point can be expressed as follows [23]:

$$m\times h_{oa}-Q_{dh}=m\times h_{Td}$$

(1)

$$h_{Td}=1.01\times Td+(2501+1.84\times Td)\times d_{oa}/1000$$

(2)

$$h_{oa}=1.01\times T_{oa}+(2501+1.84\times T_{oa})\times d_{oa}/1000$$

(3)

$$d_{oa}=622\times P_q/(101325-P_q)$$

(4)

$$\begin{array}{cc}\hfill ln\left(P_q\right)=& C_8/(Td+273.15)+C_9+C_{10}\times (Td+273.15)+C_{11}\times {(Td+273.15)}^2\hfill \\ & +C_{12}\times {(Td+273.15)}^3+C_{13}\times ln(Td+273.15)\hfill \end{array}$$

(5)

The upper formulas are simultaneously solved to obtain the cooling capacity $Q_{dh}$. The outdoor air’s moisture content $d_{oa}$ is calculated based on the outdoor air temperature $T_{oa}$ and outdoor air humidity $R{H}_{oa}$.

$$RHoa=P_q/(P_q,b)$$

(6)

$$\begin{array}{cc}\hfill ln(P_q,b)=& C_8/(T_{oa}+273.15)+C_9+C_{10}\times (T_{oa}+273.15)+C_{11}\times {(T_{oa}+273.15)}^2\hfill \\ & +C_{12}\times {(T_{oa}+273.15)}^3+C_{13}\times ln(T_{oa}+273.15)\hfill \end{array}$$

(7)

$$d_{oa}=622\times P_q/(101325-P_q)$$

(8)

Moreover, the dew point is calculated based on the moisture content.

$$\begin{array}{c}\hfill ln(101325\times d/(622+d))=C_8/(Td+273.15)+C_9+C_{10}\times (Td+273.15)\\ \hfill +C_{11}\times {(Td+273.15)}^2+C_{12}\times {(Td+273.15)}^3\\ \hfill +C_{13}\times ln(Td+273.15)\end{array}$$

(9)

When the cooling capacity is less than the dehumidification capacity, i.e., $Q_{precooling}<Q_{dh}$, the precooling coil is only used for cooling treatment. Otherwise, the precooling coil performs both cooling and dehumidification treatment. More details are provided as follows.

• Cooling only: The cooling treatment provided by the precooling coil only reduces the air temperature. Given the cooling capacity of the precooling coil denoted as $Q_{precooling}$, the energy conversion process in the precooling section can be expressed as follows:

  $$m\times h_{oa}-Q_{precooling}=m\times h_{precooled}$$

  (10)
  The air-specific enthalpy $h_{precooled}$ can be solved based on the above equation.
• Cooling with dehumidifying: The precooling coil performs both cooling and dehumidification treatment, which simultaneously reduces the air temperature and decreases the moisture content of the air. During this process, condensate water is produced, and given the cooling capacity of the precooling coil, denoted as $Q_{precooling}$, the energy conversion process in the precooling section can be expressed as follows:

  $$m\times h_{oa}-Q_{precooling}=m\times h_{precooled}+m\times c\times (d_{oa}-d_{precooled})\times T_{precooled}$$

  (11)

  $$h_{precooled}=1.01\times T_{precooled}+(2501+1.84\times T_{precooled})\times d_{precooled}/1000$$

  (12)

  $$d_{precooled}=622\times P_q/(101325-P_q)$$

  (13)

  $$\begin{array}{cc}\hfill ln\left(P_q\right)=& C_8/(T_{precooled}+273.15)+C_9+C_{10}\times (T_{precooled}+273.15)\hfill \\ & +C_{11}\times {(T_{precooled}+273.15)}^2+C_{12}\times {(T_{precooled}+273.15)}^3\hfill \\ & +C_{13}\times ln(T_{precooled}+273.15)\hfill \end{array}$$

  (14)

Therefore, the simultaneous upper formula is solved to obtain the moisture content and the air-specific enthalpy after precooling, i.e., $d_{precooled}$ and $h_{precooled}$.

3.2. The Data-Driven Model Based on Machine Learning Methods

According to the heat transfer equation, the amount of heat provided by the coil per unit of time is related to the specific heat capacity of water, the mass of the water circulating through the coil in a unit of time, and the temperature change in the water (the temperature difference between the inlet and outlet water of the coil). Among them, the mass of the water circulating through the coil in a unit of time is controlled by the coil opening and is related to the flow characteristics of the coil-regulating valve. The ice machine controls the temperature difference between the coil’s inlet and outlet water, which can be considered constant. Since there will be losses in the process of heat transfer from the coil to the air, the actual amount of heat provided to the air by the coil also needs to take into account the heat exchange efficiency of the coil. In short, each coil’s actual energy supplied to the air can be expressed as follows:

$$Q=\alpha \times c\times \rho \times f\left(TCV\right)\times \Delta T$$

(15)

In practical projects, due to the difficulty of accurately obtaining the flow rate of hot and cold water in the coil ($f\left(TCV\right)$) and the heat exchange efficiency of the coil ($\alpha$), it is often infeasible to directly apply Equation (2.1) to the calculation of coil energy supply based on the coil opening. Therefore, the relationship between coil openings and coil cooling and heating outputs was modeled using the Random Forest algorithm based on historical data. This approach allows for the calculation of coil cooling and heating outputs based on coil control valve openings, as shown in Figure 4. The next discussion will focus on three aspects: data pre-processing, comparison of different machine learning algorithms, and analysis of the best predictive model.

3.2.1. Data Analysis

The dataset comprises 51,000 records, encompassing temperature, humidity, airflow, and valve openness. Recognizing the inherent limitations and logical boundaries of these parameters—such as the valve position being constrained within the range of 0–100—enabled a thorough cleansing of the raw data. This involved the elimination of erroneous or implausible entries that did not adhere to these established norms. Post-cleaning, the refined dataset was significantly condensed yet markedly improved in quality, yielding a final tally of 25,000 valid and meaningful records. This curated dataset forms the robust foundation upon which subsequent analysis and modeling efforts are based, ensuring that the insights derived are reliable and representative of real-world conditions.

3.2.2. Data Pre-Processing

To achieve a relatively accurate prediction for full opening, it is essential to enhance the training data in advance [24]. As mentioned in Section 3.2.1, the original dataset comprises 51,000 records, while 25,000 valid and meaningful records are left after the post-cleaning stage, i.e., the refined dataset. It forms 12,500 pairs of date points, where each pair serves as the basis for linear interpolation within the valve opening range of 0–100. This process generates additional data points within the full opening range, as illustrated in Figure 5.

3.3. Machine Learning Algorithms

This study employed eight regression algorithms as the core of machine learning [25], including linear regression [26], ridge regression [27], Lasso regression [28], K-nearest neighbors regression [29], decision tree regression [30], random forest regression [31], gradient boosting regression [32,33], and AdaBoost regression [34].

3.3.1. Linear Regression

Linear regression is a fundamental machine learning algorithm used for predictive modeling. It models the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data. The equation can be written as follows:

$$y={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+...+{\beta }_n{x}_n+ϵ$$

where y is the dependent variable, $x_1,x_2,\cdots ,x_n$ are the independent variables, ${\beta }_0,{\beta }_1,{\beta }_2,\cdots ,{\beta }_n$ are the coefficients, and $ϵ$ is the error term.

3.3.2. Ridge Regression

Ridge regression, also known as Tikhonov regularization, is a variant of linear regression that includes a regularization term to prevent overfitting. It adds a penalty equal to the square of the magnitude of coefficients to the loss function:

$$\mathrm{Loss}=\sum _{i=1}^n{(y_i-\widehat{y_i})}^2+\lambda \sum _{j=1}^p{\beta }_j^2$$

where $\lambda$ is the regularization parameter controlling the strength of the penalty.

3.3.3. Lasso Regression

Lasso (Least Absolute Shrinkage and Selection Operator) regression is another regularization technique that performs both variable selection and regularization to enhance the prediction accuracy. It adds a penalty equal to the absolute value of the magnitude of coefficients:

$$\mathrm{Loss}=\sum _{i=1}^n{(y_i-\widehat{y_i})}^2+\lambda \sum _{j=1}^p\left|{\beta }_j\right|$$

The $\lambda$ parameter controls the sparsity of the coefficients.

3.3.4. K-Nearest Neighbors Regression

K-nearest neighbors (KNN) regression is a non-parametric method used for regression and classification. In KNN regression, the output is the average of the values of its K-nearest neighbors:

$$\widehat{y}={\displaystyle \frac{1}{K}}\sum _{i=1}^K{y}_i$$

where $y_i$ are the target values of the K-nearest neighbors to the input point.

3.3.5. Decision Tree Regression

Decision tree regression models the target variable by learning decision rules inferred from the features. It creates a tree structure where internal nodes represent decision rules based on features, branches represent outcomes, and each leaf node represents a predicted value:

$$\widehat{y}=\sum _{m=1}^M{c}_{m}I(x\in R_m)$$

where $c_m$ is the predicted value in region $R_m$, and I is the indicator function.

3.3.6. Random Forest Regression

Random forest regression is an ensemble learning method that constructs multiple decision trees during training and outputs the average prediction of the individual trees. It reduces overfitting and improves generalization:

$$\widehat{y}={\displaystyle \frac{1}{B}}\sum _{b=1}^B{\widehat{y}}^{\left(b\right)}$$

where B is the number of trees, and ${\widehat{y}}^{\left(b\right)}$ is the prediction of the b-th tree.

3.3.7. Gradient Boosting Regression

Gradient boosting regression builds an ensemble of trees sequentially, where each tree corrects the errors of its predecessor. It minimizes a loss function by adding weak learners using gradient descent:

$${\widehat{y}}_m\left(x\right)={\widehat{y}}_{m-1}\left(x\right)+\nu h_m\left(x\right)$$

where $h_m\left(x\right)$ is the new tree trained on the residuals of the previous model, ${\widehat{y}}_{m-1}\left(x\right)$, and $\nu$ is the learning rate.

3.3.8. AdaBoost Regression

AdaBoost (Adaptive Boosting) regression improves the performance of weak learners by focusing on the errors of previous learners. It combines the predictions of multiple learners by assigning weights to each learner based on their performance:

$$\widehat{y}=\sum _{m=1}^M{\alpha }_m{h}_m\left(x\right)$$

where ${\alpha }_m$ is the weight assigned to the m-th weak learner $h_m\left(x\right)$.

3.4. Model Configuration and Performance Evaluation

In the proposed algorithm, the random forest algorithm was chosen due to its superior performance and robustness across various predictive tasks. One of its key advantages is the ability to mitigate overfitting through the aggregation of multiple decision trees, each trained on random subsets of the data and features. This ensemble method ensures that the final model generalizes well to unseen data, providing more reliable predictions compared to single models. Additionally, the random forest algorithm excels in handling high-dimensional datasets, which is crucial given the numerous attributes in our dataset that collectively influence the predictive outcomes. It does not require extensive feature selection or pre-processing, making it both efficient and effective without compromising accuracy. Empirical results in

Table 2. Comparison of regression algorithm models on RMSE and R Squared.

Model	RMSE	R Squared
Linear Regression	15.892662	0.995577
Ridge Regression	15.892681	0.995577
Lasso Regression	15.928640	0.995557
K Neighbors Regressor	12.711077	0.997171
Decision Tree Regressor	13.526912	0.996800
Random Forest Regressor	11.162434	0.997822
Gradient Boosting Regressor	13.578922	0.996771
Adaboost Regressor	25.567316	0.988897

demonstrate that the random forest algorithm achieved the lowest root mean square error (RMSE) and the highest R Squared values among all tested models, reinforcing its selection as the optimal algorithm for our regression tasks.

Usually, some key hyperparameters of the random forest algorithm should be carefully chosen to optimize the model’s predictive capabilities. Specifically, the number of trees was set to 100, and the maximum depth of the trees was left unspecified to allow trees to grow fully. The minimum number of samples required to split an internal node was set to 2, while the minimum number of samples required at each leaf node was set to 1. To balance the trade-off between bias and variance, the maximum number of features considered for splitting a node was set to the square root of the total number of features. The model was trained using the mean squared error as the criterion for measuring the quality of splits. The dataset was split into 80% for training and 20% for testing, with a fixed random state of 42 for reproducibility. No explicit feature selection was conducted, and the model was trained on a standard desktop computer equipped with an Intel Core i7 processor and 32 GB of RAM.

The regression algorithm models utilized RMSE (root mean square error) and R Squared as the evaluation metrics for model accuracy [35]. RMSE measures the square root of the ratio of the squared deviations between predicted and actual values to the number of observations (n). It gauges the deviation between predicted and actual values and is sensitive to outliers in the data. On the other hand, R Squared, the coefficient of determination, is used in statistics to measure the proportion of the variability in the dependent variable that is explained by the independent variable. It serves to assess the explanatory power of the regression model. A lower RMSE indicates a better model, while a higher R Squared suggests a better model. The experimental results, as depicted in Table 2, show that the random forest algorithm yielded the optimal performance.

3.5. Definition of the Optimization Problem

Before applying intelligent optimization algorithms [36], it is crucial to design the proactive energy-saving optimization control of the fresh air handling unit as an optimization problem [13]. Assuming the costs of chilled water, low-temperature chilled water, and hot water per cubic unit are represented as a, b, and c, respectively, $f\left(x\right)$ represents the flow through the coil control valve at an opening of x, measured in cubic meters per hour. TCV represents the opening of the coil control valve, indicating the degree to which the valve is open. $pc$, $rc$, $ph$, and $rh$ represent the four sections in the model. The energy cost (E) of the MAU for chilled and hot water at steady state can be expressed as follows:

$$E=a\times f\left(TC{V}_{pc}\right)+b\times f\left(TC{V}_{rc}\right)+c\times \left[f\left(TC{V}_{ph}\right)+f\left(TC{V}_{rh}\right)\right]$$

(16)

Through the above model for calculating the energy cost of chilled and hot water usage in the MAU, it is possible to predict the energy cost under different combinations of control valve openings for the MAU’s chilled and hot water systems.

Given a set supply air temperature and supply air dew point, there may be multiple combinations of coil openings that satisfy the requirements. To optimize the energy cost of chilled and hot water usage in the MAU, it is necessary to find a combination of control valve openings $(TC{V}_{ph},TC{V}_{pc},TC{V}_{rc},TC{V}_{rh})$ that, while meeting the required supply air temperature and supply air dew point, minimizes the energy cost(E). Let the function for calculating the supply air temperature be denoted as $f_T(TC{V}_{ph},TC{V}_{pc},TC{V}_{rc},TC{V}_{rh})$ and the function for calculating the supply air dew point be denoted as $f_d(TC{V}_{ph},TC{V}_{pc},TC{V}_{rc},TC{V}_{rh})$. Then, the optimization problem [37] for the MAU’s energy cost of chilled and hot water usage can be expressed as follows:

$$\begin{array}{cc}\hfill & P:minE\hfill \\ \hfill & s.t.\hfill \\ \hfill & C1:f_T(TC{V}_{ph},TC{V}_{pc},TC{V}_{rc},TC{V}_{rh})=T\hfill \\ \hfill & C2:f_d(TC{V}_{ph},TC{V}_{pc},TC{V}_{rc},TC{V}_{rh})=Td\hfill \end{array}$$

(17)

By applying intelligent optimization algorithms to solve the aforementioned optimization problem of the MAU’s energy cost for chilled and hot water usage, it is possible to obtain the coil opening that minimizes the energy cost while satisfying the set supply air temperature and dew point.

This paper customizes genetic operators [21,38] to address the specific characteristics of the real-world problem. The following sections provide detailed descriptions of population initialization [39] and environmental selection [20].

3.6. Direction-Based Optimization Algorithm

Algorithm 1 gives the specific implementation details of the direction-based optimization algorithm. The problem to be optimized E is the minimum energy consumption that satisfies the constraints and has been defined above.

For the initialization of population (line 1), it is possible to sample based on the distribution of control valve openings in the dataset. The sampled results can be used as the initial population. The distribution illustrates the frequency of different control valve openings, where a higher frequency indicates more frequent usage and a greater likelihood of being a feasible solution. This approach allows for the quicker identification of feasible solutions, but caution should be taken to avoid the population becoming trapped in local optima. The population size is set to 50; therefore, 50 individuals need to be sampled as the initial population. Figure 6 depicts the sampling results at various sections.

Algorithm 1 Direction-based optimization algorithm

Input: Problem E, Population size $pop\_size$, Max generations $max\_generations$ Output: Best solution $best\_individual$   1: Initialize population P with $pop\_size$ individuals;   2: for generation $g=1$ to $max\_generations$ do   3:     for each individual $ind$ in population P do   4:         Evaluate fitness $f\left(ind\right)$;   5:     end for   6:     if convergence criteria is not met then   7:         Selected individuals $Q\leftarrow \mathrm{Select}\mathrm{the}\mathrm{top}\mathrm{half}\mathrm{of}\mathrm{population}P\mathrm{based}\mathrm{on}\mathrm{fitness}$;   8:         %Generate new population $P_{new}$ below;   9:         while $|P_{new}|<pop\_size$ do 10:            Randomly select two parents $s_1,s_2$ from Q; 11:            Perform directional crossover on $s_1$ and $s_2$ to produce children $q_1,q_2$; 12:            Apply directional mutation on $q_m$; 13:            Add $q_1$, $q_2$ and $q_m$ to $P_{new}$; 14:         end while 15:         Set $P=P_{new}$; 16:         Print the best fitness in current generation; 17:     else 18:         break; 19:     end if 20: end for

The number of iterations of the algorithm is predefined in the main loop of the algorithm (lines 2–19). And in each iteration, the fitness of the population individuals is calculated and new individuals are generated based on the better individuals using a directed learning strategy until the termination condition is reached. For constrained single-objective optimization problems, the fitness evaluation of individuals considers both the objective function value and the degree of constraint violation (lines 2–3). We use the penalty function method to transform the constraint violations into penalty values and combine them with the objective function value to compute the fitness of each individual. The formula for calculating fitness is as follows:

$$\begin{array}{cc}\hfill & P\left(ind\right)=\sum _{i=1}^m{w}_i·v_i\left(ind\right)\hfill \end{array}$$

(18)

$$\begin{array}{cc}\hfill & f\left(ind\right)=f_{obj}\left(ind\right)+P\left(ind\right)\hfill \end{array}$$

(19)

where $P\left(ind\right)$ is the sum of weighted violations of all constraints, forming the total penalty function value. Specifically, each constraint is applied to the individual, with the resulting violation multiplied by its corresponding weight. Weights range from 0 to 1, reflecting constraint importance. For instance, if two constraints are deemed equally significant, a weight of 0.5 may be assigned to both.

In addition, we improve on the traditional genetic algorithm by designing directed crossover and directed mutation operators, which can realize fast solution finding in the solution space and improve the convergence speed of the population (lines 11–16). The directional crossover process generates offspring guided by the fitness values of the parents.

3.6.1. Directional Crossover Operator

Assuming a population size of N and n decision variables, the optimization process allows both crossover and mutation to be performed in variable directions. The crossover operator primarily involves four parameters: the crossover rate $p_c$, the probability of variable direction $p_{cv}$, the direction probability $p_d$, and the multiplication factor $\alpha$. Assuming two unequal parent solutions $s_1^j$ and $s_2^j$ (where j ranges from 1 to n and is allowed to crossover), and given $s_{\mathrm{best}}^j$ and $s_{\mathrm{mean}}^j$ as the best and mean solutions in the current population, respectively, if $s_{\mathrm{best}}^j\ge s_{\mathrm{mean}}^j$, then two offspring solutions $q_1$ and $q_2$ are constructed using the following formulas:

$$val=1-{\left(0.5\right)}^{e^{\left[{\displaystyle \frac{s_1^j-s_2^j}{s_u^j-s_l^j}}\right]}}$$

(20)

$$\beta ={\displaystyle \frac{r_1}{{\alpha }^2}}$$

(21)

$$\left\{\begin{array}{c}{q}_1=val\times (s_1^j+s_2^j)+{\alpha }^{r_1}\times e^{(1-\beta )}\times (1-val)\times |s_1^j-s_2^j|\hfill \\ q_2=(1-val)\times (s_1^j+s_2^j)-{\alpha }^{(1-r_1)}\times e^{(-\beta )}\times val\times |s_1^j-s_2^j|\hfill & ,\mathrm{if}{r}_2\le p_d\hfill \end{array}\right.$$

(22)

$$\left\{\begin{array}{c}{q}_1=val\times (s_1^j+s_2^j)-{\alpha }^{r_1}\times e^{(1-\beta )}\times (1-val)\times |s_1^j-s_2^j|\hfill \\ q_2=(1-val)\times (s_1^j+s_2^j)+{\alpha }^{(1-r_1)}\times e^{(-\beta )}\times val\times |s_1^j-s_2^j|\hfill & ,\mathrm{if}{r}_2>p_d\hfill \end{array}\right.$$

(23)

where $r_1$ and $r_2$ be two distinct random numbers generated within the range [0, 1], val and $\beta$ are two intermediate parameters, $s_u^j$ and $s_l^j$ denote the upper and lower bounds of the j-th variable, respectively. In one case, if $s_{\mathrm{best}}^j<s_{\mathrm{mean}}^j$, the offspring solutions are constructed using the following formulas:

$$\left\{\begin{array}{c}{q}_1=val\times (s_1^j+s_2^j)-{\alpha }^{r_1}\times e^{(1-\beta )}\times (1-val)\times |s_1^j-s_2^j|\hfill \\ q_2=(1-val)\times (s_1^j+s_2^j)+{\alpha }^{(1-r_1)}\times e^{(-\beta )}\times val\times |s_1^j-s_2^j|\hfill & ,\mathrm{if}{r}_2\le p_d\hfill \end{array}\right.$$

(24)

$$\left\{\begin{array}{c}{q}_1=val\times (s_1^j+s_2^j)+{\alpha }^{r_1}\times e^{(1-\beta )}\times (1-val)\times |s_1^j-s_2^j|\hfill \\ q_2=(1-val)\times (s_1^j+s_2^j)-{\alpha }^{(1-r_1)}\times e^{(-\beta )}\times val\times |s_1^j-s_2^j|\hfill & ,\mathrm{if}{r}_2>p_d\hfill \end{array}\right.$$

(25)

During the directed crossover process, newly created offspring solutions are constrained by variable boundaries to avoid generating infeasible solutions, while at the same time learning from better solutions in the population to generate new ones. Additionally, the probability that $q_1$ is considered as the first offspring solution or the second offspring solution is 50%. If $q_1$ is chosen as the first offspring solution, then $q_2$ is regarded as the second offspring solution, and vice versa. This step is referred to as the offspring identification condition.

3.6.2. Directed Mutation Operator

Similar to the directed crossover operator, the directed mutation operator can adjust the directional information for the optimization problem. For the parent solution $s_i^j$ and its mutated solution $s_m$, where i represents an individual in the population from 1 to N, and j represents a decision variable from 1 to n. A random number r within the range [0, 1] is generated. If this random number is less than or equal to the mutation probability $p_m$, the parent solution $s_i^j$ is allowed to participate in the mutation operation.

The directed mutation operator requires directional information, which is collected before using the operator. The way to collect this information is by comparing the current parent solution $s_i^j$ with the best solution in the population $s_{\mathrm{best}}^j$. When it is found that the fitness of $s_{\mathrm{best}}^j$ is greater than or equal to the fitness of $s_i^j$, the mutated solution $q_m$ is created using the following formula:

$${\beta }_1=e^{\left(2r-{\displaystyle \frac{2}{r}}\right)},$$

(26)

$${\beta }_2=e^{\left(r-{\displaystyle \frac{2}{r}}\right)},$$

(27)

$$q_m=\left\{\begin{array}{cc}{s}_i^j+{\beta }_1\times \left(s_u^j-s_i^j\right),\hfill & \mathrm{if}{r}_3\le p_d\hfill \\ s_i^j-{\beta }_2\times \left(s_i^j-s_l^j\right),\hfill & \mathrm{otherwise}\hfill \end{array}\right.$$

(28)

where ${\beta }_1$ and ${\beta }_2$ are two intermediate parameters used to determine $q_m$. $r_3$ is a random number generated within the range [0, 1]. $s_u^j$ and $s_l^j$ represent the upper and lower bounds of the j-th variable, respectively. $p_d$ denotes the direction probability, typically set between 0.5 and 1. In the case wherein the fitness of $s_{\mathrm{best}}^j$ is worse compared to $s_i^j$, the mutated solution $q_m$ can be updated using the following formulas:

$$q_m=\left\{\begin{array}{cc}{s}_i^j-{\beta }_1\times \left(s_i^j-s_l^j\right),\hfill & \mathrm{if}{r}_3\le p_d\hfill \\ s_j^i+{\beta }_2\times \left(s_u^j-s_i^j\right),\hfill & \mathrm{otherwise}.\hfill \end{array}\right.$$

(29)

It is evident from the above formulas that the mutated solution is always created within the variable boundary constraints. Therefore, in this case, no boundary handling techniques are needed.

By using directed crossover and directed mutation strategies, the population can converge quickly. When the convergence degree meets the predefined requirements, it jumps out of the main loop and outputs the best individual in the population. In this article, the predetermined convergence termination condition is that, if all individuals in the population meet the constraint conditions, it can be terminated in advance. Otherwise, it will continue to run until the set number of iterations is used up.

4. Simulink Simulation Design

4.1. Simulation Model

In this section, we use Simulink to perform simulation of the designed system. Figure 7 presents the overview of our simulation model. Firstly, specific environmental conditions are given as system inputs, including temperature (T_env) and dew point temperature (Td_env). We then set our desired control results, including air temperature (T_send), air dew point temperature (Td_send), and the pre-processing stage setpoint (T_SP). Finally, we can observe how the intermediate variables change by running the system. Note that, for the setting of the setpoint in the pre-processing stage, the conventional PID control relies entirely on experience, while we use the results obtained by the intelligent optimization algorithm, which is the most significant advantage of our algorithm.

4.2. Verification of the Model’s Reliability

In Section 3.1, we described the working principle of the precooling stage of the MAU and the changes of air in this stage from a mathematical point of view. The pre-processing stage in the simulation model is built based on the mathematical descriptions. The precooling stage is chosen for detailed description because it is the most complex mechanism, and in this subsection we will use the precooling stage as a representative to verify the reliability of the overall model.

Table 3. Actual data describing changes in air properties during the precooling phase.

Air Temperature (°C)	Air Dew Point (°C)	Q (kJ/s)	Temperature After Cooling (°C)	Specific Enthalpy After Cooling (kJ/kg)
33.39	24.0880	1408.389	49.7023	17.48

shows data recorded in a real production environment describing the change in properties after the energy exchange between the outdoor air and the precooling coil, which can be checked for correctness by the mathematical model in Section 3.1. The operation of the precooling stage in the simulation model is shown in Figure 8, where it can be observed that our model can correctly calculate the properties of the treated air based on the input outside air temperature, dew point temperature, and the work accomplished by the precooling coil.

5. Experiment

In order to investigate the performance of the intelligent control method proposed in this paper from multiple perspectives, two experiments are designed in this section, including theoretical and simulation experiments. In the rest of this section, we first introduce the theoretical experimental content and then the simulation experimental content.

5.1. Data Visualization

The pre-trained random forest regression model was applied to predict the preprocessed data, and prediction was used to assess the accuracy and effectiveness of the model. The following sections will present separate analyses for the preheating, precooling, recooling, and reheating sections in the prediction model.

• Preheating: In the preheating section, out of 25,000 historical datasets, 563 did not achieve an accuracy of 90% or higher in predictions, constituting approximately 2.1% of the total data sample. The prediction accuracy in the preheating section is illustrated in Figure 9a, while the specific comparison between the predicted values and true values for both the overall prediction accuracy and the instances wherein the standard was not met is illustrated in Figure 9b.
• Precooling: In the precooling section, out of 25,000 historical datasets, 965 did not achieve an accuracy of 90% or higher in predictions, constituting approximately 3.6% of the total data sample. The specific comparison between the predicted values and true values for both the overall prediction accuracy and the instances wherein the standard was not met is illustrated in Figure 10.
• Recooling: In the recooling section, out of 25,000 historical datasets, 352 did not achieve an accuracy of 90% or higher in predictions, constituting approximately 1.3% of the total data sample. The specific comparison between the predicted values and true values for the overall prediction accuracy and the instances wherein the standard was not met is illustrated in Figure 11.
• Reheating: In the reheating stage, all 25,000 historical datasets achieved an accuracy of 90% or higher in predictions. The specific comparison between the predicted values and true values for the overall prediction accuracy and the instances wherein the standard was not met is illustrated in Figure 12.

In addition, we can see that the test and estimated values are separated at points 5 and 12 in Figure 9 and Figure 11. This separation also occurs at points 9 and 12 in Figure 10. This is mainly due to two factors: (1) There are in total 25,000 pieces of data from the actual field tests, which are subject to environmental impacts; hence, there are inevitably some unpredictable errors. (2) It is inevitable that there are some errors in machine learning-based prediction models, since it is usually hard or impossible to train the machine learning models that can fit all test datasets. Moreover, it is worth pointing out that the machine learning models in precooling mode is really not as effective as in other modes (preheating, recooling, and reheating) in terms of the prediction accuracy, as partly shown in Figure 10. This may be owing to the fact that the data collected in the precooling mode are not good enough and the precooling valve is more active.

5.2. Real Installation Design

In the real installation and deployment, we conducted tests in the central control room of a factory air conditioning system in Deqing, Zhejiang Province, China. The test time was in August. The local temperature range for a day was of 30–39 degrees Celsius, which belonged to the summer mode. The valves that should be activated were precooling, recooling, and reheating. Since the ambient temperature fluctuates during the day, in order to test the actual effect of the proposed method, we set the single test period to 24 h. The factory air conditioning system must first meet stable output temperature and dew point to ensure the normal operation of the factory. Therefore, in the actual test, we incorporated traditional PID control into the execution process. In PID control, each adjustment is made according to the current environmental conditions. In theory, even if the control effect of the intelligent optimization algorithm does not meet the requirements, it will provide a good initial result for PID control, which can reduce the PID control time and achieve energy saving.

Figure 13 shows the execution flowchart in real deployment. First, start the PLC connection and read the outside air environment data, including the outside air temperature and dew point temperature, etc. At the same time, the set temperature and dew point temperature are also obtained. Then, the intelligent optimization algorithm module is executed. The algorithm uses the Pymoo framework [40] and machine learning models to perform optimization; thereafter, the optimized valve opening can be output. The valve openings obtained by the intelligent algorithm will be written into the corresponding PLC points, and the air device system will start the corresponding valve settings to control the temperature and humidity. If the output result of the intelligent optimization algorithm cannot meet the preset temperature and dew point temperature requirements, PID control will be started to prioritize the stable temperature and dew point temperature requirements. The energy consumption at this time is calculated and written into the corresponding PLC point as a historical record. Due to the fact that it only takes about 15 s for the valve to move and achieve temperature control, in order to ensure that the current round of control is completed thoroughly, we wait for 30 s for the control to be completed. After the regulation is completed, a new round of intelligent optimization algorithm optimization control is started until it stops after 24 h of operation and all energy consumption records are output. In order to calculate the energy saving effect, we repeated the above test several times. Finally, the energy consumption generated by the proposed method was compared with the energy consumption required by the previous PID control alone.

5.3. The Experiment of Optimization Process

The experiment of optimization process is conducted with evolutionary algorithms based on the Pymoo platform [40]. The experiment starts by randomly selecting 30 original data items from the dataset. The original data include environmental temperature (T_env), environmental humidity (d_env), air supply temperature (T_send), air supply dew point (Td_send), and consumption under PID control (yuan/hour). Based on the above data, our proposed algorithm AESOC-GA can be conducted to obtain the corresponding consumption. The proposed algorithm is independently run 20 times on each data item. Instead of embedded GA in the proposed framework, we also consider Differential Evolution (DE) [41,42] and PSO [43,44] to perform the optimization process for comparison.

Table 4. Statistics of energy consumption results (mean and standard deviation) obtained by PID and DDOA with different embedded algorithms on thirty chosen original data items. The best result in each row is highlighted in boldface.

T_env	d_env	T_SP	Td_SP	kWh
				AESOC-GA	AESOC-DE	AESOC-PSO	PID
32.25	16.01	19.97	9.18	152.45 (25.19)	244.20 (6.713)	156.63 (19.26)	226.30
27.55	19.41	19.96	10.16	143.51 (2.42)	168.03 (24.10)	198.80 (13.80)	162.53
31.65	19.12	20.12	9.36	223.20 (0.82)	222.02 (0.02)	213.88 (49.91)	228.23
23.06	10.80	21.06	11.11	17.07(7.06)	15.66 (7.27)	20.94 (18.79)	76.15
22.85	15.45	18.88	10.19	51.42 (54.68)	73.87 (25.89)	72.128 (6.95)	108.13
24.41	17.82	19.15	12.02	43.24 (36.31)	61.04 (32.70)	127.51 (57.28)	54.50
23.66	10.52	21.20	10.86	13.15(3.23)	9.06 (1.68)	5.00 (9.88)	77.28
26.87	14.55	18.81	9.65	107.55 (2.42)	106.49 (12.12)	110.2 (12.89)	96.01
34.68	21.36	20.19	8.97	137.35 (169.08)	310.75 (103.84)	268.75 (96.47)	224.86
29.63	13.10	20.84	10.27	72.40 (3.06)	66.64 (4.86)	88.42 (26.67)	237.67
25.91	15.98	21.13	10.57	85.53 (20.72)	73.65 (31.73)	55.76 (51.66)	241.46
26.10	17.13	20.13	9.93	125.51 (1.74)	124.68 (4.31)	128.64 (31.70)	192.16
24.28	17.43	19.11	11.98	39.49 (40.32)	60.20 (16.66)	145.86 (52.97)	54.49
26.23	19.94	19.99	9.90	150.19 (2.59)	175.76 (21.39)	201.05 (17.57)	152.64
24.05	10.02	20.74	10.60	28.60 (14.53)	20.03 (12.63)	2.79 (8.55)	81.50
27.64	21.14	20.02	9.59	226.25 (1.07)	214.30 (49.35)	229.63 (9.67)	230.27
31.49	12.24	21.09	10.16	127.99 (1.41)	128.14 (8.49)	123.05 (29.56)	231.95
30.04	17.07	21.14	10.83	131.6 (4.22)	136.37 (11.97)	135.86 (81.54)	222.94
31.92	10.08	19.85	10.31	56.01 (17.39)	57.23 (10.03)	57.63 (2.92)	208.78
30.03	16.80	21.13	10.77	116.41 (51.03)	142.02 (14.12)	131.84 (6.18)	222.94
+/−				17/3	13/7	15/5

shows the statistical results of the traditional PID control method and our proposed intelligent control method on the 20 original data items. It can be observed that, compared to the traditional PID control method, our proposed intelligent control method significantly reduces resource consumption, regardless of whether the embedded algorithm is GA, DE, or PSO. Moreover, it can obviously show the advantage of our GA-based method using directed generic operators, i.e., AESOC-GA, compared to the other other two competitive algorithms AESOC-DE and AESOC-PSO.

5.4. Simulation Experiment

The simulation experiment plan is based on Simulink to compare the energy consumption of traditional PID control methods and intelligent control methods. In this experiment, the main difference between the two control methods lies in the determination of the setpoint during the pre-processing stage: in the traditional PID control method, the setpoint is determined by expert experience, while in the intelligent control method, the setpoint is determined by an intelligent optimization algorithm. Subsequently, the experimental method will be introduced in detail, and the results are presented.

The experimental data used in

Table 5. The data used are collected from real-world scenarios. For the traditional PID control, the setpoint for the pre-processing stage is set to 21 °C, as used on-site. For the intelligent optimization control, the algorithm determines the setpoint for the pre-processing stage.

Air Temperature (°C)	Air Dew Point (°C)	Post-Processing Temperature (°C)	After-Cooling Temperature (°C)	Delivery Air Temperature (°C)	Delivery Air Dew Point (°C)
29.93	16.40	17.70	11.06	20.99	11.06

were measured by the sensors attached to the MAUs in the actual production environment, where the dew point temperature and temperature of the outdoor ambient air were measured by the dew point/temperature sensors of the model EE210-HT6xPCxDx-Td048-Tx003M + HA010502, and the data of the air in the other MAUs were measured by the air sensors of the corresponding positions of the model EE210- HT6xPCxDx-Txd004-Tx004M + EE215-HTxD model dew point/temperature sensors in the corresponding locations. The PID controller coefficients were tuned using the Z-N method, based on time response and experience [45,46]. The PID controller coefficients for the pre-process section, recooling section, and reheat section are set as shown in

Table 6. The setting of the PID controller coefficients.

	Proportional (P)	Integral (I)	Derivative (D)
preprocess	1	1	0
recool	1	1.2	0
reheat	1	1.2	0

, with the same settings used for both the traditional PID control method and DDOA.

There are three control variables which are the setpoints of the PIDs for the different stages, i.e., the temperature setpoint for the pre-processing stage, the supply air dew point temperature setpoint for the re-cooling stage, and the supply air temperature setpoint for the reheating stage.

• Experiment method:

  (a)

  Traditional PID control:

  • Select several representative data from the dataset for the experiment.
  • Run the simulation system based on the selected data using the traditional PID control method. This allows us to observe the energy consumption of the PID control method.

  (b)

  Intelligent optimization control:

  • Run the proposed algorithm based on the selected data to obtain the setpoint for the pre-processing stage.
  • Run the simulation system based on the selected data and the setpoint obtained from the pre-processing stage. Then, we can observe the energy consumption of the intelligent control method.

• Experiment result:

  (a)

  Experiment data:

  (b)

  Experimental configuration for traditional PID control:

  • Preprocessing stage setpoint: $21.00 °$C;
  • Supply air dew point: $11.06 °$C;
  • Supply air temperature: $21.00 °$C.

  (c)

  Experimental configuration for intelligent optimization control:

  • Preprocessing stage setpoint: $15.07 °$C;
  • Supply air dew point: $11.06 °$C;
  • Supply air temperature: $21.00 °$C.

  (d)

  Comparison of experimental results:

Figure 14 shows the control comparison of the air temperature variables under conventional PID control (precool, recool, and reheat) and under DDOA-based intelligent control (precool_DDOA, recool_DDOA, and reheat_DDOA), respectively. It can be observed that, under DDOA control, the air temperature in the recooling section converges to the set value more quickly, which is likely due to the lower setpoint of the precooling section PID. This also explains why the energy consumption is lower under the proposed DDOA control. Moreover, Figure 15 shows the comparison of the energy consumption curve between PID and DDOA control methods. It is obvious that the proposed DDOA method can reduce the energy consumption significantly, as compared to the PID control. To be specifically, the DDOA method can achieve up to 27.3% of energy savings as well as the related amount of overall saved money.

5.5. Detailed Analysis and Discussion of Experimental Results

We have conducted two kinds of experiments in this study: (1) the theoretical experiment based on Pymoo, and (2) the simulation experiment based on Simulink. These two experiments complement each other. The theoretical experiment based on Pymoo directly uses the optimal solution obtained by the intelligent optimization algorithm as the final result. However, due to the limitation in the accuracy of the prediction model, there is a slight deviation between this result and the actual outcome. Therefore, it is necessary to conduct a simulation experiment to further analyze the performance of the proposed algorithm. Using the result from the intelligent optimization algorithm as the foundation, we fine-tune it with a PID controller in the simulation environment to better match the actual production conditions, and then compare it with the traditional pure PID control method. The results are shown in Figure 14 and Figure 15. In Figure 15, it is visually evident that the proposed DDOA control method requires lower energy consumption compared to the traditional PID control algorithm, while Figure 14 explains the reason. For the traditional PID control method, the setpoints are typically determined based on expert experience, with the setpoints for the preprocessing stage set to be around 20 °C, as shown in recool, recool, and reheat of Figure 14. In contrast, the result obtained by the DDOA method adjusts the PID setpoints for the pre-processing stage to be around 15°C, as shown in recool_DDOA, recool_DDOA, and reheat_DDOA of Figure 14. Since the saturation vapor pressure of air increases exponentially with temperature, higher temperatures allow air to hold more water vapor. Therefore, setting the pre-processing stage setpoint to 20 °C leads to excessive humidification during the humidification stage, which results in the need for more energy for dehumidification during the cooling stage. The proposed DDOA method replaces expert experience with the intelligent optimization algorithm, and hence make the more reasonable PID setpoints, which helps avoid the aforementioned issue. Therefore, it is more energy-efficient compared to the traditional PID control algorithm.

6. Conclusions

This algorithm includes a method for modeling the relationship between the cold and hot coil opening and the energy based on machine learning and an optimization method for minimizing the energy cost of cold and hot water usage based on intelligent optimization algorithms. It successfully achieves real-time adjustment of the coil opening of the MAU in response to changes in outdoor air conditions. This optimization ensures that the supply air temperature and dew point meet the requirements, ultimately reducing the energy cost of the cold and hot water usage in the MAU.

The experimental results indicate that the intelligent optimization algorithm can output the coil opening, which minimizes the energy cost of the cold and hot water usage in the MAU. Additionally, the designed energy-saving optimization control method is compared with the commonly used PID control method through simulation experiments. The results demonstrate improvements in adjustment speed and energy cost of cold and hot water usage for the energy-saving control method compared to the PID control method. To be specific, the proposed strategy can achieve up to 27.3% of saved energy and the related amount of money.

Furthermore, it is very interesting to explore the integration of other energy-saving techniques into the MAU system. For example, natural cooling energy [47] and high-efficient radiant cooling techniques [48] are essential to mitigate energy resources shortage crises, a breakthrough for traditional convective air conditioning systems in isolation between indoor and outdoor environment with high indoor air quality.