Artificial Intelligence-Assisted Heating Ventilation and Air Conditioning Control and the Unmet Demand for Sensors: Part 1. Problem Formulation and the Hypothesis

In this study, information pertaining to the development of artificial intelligence (AI) technology for improving the performance of heating, ventilation, and air conditioning (HVAC) systems was collected. Among the 18 AI tools developed for HVAC control during the past 20 years, only three functions, including weather forecasting, optimization, and predictive controls, have become mainstream. Based on the presented data, the energy savings of HVAC systems that have AI functionality is less than those equipped with traditional energy management system (EMS) controlling techniques. This is because the existing sensors cannot meet the required demand for AI functionality. The errors of most of the existing sensors are less than 5%. However, most of the prediction errors of AI tools are larger than 7%, except for the weather forecast. The normalized Harris index (NHI) is able to evaluate the energy saving percentages and the maximum saving rations of different kinds of HVAC controls. Based on the NHI, the estimated average energy savings percentage and the maximum saving rations of AI-assisted HVAC control are 14.4% and 44.04%, respectively. Data regarding the hypothesis of AI forecasting or prediction tools having less accuracy forms Part 1 of this series of research.


Introduction
Heating, ventilation, and air conditioning (HVAC) systems provide a suitable living environment with thermal comfort and air quality. These mechanic-electrical systems include several types, such as air conditioners, heat pumps, furnaces, boilers, chillers, and packaged systems [1]. In most of the countries, the building sector accounts for nearly 40% of the total consumed energy [2]. For every building type, HVAC and lighting systems occupy more than half of the energy consumption [3]. A large fraction of the increasing energy expenditure for the buildings was because of the extending HVAC installations for better thermal comfort and air quality [4]. Therefore, the HVAC system plays an important role in the energy efficiency of buildings. Improving the control of HVAC operations and the efficiency of the HVAC system can save significant energy, increase thermal comfort, and contribute to improved indoor environmental quality (IEQ) [5]. Artificial intelligence (AI) was founded as an academic discipline in 1956. In contrast to human intelligence, AI demonstrates machine intelligence and imitates human behaviors through mathematical coding and mechanical works. In 1997, an AI program known as Deep Blue defeated the reigning world chess champion, Garry Kasparov [6].

Genetic algorithm (GA), cost estimation and model-based predictor
Simulation results show that the overall energy savings were 0.1%, 0.2%, 1.8% and 1.9% less than the original status [14] 2001 Prediction of heating and cooling loads at residential buildings Static neuro network (SNN) development for prediction Load curve fitting with an R-square value up to 0.9887 Prediction error ranges from 2.5% to 8.7% [15] 2001 Use of artificial neuro networks (ANNs) in solar radiation and wind speed prediction, photovoltaic systems, building services, and load forecasting and prediction ANNs for modeling a solar steam generator, modeling of solar domestic water heating systems, and forecasting the building thermal loads R-square value of load fitting ranges from 0.9733 to 0.9940. The prediction errors are within 1.9-5.5%. [16] 2001 Optimal heating control of a passive solar commercial building Smart heating controller with the cost function can combine comfort level and energy consumption Energy savings of maintaining or improving a thermal comfort are about 9% [17] 2002 House_n demonstration at Massachusetts Institute of Technology Saving energy, maintaining air quality and thermal comfort using data analysis Energy savings are about 14% [18] 2002 SNN for analyzing energy consumption in residential buildings Model-based control for energy savings Energy savings range from 5% to 15% [19] 2003 Building automation and energy management using AI Distributed AI development for demand-side management (DSM) and scheduling energy consumption according to energy tariff DSM-abled devices can save up to 40% on energy costs based on 24-h analysis [20] 2003 Fuzzy controller for the management of an indoor environment Five fuzzy controllers include fuzzy P, fuzzy proportional-integral-differential (PID), fuzzy PI, fuzzy PD and adaptive fuzzy PD While maintaining predicted mean vote (PMV) within 0-0.1 and indoor CO 2 ppm increased less than 20 ppm, fuzzy P controller had the best performance, heating and cooling energy can be reduced up to 20.1%. [21] 2003 ANNs in the optimal operation of HVAC equipment ANN was developed for predicting the optimal start times of a heating system in a building In 27 instances, a clear linear relationship between prediction and real data was shown by the R-square values ranging from 0.968 to 0.996. [22] 2004 ANNs for load forecasting of Taiwan  power system An integrated, evolving fuzzy neuro network and simulated annealing (AIFNN) developed for load forecasting Compared with traditional ANNs, AIFNN can reduce prediction errors up to 3% [23]  The prediction accuracy is measured by the coefficient of variation (CV) and the root mean square error (RMSE). For the Laval building case, the CV is 0.20 and the RMSE = 27.0 kW. With respect to the total power consumption~180 kw, the prediction error is 15%. [24] 2005 Energy forecast of intelligent buildings located at US and United Kingdom (UK) Increased return on investment (ROI) by using fuzzy multi-criteria decision-making method (DMM) 3% cost savings can be achieved with AI-assisted decision making. [25] 2005 Adaptive control of home environment (ACHE) at Colorado Distributed AI development and integrated with sensors Sensors of electrical consumption with ANN adapt to the habits of inhabitants [26] 2005 Predicting hourly energy consumption in buildings ANN development for predicting short-term energy consumption and feedback control Feedback ANN for highly efficient energy supply [27] 2005 Prediction of building energy consumption in tropical regions Support vector machine (SVM) development for accurate prediction based on weather forecast data Summertime energy consumption can be accurately predicted within an error rate of less than 4.5% [28] 2005 Prediction of daily heating loads of UK buildings SNN development for daily heating load predictions based on one year of sensor data Prediction error rate of less than 3.0% [29] 2006 Electric load forecasting through the use of data from the

2012
Forecasting household electricity consumption RNN development for the short-term (one hour ahead) forecasting of the household electric consumption The house is located in a suburban area in the neighbors of the town of Palermo, Italy. The prediction errors range from 1.5% to 4.6% [60] 2012 Model-based control of a HVAC system in a single zone of a building Multi-objective GA development for predicting air temperature and relative humidity MAE of temperature prediction is 0.1-0.6 • C. Relative humidity is 0.5-3.0% [61] 2012 Coordinating occupants' behaviors for building energy and comfort management Distributed AI development to achieve multi-agent comfort management Reducing 12% energy consumption while keeping thermal comfort with the variation less than 0.5% [62] 2012 Optimization of chiller operation at the office building of the company Imel in New Belgrade GA development for the optimization of chiller operation 2% energy saving during warmest summer days, and up to 13% during the transition period at lower average external temperatures [63] 2012 Energy efficiency enhancement of a decoupled HVAC system Wavelet-based ANN development for optimization of scheduling control In mid-season operation, daily operation cost can be saved from 5.88% to 11.16% [64] 2012 Hourly thermal load prediction Autoregressive with exogenous terms (ARX) model development for thermal load prediction MAPE ranges from 9.5% to 17.5% [65] 2013 Multi-agent system (MAS) application in a commercial building owned by Xerox Palo Alto Research Center (PARC) in the US MAS development for constructing a building comfort and energy management system (BECMS) Constructing a hierarchical function decomposition to provide user solution [66]

2013
Three typical residential buildings with 3.3-kWp photovoltaic (PV) plant located at Ripatransone (AP), Italy Radial basic function (RBF) network development for monitoring home loads, detecting and forecasting PV energy production and home consumptions, informs and influences users on their energy choices MAPE of home load prediction for next three hours is 9.70%, eight hours is 12.20%, and 18 h is 16.30%. MAPE of PV energy production for the next three hours is 7.70%, eight hours is 9.30%, and 18 h is 11.80%.
[67] [68] 2013 Smart homes in a smart grid Supervisory control and data acquisition + house intelligent management system = SHIM for charge and discharge of the electric or plug-in hybrid vehicles, and the participation in demand response (DR) programs

2013
Optimal energy management by load shift GA development for load shift control 35% load shift is possible under a reasonable storage capacity [74] 2014 Dynamic fuzzy controller development to meet thermal comfort ANN performs indoor temperature forecasts to deed a fuzzy logic controller Thermal comfort is very subjective, and may vary even in the same object [75] 2014 Electricity demand prediction of the center of investigation on energy solar (CIESOL) bioclimatic building Short-term predictive neural network model development With a short-term prediction horizon equal to 60 min, the mean error is 11.48% [76] 2014 An autonomous hybrid power system PSO development for predicting weather conditions Techno-socio-economic criterion for the optimum mix of renewable energy resources [77] 2014 Energy consumption prediction of a commercial building that has a total floor area of 34,568 m 2 and is located in Montreal, Quebec Case-based reasoning (CBR) model development for predicting following three-hour weather conditions and indoor thermal loads During occupancy, 07:00-18:00, the coefficient of variation of the root mean square error (CV-RMSE) is below 13.2%, the normalized mean bias error (NMBE) is below 5.8%, and the root mean square error (RMSE) is below 14 kW [78] Sensors 2019, 19,1131  Peak difference in hourly prediction of different models can be as high as 90%. Monthly prediction is 40% and annual variation is 7% [82] 2014 Energy management optimization of a building that has wooden external walls of 9 cm and a wooden external roof of 9 cm.
Distributed AI development Distributed AI in the end control devices can save up to 39% energy through the generation of optimal set points [83] 2015 Real-world application for energy savings in a smart building at a Greek university Rule-based approach development for optimized scheduling control Daily energy saving can reach up to 4% [84] 2015 100 load curves in a smart grid ANN development for DSM Prediction error is less than 5.5% [85] 2015 Five AI algorithms conducted in a one-story test building with a double skin; the building is 4.2 m wide, 4.5 m deep, and 3.05 m high.
AI theory-based optimal control algorithm development for improving the indoor temperature conditions and heating energy efficiency Compared with the transitional algorithm, this novel algorithm can increase thermal comfort by around 2.27% [86] 2015 Solar combi-system combined with a gas boiler or a heat pump ANN model development for predicting thermal load Based on a learning sequence lasting only 12 days, the annual prediction errors are less than 10% [87] 2015 Home energy management system in 25 households in Austria Short-term smart learning electrical load algorithm development to increase flexibility to fit more the generation from renewable energies and micro co-generation devices Prediction error is less than 8.2% [88] 2015 Three houses with wireless sensors for detecting use occupancy and activity patterns

2016
Hot water demand prediction model development for residential energy management systems Bottom-up approach development Total energy savings of 18.25%. Among them, 1.46% of that is attributed to the use of AI tools, compared with linear-up prediction. [94] 2016 Hybrid forecasting model based on data preprocessing, optimization, and AI algorithms AI-assisted data fusion MAPE ranges from 4.57% to 5.69% [95] 2017 Estimation of the energy savings potential in national building stocks AI for analyzing user behaviors User-behavior trends were taken into account and up to a 10% improvement of prediction accuracy resulted [96] 2017

AI Developments and the Applications for HVAC Systems
In this study, keywords including AI, machine learning, heating, ventilation, and air conditioning, were utilized to conduct a paper survey from the Science Direct on Line (SDOL), IEEE Xplore (IEL Online), and MDPI databases. Initially, 737 papers were found from SDOL fitting the criteria of our paper survey, while 34 were found from IEEE Xplore, and 12 were found from MDPI. After further review, articles that were not related to HVAC control or methods to enhance performance were separated out. A total of 79 articles fit the requirements of either (1) describing the applying factory; (2) developing innovative AI tools and their use involving HVAC control; and (3) depictions describing the overall performance of an HVAC system after applying AI control tools. These articles were chosen for further exploration.

Study Case
The published year, HVAC system, developed AI technology, and key results of the collected 79 articles are listed in Table 1.

Developed AI Tools
In the second column of Table 1, there are 18 AI tools for HVAC systems. Among them, the most well-known AI tools are neuro networks (NN), including artificial neuro networks (ANN), recurrent neuro networks (RNN), spiking neuro networks (SNN), and wavelet ANN [15,16,19,[22][23][24]27,29,34,35,37,39,40,44,[51][52][53]59,60,64,76,79,81,82,85,87,[98][99][100]102]. ANN is based on the nervous system, the human brain architecture, and the learning processes. A set of interconnected neurons can be separated into three layers, which are composed of input, output, and hidden layers. The HVAC system inputs, network weights, and the transfer functions of the network lead to the output of ANN. The ANN controller doesn't need to identify the control model. The weight coefficient can be regulated to minimize the costs. ANN can simulate the working procedure of the human brain; therefore, it has the capability of having insight into a complex system. However, the brain-like controller has disadvantages due to having to take a lot of time for off-line training as well as requiring a large amount of data for the system to make quality predictions.
The second AI tool is used for the predictive control functions of ANN: fuzzy or model-based predictive control (MPC) [32,42,47,48,50,65,72,75,87,92,94,101,103,104]. Predictive control provides feedback of the results of the prediction to the system to allow for the adjustment of a system's control parameters. The predictive feedback system is different from previous control systems due to the design of the feedback sensor. Collotta etc. created a non-linear autoregressive neural network auto regressive external type (NNARX-type) structure in 2014 for indoor temperature prediction [75]. In addition to enhancing the control performance, the signal of a predictive control system could be discontinuous for a non-linear system. This is different from the continuous signals that are needed for a linear system managed by a traditional PID controller, which is based on the Laplace transform and linear transfer functions. The insight ability of the ANN is similar to the human insight process, and is a smart way to improve the performance of a non-linear system commanded by predictive control.
The third type of AI tool is known as distributed AI and the multi-agent system (MAS) [20,26,31,57,58,62,66,72,73,83]. In addition to strengthening the entire performance of a system using ANN or predictive control, the subsystems, sensors, and actuators of an HVAC system are able to communicate and interact with each other and become an even more intelligent system through the use of MAS.
The fourth type of AI tool is what is known as the genetic algorithm (GA) method, which is based on biological evolution theory [14,45,54,59,61,63,74,82,93]. The GA method utilizes global non-derivative-based optimization to tune the set points of HVAC systems and meet the thermal comfort requirements without the use of a mathematical model of the system. However, the problem with the GA method is that it requires massive calculations and long run times. Therefore, the GA method might be inappropriate for the real-time operation of an HVAC system.
The fifth type of AI tools is employed for fuzzy control [21,32,33,46,51,59,102], support vector machines (SVM), and R [28,30,38,56,79,82,89]. These two AI tools have the same amount of published articles. A fuzzy logic controller (FLC) is similar to human reasoning and can be used to control a complex system by using the rules of the IF-THEN algorithm. The utilization of fuzzy logic grades and rules yields a low real-time response speed. This situation limits the application of the FLC onto HVAC systems. However, SVM and R could be used in conjunction with the FLC for data classification by finding the hard margins of various data sets to determine the proper control methodologies, modeling, or regression for decision making. This method is used mainly for analyzing huge amounts of data, modeling, and decision making, but is rarely used for HVAC system applications.
The seventh AI tools are model-based controls [10,17,18,69,91] and deep learning (DL, or reinforced learning) [36,49,88,97,98]. The model-based control models, when used with the SVM and R tools, collect and analyze data utilizing the distributed AI tool, and communicate and interact with the MAS tool. The advantage of model-based control is its predictive strategy and high capability of observation. However, the model-based control is a feedback control methodology that can only be applied to a time-independent system. It can't solve problems within a non-linear time-variable system. A deep learning tool could determine a control strategy according to a system's present conditions and information from previous cases through a learning process without the use of modeling. Deep learning is one of the broader machine learning methods, which is based on learning data representations, as opposed to following task-specific algorithms. The learning types are supervised, semi-supervised, or unsupervised. For an HVAC system, deep learning is a novel methodology to achieve more intelligent control.
The knowledge-based system (KBS) [11][12][13]43] is similar to the DL tool. However, the difference between them is that the DL tool is for controlling the system, and KBS is used for building various SVM and R knowledge databases. KBS could provide an optimal control strategy for various HVAC systems through the expert system. KBS and DL are mostly used for problem-solving procedures and to support human learning, decision making, and actions. Another key tool is case-based reasoning (CBR) [78]. However, there are not many published articles regarding this. CBR is able to analyze a control strategy and provide the most optimal one in conjunction with KBS or model-based control in certain cases. Nevertheless, KBS, DL, and CBR tools all need a large amount of data to learn from, and will require a lot of time to collect the control data, which will increase initial installation costs.
The use of AI tools applied onto commercial and residential buildings will be discussed, due to the different occupant behavior patterns between the two building types. The occupants of commercial buildings operate within the confines of working in the numerous companies within a commercial building with a fixed office schedule, and therefore have more predictive air-conditioning demands. The HVAC systems of most commercial buildings are operated by professional energy managers under certain routines and energy-saving targets. Yet, the occupants of residential buildings, being residents, have different air-conditioning behaviors and demands. In general, the HVAC systems of most residential buildings are not operated by professional energy managers.
As mentioned in the previous section, ANN + fuzzy tools are the most widely utilized AI tools for commercial and residential buildings. The adoption ratios for these two types of buildings are 34.5% (10/29) and 24.2% (8/33), respectively. The ANN tool can imitate the operating model of the human brain to implement complex control strategies by learning and analyzing large amounts of data. This is suitable for commercial buildings due to the predictive nature of the occupants. Unfortunately, the ANN tool is not suitable for use in residential buildings. The ANN tool combined with DL, reinforced learning, or deep reinforcement learning (DFL) equips the system with the capability of feature extraction to analyze data and make control decisions, which replaces the need for a professional energy manager.
For commercial buildings, CBR and KBS tools operate alongside ANN + fuzzy tools. CBR and KBS tools can practice model base control and forecast several conditions, including weather, occupancy, and energy consumption, optimize control set points, improve the energy efficiency of an HVAC system, and ensure thermal comfort [13,22,24,27,29,35,43,44,53,64,76,78,84,100,105]. Based on the cases utilizing ANN, CBR, and KBS tools, the ability to make predictions is the most significant function of these AI tools. For residential buildings, DL, distributed AI, and MAS tools function alongside ANN + fuzzy tools. If the fundamental devices of HVAC systems are equipped with distributed AI tools for saving energy and ensuring the thermal comfort, and are able to interact with each other through an MAS tool, then predictive control and the prediction of future environmental conditions for enhancing a system's overall performance could be achieved.
Finally, the most recent development of AI tools applied onto composite buildings is predictive control [50,103,104], which improves the control performance of an HVAC system by having the ability to make predictions. Composite building systems are a mix of residential commercial building systems.

Theoretical Analysis of AI Assisted HVAC Control
In this section, the control performance differences between typical HVAC controls and AI-assisted HVAC controls are analyzed quantitatively. The control outputs were calculated by the common analytic solutions of the AI-assisted HVAC controls in Table 1, which were then compared with those of the on-off and proportional-differential-integral (PID) controls.

Typical HVAC Control
Typical HVAC controls for residential and commercial buildings utilize on-off and PID control algorithms [106] in addition to sensor feedback controls to have the ability to control parameters such as a system's temperature, humidity, and ventilation. The controllable structure is presented in Figure 1.
The control block diagram in Figure 1 runs PID or an on-off algorithm by comparing the set point values and sensor feedback values, and then providing the subsequent output control signals to an HVAC system.
The on-off control output values are calculated according to the following Equation: where σ is the step function corresponding to the difference reading of the sensor feedback, S(t), and the set point, SP, of an HVAC system. If the difference value is larger than the designed threshold value, the value of σ is one. If the difference value of S(t) and SP is within the standard variation of S(t), the value of σ is zero. The modification of on-off control is that, instead of being zero, the value of σ is located within the range of 0.5~0.7 when the difference value is within the standard variation of S(t). This is the so-called floating control to avoid the large oscillation of a control signal of the HVAC system. However, no matter how the typical on-off control or floating control is utilized, the final control signal is determined by the difference of S(t) and SP, as shown in Equation (1).

Theoretical Analysis of AI Assisted HVAC Control
In this section, the control performance differences between typical HVAC controls and AIassisted HVAC controls are analyzed quantitatively. The control outputs were calculated by the common analytic solutions of the AI-assisted HVAC controls in Table 1, which were then compared with those of the on-off and proportional-differential-integral (PID) controls.

Typical HVAC Control
Typical HVAC controls for residential and commercial buildings utilize on-off and PID control algorithms [106] in addition to sensor feedback controls to have the ability to control parameters such as a system's temperature, humidity, and ventilation. The controllable structure is presented in Figure 1.
where σ is the step function corresponding to the difference reading of the sensor feedback, S(t), and the set point, SP, of an HVAC system. If the difference value is larger than the designed threshold value, the value of σ is one. If the difference value of S(t) and SP is within the standard variation of The output of PID control, as shown in Figure 1, is calculated according to the following equation: where K P is the proportional constant, K I is the integral constant, and K D is the differential constant. The differentiation between S(t) − SP is able to predict the controlling oscillation of the next stage and eliminate it within a short period. The integration of S(t) − SP is capable of providing a stable output of PID control and reaching the final state of S(t) − SP → 0 after a longer period.

AI-Assisted HVAC Control
The block diagram of AI-assisted HVAC control resulting from the collected articles is shown in Figure 2.
The core of AI assisted HVAC control is the ANN tool illustrated as controller #1 in Figure 2. The output, y, of the ANN tool is produced through many processes, or neurons, and these neurons interconnect with each other by multiplying with the weights, ω, as shown in the following equation [9,15,16,[22][23][24]27,29,44,47,51,52,64,75,81,85,87,99]: where ω 0 , ω 1 , . . . and ω n are the weighting coefficients, and g is a non-linear activation function, which is usually a step or a sigmoid function, as illustrated by the following equation: The neuron output, y, is unidirectional both for feedback or feedforward control. The ANN tool is skilled at solving data-intensive problems within the categories of pattern classification, clustering, function approximation, prediction, optimization, content retrieval, and process control. It is similar to the human ability to make a single decision based on multiple inputs. Therefore, the main characteristic of AI-assisted HVAC control is its multiple sensor feedback, as shown in Figure 2. The multiple feedback sensor collects several sensor inputs, including controllable and uncontrollable parameters, to build a database. AI tools are not only in the central control port, as shown in controller #1 of Figure 2, but they are also applied in the sensor port, as shown in controller #2 of Figure 2, for more intelligent control.  (2) where K is the proportional constant, K is the integral constant, and K is the differential constant. The differentiation between S(t) − SP is able to predict the controlling oscillation of the next stage and eliminate it within a short period. The integration of S(t) − SP is capable of providing a stable output of PID control and reaching the final state of S(t) − SP → 0 after a longer period.

AI-Assisted HVAC Control
The block diagram of AI-assisted HVAC control resulting from the collected articles is shown in Figure 2. The core of AI assisted HVAC control is the ANN tool illustrated as controller #1 in Figure 2. The output, y, of the ANN tool is produced through many processes, or neurons, and these neurons interconnect with each other by multiplying with the weights, ω, as shown in the following equation [9,15,16,[22][23][24]27,29,44,47,51,52,64,75,81,85,87,99]: where , , … and are the weighting coefficients, and g is a non-linear activation function, which is usually a step or a sigmoid function, as illustrated by the following equation: g(x) = 1 1 + e β > 0 (4) Figure 2. AI-assisted HVAC controls for residential and commercial buildings.
The most utilized intelligent control functions are the optimized setting and predictive control functions, as shown in Figure 2. First, the optimized setting function utilizes the KBS [11][12][13]43,67,68,84] or CBR [34,78,105] tools from the database block to determine the set point (SP). The similarity index (SI) is employed during the calculation process, as shown in the following equation: where y ic and y ip are the neuro outputs of the variable i for the control and past case, respectively. MV i is the mean difference of the variable i in the database. The function f maps the control case to the whole case difference. Based on SI, the global similarity (GS) is calculated according to the following equation: where n is the number of the controlled case and ω i is the weighting coefficient. The proportion P j of the prediction from the past case j is: where GS T is the sum of the global similarities between the selected m cases. Then, the optimized setting point (SP opm ) can be determined by the following equation: where SP j is the set point of past case j. The optimized set point is determined from the built database, including the previous controllable and uncontrollable parameters, and the desired SP value.
In addition to the optimized settings, other intelligent control functions are the predictive controls, which utilize the ANN + fuzzy tool as the central controller, as shown in controller #1 of Figure 2. This tool employs an IF-THEN algorithm to enhance the control performance by predicting the likelihood of future errors effectively and providing proper feedback. The SVM and R tool [28,30,38,56,79,82,89] and autoregressive with exogenous terms (ARX) tool [65] are also suitable for central and edge computing ports, respectively.
The first step of predictive control is to determine probability. After comparing the calculation methods of several articles, the suggested equation is shown in the following: where i indicates the ith sensor for detecting controllable or uncontrollable parameters. S i,k (t) is the ith sensor value, τ i,k is the pheromone intensity, and α and β are the experience parameters. In addition to the probability value, a Guess value is also necessary for predictive control. It is calculated after the ANN runs [9,15,16,[22][23][24]27,29,44,47,51,52,64,75,81,85,87,99] according to the following equation: where ω 0 , ω 1 , . . . and ω n are the weighting coefficients, and g is the non-linear activation function, as illustrated above. The following equation is able to predict the sensor output of the next stage.
where a is the momentum parameter, b is the self-influence parameter, and c is the measure insight. R 1 and R 2 are the random numbers within [0,1] for predictive control.

Control Performance Index
The Harris index (H) and normalized Harris index (NHI) [107,108] are utilized for evaluating the performances of typical and AI-assisted HVAC control outputs, as shown in the following equations: where V 1 = Var[y|initial condition]. The Harris index compares the variations between the initial control y(0) and y(t + 1). There are several articles discussing the effect of rising time, settling time, and overshooting [32] on the control performance of the linear system. However, the Harris index and NHI are able to assess the performance of linear, non-linear, feedforward, and feedback control systems [109], as well as thermal comfort and energy efficiency, etc.

Results and Discussions
In this study, the Harris index and NHI are employed to estimate the performance of HVAC systems in Table 1 managed by On-Off, PID, and AI-assisted control. The sensor signal outputs of the On-Off and PID controls, as shown in Equations (1) and (2), have a positive linear relationship with the Harris index. Therefore, the sensor types mentioned in the articles in Table 2 will be indicated and, then, the sensor errors will be calculated. 2005 Internet-based HVAC system allows authorized users to keep in close contact with a building automation system Optimized setting • Web-enabled controller with pressure, temperature, and flow sensors [25] 2006 Centralized HVAC system with multi-agent structure Distributed AI • Simulation based on thermal comfort related sensors [31] 2006 Predictive control system development for a building heating system Predictive control • Temperature sensor [32] 2006 Indoor thermal comfort controller development Fuzzy indoor thermal comfort controller development by simulation software • Simulation based on inputs from light sensor, outdoor temperature sensor, relative humidity sensor, air flow/hotwire anemometer, and CO 2 sensor [33] 2006 Cooling load prediction of an existing HVAC system in China Load prediction • Multiple sensor data input includes temperature, relative humidity, and pressure [34]     In addition, one commercialized product, Ambi Climate, with a geolocation sensor and applied sensors for the academic cases are analyzed in Table 2. The sensor types and the individual sensor errors are illustrated in Figure 3. In addition, one commercialized product, Ambi Climate, with a geolocation sensor and applied sensors for the academic cases are analyzed in Table 2. The sensor types and the individual sensor errors are illustrated in Figure 3. The performance indexes of On-Off and PID controls are calculated by the sensor errors, as shown in Figure 3. However, instead of sensor errors, the Harris indexes of the optimized settings and predictive controls are determined by the predictive errors, as shown in Equations (8) and (11). The collected prediction or forecast errors of AI-assisted HVAC controls in Table 1 are shown in  The performance indexes of On-Off and PID controls are calculated by the sensor errors, as shown in Figure 3. However, instead of sensor errors, the Harris indexes of the optimized settings and predictive controls are determined by the predictive errors, as shown in Equations (8) and (11). The collected prediction or forecast errors of AI-assisted HVAC controls in Table 1 are shown in Figure 4.
For the On-Off control variables of V 1 and Var[y(t + 1)], both are directly proportional to any sensor errors. Therefore, the calculated H is equal to one, and it becomes the comparison reference. For PID control, when the damping ratio is located in a lower damping ratio range from 0.5 to 1.5, the Var[y(t + 1)] is able to reduce sensor errors by up to 30%, which will in turn enhance the H index value. Due to the reduction of the steady-state error by the integral (K I ) control, a PID control has a better control ability than that of an On-Off control system, when the damping ratio is located within normal to lower value ranges. For higher damping ratio systems, the initial stage V 1 , the final stage Var[y(t + 1)], and the NHI value of the PID control will fluctuate due to variations of the proportional (K P ) and differential (K D ) control within a range of [0.2-0.69]. For AI-assisted HVAC control, the Var[y(t + 1)] is estimated from the sensor output S(t+1), and the assumption is that the NHI is equal to one, as illustrated in Equations (12) and (13). However, the prediction or forecast errors of the AI controls fluctuate at certain ranges and cause variations of the NHI. This occurs particularly when the AI control utilizes human behavior algorithms or thermal comfort prediction algorithms, and the NHI is even lower than that of the PID control. The NHIs of On-Off, PID, and AI-assisted HVAC controls are shown in Figure 5.  For the On-Off control variables of V and Var[y(t + 1)], both are directly proportional to any sensor errors. Therefore, the calculated H is equal to one, and it becomes the comparison reference. For PID control, when the damping ratio is located in a lower damping ratio range from 0.5 to 1.5, the Var[y(t + 1)] is able to reduce sensor errors by up to 30%, which will in turn enhance the H index value. Due to the reduction of the steady-state error by the integral (KI) control, a PID control has a better control ability than that of an On-Off control system, when the damping ratio is located within normal to lower value ranges. For higher damping ratio systems, the initial stage V , the final stage Var[y(t + 1)], and the NHI value of the PID control will fluctuate due to variations of the proportional (KP) and differential (KD) control within a range of [0.2-0.69]. For AI-assisted HVAC control, the Var[y(t + 1)] is estimated from the sensor output S(t+1), and the assumption is that the NHI is equal to one, as illustrated in Equations (12) and (13). However, the prediction or forecast errors of the AI controls fluctuate at certain ranges and cause variations of the NHI. This occurs particularly when the AI control utilizes human behavior algorithms or thermal comfort prediction algorithms, and the NHI is even lower than that of the PID control. The NHIs of On-Off, PID, and AI-assisted HVAC controls are shown in Figure 5.   For the On-Off control variables of V and Var[y(t + 1)], both are directly proportional to any sensor errors. Therefore, the calculated H is equal to one, and it becomes the comparison reference. For PID control, when the damping ratio is located in a lower damping ratio range from 0.5 to 1.5, the Var[y(t + 1)] is able to reduce sensor errors by up to 30%, which will in turn enhance the H index value. Due to the reduction of the steady-state error by the integral (KI) control, a PID control has a better control ability than that of an On-Off control system, when the damping ratio is located within normal to lower value ranges. For higher damping ratio systems, the initial stage V , the final stage Var[y(t + 1)], and the NHI value of the PID control will fluctuate due to variations of the proportional (KP) and differential (KD) control within a range of [0.2-0.69]. For AI-assisted HVAC control, the Var[y(t + 1)] is estimated from the sensor output S(t+1), and the assumption is that the NHI is equal to one, as illustrated in Equations (12) and (13). However, the prediction or forecast errors of the AI controls fluctuate at certain ranges and cause variations of the NHI. This occurs particularly when the AI control utilizes human behavior algorithms or thermal comfort prediction algorithms, and the NHI is even lower than that of the PID control. The NHIs of On-Off, PID, and AI-assisted HVAC controls are shown in Figure 5.  The NHI is utilized to evaluate the performance of the control tools, and especially focuses on the energy-saving percentages, because of its capability to estimate the performance of linear and non-linear control systems. In Table 1, there are only 24 cases [11,12,14,19,21,44,50,57,58,62,63,72,73,83,84,[92][93][94]97,98,101,103,105] that have references to the energy-saving percentages of AI-assisted HVAC controls. The average energy saving percentages of these 24 cases are shown in Figure 6, and a maximum energy savings of 41% is achieved by decision making through the MAS and CBR tools.
In Figure 6, the average energy savings percentage when using AI-assisted HVAC control is 14.02%. Of the 24 cases, 83% were comprised of On-Off control, and 17% were comprised of PID control. Based on the NHI, the estimated average energy savings percentage, variations in energy savings, and the maximum energy savings of AI-assisted HVAC control are 14.4%, 22.32%, and 44.04%, respectively. Comparing these results with the experimental data of 14.02%, 24.52%, and 41.0% in Figure 6, the errors are 3%, 9%, and 7%, respectively. the energy-saving percentages, because of its capability to estimate the performance of linear and non-linear control systems. In Table  1, there are only 24 cases [11,12,14,19,21,44,50,57,58,62,63,72,73,83,84,[92][93][94]97,98,101,103,105] that have references to the energy-saving percentages of AI-assisted HVAC controls. The average energy saving percentages of these 24 cases are shown in Figure 6, and a maximum energy savings of 41% is achieved by decision making through the MAS and CBR tools. In Figure 6, the average energy savings percentage when using AI-assisted HVAC control is 14.02%. Of the 24 cases, 83% were comprised of On-Off control, and 17% were comprised of PID control. Based on the NHI, the estimated average energy savings percentage, variations in energy savings, and the maximum energy savings of AI-assisted HVAC control are 14.4%, 22.32%, and 44.04%, respectively. Comparing these results with the experimental data of 14.02%, 24.52%, and 41.0% in Figure 6, the errors are 3%, 9%, and 7%, respectively.

Conclusions
The presented NHI in this research can be used to evaluate the performance of AI-assisted HVAC control effectively, especially for non-linear control systems assisted by the optimized setting with CBR or KBS tools, or predictive control with the distributed AI and fuzzy algorithm. In order to calculate the NHI, the following hypotheses are made: (1) If the prediction/forecast accuracy could reach 3.5%, which approaches the thresholds of weather forecast accuracy and the accuracies of several types of sensors, including the thermistor, chip type temperature sensor, and humidity sensor, the performance of AI-assisted HVAC control will be enhanced. When compared with the On-Off and PID control strategies, the performance of the AI-assisted HVAC control had an increase of 57.0% and 44.64%, respectively. The increased energy saving percentages are above the average, and even above the maximum energy savings that were found in any of the published articles from 1997 to 2018.
(2) In this study, the lower accuracy of the prediction tools and the resulting poor energy savings of HVAC systems are hypothesized. This hypothesis is from the collected articles, and forms the qualitative research in this paper. In the future, based on the hypothesis, the performance improvement of AI-assisted HVAC control will depend on the prediction accuracy of the sensors, which will be evidenced through the numerical simulation in Part 2 and the confirming experiments in Part 3.

Conclusions
The presented NHI in this research can be used to evaluate the performance of AI-assisted HVAC control effectively, especially for non-linear control systems assisted by the optimized setting with CBR or KBS tools, or predictive control with the distributed AI and fuzzy algorithm. In order to calculate the NHI, the following hypotheses are made: (1) If the prediction/forecast accuracy could reach 3.5%, which approaches the thresholds of weather forecast accuracy and the accuracies of several types of sensors, including the thermistor, chip type temperature sensor, and humidity sensor, the performance of AI-assisted HVAC control will be enhanced. When compared with the On-Off and PID control strategies, the performance of the AI-assisted HVAC control had an increase of 57.0% and 44.64%, respectively. The increased energy saving percentages are above the average, and even above the maximum energy savings that were found in any of the published articles from 1997 to 2018. (2) In this study, the lower accuracy of the prediction tools and the resulting poor energy savings of HVAC systems are hypothesized. This hypothesis is from the collected articles, and forms the qualitative research in this paper. In the future, based on the hypothesis, the performance improvement of AI-assisted HVAC control will depend on the prediction accuracy of the sensors, which will be evidenced through the numerical simulation in Part 2 and the confirming experiments in Part 3. (3) The existing sensors are designed for accurate sensing, but not for accurate prediction, and this causes an unmet demand of the sensors. Improved sensors for AI-assisted HVAC controls should be able to provide the ability of more accurate prediction. Based on Bayes' theorem, accurate prediction depends on the conditional probability. The priori probability can be utilized to determine the posterior possibility, and the consistent prediction can be achieved by aggregation. The priori information notice (PIN) design for sensors are provided in this study to decrease the prediction errors to as low as 3.5% or less. The details of the PIN sensor will be discussed in Part 2 of the serial research.