Prediction and Comparison of In-Vehicle CO₂ Concentration Based on ARIMA and LSTM Models

Abstract

An increase in the carbon dioxide (CO₂) concentration within a vehicle can lead to a decrease in air quality, resulting in numerous adverse effects on the human body. Therefore, it is very important to know the in-vehicle CO₂ concentration level and to accurately predict a concentration change. The purpose of this research is to investigate in-vehicle concentration levels of CO₂, comparing the accuracy of an autoregressive integrated moving average (ARIMA) model and a long short-term memory (LSTM) model in predicting the change in CO₂ concentration. We conducted a field test to obtain in-vehicle original concentration data of CO₂ while driving, establishing a prediction model of CO₂ concentration with ARIMA and LSTM. We selected mean absolute percentage error (MAPE) and root mean squared error (RMSE) as the evaluation indicators. The findings indicate the following: (1) With the vehicle windows closed and recirculation ventilation mode activated, in-vehicle CO₂ concentration increases rapidly. During testing, CO₂ accumulation rates were measured at 1.43 ppm/s for one occupant and 3.52 ppm/s for three occupants within a 20 min driving period. Average concentrations exceeded 1000 ppm, so it is recommended to improve ventilation promptly while driving. (2) The MAPE of ARIMA and LSTM prediction results are 0.46% and 0.56%, respectively. The RMSE results are 19.62 ppm and 22.76 ppm, respectively. The prediction results demonstrate that both models effectively forecast changes in a vehicle’s interior environment CO₂, but the prediction accuracy of ARIMA is better than that of LSTM. The research findings provide theoretical guidance to traffic safety managers in selecting suitable models for predicting in-vehicle CO₂ concentrations and establish an effective in-vehicle ventilation warning control system.

1. Introduction

Individuals spend a significant amount of time in indoor environments, including automobiles. A survey conducted among Americans revealed that 88% of their day is spent indoors, and 7% is spent in a vehicle [1,2]. Therefore, indoor air quality is closely linked to the health, comfort, well-being, and productivity of occupants [3]. Furthermore, the air pollution levels within a vehicle’s interior environment exceed those of indoor living environments [4]. Therefore, we should pay attention to the air quality issue within the vehicle’s interior environment, and the number of studies in this field is increasing [5]. To ensure thermal comfort while driving, people will close windows and use air conditioning, particularly during winter and summer. In a tropical country like Thailand, air conditioning is utilized throughout almost the entire year due to the hot climate, and people commonly utilize recirculation (RC) ventilation mode because it can reduce fuel consumption [6]. When occupants operate air conditioning based on their personal preferences in a vehicle, they may not be aware of the issues caused by RC ventilation mode and closed windows: the elevated concentration of carbon dioxide (CO₂) in a vehicle due to human respiration within a small, enclosed space and a low air ventilation rate. In order to investigate the level of CO₂ concentration in vehicles during driving, numerous scholars have conducted field measurements of CO₂ concentration in small vehicles. For instance, Tolis et al. [7] observed that after 15 min of driving, the CO₂ concentration in a vehicle reached 5000 ppm. Luangpresert et al. [6] observed that the concentration of CO₂ increased to 10,000 ppm after 33 min of driving. In a survey of taxi air quality, it was discovered that CO₂ levels reached 3000 ppm within 45 min of operation and remained above this threshold for over four hours [8]; Barnes et al. [9] conducted a random selection of 51 private vehicles and monitored their CO₂ levels during daily driving, revealing that 96% of the vehicles exceeded 1000 ppm, and 16% surpassed the threshold of 5000 ppm. In addition to small vehicles, CO₂ concentrations in large vehicles have also attracted the attention of numerous scholars. Chan [10] discovered that the concentration of CO₂ reached 4000 ppm when a bus was fully loaded, which is ten times higher than the ambient concentration; Chiu et al. [11] conducted an investigation on the concentration of CO₂ in a campus tour bus. Throughout the test, the maximum and average CO₂ concentrations in the driver zone were 2511 ppm and 1831 ppm, respectively. Meanwhile, the passenger zone reached 2647 ppm and 2047 ppm, respectively. Querol et al. [12] monitored the concentration of CO₂ in buses during peak commuting hours and found a mean value of 1039 ppm. However, few of the above-mentioned studies have focused on variations in CO₂ concentrations across diverse driving conditions. Furthermore, CO₂ and particulates are key indicators for assessing in-vehicle air quality [13]. Current research has shown that there are fewer studies on in-vehicle CO₂ concentrations compared to in-vehicle particulate studies [14]. This indicates a relative scarcity of in-vehicle CO₂ research.

Currently, there are a limited number of standards pertaining to CO₂ concentration in passenger vehicles. Consequently, reference is generally made to indoor air quality standards.

Table 1. CO₂ standards established by various institutions.

Institution	Regulated or Suggested Concentration of CO2 (ppm)
The American Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHRAE)	1000 [15]
U.S. Occupational Safety and Health Administration (OSHA)	1000–1500 [16]
National Bureau of Disease Control and Prevention of China	1000 (1 h average) [17]
French rules	1000 (Non-residential buildings) 1300 (No smoking area) [18]
Taiwan Environmental Protection Administration in China	1000 (8 h CO2) [11]
Hong Kong Environmental Protection Administration in China	2500 (1 h CO2 for level 1 for buses) [11]

presents the recommended or specified CO₂ values proposed by various institutions.

Among them, the carbon dioxide concentrations specified by ASHRAE, OSHA, the Chinese National Center for Disease Control and Prevention, French rules, and the Taiwan Environmental Protection Administration in China pertain to indoor air quality. The Hong Kong Environmental Protection Administration in China has developed specific standards for CO₂ levels in buses. The majority of standards prescribe a CO₂ concentration of 1000 ppm. Based on the aforementioned measurement results, it was observed that in most cases, both small and large vehicles exhibited a CO₂ concentration exceeding 1000 ppm during operation, with some even surpassing 5000 ppm. Comparing the existing standards, it was observed that the concentration of CO₂ in numerous test vehicles exceeded the prescribed levels stipulated by the standards. Although the duration of actual tests rarely exceeds 1 h or 8 h, studies have indicated that exposure to 1000 ppm to 5000 ppm can impact both health and driving behavior. ASHRAE reports that indoor CO₂ concentrations are linked to an increased occurrence of self-reported sick building syndrome symptoms [15]. Additionally, the in-vehicle CO₂ may affect the body’s perception of comfort [18], and it may cause an increase in diastolic blood pressure [19], affecting ride comfort. It can lead to fatigue and drowsiness, impacting cognitive capabilities, which reduce reaction time and concentration. Ultimately, this affects the driver’s decision-making ability and judgment, creating a potential hazard for traffic safety [20,21,22]. Some authority agencies have pointed out that this negative impact can lead to traffic accidents., as noted by the Royal Malaysian Traffic Police, who identify driver fatigue and inattention as primary causes of such incidents [23]. A study conducted by the American Automobile Association revealed that fatigued drivers were responsible for three-and-a-half times more crashes than that reported in news accounts from 1999–2008 [24]. A report released by the National Highway Traffic Safety Administration (NHTSA) indicated that at least 83,000 vehicle accidents were caused by driver fatigue and drowsiness; these accidents led to 37,000 injuries and 900 fatalities [25].

In order to mitigate the occurrence of traffic accidents and maintain a comfortable cabin environment, it is important to precisely forecast and regulate the in-vehicle CO₂ concentration level, while also alerting occupants prior to reaching levels that may impact behavior or physical health. Consequently, several scholars have conducted research on models for calculating the CO₂ concentration in vehicles. Jung [26] developed a mathematical model that accurately predicts the concentrations of CO₂ during RC ventilation mode; Luangprasert et al. [6] employed a first-order mass balance equation to simulate variations in CO₂ inside a vehicle while driving; Mathur [27] developed a more comprehensive calculation model, including passenger count, cabin volume, and leakage rate, among others; Zhao et al. [13] investigated the impact of seasonal variations and developed a semi-empirical model. These models were developed based on the principles of CO₂ mass balance or control volume-mass conservation. Furthermore, Hudda and Fruin [22] integrated the CO₂ generation rate with the air change rate, vehicle characteristics, and driving conditions to develop a model for assessing in-vehicle CO₂ accumulation. Though these physically driven models can ensure a certain level of accuracy, they also have some limitations: determining the parameters required by the model is difficult, and the assumptions necessary for establishing the model can result in inaccurate calculation results.

The increase in CO₂ concentration is directly proportional to the duration of driving time when using the RC ventilation mode, exhibiting typical characteristics of time series data, so it can be considered as a time series dataset [23,28]. This illustrates the feasibility of using a time series prediction model for forecasting the in-vehicle CO₂ concentration. The autoregressive integrated moving average model (ARIMA) is a classical time series forecasting model that falls under the umbrella of traditional statistical analysis methods. Its ability to analyze seasonality, periodicity, and trends in data make it highly versatile with accurate predictive effect. It has been utilized for morbidity prediction in medical research [29,30], commodity price and stock price forecasting in finance [31,32,33,34], as well as for applications in geology [35,36], transportation [37,38], electricity [39,40], sound recognition [41], atmospheric environment research [42], and other disciplines. In recent years, the rapid development of big data and artificial intelligence has led to long short-term memory (LSTM), a modified version of a recurrent neural network (RNN), becoming a prominent research topic. Due to its powerful feature extraction capability, LSTM has become a common method for analyzing time series data [43,44]. LSTM is proficient in capturing long-term dependencies and non-linear relationships from historical data, thereby enabling accurate prediction of future changes [45]. The LSTM also has a wide range of applications: it has been successfully applied to prediction in various fields such as medicine [30,46,47,48], finance [49,50], transportation [51,52], acoustics [53], hydrology [54], and marine science [55]. From the above research, it is evident that ARIMA and LSTM share similar application areas. Therefore, numerous studies have applied both models to the same dataset to compare the differences in prediction accuracy. Tsan et al. [56] predicted the number of upper respiratory illnesses in Taiwan, China. Xiao and Su [57] used stock price data from the New York Stock Exchange and made predictions. Both studies found that LSTMs exhibited superior predictive performance. Elsaraiti and Merabet [58] compared the accuracy of the two models in predicting wind speed. The root mean squared error (RMSE) values of LSTM and ARIMA were 3.423 and 3.124 respectively, and the mean absolute error (MAE) values were 2.772 and 2.457 respectively. From these three studies, it was found that LSTM prediction accuracy was higher than that of ARIMA. However, some scholars have discovered that ARIMA exhibits higher prediction accuracy than LSTM: Long et al. [45] conducted a comparison of the predictive accuracy between ARIMA and LSTM models for monkeypox incidence in the United States. The results showed that ARIMA had lower RMSE and MAE values of 100.38 and 80.79, respectively, compared to LSTM’s values of 208.58 and 193.19. Similarly, Xu and Chen [59] predicted quarterly GDP changes in China using ARIMA, with an RMSE value of 218.203, which was lower than LSTM’s value of 609.356. Ning et al. [60] have demonstrated that ARIMA outperforms other methods in predicting oil production. Other scholars have utilized both LSTM and ARIMA models to predict price changes in more than 70 types of vegetables, with the proportion of mean absolute percentage error (MAPE) values less than 10% being 0.436 and 0.694, respectively [61]. In addition, some researchers have found that each of the two models has its own advantages. Zhang et al. [62] demonstrated that ARIMA outperformed LSTM in predicting monthly and weekly incidence of hemorrhagic fever, whereas LSTM exhibited superior performance in daily incidence prediction compared to ARIMA. Wang and Mi [63] applied both models to forecast user demand for vehicle sharing and found that LSTM was more accurate in predicting the demand for each type of user individually, whereas ARIMA performed better when forecasting the overall demand across all users. The findings, advantages, and limitations of the aforementioned model comparison studies are summarized in

Table 2. Summary of model comparison studies.

Literatures	Comparison of Model Prediction Results	Advantages	Limitations
Tsan [56]	LSTM better than ARIMA	The prediction model was established using air pollutants as input variables and the number of diseases as the output variable	Only supports univariate input
Xiao and Su [57]	LSTM better than ARIMA	Developed a hybrid ARIMA-LSTM model for accurate stock price prediction	The analysis was limited to data collected from 2010 onwards
Elsaraiti and Merabet [58]	LSTM better than ARIMA	Comparing the predictive accuracy of ARIMA and LSTM in wind speed	The conclusions need to be confirmed through comparisons with other studies
Long et al. [45]	ARIMA better than LSTM	The first application of machine learning to predict monkeypox cases	The influence of temperature and air passenger traffic on cases was not taken into account
Xu and Chen [59]	ARIMA better than LSTM	Utilizing time series forecasting models to predict the trend in macroeconomic indicators	The influencing factors were not taken into consideration
Ning et al. [60]	ARIMA better than LSTM	Considering the seasonal impact on oil production	R-squared is not appropriate in evaluating nonlinear regression
Peng et al. [61]	ARIMA better than LSTM	Establishing an accurate vegetable price prediction model	Forecast accuracy needs to be improved
Zhang et al. [62]	Monthly and weekly incidence prediction: ARIMA better than LSTM Daily incidence prediction: LSTM better than ARIMA	Compared the prediction models based on data at different time scales	The influencing factors were not taken into consideration
Wang and Mi [63]	Predicting the overall demand: ARIMA better than LSTM Predicting the individual demand: LSTM better than ARIMA	Anticipating future demand for shared cars among users	The data preprocessing stage exhibits certain inadequacies

. In conclusion, though both ARIMA and LSTM models demonstrate accurate predictions for time series data, their prediction performance varies across diverse datasets.

According to the current research status, we found that:

• There are fewer studies on in-vehicle CO₂ concentrations compared to studies on in-vehicle particulates.
• The models for in-vehicle CO₂ concentration primarily rely on computational models that consider physical influencing factors, but these models still have some limitations.
• Due to their similar application domains, ARIMA and LSTM are frequently employed for comparative analysis of forecasting accuracy.

There exists a knowledge gap in this area, with inadequate comprehension of in-vehicle CO₂ concentration levels across diverse driving conditions, and there is a lack of studies utilizing data-driven time series analysis methods to build prediction models for the in-vehicle CO₂ concentration. Based on the aforementioned description, the cross-application of time-series forecasting models and traffic environmental science warrants in-depth investigation. It is feasible to apply ARIMA and LSTM to predict CO₂ concentrations in vehicles, and further comparative experiments are necessary to verify the accuracy of both models.

According to the current research status, the purpose of this research is to enhance our understanding of in-vehicle CO₂ concentrations under various driving conditions, to establish a precise time series predictive model for the in-vehicle CO₂ concentration, and to compare the accuracy of these models. In order to achieve this objective, this research conducted field tests to obtain in-vehicle CO₂ concentration data under different driving conditions, used the statistical prediction algorithm ARIMA and the deep-learning algorithm LSTM to build a predictive model of the in-vehicle CO₂ concentration, compared the prediction accuracy of the two models, and we explore the application scope of the models. The findings of this research offer suggestions to traffic safety managers for selecting suitable early warning models for in-vehicle CO₂ concentrations and provide theoretical guidance for establishing an effective in-vehicle ventilation control system, which can help reduce the incidence of traffic accidents. Furthermore, this research can also serve as a data reference for establishing in-vehicle CO₂ concentration standards in the automotive industry.

2. Materials and Methods

2.1. In-Vehicle CO₂ Concentration by Field Dynamic Testing

The original CO₂ concentration data for this research were acquired through field tests. Driving the vehicle in accordance with the predetermined driving route and placing a monitoring instrument inside the vehicle, real-time changes in CO₂ concentration within the vehicle are recorded by the instrument, thereby obtaining data on the CO₂ concentration levels while driving.

2.1.1. Test Subjects and Instrument Layout

The two test vehicles used in this research were common 1.5 L 5-seater family vehicles, namely, the Nissan-Sylphy and Honda-Fit. Both gasoline-powered vehicles use Euro VI 92.

Table 3. Vehicle technical parameters.

Vehicle Parameters	Nissan-Sylphy [64]	Honda-Fit [65]
Engine	Type: petrol engine, model: HR16 Displacement: 1.6 L Number of cylinders: 4 Maximum power: 90 KW Maximum torque: 155 n·m	Type: petrol engine, model: L15BU Displacement: 1.5 L Number of cylinders: 4 Maximum power: 96 KW Maximum torque: 155 n·m
Transmission	Continuously variable transmission (CVT, no gear number)	Continuously variable transmission (CVT, no gear number)
Vehicle body features	Length, width, and height: 4631 mm × 1760 mm × 1503 mm Wheelbase: 2700 mm Vehicle weight: 1230 kg Age of vehicle: 2 years Approximate cabin volume: 3.5 m3 Odometer: 58,682 km	Length, width, and height: 4109 mm × 1694 mm × 1537 mm Wheelbase: 2530 mm Vehicle weight: 1107 kg Age of vehicle: 1.5 years Approximate cabin volume: 3.2 m3 Odometer: 52,439 km
Performance parameters	Acceleration time from 0 to 100 km/h: 12.1 s Maximum speed: 182 km/h Fuel consumption of official WLTC: 6.09 (L/100 km), 45.07(g/km) [66] Fuel consumption of our testing: 7.12 (L/100 km), 52.61 (g/km, per hour)	Acceleration time from 0 to 100 km/h: 10.6 s Maximum speed: 190 km/h Fuel consumption of official WLTC: 5.57 (L/100 km), 41.22 (g/km) [66] Fuel consumption of our testing: 6.85 (L/100 km), 50.69 (g/km, per hour)
Suspension and braking systems	Type of front suspension: MacPherson independent suspension Type of rear suspension: torsion beam non-independent suspension Front brake system: ventilated disc brakes; rear brake system: disc brakes	Type of front suspension: MacPherson independent suspension Type of rear suspension: torsion beam non-independent suspension Front brake system: ventilated disc brakes; rear brake system: drum brakes
Fuel type and tank capacity	Fuel type: gasoline fuel, tank volume: 50 L	Fuel type: gasoline fuel, tank volume: 40 L
Security configuration	Main and passenger airbags, ABS	Main and passenger airbags, ABS
Number of seats and seat configuration	Number of seats: 5-person seat configuration; fabric, manual adjustment, no heating or cooling equipment	Number of seats: 5-person seat configuration; fabric, manual adjustment, no heating or cooling equipment

presents detailed information about these vehicles. The data on the concentration of CO₂, temperature, and humidity in the vehicle were collected using a HOBO tester (Figure 1), and fan speed at the air outlet was measured using a smart sensor anemometer (Figure 2). Instrument parameters are provided in

Table 4. Test instrument models and parameters.

Instrument Name	Model Measuring	Parameters	Measuring Range	Measuring Accuracy
HOBO CO2 concentration recorder	MX1102A	CO2 Temperature Relative humidity	0–5000 ppm −20–70 °C 5–95%	CO2: ±50 ppm +5% of reading at 25 °C (77 °F), less than 90% RH (noncondensing) and 1013 mbar Temperature: ±0.21 °C from 0° to 50 °C (±0.38 °F form 32° to 122 °F) Relative humidity: ±2% from 20% to 80% typical to a maximum of 14.5% including hysteresis at 25 °C (77 °F); below 20% and above 80% ± 6% typical
Sigma digital wind speed and volume meter	AS856	Outlet air speed	0.0–45.0 m/s	± (0.5 m/s + 0.05 × indicated wind speed)

. The study utilized mobile phone software capable of satellite connectivity to record real-time vehicle speed; the software is based on the Android platform. To avoid the impact of occupant respiration and solar radiation on data recording, the instrument is positioned at the center of the vehicle, aligned with the right shoulder height of the front row. The location of the testing device is illustrated in Figure 3. A total of three occupants participated in this field test, with one occupant seated on the right side of the front row, another on the left side of the rear row, and a designated driver included. The participants in this field test were exclusively male. The weight, height, and age of the participants were strictly controlled to fall within the ranges of 65–70 kg, 165–170 cm, and 24–26 years old, respectively, in order to minimize the impact of weight, body composition, sex, and other physiological factors on CO₂ exhalation levels. Additionally, none of the three subjects engaged in strenuous physical activity prior to testing.

2.1.2. Test Location and Process

The field test site was situated in Guilin, Guangxi, and the test was conducted on 14–15 December 2022, under clear weather conditions. Given that the concentration of CO₂ inside a vehicle is influenced by various factors such as ventilation settings, the number of occupants, driving speed, and vehicle characteristics [13,14], this research monitored changes in CO₂ concentration across these different variables. We conducted a total of six field tests, and the specific operational conditions during each test are presented in

Table 5. Test conditions.

Test Variable	Test Number	Test Vehicle	Fan Speed	Driving Road	Number of Occupants
Fan speed	T1	Nissan-Sylphy	S1	Urban road	3
	T2	Nissan-Sylphy	S4	Urban road	3
Number of occupants	T3	Nissan-Sylphy	S1	Urban road	1
Driving speed	T4	Nissan-Sylphy	S1	Suburban road	3
	T5	Nissan-Sylphy	S1	Expressway	3
Vehicle volume	T6	Honda-Fit	S1	Urban road	3

. T1–T2 were designed to monitor and compare the impact of varying fan speeds on the rate of CO₂ increase. The fan speed of the Nissan-Sylphy is categorized into seven different levels. We selected level 1 (S1) and level 4 (S4) for the purpose of testing. The fan speeds at the vents of S1 and S4 were measured as 0.756 m/s and 1.648 m/s, respectively. The purpose of T3 and T1 is to monitor and compare the impact of varying numbers of passengers on the rate of CO₂ increase. T4–T5 were designed to monitor and compare the impact of varying vehicle speeds on the rate of CO₂ increase. T1–T5 were conducted in a Nissan-Sylphy, and T6 in a Honda-Fit to assess the effect of different interior spaces on the rate of increase in CO₂. The S1 fan speed at the air vent of the Honda-Fit was measured to be 0.723 m/s, which is approximately equivalent to that of the Nissan-Sylphy. The reference data for this research were obtained from the T1 test results, with all other tests compared against it. Our field test design refers to the test methodology described in reference 14.

We selected three driving routes: 12 km of urban roads, with a speed range of 0–40 km/h; 15 km of suburban roads, with a speed range of 0–80 km/h; and 28 km of highways, with a speed range of 60–120 km/h. The duration for each test was controlled at 20 min, and the driving route is illustrated in Figure 4. During the test, the windows were closed, and the air conditioning system was set to internal circulation mode. Prior to each experiment, the instrument underwent calibration in an outdoor open area. Subsequently, fresh air was introduced into the vehicle by opening its doors and windows until the CO₂ concentration inside reached an equilibrium with that of its surroundings. Only then did all personnel enter the vehicle and commence testing. Each measurement lasted for a duration of 20 min, during which data were recorded at intervals of 5 s, resulting in a total collection of 1440 sets of data.

2.2. Prediction Models

This research utilizes the ARIMA model and LSTM model to predict in-vehicle CO₂ concentration. Specifically, it aims to identify regularity among the previous moment data (t₀, t₁, t₂, …, t_n−1, t_n) and to predict the subsequent moment data (t_n+1). The research was implemented using Python 3.8 for modeling and simulation in order to achieve accurate predictions of in-vehicle CO₂ concentration changes.

2.2.1. ARIMA Model

The ARIMA model is a statistical model that combines autoregressive (AR) and moving average (MA) models to predict stochastic time series data. It was first proposed by Box, an American researcher, and Jenkins, a British statistical researcher, in the 1970s [67]. The model identifies intrinsic relationships between historical and current values to forecast future data.

The AR model is based on a mathematical equation to describe the autocorrelation in a time series, i.e., the relationship between the current moment (t) and the previous moment (p) values. The autoregressive model of order p is denoted as AR(p) and is expressed as shown in Equation (1):

$$Y_t=c+{\alpha }_1{Y}_{t-1}+{\alpha }_2{Y}_{t-2}+{\alpha }_3{Y}_{t-3}+\dots +{\alpha }_p{Y}_{t-p}+{\epsilon }_t$$

(1)

The MA model is known as a moving average model and represents a weighted average sum of several white noises. The q–th order moving average model is denoted as MA(q), as shown in Equation (2):

$$Y_t={\beta }_1{\epsilon }_t{}_{-1}-{\beta }_2{\epsilon }_{t-2}-{\beta }_3{\epsilon }_t{}_{-3}-\dots -{\beta }_q{\epsilon }_t{}_{-q}+{\epsilon }_t$$

(2)

Combining the AR model with the MA model yields the ARMA model, as shown in Equation (3):

$$Y_t=c+{\alpha }_1{Y}_{t-1}+{\alpha }_2{Y}_{t-2}+{\alpha }_3{Y}_{t-3}+\dots +{\alpha }_p{Y}_{t-p}+{\epsilon }_t-{\beta }_1{\epsilon }_t{}_{-1}-{\beta }_2{\epsilon }_{t-2}-{\beta }_3{\epsilon }_t{}_{-3}-\dots -{\beta }_q{\epsilon }_t{}_{-q}$$

(3)

The ARIMA model is the model calculated by differencing the data d times using the ARMA model, denoted as ARIMA (p, d, q). The ARIMA model is used for time series forecasting in the following steps:

• Data stationarity analysis: Prior to establishing an ARIMA prediction model, it is imperative to evaluate the stationarity of the data. The augmented Dickey–Fuller test (ADF) is employed to estimate whether the data are stationary or not in this research. If the data exhibit stability, the significance p-value should be less than 0.05; otherwise, differencing must be applied to non-stationary data until they achieve stationarity.
• Estimation of model hyperparameters: The stationary time series data are further processed to obtain the autocorrelation coefficient (ACF) and partial autocorrelation coefficient (PACF). After determining the range of hyperparameters p and q, it is necessary to continuously try to determine the combination of model hyperparameters with the highest accuracy, but this method has an interference of certain human factors. Therefore, the “auto. arima” function in Python can be utilized to automatically determine the optimal combination of hyperparameters, selecting the optimal model by means of the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), thereby eliminating any potential influence from human factors during the selection process. The range of AIC and BIC values is not fixed but varies across different datasets. Usually, the combination of hyperparameter p and q that yields the smallest AIC and BIC values represents the most suitable model. The calculation method for AIC and BIC is shown in Equations (4) and (5):

$$\mathrm{AIC}=2k-2ln(L)$$

(4)

$$\mathrm{BIC}=kln(n)-2ln(L)$$

(5)

• Test the validity of the optimal model: Before forecasting, the effectiveness of the optimal model needs to be tested. Firstly, the Ljung–Box test method is used to judge whether the residual of the prediction model is a white noise sequence. If p-value > 0.05, it can be considered that the residual is a white noise sequence. Then, the Q test is used to check the normal distribution of the model residuals, and a Q–Q diagram is drawn to observe the distribution of the residuals.
• Forecast the data: After completing the aforementioned actions, predictions can be made.

2.2.2. LSTM Model

In 1997, Sepp Hochreiter and Jurgen Schmidhuber proposed the LSTM neural network [68], which is an improved version of a recurrent neural network (RNN). The single-cell structure of the LSTM cell structure is shown in Figure 5, with each cell having three gates: the “input gate”, the “forget gate”, and the “output gate”. This “gate” can be opened or closed to determine whether the output of the memory state (the previous state of the network) of the model neural network reaches a threshold value at that layer, so that it can be added to the current calculation of that layer [69]. Each gating unit is a sigmoid activation function that controls the flow of information. In the LSTM model, each time step has a hidden state h_t and a cell state C_t. Cell states are a central part of the LSTM model, which allows the neural network to selectively forget or preserve information. The cell state C_t at each time step depends on the cell state C_t−1 at the previous time step, the input x_t at the current time step, and the output of the gating unit. LSTM’s cell states can pass information between multiple time steps, allowing the neural network to capture long-term dependencies. It is possible to keep the important information and forget the minor information, to be able to identify the regular changes in time series data, and to realize the prediction. The training process of the LSTM neural network uses a back propagation algorithm combined with gradient cropping to address the shortcomings of traditional recurrent neural network gradient explosion.

The mathematical formulations for the input gate (i_t), forgetting gate (f_t), and output gate (o_t) are presented in Equations (6)–(8). The memory cell C is utilized for the storage and transmission of long-term information within the network, with mathematical expressions depicted in Equations (9) and (10). Equation (11) depicts the output h_t generated by the LSTM network:

$$i_t=\sigma (W_i\cdot [h_{t-1},x_t+b_i])$$

(6)

$$f_t=\sigma (W_f\cdot [h_{t-1},x_t]+b_f)$$

(7)

$$o_t=\sigma (W_o\cdot \left[h_{t-1},x_t\right]+b_o)$$

(8)

$$C_t=f_t\cdot C_{t-1}+i_t\cdot C_t^{{}^{\prime }}$$

(9)

$$C_t^{{}^{\prime }}=tanh(W_c\cdot [h_t,x_t]+b_c)$$

(10)

$$h_t=o_t\cdot tanh(C_t)$$

(11)

The key steps for time series prediction using LSTM are as follows:

• Data preprocessing: Data preprocessing can effectively reduce noise, eliminate redundant information, and extract key features from data to enhance the training and prediction performance of neural network models. This research employs the max-min normalization method for data preprocessing. This process ensures that all data values are reflected within the [0, 1] interval. The calculation method for normalization is as follows:

$$y_i=\frac{x_i-\min (x_i)}{\max (x_i)-\min (x_i)}$$

(12)

• Determining the neural network structure: Determine the inputs and outputs of the neural network and the number of neurons in the hidden layer.
• Network training: Determine the loss function, activation function, optimizer, and other parameters utilized for training the LSTM network. The loss function adopts the mean squared error (MSE) as the criterion for evaluation. The computation of the MSE is illustrated below:

$$\mathrm{MSE}=\frac{1}{n}{{\displaystyle \sum }}_{i=1}^n{(y_i-\widehat{y_i})}^2$$

(13)

MSE, which stands for mean squared error, is a metric used to assess the accuracy of a model’s predictions. It is calculated by averaging the squared differences between the predicted and true values. The activation functions use the sigmoid function. The adaptive moment estimation (Adam) was selected as the optimizer for this research. The Adam optimizer is suitable for problems where the gradient is sparse or noisy. The update of its parameters is not affected by the gradient scaling transformation. It is a commonly used optimizer for deep learning.

• Make predictions: After the aforementioned steps have been completed, the trained model can be utilized for predictions.

2.3. Evaluation Indicators

The model forecasts are evaluated for accuracy using MAPE and RMSE, which are calculated as shown below:

$$\mathrm{MAPE}=\frac{100\%}{n}{{\displaystyle \sum }}_{i=1}^n\mid \frac{{\widehat{y}}_i-y_i}{y_i}{\displaystyle \mid }$$

(14)

$$\mathrm{RMSE}=\sqrt{\frac{1}{n}{{\displaystyle \sum }}_{i=1}^n{\left({\widehat{y}}_i-y_i\right)}^2}$$

(15)

3. Results

3.1. Analysis of In-Vehicle CO₂ Concentration

The mean values of temperature, humidity, CO₂ concentration, and rate of CO₂ increase during the six field tests are presented in

Table 6. Average temperature and humidity and CO₂ concentration of each test.

Test Number	Temperature (°C)	Relative Humidity (%)	CO2 (ppm)
T1	22.78	32.07	2734
T2	25.10	37.69	2489
T3	17.14	38.84	1161
T4	18.49	36.75	2427
T5	25.21	28.69	1905
T6	23.82	28.70	2866

. Temperature and humidity remained relatively stable due to the operation of the vehicle’s air conditioning system. The CO₂ concentration measurements for each field test are presented in Figure 6. During testing, the windows were closed, and internal circulation was activated, resulting in an increase in the CO₂ concentration over time. Due to real-time changes in vehicle speed causing an unstable air change rate, there were fluctuations observed during the growth process of CO₂ concentrations, similar to the field test results from Luangprasert et al., Lohani et al., and Zhao et al. [6,13,28]. The impact of different fan speeds on the increase in the in-vehicle CO2 concentration is illustrated in Figure 6a. After 20 min, the CO₂ concentration levels exceeded 4000 ppm in T1–S1 and T2–S4, with rates of CO₂ increase of 3.52 ppm/s and 3.02 ppm/s, respectively. The higher air speed at the air conditioning outlet in S4 results in an increased frequency of air exchange between the cabin and its surrounding environment, leading to a lower rate of CO₂ increase. The impact of different numbers of occupants on the increase in the in-vehicle CO₂ concentration is illustrated in Figure 6b. With three occupants, the CO₂ concentration reaches 4633 ppm after 20 min, exhibiting a rate of CO₂ increase of 3.52 ppm/s. With one occupant, the CO₂ concentration increases to 2152 ppm at a rate of 1.43 ppm/s after 20 min. The comparison indicates that with three occupants in the vehicle, the CO₂ concentration attained after 20 min is 2.53 times higher than that with only one occupant, and the rate of CO₂ increase is 3.03 times greater. Figure 6c illustrates the rate of CO₂ increase within a vehicle at varying driving speeds. Disregarding the impact of road conditions, when traveling at an average speed of 85.89 km/h on an expressway, the CO₂ concentration reaches 3176 ppm after 20 min, with a rate of CO₂ increase of 2.30 ppm/s. When traveling at an average speed of 55.85 km/h on a suburban road, the CO₂ concentration reaches 4228 ppm, with a rate of CO₂ increase of 3.17 ppm/s after 20 min of driving. The test data showed that a lower rate of CO₂ increase will be caused by increasing driving speed, and a lower concentration level will be reached over the same period. The phenomenon can be attributed to the reason that as the speed of driving increases, so does the external dynamic pressure. The static pressure decreases, and the leakage of air from the inside to the outside of the vehicle is accelerated, resulting in a reduction in the rate of CO₂ increase. The impact of different interior vehicle volumes on the increase in the in-vehicle CO₂ concentration is illustrated in Figure 6d. The T6–Honda Fit exhibits a CO₂ concentration of 4870 ppm after 20 min, with a rate of CO₂ increase of 3.72 ppm/s. Compared to the T1–Nissan Sylphy, which reaches 4633 ppm of CO₂ concentration after 20 min, the concentration of the Nissan-Sylphy is 237 ppm smaller than that of the Honda-Fit. Since the interior space of the Nissan-Sylphy is 0.3 m³ larger than that of the Fit, the calculation shows that each 1 m³ increase in the volume of the vehicle reduces the CO₂ concentration by 790 ppm.

The majority of indoor CO₂ concentration standards, as summarized in the preceding introduction section, are set at 1000 ppm. Hudda and Fruin [22] indicated a concentration threshold of 2500 ppm for automotive CO₂ concentrations, above which negative effects can occur. Therefore, we used 1000 ppm and 2500 ppm as the evaluation criteria. From the test data, it is found that the rate of CO₂ increase in the vehicle is rapid when the RC ventilation mode is turned on. When there are three occupants in the vehicle, the rate of CO₂ increase for the T6–Honda Fit artificial condition is the fastest, reaching 1000 ppm in 160 s (about 2.5 min) and 2500 ppm in 470 s (about 8 min); the T3–1 artificial condition has the slowest rate of CO₂ increase, reaching 1000 ppm within 500 s (about 8 min). The CO₂ concentration reached 1000 ppm within a range of 120–245 s during the T1–S1, T2–S2, T4–suburban road, and T5–expressway tests. The average concentration within 20 min of the six groups of working conditions all exceeded 1000 ppm, and the T1–S1, T6–Honda Fit working conditions even exceeded 2500 ppm, with the proportion of time exceeding 2500 ppm in the test process exceeding 59%. CO₂ concentration is a key indicator for judging the degree of ventilation in a vehicle [13]. Therefore, when the windows are closed, and internal air circulation is activated, the concentration of CO₂ can easily exceed safe levels, posing a potential hazard to driving safety. A timely increase in ventilation is necessary to reduce the in-vehicle CO₂ concentration.

3.2. Fitting Models and Prediction Result Analysis

3.2.1. ARIMA Model

Using the ADF test to all datasets revealed a p-value exceeding 0.05, meaning that all datasets are non-stationary, meaning that the data required differencing. The ADF test is applied again after all data are first differenced, and the test results are shown in

Table 7. ADF test results after differencing processing.

Datasets	The Order of Diffrence	t	p-Value	Critical Value
				1%	5%	10%
T1	1	−3.717	0.004 ***	−3.459	−2.874	−2.573
T2	1	−6.516	0.000 ***	−3.459	−2.874	−2.573
T3	1	−15.166	0.000 ***	−3.458	−2.874	−2.573
T4	1	−17.375	0.000 ***	−3.458	−2.874	−2.573
T5	1	−4.575	0.000 ***	−3.459	−2.874	−2.573
T6	1	−5.11	0.000 ***	−3.459	−2.874	−2.573

*** in the table represent the significance levels of 1%, 5%, and 10%, respectively.

. The p-value is lower than the significance level of 0.05, and the t statistic is smaller than 1%, 5%, and 10%. The null hypothesis of non-stationarity in the time series should be rejected. It is indicated that the data after difference have been stabilized, and the mean and variance do not change with time, which meets the prerequisites for forecasting using the ARIMA model. Therefore, we set the order of difference d = 1 for all the datasets.

Table 8. Optimal ARIMA model parameters and effectiveness test results.

Datasets	Optimal Model	AIC	BIC	p-Value
T1	ARIMA (3, 1, 1)	1401.47	1417.06	0.74
T2	ARIMA (4, 1, 3)	1433.24	1458.19	0.62
T3	ARIMA (1, 1, 1)	1186.36	1195.72	0.93
T4	ARIMA (5, 1, 4)	1446.43	1477.61	0.57
T5	ARIMA (5, 1, 3)	1427.32	1455.38	0.36
T6	ARIMA (3, 1, 3)	1405.53	1427.36	0.68

displays the AIC and BIC values corresponding to the optimal model hyperparameter combinations and the significance p-values after the Ljung–Box test. The p-values of the six models are greater than 0.05, indicating that the prediction residuals of the models conform to a sequence of random numbers and support the assumption that they are white noise.

Figure 7 shows the Q–Q plots of predicted residuals for six optimal models. The x-axis in the Q–Q graph represents the quantile of the theoretical distribution, the y-axis represents the quantile of the model prediction residual, the red straight line is the normal distribution line, and the solid blue dot is the model prediction residual value. The closer the solid blue dot is to the red straight line, the more it conforms to the standard normal distribution. It can be seen from the figure that most of the solid blue dots are located on the red straight line, indicating that the predicted residual values of the best model obey the normal distribution. To conclude, the residuals satisfy the requirements of a white noise sequence and conform to a normal distribution. Therefore, the model is suitable for prediction.

3.2.2. LSTM Model

After multiple attempts, the following LSTM network structure settings were used for CO₂ concentration prediction:

• Input layer: After continuous debugging of the size of the time window, it was found that the error is the smallest when the number of time windows is three. Therefore, the neuron dimension of three has been selected for our input layer.
• Output layer: Since our goal is to forecast CO₂ concentration for future moments, the number of neurons in the output layer is therefore determined to be one.
• Hidden layer: In this research, we utilized a sequential model in Keras, which is comprised of one LSTM layer and one dense layer. The neuron dimension of the first hidden layer is 64, and the second hidden layer has a neuron dimension of 1.

Therefore, this research chose three as the number of neurons in the input layer, namely, X_t = f (X_t−1, X_t−2, X_t−3). This is utilizing the preceding three data points to forecast the next one data point. The other parameters are configured as follows: The learning rate is set to 0.002. The maximum number of iterations (epoch) is set to 200, and the number of samples passed to the model for training each time (batch size) is 32. This network architecture exhibits the lowest RMSE and is well suited for predicting CO₂ concentration.

In summary, the final model structure of the LSTM neural network is as follows:

The neuron dimension of the input layer is three, and the neuron dimension of the output layer is one. It consists of a LSTM layer and a dense layer. The neuron dimension of the LSTM layer is 64, and the neuron dimension of the dense layer is 1. The optimizer chosen is Adam. The learning rate is set to 0.002. The epoch is set to 200, and the batch size is 32. This model has the smallest error, a high fitting degree, and high prediction accuracy, so this structure is used for prediction.

3.2.3. Results of Model Predictions and Comparative Analysis

The duration of each field test is 1200 s (20 min), with a data collection interval of 5 s. A total of 240 sets of data were collected in each test, which are then divided into training and testing sets at a seven-to-three ratio to evaluate the predictive performance of two models—ARIMA and LSTM. Figure 8 illustrates the comparison between predicted values and actual values for both models. The two models effectively learned the regular patterns in the historical data and are capable of accurately predicting variations in CO₂ concentration under different fan speeds, occupancy levels, driving speeds, and vehicle volumes. Furthermore, their prediction curves closely align with the actual value curves, obtaining an accurate prediction result. The prediction results demonstrate the accuracy and good generalization ability of both models in predicting changes in CO₂ concentration within a vehicle, effectively capturing fluctuations during driving. The predicted curve closely aligns with the actual curve and exhibits excellent fitting effects. The two models are capable of forecasting variations in CO₂ concentration across diverse vehicle models and driving scenarios. However, in terms of the prediction results for the T2, T3, and T5 datasets, the ARIMA prediction curves show a closer alignment with the actual values compared to LSTM.

The RMSE and MAE values for the prediction results of both models are presented in

Table 9. Comparison of model prediction results.

Datasets	MAPE (%)		RMSE (ppm)
	ARIMA	LSTM	ARIMA	LSTM
T1	0.48	0.49	25.37	25.11
T2	0.52	0.65	23.02	29.37
T3	0.42	0.65	9.25	13.51
T4	0.54	0.52	23.34	24.57
T5	0.49	0.65	17.55	23.09
T6	0.35	0.39	19.19	20.93
Average value	0.46	0.56	19.62	22.76

. The ARIMA model exhibits superior performance, with an average MAPE of 0.46% and RMSE of 19.62 ppm, respectively, compared to the LSTM model’s values of 0.56% and 22.76 ppm. The MAPE metric reflects the accuracy of the model’s predictions, and the RMSE metric measures the average deviation between predicted and true values. Lower values indicate better performance. The ARIMA model exhibits lower MAPE and RMSE values compared to the LSTM model, indicating superior prediction accuracy in forecasting CO₂ concentration changes within a vehicle. And the degree of deviation between the predicted value of ARIMA and the true value is also lower than that of LSTM.

4. Discussion

The CO₂ concentration in vehicles is affected by factors such as ventilation settings, the number of passengers, driving speed, vehicle characteristics, etc. There are many influencing factors, and they are coupled with each other. Parameters such as the amount of air leakage in a vehicle are difficult to obtain [27], and the accuracy of the model needs to be calibrated with data from multiple studies [13]. Therefore, the utilization of conventional mathematical models for computations encounters certain challenges. When utilizing ARIMA and LSTM for prediction, it is not necessary to deeply explore the impact of various influencing factors on CO₂ concentration. Instead, future trends can be predicted by capturing historical data and analyzing its correlation, seasonal and periodic fluctuations, as well as noise characteristics, leading to accurate prediction results. Additionally, ARIMA and LSTM have demonstrated their reliability in accurately predicting unconventional fluctuations in data [60]. In this research, we utilized ARIMA and LSTM models to build a predictive model for in-vehicle CO₂ concentrations, which yielded accurate forecast results. Predicting in-vehicle CO₂ levels can assist in maintaining a favorable in-vehicle environment, improving traffic safety, and enhancing driving comfort. Lohani et al. [28] employed the ARIMA (0, 1, 0) model to forecast the variation in the CO₂ concentration in a vehicle, yielding MAPE and RMSE values of 3.79% and 55.32 ppm, respectively. Compared to this result, the ARIMA model employed in our research yielded more precise prediction outcomes, which may indicate that our model, which considers the autoregressive and moving average items, can better capture the correlations and trends in historical data, whereas ARIMA (0, 1, 0) only performs differential processing on the data and does not consider the correlation with historical data.

The prediction principle of ARIMA is to filter the high-frequency noise in the data, detect the linear correlation in the historical data, and use this correlation to predict the future development trend. The prediction principle of RNN involves combining the current input with the previous hidden state to establish temporal dependencies in time series data, which can capture nonlinear relationships within the data. LSTM builds upon this by introducing gating mechanisms that enable memory cells to retain relevant information over longer periods of time, making it particularly effective for large datasets and mitigating issues related to vanishing gradients in traditional RNNs. In our research, the predictive accuracy of LSTM was inferior to that of ARIMA. The possible reasons contributing to this outcome are as follows: (1) The linear relationship of in-vehicle CO₂ concentration data is strong, and there is a clear upward trend in the concentration. ARIMA effectively captures the linear law within time series data, whereas LSTM excels at predicting complex nonlinear patterns. (2) The in-vehicle CO₂ concentration is a one-dimensional time series form of data. Due to the rapid growth process, the amount of data collected at intervals of 5 s within 20 min is only 240 sets. The learning ability of LSTM is restricted by the insufficient amount of data. When predicting data with a limited number of samples and only one dimension, the prediction accuracy of ARIMA may surpass that of LSTM. LSTM requires a large amount of data for training, and the larger the training volume, the higher the prediction accuracy of LSTM. Therefore, using LSTM has a better effect when predicting datasets with a large amount of data [46]. Even though LSTM’s prediction accuracy is somewhat lower than that of ARIMA, it still has numerous advantages as a deep-learning model compared to ARIMA. Firstly, the process of utilizing ARIMA prediction is more intricate than that of LSTM. It involves a series of steps such as time series stabilization detection, model order determination, and validity inspection. In contrast, LSTM can detect regularity in raw data without any mathematical processing, making the prediction process more convenient. Secondly, the use of ARIMA prediction must ensure that the data are stationary. Not all data can be stable after differencing processing, and the data may lose important information after differencing processing, which means that ARIMA may not be able to achieve good results when predicting certain types of data. However, LSTM can be used for non-stationary data prediction. Finally, due to its memory units and gating mechanisms, LSTM is capable of predicting complex multivariate nonlinear data, whereas ARIMA, being a linear model, falls short in this regard. The non-linear nature of the changes in data renders ARIMA incapable of producing accurate predictions for complex multivariate time series data [62], which demonstrates the broader applicability of LSTM. Furthermore, both models have their respective shortcomings. The ARIMA model is not well suited for analyzing data with long-term dependencies, and its predictive capability for nonlinear data is limited. The model’s predictive performance tends to degrade when handling large datasets. On the other hand, LSTM models involve a significant number of hyperparameters that require tuning. They are computationally expensive and demand considerable computational resources compared to simpler models like ARIMA.

From the comparative research of the two models, it is found that machine learning is not superior to traditional statistical models in all cases, and it is necessary to select an appropriate prediction model according to the amount of data. When the amount of data used for training reaches 1000, LSTM shows better predictive performance [57,58,70,71,72]. Both of these two models have their advantages when the amount of training data is between 100 and 1000 [44,45,71,72,73,74,75]. ARIMA exhibits better accuracy when the amount of training data is less than 100 [59,60,76,77]. In addition, although our research focuses on the in-vehicle CO₂ concentration in a Nissan-Sylphy and a Honda-Fit under the driving conditions outlined in Table 3, the prediction method used is also applicable to the prediction of CO₂ concentration changes in different vehicles under other driving conditions.

The research findings can provide a theoretical foundation for the development of more complex prediction models in the future and serve as crucial evidence for establishing a CO2 concentration prediction model within the traffic safety management system. However, this research also has several limitations. Firstly, our anemometer lacks the capability to record airflow data. Secondly, our prediction model solely relies on historical data for forecasting future trends, without considering influential factors or elucidating the underlying mechanisms. Therefore, forthcoming research should incorporate influential factors and establish multivariable time series prediction models.

5. Conclusions and Future Work

This research focuses on the concentration of CO₂ in vehicles as its research subject. Through field tests, data on the CO₂ concentration within vehicles were obtained and established using both ARIMA and LSTM prediction models for forecasting changes in CO₂ concentration. The accuracy of these two models was analyzed and compared, with differences in performance discussed. The main conclusions are as follows:

• The measured data indicate that with closed vehicle windows and internal circulation turned on, the concentration of CO₂ in a vehicle increases proportionally to driving time. Under all test conditions, the average CO₂ concentration within 20 min exceeds the standard limit of 1000 ppm. During driving, it is necessary to improve vehicle ventilation by opening windows, switching to outside air mode, and using other methods.
• Both the ARIMA and LSTM models are capable of accurately predicting changes in the CO₂ concentration within a vehicle. However, the MAPE and RMSE values obtained from the ARIMA model’s predictions are lower than those produced by the LSTM model. Therefore, the ARIMA model is more accurate in predicting changes in the CO₂ concentration within a vehicle compared to the LSTM model.
• The prediction performance of LSTM is not always better than the ARIMA model, and the two models need to be selected according to the characteristics of the data. When the amount of data used for training reaches 1000, it is better to use LSTM, and it is more appropriate to use ARIMA when the amount of data is within 100, but comparative analysis is required when the amount of data is within 100–1000.

Predicting the change in CO₂ can remind the people in a vehicle to take control measures before the concentration exceeds the standard. This research provides a critical theoretical basis for the future selection of early warning prediction models for in-vehicle CO₂ concentrations and for establishing efficient in-vehicle ventilation control systems.

In future research, we should develop an in-vehicle ventilation management system that integrates predictive capabilities with control functionalities. Furthermore, we should comprehensively consider the influencing factors of in-vehicle CO₂ concentration and develop a time series prediction model that incorporates multiple input variables to investigate whether these models can provide more accurate predictions of in-vehicle CO₂ concentration.