IoT-Based Bi-Cluster Forecasting Using Automated ML-Model Optimization for COVID-19

Abstract

The current COVID-19 pandemic has raised huge concerns about outdoor air quality due to the expected lung deterioration. These concerns include the challenges associated with an increase of harmful gases like carbon dioxide, the iterative/repetitive inhalation due to mask usage, and harsh environmental temperatures. Even in the presence of air quality sensing devices, these challenges can hinder the prevention and treatment of respiratory diseases, epidemics, and pandemics in severe cases. In this research, a dual time series with a bi-cluster sensor data-stream-based novel optimized regression algorithm was proposed with optimization predictors and responses that use an automated iterative optimization of the model based on the similarity coefficient index. The algorithm was implemented over SeReNoV2 sensor nodes data, i.e., a multi-variate dual time-series sensor, of the environmental and US Environmental Protection Agency standard, which measures variables for the air quality index using air quality sensors with geospatial profiling. The SeReNoV2 systems were placed at four locations that were 3 km apart to monitor the air quality and their data was collected at Ubidots IoT platform over GSM. The results have shown that the proposed technique achieved a root mean square error (RMSE) of 1.0042 with a training time of 469.28 s for the control and an RMSE of 1.646 in a training time of 28.53 s when optimized. The estimated R-Squared error was 0.03, with the Mean-Square Error for temperature being 1.0084 °C, and 293.98 ppm for CO2. Furthermore, the Mean-Absolute Error (MAE) for temperature was 0.66226 °C and 10.252 ppm for the correlated-CO2 at a predicted speed of ~5100 observations/s. In the sample cluster for temperature, 45,000 observations/s for CO2 was achieved due to the iterative optimization of the training time (469.28 s). The correlated temperature and a time of 28.53 s for CO2 were very promising in forecasting COVID-19 countermeasures before time.

1. Introduction

According to the WHO and US Environmental Protection Agency (EPA) guidelines, the future of air quality and climatic conditions are a signature of life security for healthy respiration. The quality of respiration and its associated life processes are directly related to air quality, specifically in regard to oxygen (O2) and carbon dioxide (CO2) in a particular geo-location at a tolerable temperature (WHO, 2021) [1]. The National Ambient Air Quality Standards (NAAQS) report that the gradual deterioration in urban air quality is ambient each year due to the increasing population, chemical emissions from machinery, and depreciation in green ecology [2]. Several studies have concluded that a poor air quality index (AQI) refers to a higher concentration of CO2 in the atmosphere and that temperature extremities are more likely to be disastrous and fatal when it is inhaled/exhaled. Therefore, its real-time monitoring is key to public safety [3]. Mandated measurement methods, like geo-spatially sensed outdoor gases, are a critical decision source in forecasting the COVID-19 threat intensity at lower temperatures and higher CO2 concentrations [4]. Flu-based pandemics and COVID-19 are becoming an increasing problem worldwide and so require a more widespread research approach.

Globally, CO2 sensing time-series analysis and forecasting are the most widely capitalized approach in respiratory research i.e., an ensemble time-series model with machine learning approaches as the projection benchmark has shown that China’s carbon peak will be achieved by 2021–2026 with  >80% probability [5] by using the logged dataset with a gap in real-time CO2 sensing at regional temperatures. The Long Short-Term Memory (LSTM) networks, DeepLMS, resulted in an average testing Root Mean Square Error (RMSE) < 0.009, and an average correlation coefficient between ground truth and predicted values r ≥ 0.97 (p < 0.05) when tested on logged data from one database pre-COVID-19 and two during COVID-19 pandemic years [6]. This study [6] had challenges with data interpretation and collective forecasting from multiple real-time CO2 and temperature sensing units due to data structuring challenges. The first step has been structuring the dual-series sensor data into a decomposed time series, as mentioned in the reviews as either additive or multiplicative by valued research [7,8,9].

The second challenge was to sort the time-series in preparation for the next stage, called the time-series trend assessment using Theil-Sen’s Slope (TSS), Mann-Kendall (MK), Modified Mann-Kendall (MMK), and Kendall Rank Correlation (KRC) tests, which need the incorporation of improved trending for seasonality tests [8,9]. Several studies used the above-mentioned tests effectively for the logged data but they had challenges with real-time sensor data. The real-time processing, time-series decomposition methods (REG and GAM based on OLS; FFT, FFT, AVG, LOESS, and LHM based on Backfitting [10]) had challenges with the stationarity assessment. Various time-series hypothesis tests, the Durbin-Watson test (DWT), Box-Pierce (BPT), Ljung-Box tests (LBT), Breusch-Godfrey test (BGT), Jarque-Bera test (JBT), and Augmented Dickey-Fuller test (ADFT) were used for stationarity and seasonality assessment and are useful for the auto-regressive moving average (ARIMA); however, the advanced Seasonal autoregressive integrated moving average model (SARIMA) [11] needed a clustered approach for real-time forecasting of multi-variate sensor data. The statistical techniques and machine learning approaches mentioned above were found to have the sensors’ dependent and wireless sensor network-based anomalies’ dependent results.

The third major challenge was the absence of an optimized and adaptive real-time forecasting approach for the networked CO2 and temperature measurement sensor nodes. For this, many air quality sensing systems were studied. The top sensing systems AirNut, PA-I and PA-II, Egg, PATS+, and S-500, CairClip, Portable ASLUNG, AirSensEUR, Met One, AQY v0.5, Vaisala AQT410, 2B Tech, and AQMesh V3.0 systems had measurement capabilities for specific pollutants and gases [12]. This was impacted by real-time health monitoring systems [13] and the infrastructure and architectures of specialized platforms [14]. FIS SP-61, O3-3E1F, AirSensEUR v.2, S-500, and AirSensEUR used a built-in AlphaSense OX-A431 limited to O₃ [15]. Likewise, the PMS1003 and PMS3003 by Plantower; DC1100 PRO and DC1700 by Dylos; and OPC-N2 by AlphaSense only had sensing support for particulate matter (PM) and so, from a multi-agent perspective, had challenges in the clinical biomarker space of COVID-19 using feature selection and prognosis classification for the time-series forecasting problem [16]. The networked sensing errors found in the previously mentioned works using CO-3E300 by City Technology; CO-B4 by Alphasense, MICS-4515 by SGX Sensortech, and Smart Citizen Kit by Acrobotic, and the RAMP had wireless sensor network errors that can be corrected by the multi-objective prediction monitoring algorithm [17,18,19]. All the above-mentioned research was suited for a fixed network of sensing systems but had to face the challenge of threshold updates that gave errors in forecasting spatially placed sensing node clusters [20].

In clustered sensing for CO2 and temperature, there was a pressing need for a concurrent forecasting chain in addition to a dimensionality reduction using matrix factorization (MF) [21] for the air quality nodes, with parametric ML model deployment support on embedded systems like SeReNoV2 [22]. Considering the recent studies conducted at the European Commission, Joint Research Centre (JRC) [23] on the impact of masks on CO2 concentration zones in the breathing zones, it was concluded that the increase in CO2 was due to breathing exhaled air temperature as well [24].

The existing O-AQNs, Urban AirQ, Smart Citizen Kit, Air SensUR 4.0, SeReNo V1, and AirQ Mesh needed improvement for the AQI-dependent principal component approach [25] in the scope of automated optimization of forecasting. The multi-time series-based forecasting required a novel melioration in linear regression and a tree-based time-series learning, regression, and forecasting tree to be an innovative step in the SeReNoV2 AQM systems.

The recent environmental data forecasting works (2022, 2023) were also reviewed. The hybrid additive regression and data-driven models [26,27] were monthly based and for arid environmental conditions had the gap of annual forecasting using real-time sensing systems [12,13,14,15,16,17,18,19]. The hybrid metaheuristic algorithms-based estimation of reference evapotranspiration [28] had challenges in real-time IoT-based sensing. The hybrid machine learning-pedotransfer Function (ML-PTF) based on a novel Genetic Algorithm (GA) for the prediction of the spatial pattern of saturated hydraulic conductivity [29] was more concentrated in the water patterns and needed improvements in real-time IoT-based environmental systems integrated data. The recent work in Runoff-Rainfall (R-R) [30] was a better contestant for several data-driven models, namely, multiple linear regression (MLR), multiple adaptive regression splines (MARS), support vector machine (SVM), and random forest (RF), but needs improvement in the IoT-based environmental and health integrated forecasting domain. Furthermore, very recent work in forecasting conducted a feasibility study to examine the feasibility and effectiveness of the Random Subspace (RSS) model and its hybridization with the M5 Pruning tree (M5P), Random Forest (RF), and Random Tree (RT). It was based on the data from the Standardized Precipitation Index (SPI) [31] case study in Jaisalmer, India and needed improvements in real-time IoT-based environmental sensing. A noticeable work was a study of the evaluation of the adaptive neuro-fuzzy inference system (ANFIS)-, artificial neural network (ANN)-, and wavelet-based artificial neural system (WANN)-based models [32] that estimated the discharge by using 12 years of daily data (2007–2018) but needed improvement in the IoT-based real-time sensing data and health integration application domain. The study of two different agro-climatic zones, that employed the data intelligence model and meta-heuristic algorithms-based pan evaporation modelling using the data from a case study from Northern India [33], needed an investigation into the same methods of the real-time IoT-based environmental data. The summary of enhancements is presented in

Table 1. A Summary of the Enhancements in Methods from the Literature Review.

Authors	Methods	Enhancements
Jiandong, C et al. (2022) [5]	LSTM with RMSE estimation	Real-time CO2 data processing
Sofia, B. et al. (2020) [6]	DeepLMS Attendance in COVID era	CO2 and temperature forecasting with respect to COVID-19
Zhou, Y. et al. (2020) [7]	Regression Analysis for CO2 Emissions	CO2 and temperature co-related forecasting for COVID-19.
Malik, A et al. (2020) [8]	Spatio-temporal analysis using parametric/non-parametric tests	Real-time data pre-processing for dual variable forecasting.
Abbasi, S. (2014) [9]	Statistical analysis using two-component measurement error	Real-time IoT-based sensor data
Santiago, M.-C. (2020) [10]	REG and GAM based on OLS; FFT, FFT, AVG, LOESS, and LHM based on Backfitting	Real-time IoT-sensor data for COVID-19
Stanislaus, S. U. (2020) [11]	Durbin-Watson test (DWT), Box-Pierce (BPT), and Ljung-Box tests (LBT), Breusch-Godfrey test (BGT), Jarque-Bera test (JBT), and Augmented Dickey-Fuller test (ADFT)	Real-time IoT sensors data for COVID-19
Mehrpooya, A., et al. (2022) [18]	Dimensionality reduction by matrix factorization	Dual-time series real-time sensor data
Tariq. H. et al. (2019) [19]	4th other stationarity and differential time-series analysis for prediction	Multi-variate time-series forecasting
Sadeghi, G., et al. (2022) [20]	Data mining approaches for pre-processing of data forecasting	Forecasting on real-time data from COVID-19 prospective
Najafzadeh, M. (2022) [21]	Reviewed AI-techniques for temperature forecasting	Forecasting on real-time data from COVID-19 prospective
Tariq, H. et al. (2020) [22]	Multi-variate AQI mapping using dual time-series	Forecasting on real-time data from COVID-19 prospective
Geiss, O [23] 2020	Studied effect of face mask on CO2 in breathing	Forecasting on real-time IoT data
Michelle, S. et al. (2021) [24]	Studied impact of face masks increase as per NIOSH definitions	Forecasting on real-time IoT data
Abdaoui, A. et al. (2020) [25]	Co-variance based gradient estimation of real-time sensor data for AQI	Forecasting on real-time data from COVID-19 prospective
Tariq, H. et al. (2019) [26]	Developed real-time CO2 and temperature sensing devices used in this work for forecasting	Forecasting on real-time data from COVID-19 prospective
Elbeltagi, A. (2023) [27]	Additive regression for forecasting monthly data	Real-time IoT sensors data for COVID-19 forecasting
Elbeltagi, A. (2022) [28]	Hybrid metaheuristic algorithms for reference evaporation estimation	Real-time IoT sensors data for COVID-19 forecasting
Singha, V.K. et al. (2022) [29]	Genetic Algorithm based on hybrid machine learning pedo-transfer functions.	Real-time IoT sensors data for COVID-19 forecasting
Singh, A.K. et al. (2022) [30]	Statistical machine learning approaches for run-off water forecasting	Real-time IoT sensors data for COVID-19 forecasting
Elbeltagi, A. et al. (2023) [31]	Random Subspace (RSS) model and its hybridization with the M5 Pruning tree (M5P), Random Forest (RF).	Real-time IoT sensors data for COVID-19 forecasting
Shukla, R. et al. (2022) [32]	ANN, ANFIS, and WANN for dual time-series	Real-time IoT sensors data for COVID-19 forecasting
Kushwaha, N.L. et al. (2021) [33]	Data intelligence model and meta-heuristic algorithms for two different data sets.	Real-time IoT sensors data for COVID-19 forecasting

.

The above literature review shows that COVID-19 and pandemics are an increasing problem and that these diseases need a novel and ubiquitous solution. The main drive behind this work is to support EPAs and state health agencies worldwide in improving global healthcare and welfare by using out-of-the-box techniques that enable adequate forecasting and healthcare management. The innovative aspects and novel contributions of this research are: (a) bi-cluster regression, i.e., real-time CO2 and temperature sensing systems placed at different locations with different surroundings (different CO2 and temperature curves) to be used for evaluation as a bi-cluster time-series interpolated with air quality index (AQI) from principle pollutants; (b) a networked assessment to have multiple sensing sources based on the dual-redundancy and resilience of real-time forecasting and machine learning model (MLM) training; (c) the automated optimization to tune the scalable spatial gradients with different thresholds; (d) automated iteration to achieve the minimum RMSE and MAE for the trackable similarity coefficient index (SCI) for accurate forecasting. The research work is organized as:

• The Real-time Gradient Aware Multi-Variable Sensing Model (GAM-VSM)
• The Optimized Bi-Cluster Regression Machine Learning Model (OBR-MLM)
• Case Study: Urban Scale IoT-based AQI Monitoring System.

The list of acronyms is presented in

Table 2. List of Acronyms.

Acronyms	Description
IoT	Internet of Things
COVID	Corona Virus Disease
CO2	Carbon Dioxide
NAAQS	National Ambient Air Quality Standards
FFT	Fast-Fourier Transform
REG	Regression
DeepLMS	Deep Learning Management Systems
TSS	Theil-Sen’s Slope
MK	Mann-Kendall Method
MMK	Modified Mann-Kendall Method
KRC	Kendall Rank Correlation
DWT	Durbin-Watson test
BPT	Box-Pierce Test
LBT	Ljung-Box tests
BGT	Breusch-Godfrey test
JBT	Jarque-Bera test
ADFT	Augmented Dickey-Fuller test
ARIMA	Auto-regressive moving average
OLS	Ordinary Least Squares Regression
LHM	Linear Hinges Model
LOESS	Locally estimated scatterplot smoothing
WHO	World Health Organization
EPA	Environmental Protection Agency
GSM	Global Service for Mobile
AQI	Air Quality Index

given below.

2. Materials and Methods

The materials in this work are comprised of a real-time air quality monitoring system and the methods consist of GAM-VSM and OBRM-MLM. The results section gives further insights into this contribution

2.1. The Real-Time Multi-Variable Geospatial Gradient-Aware AQI Sensing Model (GAM-VSM)

To measure the precise impact of CO2 and temperature on COVID-19, a real-time multi-variable structured data time-series vector was needed to proceed with the geospatial profiling of gradient awareness as per our past work [25,26]. Let us consider an EPA standard outdoor air quality index (O-AQI) real-time variables as temperature T in centigrade, pressure P in pascals, humidity H in %, volatile organic compounds VoC (ppm), particulate matter as PM (ppm), Ozone as O3 (ppm), Nitrogen Dioxide as NO2 (ppm), Carbon Monoxide as CO2 (ppm), and Sulphur Dioxide as SO2(ppm). The real-time O-AQI data was proposed as a commutative time series multi-variable vector V_O-AQI of two non-linear time-series with t₁ and t₂ of environmental E and gas G sensors data at a particular geo-location L, given as:

V_O-AQI (t) = [E(t₁), G(t₂)]: L(t)

(1)

where t = (0, 1, 2, 3, …}

The practicality of the response time of the heterogeneous sensors was taken into account for the non-linear time-series decomposition t, with the gas sensor response time t₂ being greater than the response time of environmental sensors t₁ with a relationship t₂ > t₁ given as:

t₂ = 3t₁

(2)

where [t₁, t₂] ϵ t

The environmental sensor variables function E for sensor array A_E (T, P, H, VoC, PM) as E (A_E, t₁); and gas sensors array A_G (O3, NO2, SO2, CO) as G(A_G, t₂) and position vector L as reference function GPS using GSM network cell locations (using AT + CIPGSMLOC = (1, 1)) for L_GPRS and GPS module as L_GPS (using AT + CGPSINF). For precise AQM the L_GPS must belong to the slope of L_GPRS1 and L_GPRS2 in a particular slope format by NEMEA specifier for consecutive cells and is given as:

L_GPS (X, Y) ϵ [L_GPRS1(X2, Y2), L_GPRS2(X1, Y1)]

(3)

The agreed L_GPS was termed as L(t) where condition (3) was satisfied. From Equations (1)–(3) the finalized AQM vector of V_O-AQI was derived as:

V_O-AQI (t) = [E(A_E(T, P, H, VoC, PM),t₁), G(A_G(O3, NO2, SO2, CO), t₂)]: L(t)

(4)

Three bounded value conditions were applied on GAM programmed in the SeReNo V2 firmware are presented in Figure 1:

(a)

The mandatory gradient unit Δ₁CO2 to monitor the CO2 gradient from inhaled air at temperature Δ₁T.

(b)

The role of the gradient of the temperature of exhaled air Δ₂T with Δ₂CO2 recycled in the breathing zone due to a mask.

The optimization scalar is presented as (CO2 is in ppm):

Mask(ΔCO2) = Δ₁CO2 × Δ₁T + Δ₂CO2 × Δ₂T

(5)

2.2. The Optimized Bi-Cluster Regression Machine Learning Model (OBR-MLM)

The GAM reduced the bulk time-series curation operations needed for forecasting. The dual time-series data was queued to OBRM with (AQI, CO2) and (AQI, Temperature) vectors at the same time with the t₁ and t₂ time series. The iterative regression parameter setting was performed based on default parameters (RMSE, RSS, and MAE). On every cycle, these parameters were optimized as per the KPI requirements. The two simultaneous regression models were trained for A_E(t₁) and A_G(t₂) vectors. The root-mean-square error (RMSE), and mean absolute error (MAE) were the common KPIs that were analyzed before model approval. The approved model was set for forecasting from the SeReNoV2 test data and disapproved data was fed to an optimizer that used a configurable tree-based machine learning approach by variable iterations based on the similarity coefficient index (SCI). The generic regression model Y for

$$\mathrm{Yt}={{\displaystyle \sum }}_{m=1}^i{\mathsf{\beta }}_m{\mathrm{X}}_{m,t}+\mathsf{\epsilon } =\mathsf{\beta }1{\mathrm{X}}_{1,\mathrm{t}}+\mathsf{\beta }2{\mathrm{X}}_{2,\mathrm{t}}+\dots +\mathsf{\beta }{\mathrm{iX}}_{\mathrm{i},\mathrm{t}}+\mathsf{\epsilon }$$

(6)

The flowchart of OBRM is presented in Figure 2 below.

As per the proposed bi-cluster networked forecasting of the regression models Y_t-CO2 (AQI, CO2) and Y_{t-Temperature} (AQI, Temperature), the regression models must have an acceptable similarity of >85%. If the forecasted time-series curves from two similar sensors installed at two different locations have curve-similarity concerning their AQI curves, termed as similarity coefficient index (SCI) as less than 85%, the iterations will keep running automatically. For RMSE < 1.5, statistically the SCI < 0.85 conditions should be satisfied in real-time. The US EPA AQI standard for outdoor air quality is presented in

Table 3. Pollutants and Epidemiological Baseline.

Breakpoints							AQI	Epidemiological Impact/Category
O3 (ppm) 8-h	O3 (ppm) 8-h	PM10 (µg/m3)	PM2.5 (µg/m3)	CO (ppm)	SO2 (ppm)	NO2 (ppm)
0–0.064	–	0–54	0–15.4	0–4.4	0–0.034	(2)	0–50	Good
0.65–0.84	–	55–154	15.5–40.4	4.5–9.4	0.035–0.144	(2)	51–100	Moderate
0.85–0.104	0.125–0.164	155–254	40.5–65.4	9.5–12.4	0.145–0.224	(2)	101–150	Unhealthy for sensitive groups
0.105–0.124	0.165–0.204	255–354	65.5–150.4	12.5–15.4	0.225–0.304	(2)	151–200	Unhealthy
0.125–0.374 (0.155–0.404) 4	0.205–0.404	355–424	150.5–250.4	15.5–30.4	0.305–0.604	0.65–1.64	201–300	Very Unhealthy
(3)	0.405–0.504	0.425–0.504	250.5–350.4	30.5–40.4	0.605–0.804	1.25–1.64	301–400	Hazardous
(3)	0.505–0.604	0.505–0.604	350.5–500.4	40.5–50.4	0.805–1.004	1.65–2.04	401–500	Hazardous

below:

The AQI is generically estimated as:

$$I_P=[(I_{high}-I_{low})/{(B}_{P-high}{- B}_{P-low}\left)\right]\times (C_P-B_{P-low})+I_{low}$$

(7)

Every pollutant was formulated using Equation (7) and given by Equations (8) to (12).

$$I_{PM}=[(I_{high}-I_{low})/(B_{PM-high}-B_{PM-low}\left)\right]\times (C_{PM}-B_{PM-low})+I_{low}$$

(8)

$$I_{\mathrm{NO}2}=[(I_{high}-I_{low})/(B_{\mathrm{NO}2-high}-B_{\mathrm{NO}2-low}\left)\right]\times (C_{\mathrm{NO}2}-B_{\mathrm{NO}2-low})+I_{low}$$

(9)

$$I_{\mathrm{SO}2}=[(I_{high}-I_{low})/(B_{\mathrm{SO}2-high}-B_{\mathrm{SO}2-low}\left)\right]\times (C_{\mathrm{SO}2}-B_{\mathrm{SO}2-low})+I_{low}$$

(10)

$$I_{\mathrm{O}3}=[(I_{high}-I_{low})(B_{\mathrm{O}3-high}-B_{\mathrm{O}3-low}\left)\right]\times ({\mathrm{C}}_{\mathrm{O}3}-B_{\mathrm{O}3-low})+I_{low}$$

(11)

$$I_{\mathrm{C}\mathrm{O}}=[(I_{high}-I_{low})/(B_{\mathrm{C}\mathrm{O}-high}-B_{\mathrm{C}\mathrm{O}-low}\left)\right]\times (C_{\mathrm{C}\mathrm{O}}-B_{\mathrm{O}3-low})+I_{low}$$

(12)

From the AQI equations the resulting relative regression models for CO2 (${\mathrm{I}}_{m-\mathrm{CO}2,t})$ and Temperature (${\mathrm{I}}_{m-T,t})$ are given as:

$${\mathrm{Y}}_{\mathrm{t}-\mathrm{CO}2}={{\displaystyle \sum }}_{m-\mathrm{CO}2=1}^i{\mathsf{\beta }}_{m-\mathrm{CO}2}{\mathrm{I}}_{m-\mathrm{CO}2,t}+{\mathsf{\epsilon }}_{\mathrm{CO}2}$$

(13)

= β_1-CO2I_1-CO2,t + β_2-CO2I_2-CO2,t + … + β_i-CO2${\mathrm{I}}_{\mathrm{i}-\mathrm{CO}2,\mathrm{t}}+{\mathsf{\epsilon }}_{\mathrm{CO}2}$

$${\mathrm{Y}}_{\mathrm{t}-\mathrm{T}}={{\displaystyle \sum }}_{m-T=1}^i{\mathsf{\beta }}_{m-T}{\mathrm{I}}_{m-T,t}+{\mathsf{\epsilon }}_T {\mathrm{I}}_{\mathrm{i}-\mathrm{T},\mathrm{t}}+{\mathsf{\epsilon }}_T$$

(14)

= β_1-TI_1-T,t + β_2-TI_2-T,t + … + β_i-TI_i-T,t + ε_T

The function Iµ has been used to express the rate of change in AQI at the corresponding time derivative.

$${\left(I\mu \right)}^n=\frac{\Delta \mathrm{AQI}}{\Delta t}=\frac{2kr{e}^2}{ {(1+e^{-rt})}^2}\times t+\dots =0, 1, 2\dots$$

(15)

To compare the relative influence level among the various influencing factors, the regression coefficients were normalized.

$${\mathsf{\beta }}_{\mathrm{m}}^{\prime }={\mathsf{\beta }}_{\mathrm{m}}\times \frac{\mathsf{\sigma }\mathrm{Xm}}{\mathsf{\sigma }\mathrm{Y}}$$

(16)

where β’_m is the normalized regression coefficient of the mth driving force, and β_m is the regression coefficient of the driving force. σX_m is the standard deviation of the driving force, and σ_Y is the standard deviation of the dependent variable. The RMSE will be the first step in ML model testing and optimization and is given as:

$$\mathrm{RMSE}=\sqrt{\frac{1}{n}{{\displaystyle \sum }}_{i=1}^n{(M_{\mathrm{i}}-R{M}_i)}^2}$$

(17)

This indicates the magnitude of the error and retains the variable’s unit; is sensitive to extreme values and outliers; tends to vary as a function of the standard deviation of the RM. Based on the RMSE the iteration will be performed by eliminating the temperature effect E_T and CO2 E_CO2 effect respectively from Equations (13) and (14) using:

$${\mathrm{E}}_{\mathrm{T}}=\frac{n{{\displaystyle \sum }}_{i=1}^n{Y}_{i-T}{C}_i-{{\displaystyle \sum }}_{i=1}^n{Y}_{i-T}{{\displaystyle \sum }}_{i=1}^n{C}_i}{n{{\displaystyle \sum }}_{i=1}^n{\left(Y_{i-T}\right)}^2-{({{\displaystyle \sum }}_{i=1}^n{Y}_{i-T})}^2}$$

(18)

$${\mathrm{E}}_{\mathrm{CO}2}=\frac{n{{\displaystyle \sum }}_{i=1}^n{Y}_{i-\mathrm{CO}2}{C}_i-{{\displaystyle \sum }}_{i=1}^n{Y}_{i-\mathrm{CO}2}{{\displaystyle \sum }}_{i=1}^n{C}_i}{n{{\displaystyle \sum }}_{i=1}^n{\left(Y_{i-\mathrm{CO}2}\right)}^2-{({{\displaystyle \sum }}_{i=1}^n{Y}_{i-\mathrm{CO}2})}^2}$$

(19)

sensitivity coefficient C for the measurement influencing variable and finally:

$$\mathrm{RSS}={{\displaystyle \sum }}_{i=1}^{\infty }{\left({\mathsf{\gamma }}_{\mathrm{i}}{-\mathrm{b}}_0-{\mathrm{b}}_1{\mathrm{x}}_{\mathrm{i}}\right)}^2$$

(20)

The RSS is measured as the sum of the square of residuals as the final step in the iterative optimization. In the results section, an ambient role of magnitudes of two variables can be observed, but the RMSE and MAE are not enough to resolve the sensor data with different scales and orders of magnitude for this SCI. The SCI for CO2 (SCI_CO2) and temperature (SCI_T) will be the tacking gradient (real-time difference divided by their average) ratio of two cluster nodes 1 and 2 given as:

$${\mathrm{SCI}}_{\mathrm{CO}2}=2 \times |\frac{{\mathrm{SCI}}_{\mathrm{CO}2-1}{- \mathrm{SCI}}_{\mathrm{CO}2-2}}{{\mathrm{SCI}}_{\mathrm{CO}2-1}{+\mathrm{SCI}}_{\mathrm{CO}2-2}}|$$

(21)

$${\mathrm{SCI}}_{\mathrm{T}}=2 \times |\frac{{\mathrm{SCI}}_{\mathrm{T}-1}{- \mathrm{SCI}}_{\mathrm{T}-2}}{{\mathrm{SCI}}_{\mathrm{T}-1}{+\mathrm{SCI}}_{\mathrm{T}-2}}|$$

(22)

$$\mathrm{SCI}={\mathsf{\beta }}_{\mathrm{m}}^{\prime } \times |\frac{{(\mathrm{SCI}}_{\mathrm{T}}{ \times \mathrm{E}}_{\mathrm{CO}2})+({\mathrm{SCI}}_{\mathrm{T}}\times {\mathrm{E}}_{\mathrm{CO}2})}{2}|$$

(23)

The present probability of infection (P_{Infection-Present}) is based on present data and the future probability of infection (P_{Infection-Future}) is based on forecasted data. Based on previous research mentioning the COVID-19 relationship with temperature and CO2 and Mask(ΔCO2) (cycling the CO2 into the lungs that gradually weakens the lungs) from Equation (5) and relative influence level based on β′_m (Equation (16)) the probability (P_Infection) of trans-respiratory pandemics and COVID-19 is given by:

$${\mathrm{P}}_{\mathrm{Infection}-\mathrm{Present}}=|\frac{\mathrm{SCI}}{{\mathrm{RMSE} \times \mathrm{I}}_{\mathsf{\mu }}}|$$

(24)

$${\mathrm{P}}_{\mathrm{Infection}-\mathrm{Future}}=({\mathrm{P}}_{\mathrm{Infection}-\mathrm{Present}}\times \frac{1}{{ \mathrm{I}}_{\mathsf{\mu }}})+(\mathrm{Mask}(\mathsf{\Delta }\mathrm{CO}2)\times |\frac{{\mathrm{Y}}_{\mathrm{t}-\mathrm{CO}2}}{{\mathrm{Y}}_{\mathrm{t}-\mathrm{T}}}|)$$

(25)

The proposed automated iterative optimization for COVID-19 and other pandemics that are based on some sensing variables is independent of personal immunity and the infection capability or the strength of pathogens as a medical science research area.

2.3. A Case Study: Urban Scale IoT-Based AQI Monitoring System

The proposed model and applied algorithm were tested and validated using our TRL7 autonomous AQI mapping system from past research [25,26]. A 1-1 correspondence electronics and instrumentation system was designed in a single package, i.e., SeReNoV2 presented in Figure 3 presented below.

Three SeReNo V2 nodes were fabricated and deployed in QU for outdoor testing. The fabricated SeReNo V2 was deployed based on the efficient utilization of GAM, i.e., QU Greenhouse exhibited in the Figure 4 below.

The GAM reduced the bulk time-series curation operations needed for forecasting. The dual time-series data was queued to OBRM with (AQI, CO2) and (AQI, Temperature) vectors at the same time with the t₁ and t₂ time series. The iterative regression parameter setting was performed based on default parameters (RMSE, RSS, and MAE). On every cycle, these parameters were optimized; AQI refers to a structured chart with a bio-tolerable threshold of specific pollutants and bio-hazardous gases recommended by EPA in the area under a specified border agency18–24. The top 10 environmental protection agencies (EPAs) unanimously agreed on the standard of four core gases for outdoor.

3. Results and Discussion

After the long-haul deployment of six months, the data results obtained were displayed on the Ubidots IoT platform as shown in Figure 5.

The eleven real-time variables were exhibited in Figure 4, sending data through the GSM model QuecTel M10. The bi-cluster is considered in this special data-fusion case for data collected at the central site, i.e., QU Greenhouse. The two variables CO2 and temperature were double interpolated from four sites (top: QU H10 and QU C05) and presented in Figure 6 below from the Ubidots IoT platform.

Since trans-respiratory diseases, as per WHO and US EPA, get worst due to poor AQI, from (8) to (12) the Cumulative AQI of four sites is given in Figure 7.

The application of GAM enabled only meaningful data to be sent to the cloud, which made the time series more non-linear as only gradient-impacted values were being transmitted. The accuracy of bi-clustered data measurements in terms of the autonomous AQI system by applying our previous work is exhibited in Figure 7. The following plots of individual variables give more insight into GAM in the SeReNoV2. The KPIs of GAM contributed to the accuracy and efficiency of the OBRM.

The impact of GAM can be warm times below 1.83 s throughout 5 months. The reduced warm-up times reduce the boot time power spike and result in the stable voltage above 3.3 V needed for the sensors. The typographic error observed is around 3.1 to 3.4, which is much less. A minute typographic error can be observed due to the correlation of the GPS and GPRS-assisted cell network locations scheme. The key performance indicators (KPIs) of GAM efficiency on SeReNoV2 were the major contribution that enabled all the outcomes presented in Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16 and Figure 17, as detailed in Figure 17.

The dual-time series regression of OBRM is presented as CO2 being the top concern in Qatar. This outcome contributed to potential safety precautions during COVID-19. A four-step procedure was followed for OBRM. First, the predicted response was assessed and the ML KPIs, mentioned in Table 1, were streamlined. Then the comparison was performed between real and predicted; at this step, the trained model residuals were estimated and finally, the optimization was performed as per conditions.

Figure 9a exhibits the temperature response for model 1, termed OBRM1. The real data is in blue and the predicted is in orange. It was measured for one month. The RMSE of 1.0042 was almost ideal and needed no further tuning and verification. Figure 9b is a realization of a close prediction, as the predicted and actual are almost overlapping with RMSE 1.7+.

In Figure 10a, the wrapping of blue markers or bubbles over the ideal or accurate prediction shows the accuracy of the prediction using customized linear regression. Maximum similarity can be observed in magnitudes of 21 °C to 24.5 °C. In the next process, the residual was estimated as the vertical distance between a data point and the regression line. Each data point has one residual. They are positive if they are above the regression line and negative if they are below the regression line. If the regression line passes through the point, the residual at that point is zero.

The RMSE of 1.7+ is extremely small for magnitudes like 6000, thus the comparative plot for the predicted and true is almost overlapping in Figure 10b.

In Figure 11a, the magnitudes of 9+ for residuals are non-convex and impact the error in the prediction by OBRM1 for temperature. The A_E(t₁) cluster was not optimized due to RMSE 1.0042. The optimization was performed for RMSE > 1.5 for A_G(t₂), presented in Figure 9, Figure 10, Figure 11 and Figure 12. The residuals for temperature and CO2 are presented in the Figure 11.

The 200 residual magnitudes for amplitudes of PPM like 4500+ are minute, i.e., 200/4500 = 0.044 shown in Figure 11b.

The results in Figure 12 lead to level 2 optimization of the OBRM1 based on the leaf size 3.

The tracking and alignment performed by OBRM3 for the observed and predicted CO2 (PPM) is up to 4400 ppm in Figure 13.

The offset or residual of 150/4800 = 0.03125 ppm is almost perfect or accurate as examined in Figure 14. The 200 residual magnitudes for amplitudes of PPM like 4500+ are minute, i.e., 200/4500 = 0.044 shown in Figure 14.

The leaf size of 2 with 100 iterations delivered fine-tuned optimization and tracking for the precise prediction observed in Figure 16. Later, the generated model was tested over test data for predicting the CO2 for the years 2021 and 2022. This is presented in Figure 16.

The P_{Infection-Future} for CO2 by OBRM3 was almost similar; it was ambient from Figure 16 with a numerical explanation and highlights for SCI computation. The OBRM3 had a very minute difference between the present and forecasted data.

The parameter setting for an optimized linear regression and optimized tree are presented in

Table 4. Regression Parameter Setting.

	Optimized Bi-Cluster Regression MLT
Parameters	SWL (Temperature)	OBRM3 (CO2)
Time Series Vector	[E(AE(T, P, H, VoC, PM),t1)]	[G(AG(O3, NO2, SO2, CO), t2)]
No. of Predictors	11	11
RMSE	1.0042	1.646
R-Squared	0.97	1.0
MSE	1.0084	293.98
MAE	0.66226	10.252
Prediction Speed	~5100 obs.s	~45,000 obs/s
Training Time	469.28	28.53
Model Type	Step-wise Linear	Surrogate Split
Steps	1000	N/A
Iterations	N/A	100
Hyperparameter	N/A	LS (1~577)

. The training time and predicted speed are related as they are reciprocal to each other.

The probability of errors in the magnitude range set {0.06, 0.15} is 0, observed in Figure 17. A comparison of the results with other studies was not possible, as shown in Table 1, because none of the past studies used real-time sensor data forecasting for two time-clustered IoT node measurements, and so these results are exclusively based on our data.

4. Limitations and Future Recommendation

This experiment and study were based on AQI sensing at different locations within Qatar University. The 4 SeReNo V2 AQI sensors nodes were in two buildings with similar conditions and two buildings with different conditions. A dual installation was performed to avoid any measurement errors, as per Figure 9, based on previous studies (Hasan et al., 2020). Since the trans-respiratory pandemics, especially COVID-19, are more impactful at gatherings and populated premises, the university was chosen and the equations and their respective figures provided a precise route map of forecasting. Based on Equations (24) and (25) using SCI, countermeasures can be easily taken by raising the temperature to the un-survivable limit for COVID-19 pathogens and by using CO2-capturing units and O2 cylinders to cycle fresh air.

This study will be more impactful if such AQI nodes are installed in hospitals and measured for COVID-19-tested positive and negative patients. Our research group is looking forward to conducting this research in hospitals which was not possible during the pandemic times due to social isolation.

5. Conclusions

A novel similarity coefficient index-based forecasting method for COVID-19 and trans-respiratory pandemics is proposed using the SeReNoV2 nodes. A multi-time series-parallel automated iterative optimization of regression models was performed with interesting results. The presented work highlighted the practical time-series challenge of duality and multi-cluster vector forecasting for COVID-19 safety with the impact of masks. To the best of our knowledge, this is the first real-time bi-cluster dual time-series forecasting machine learning approach for real-time multi-source sensor temporal data forecasting. The results can be summarized in three key milestones. The optimized regression methodology was able to: (1) implement a dual-time series analysis for a non-linear composite time series vector, compensating for the commutative anomalies in the bi-cluster sensor network; (2) the selected KPIs for the data preprocessing by hardware resulted in reduced training time and improved prediction speeds of the machine learning model training; (3) the forecasted results were overlapping being a justified precision in forecasting methodology accuracy for COVID-19 infections. The proposed method can serve as a role model for dual time-series problems in COVID-19 and other complex pandemics.