Prediction of Groundwater Level Using Machine Learning

<p>Accurate water level (WL) forecasting is important for water resources management and planning purposes in the Great Lakes. The objectives of this research are two-fold.  The first objective is to apply machine learning (ML) (i.e., random forest (RF) and support vector regression (SVR)) and hybrid convolutional neural network(CNN)-long-short term memory (LSTM) deep learning (DL) models for multi-step (i.e., one-, two- and three-monthly step ahead) WL forecasting in the Great Lakes (Michigan and Ontario). The second objective is to integrate the boundary corrected (BC) maximal overlap discrete wavelet transform (MODWT) with SVR, RF, and CNN-LSTM models to improve the performance of the individual models. By employing a BC-wavelet decomposition method, the ‘future data’ issue (i.e., data from the future that is not available), often overlooked in the literature and a major barrier to achieving realistic forecasting performance is overcome. </p><p>For Lakes Michigan and Ontario, 1212 monthly WL (m) records (spanning Jan 1918–Dec 2018) were used to develop the models. For the non-wavelet-based models (SVR, RF, and CNN-LSTM), candidate model inputs included the WL recorded over the previous 12 months.  For the BC-MODWT-based models (BC-MODWT-SVR, BC-MODWT-RF, and BC-MODWT-CNN-LSTM), the lagged input time series were decomposed into BC-wavelet and scaling coefficients by using different mother wavelets (Haar, Daubechies, Symlets, Fejer-Korovkin and Coiflets), filter lengths (from two up to 12) and decomposition levels (from one up to seven).  For each method (SVR, RF, and CNN-LSTM), mother wavelet, and decomposition level a model was generated.  For both wavelet- and non-wavelet-based models, the particle swarm optimization (PSO) method was used to select the most appropriate inputs to include in the proposed multi-step WL forecasting models.</p><p>The datasets were partitioned into calibration and validation subsets. After calibrating the models, various performance evaluation metrics, e.g., coefficient of determination (R<sup>2</sup>), root mean square error (RMSE), mean absolute error (MAE), root mean square percentage error (RMSPE), mean absolute percentage error (MAPE) and the Nash-Sutcliffe efficiency coefficient (NSC) were used to assess model accuracy.</p><p>Of the ML models, the SVR outperformed RF while the DL models outperformed the ML models for each forecast lead time (one-, two-, and three-step(s) ahead). Results from this case study indicate that not all wavelet families and decomposition levels perform equally and in some cases, the wavelet-based models do not improve performance over the non-wavelet-based models. However, the BC-MODWT-CNN-LSTM using suitable mother wavelets (e.g., Haar) outperforms the individual ML and BC-MODWT-ML-based models. More accurate forecasts were obtained for Lake Michigan although the performance in both Great Lakes was accurate. The outcomes of this research indicate that the BC-MODWT-CNN-LSTM model is a promising tool for generating accurate WL forecasts.</p>

Monkeypox virus is gaining attention due to its severity and spread among people. This study sheds light on the modeling and forecasting of new monkeypox cases. Knowledge about the future situation of the virus using a more accurate time series and stochastic models is required for future actions and plans to cope with the challenge. We conduct a side-by-side comparison of the machine learning approach with the traditional time series model. The multilayer perceptron model (MLP), a machine learning technique, and the Box-Jenkins methodology, also known as the ARIMA model, are used for classical modeling. Both methods are applied to the Monkeypox cumulative data set and compared using different model selection criteria such as root mean square error, mean square error, mean absolute error, and mean absolute percentage error. With a root mean square error of 150.78, the monkeypox series follows the ARIMA (7,1,7) model among the other potential models. Comparatively, we use the multilayer perceptron (MLP) model, which employs the sigmoid activation function and has a different number of hidden neurons in a single hidden layer. The root mean square error of the MLP model, which uses a single input and ten hidden neurons, is 54.40, significantly lower than that of the ARIMA model. The actual confirmed cases versus estimated or fitted plots also demonstrate that the multilayer perceptron model has a better fit for the monkeypox data than the ARIMA model. When it comes to predicting monkeypox, the machine learning method outperforms the traditional time series. A better match can be achieved in future studies by applying the extreme learning machine model (ELM), support vector machine (SVM), and some other methods with various activation functions. It is thus concluded that the selected data provide a real picture of the virus. If the situations remain the same, governments and other stockholders should ensure the follow-up of Standard Operating Procedures (SOPs) among the masses, as the trends will continue rising in the upcoming 10 days. However, governments should take some serious interventions to cope with the virus. In the ARIMA models selected for forecasting, we did not incorporate the effect of covariates such as the effect of net migration of monkeypox virus patients, government interventions, etc.

Full text Figures and data Side by side Abstract Editor's evaluation Introduction Materials and methods Results Discussion Data availability References Decision letter Author response Article and author information Metrics Abstract Background: Oxygen uptake (VO2) is one of the most important measures of fitness and critical vital sign. Cardiopulmonary exercise testing (CPET) is a valuable method of assessing fitness in sport and clinical settings. There is a lack of large studies on athletic populations to predict VO2max using somatic or submaximal CPET variables. Thus, this study aimed to: (1) derive prediction models for maximal VO2 (VO2max) based on submaximal exercise variables at anaerobic threshold (AT) or respiratory compensation point (RCP) or only somatic and (2) internally validate provided equations. Methods: Four thousand four hundred twenty-four male endurance athletes (EA) underwent maximal symptom-limited CPET on a treadmill (n=3330) or cycle ergometer (n=1094). The cohort was randomly divided between: variables selection (nrunners = 1998; ncyclist = 656), model building (nrunners = 666; ncyclist = 219), and validation (nrunners = 666; ncyclist = 219). Random forest was used to select the most significant variables. Models were derived and internally validated with multiple linear regression. Results: Runners were 36.24±8.45 years; BMI = 23.94 ± 2.43 kg·m−2; VO2max=53.81±6.67 mL·min−1·kg−1. Cyclists were 37.33±9.13 years; BMI = 24.34 ± 2.63 kg·m−2; VO2max=51.74±7.99 mL·min−1·kg−1. VO2 at AT and RCP were the most contributing variables to exercise equations. Body mass and body fat had the highest impact on the somatic equation. Model performance for VO2max based on variables at AT was R2=0.81, at RCP was R2=0.91, at AT and RCP was R2=0.91 and for somatic-only was R2=0.43. Conclusions: Derived prediction models were highly accurate and fairly replicable. Formulae allow for precise estimation of VO2max based on submaximal exercise performance or somatic variables. Presented models are applicable for sport and clinical settling. They are a valuable supplementary method for fitness practitioners to adjust individualised training recommendations. Funding: No external funding was received for this work. Editor's evaluation The authors have established new formulas to predict maximum oxygen uptake for cyclists and runners based on submaximal exercise testing and anthropometric characteristics. This is an important study with a large and comprehensive dataset, which may be helpful for many exercise labs. The work is convincing, using appropriate and validated methodology in line with the current state-of-the-art, as shown by references to common exercise books. https://doi.org/10.7554/eLife.86291.sa0 Decision letter Reviews on Sciety eLife's review process Introduction The oxygen uptake (VO2) is considered an important metric in assessing cardiorespiratory fitness, health status, or endurance performance potential (Guazzi et al., 2012). With the application of standardised procedures and interpretation protocols, during graded exercise tests (GXT), the (maximal oxygen uptake) VO2max can be established (Bentley et al., 2007). GXT is the most widely used assessment to examine the dynamic relationship between exercise and integrated physiological systems (Albouaini et al., 2007; Bentley et al., 2007). The information from GXT during cardiopulmonary exercise testing (CPET) can be applied across the spectrum of sport performance, occupational safety screening, research, and clinical diagnostics (Guazzi et al., 2017). VO2 max is often used as a boundary between severe and extreme intensity domains and by definition requires maximal effort from the tested subject (Gaesser and Poole, 1996). However, it is not always recommended or possible to undertake a test to exhaustion (Guazzi et al., 2012). For the athletes, the proximity of competition or injury history can allow submaximal testing, but not testing to exhaustion (Sassi et al., 2006). Testing that requires maximal effort may be disruptive to the training process or interfere with race performance (Coutts et al., 2007; Lamberts et al., 2011). Due to practical constraints, tests to exhaustion or peak-power-output tests are often performed only two or three times a year (Coutts et al., 2007). However, VO2 values are widely used in sport science and the decision-making process (Mann et al., 2013). VO2 is widely considered one of the major endurance performance determinants (Joyner and Coyle, 2008). Using VO2max to guide the selection process, prescribing training intensity, assessing training adaptations, or predicting race times is a common practice in high-performance sports (Bassett and Howley, 2000; Bentley et al., 2007; Hawley and Noakes, 1992; Noakes et al., 1990). VO2max is also one of the critical vital signs coordinating the function of the cardiovascular, respiratory, and muscular systems, it is an indicator of overall body health status (Kaminsky et al., 2017). Quantifying VO2max provides additional input regarding clinical decision-making, risk stratification, evaluation of therapy, and physical activity guidelines (Guazzi et al., 2012). For patients undertaking a test to exhaustion is rarely needed or possible due to health restraints or cardiac risk (Guazzi et al., 2016). For many years researchers have studied indirect methods of estimating VO2max(Sartor et al., 2013). Protocols such as the Astrand-Ryhming Test, Six-Minute Walk Test, or YMCA Step Test have been established and validated (Astrand and Ryhming, 1954; Beutner et al., 2015; Carey, 2022; Jalili et al., 2018). Moreover, estimation of the VO2 and heart rate (HR) values below the ventilatory threshold can be based on cardiorespiratory kinetics assessment using randomised changes in the work rate known as a pseudo-random binary sequences testing (Hoffmann et al., 2022). However, with the development of technology, the accessibility of laboratory testing and mobile testing improved (Montoye et al., 2020; Pritchard et al., 2021). Therefore, new opportunities to develop more precise yet simple and accessible methods and models to assess VO2max occur (Jurov et al., 2023). This appears to be especially important considering the low prediction accuracy of most of the VO2max formulae that were validated in our previous study (Wiecha et al., 2023). Recently, we have been observing the development of prediction methods with the usage of machine learning (ML) and artificial intelligence (AI) (Ashfaq et al., 2022). Both ML and AI are used in sport science as forecasting and decision-making support tools (Abut and Akay, 2015; Bobowik and Wiszomirska, 2022; Chmait and Westerbeek, 2021; Hammes et al., 2022; Rossi et al., 2021). There is growing evidence that VO2max prediction based on ML models, especially support vector ML and artificial neural network models, exhibits more robust and accurate results compared to MLR only (Abut and Akay, 2015; Ashfaq et al., 2022). Therefore, in this research, with the support of ML, we look for algorithms and prediction patterns that allow us to use values obtained during submaximal CPET and somatic measurements to estimate maximal VO2max values in male runners and cyclists. We stipulate that prediction models allow for accurate calculation of VO2max based on somatic or submaximal CPET variables. Materials and methods We have applied the development and validation of the prediction TRIPOD guidelines to conduct the study (see Supplementary Material 1TRIPOD Checklist for Prediction Model Development and Validation) (Collins et al., 2015). The study is based on retrospective data analysis from the CPET registry collected from 2013 to 2021 at the medical clinic (Sportslab, Warsaw, Poland). All CPET have been performed at the individual request of participants, as a part of regular training monitoring or performance assessment. Ethical approval Request a detailed protocol The Institutional Review Board of the Bioethical Committee at the Medical University of Warsaw (AKBE/32/2021) has approved the study protocol. The regulations of the Declaration of Helsinki were met during all parts of the study. Each study participant delivered written consent to undergo CPET and participate in the study. Derivation cohort Request a detailed protocol We selected the cohort with the use of rigorous exclusion/inclusion criteria. Due to the insufficient number of women in our database and the number of potential variables in the regression models for adequate power, we had to limit ourselves to conduct analysis in the male population only (Martens and Logan, 2021). Out of 6439 healthy, adult male cyclists and long-distance runners that undergone CPET, 4423 met the criteria as further: (1) age ≥18 years, (2) declared regular cycling or running training for ≥3 months, (3) had no extreme outliers ≤ or ≥±3 standard deviations (SD) from mean for all of the testing variables (beyond ≥±3 SD in VO2max), (4) lack of any injury, medical condition, or addiction in medical history that may affect exercise capacity, (5) not taking any medications with a modifying effect on exercise capacity, (6) maximum exertion achieved during CPET. We defined the maximum exertion in CPET as the fulfilment of the minimum six of the following criteria: (1) respiratory exchange ratio (RER) ≥1.10, (2) present VO2 plateau (growth <100 mL·min–1 in VO2 despite increased running speed or cycling power), (3) respiratory frequency (fR) ≥45 breaths·min–1, (4) declared subjective exertion intensity during CPET ≥18 in the Borg scale (Borg, 1970), (5) blood lactate concentration [La-]b ≥8 mmol·L–1, (6) growth in speed/power ≥10% of respiratory compensation point (RCP) values after exceeding the RCP, (7) peak heart rate (HRpeak) ≥15 beats·min–1 below predicted maximal heart rate (HRmax) (Lach et al., 2021). Participants’ selection procedure has been shown in Figure 1. Figure 1 Download asset Open asset Flowchart of the preliminary inclusion and exclusion process. Abbreviations: EA, endurance athlete; CPET, cardiopulmonary exercise testing; SD, standard deviation; TE, treadmill; RER, respiratory exchange ratio; VO2, oxygen uptake (mL·min−1·kg−1); [La−]b, lactate concentration (mmol·L−1); fR, breathing frequency (breaths·min−1); RCP, respiratory compensation point; HRpeak, peak heart rate (beats·min−1); HRmax, maximal heart rate (bpm). At both stages of the selection, some participants met several (>1) exclusion criteria. Somatic measurements and CPET protocols Request a detailed protocol Body mass was measured with a body composition (BC) analyser (Tanita, MC 718, Japan) with the multifrequency of 5 kHz/50 kHz/250 kHz via the bioimpedance analysis and normal testing mode. The participants’ skin was cleaned with alcohol before placing the electrodes on the skin. Prior to the test, the participants received instructions to refrain from exercising for 2 hr, consume a light meal rich in carbohydrates 2–3 hr beforehand, and maintain hydration by drinking isotonic beverages. Additionally, they were advised to abstain from medications, caffeine, and cigarettes on the day of the test. Running CPET (TE) was performed on a mechanical treadmill (h/p/Cosmos Quasar, Germany). Cycling CPET (CE) was performed on Cyclus-2 (RBM elektronik-automation GmbH, Leipzig, Germany). Hans Rudolph V2 mask (Hans Rudolph, Inc, Shawnee, KS, USA), breath-by-breath method with Cosmed Quark CPET gas exchange analysing device (Cosmed Srl, Rome, Italy), and Quark PFT Suite to Omnia 1.6 software were utilised. The gas analyser device was regularly calibrated with the reference gas (16% O2; 5% CO2) in accordance with the manufacturer’s instructions (Airgas USA, LLC, Plumsteadville, PA, USA). From 2013 to 2021, three Cosmed Quark CPET units were used. HR was measured with the Cosmed torso belt (Cosmed srl, Rome, Italy). [La-]b was measured via enzymatic-amperometric electrochemical technique with Super GL2 analyser (Müller Gerätebau GmbH, Freital, Germany). The [La-]b analyser was regularly calibrated before each measurement series. The 40 m2 indoor, air-conditioned laboratory with 20–22°C temperature and 40–60% humidity, and 100 m ASL provided the same conditions for all BC and CPET. Each CPET began with a 5 min personalised warm-up (walk or easy jog with ‘conversational’ intensity for running, easy pedalling with ‘conversational’ intensity for cycling). Then after the preparation (about 5 min), the continuous progressive step test was conducted. Due to the population diversity (training status), the running test speed started from 7 to 12 km·hr–1 with a 1% treadmill incline. The choice of initial starting speed was determined by the interview and sports results achieved. For example, those running less than 60 min at a distance of 10 km started the test at 7 km/hr, while those running 10 km for less than 35 min started the test at an initial speed of 12 km/hr. The pace increased by 1 km·hr–1 every 2 min with no change in incline. The cycling test began at 60–150 W, depending on the athletes training status. The power increased by 20–30 W every 2 min. It was recommended to maintain a constant cadence of 80–90 (repetition·min–1) during the test. The tests were terminated due to exhaustion: volitional inability to continue the activity or/and VO2 and HR plateau with increasing load or/and observed disturbance of coordination in running or/and inability to maintain the set cadence. Due to the graded protocol used, the cycling power and running speed values have been calculated as a function of time to better reflect the actual level for the test moment being determined (Kuipers et al., 1985). Before the test, after every step, and 3 min after the termination of the effort technician took a 20 µL blood sample from a fingertip. Samples were collected during the test without interrupting the effort. The samples were taken from the initial puncture. The first blood drop was collected into the swab and the second blood drop was drawn for further analysis into the capillary. VO2max was recorded as the highest value (15 s intervals) before the termination of the test. HRmax was recorded as the highest value obtained at the end of the test, without averaging. The anaerobic threshold (AT) was established with the following criteria: (1) common start of VE/VO2 and VE/VCO2 curves, (2) end-tidal partial pressure of oxygen raised constantly with the end-tidal partial pressure of carbon dioxide (Beaver et al., 1986). The was established with the following criteria: (1) PetCO2 must decrease after reaching maximal amount, (2) the presence of fast nonlinear growth in VE (second deflection), (3) the VE/VCO2 ratio achieved minimum and started to rise, and (4) a nonlinear increase in VCO2 versus VO2 (lack of linearity) (Beaver et al., 1986). The [La-]b was estimated for AT and RCP in relation to power or speed (Wiecha et al., 2022). Data analysis Request a detailed protocol Our comprehensive ML approach enables the evaluation of each formula by preliminary variables precision (at the stage of selection), then accuracy (during the model’s building) and recall (in internal validation). Individual CPET results were saved into the Excel file (Microsoft Corporation, Redmond, WA, USA) and a custom-made script was used to generate the database in Excel (Python programming). Further, mean, SD, and 95% confidence intervals (CI) were calculated. The normality of the distribution of the data was examined using the Shapiro-Wilk test and intergroup differences were calculated using the Student’s t-test for independent variables. Three-step variable selection procedures based on random forests were applied using the R package VSURF in RStudio software (R Core Team, Vienna, Austria; version 3.6.4) (Genuer et al., 2016). For each level of measurement (AT, RCP) and their combination (AT+RCP), significant variables were identified separately. The first step was dedicated to eliminate irrelevant variables from the dataset. Second step aimed to select all variables related to the response for interpretation purposes. The third step refined the selection by eliminating redundancy in the set of variables selected by the second step, for prediction purposes (Genuer et al., 2017). Each time for variables selection, the anthropometric variables as in Tables 1–2 and the CPET parameters given in Tables 3–4 from a specific level of measurement (AT; RCP) and their combinations were visible. Table 1 Basic anthropometric characteristics for runners. Variable (unit)Derivation group n=1998Testing group n=666Validation group n=666MeanCISDMeanCISDMeanCISDAge (years)36.235.6–36.98.4535.935.5–36.38.0535.534.9–36.28.14Height (cm)180.0179.6–180.56.04179.4179.1–179.76.13179.7179.2–180.26.61BM (kg)77.777.0–78.49.3577.777.3–78.19.2977.977.1–78.610.1BMI (kg·m–2)23.923.8–24.12.4324.124.0–24.22.4124.123.9–24.32.56BF (%)15.415.1–15.74.5515.515.3–15.74.5215.415.1–15.84.55FM (kg)12.211.9–12.64.6812.312.1–12.54.6512.311.9–12.74.92FFM (kg)65.565.0–66.06.4365.465.1–65.76.3165.665.1–66.16.86 BM, body mass; BMI, body mass index; BF, body fat; FM, fat mass; FFM, fat-free mass; CI, 95% confidence interval; SD, standard deviation. Table 2 Basic anthropometric characteristics for cyclists. Variable (unit)Derivation group n=656Testing group n=219Validation group n=219MeanCISDMeanCISDMeanCISDAge (years)37.336.6–38.09.1337.135.9–38.49.5037.636.5–38.88.46Height (cm)179.9179.4–180.46.27180.1179.2–181.06.96180.2179.4–181.06.13BM (kg)78.878.1–79.69.8079.177.7–80.510.479.878.4–81.310.9BMI (kg·m–2)24.324.1–24.62.6324.424.0–24.72.8024.624.2–25.02.96BF (%)16.415.7–17.14.9916.115.7–16.54.8116.215.5–16.84.87FM (kg)13.312.6–14.15.6613.012.6–13.45.2713.312.5–14.05.85FFM (kg)65.864.9–66.66.2565.865.4–66.36.0666.665.7–67.46.58 BM, body mass; BMI, body mass index; BF, body fat; FM, fat mass; FFM, fat-free mass; CI, 95% confidence interval; SD, standard deviation. Table 3 Cardiopulmonary exercise testing (CPET) characteristics for runners. Variable (unit)Derivation group n=1998Testing group n=666Validation group n=666MeanCISDMeanCISDMeanCISDrVO2AT (mL·min–1·kg–1)38.438.1–38.85.0138.538.3–38.74.8838.137.7–38.55.16RERAT0.870.86–0.870.040.870.86–0.870.040.870.86–0.870.04HRAT (beats·min–1)151.5150.8–152.310.3151.0150.6–151.510.8152.0151.2–152.810.8VEAT (L·min–1)79.178.1–80.012.278.377.8–78.912.077.276.3–78.212.0SPEEDAT (km·h–1)11.010.9–11.11.4511.011.0–11.11.3610.910.8–11.01.42LAAT (mmol·L–1)2.082.02–2.140.631.801.76–1.830.622.352.27–2.420.72rVO2RCP (mL·min–1·kg–1)47.547.0–48.05.8847.747.4–48.06.1547.346.8–47.86.16RERRCP1.001.00–1.000.041.001.00–1.000.041.001.00–1.000.03HRRCP (beats·min–1)173.4172.7–174.19.21173.2172.8–173.69.30174.3173.5–175.09.50VERCP (L·min–1)114.7113.5–116.015.9113.9113.1–114.616.7112.7111.4–114.016.2SPEEDRCP (km·h–1)14.013.9–14.11.7714.114.0–14.11.7013.913.8–14.11.75LARCP (mmol·L–1)4.724.63–4.821.044.404.34–4.451.044.814.69–4.931.14rVO2max (mL·min–1·kg–1)53.853.3–54.36.6754.354.0–54.66.9553.853.3–54.37.09 CI, 95% confidence interval; SD, standard deviation; rVO2AT, oxygen uptake at anaerobic threshold relative to body mass; RERAT, respiratory exchange ratio at anaerobic threshold; HRAT, heart rate at anaerobic threshold; VEAT, pulmonary ventilation at anaerobic threshold; SPEEDAT, velocity at anaerobic threshold; LAAT, blood lactate concentration at anaerobic threshold; rVO2RCP, oxygen uptake at respiratory compensation point relative to body mass; RERRCP, respiratory exchange ratio at respiratory compensation point; HRRCP, heart rate at respiratory compensation point; VERCP, pulmonary ventilation at respiratory compensation point; SPEEDRCP, velocity at respiratory compensation point; LARCP, blood lactate concentration at respiratory compensation point; rVO2max, maximal oxygen uptake relative to body mass. Table 4 Cardiopulmonary exercise testing (CPET) characteristics for cyclists. Variable (unit)Derivation group n=656Testing group n=219Validation group n=219MeanCISDMeanCISDMeanCISDrVO2AT (mL·min–1·kg–1)33.032.5–33.45.8433.232.4–33.95.6833.732.9–34.55.89RERAT0.870.87–0.870.040.870.87–0.880.040.870.87–0.880.04HRAT CI, 95% confidence interval; SD, standard deviation; rVO2AT, oxygen uptake at anaerobic threshold relative to body mass; RERAT, respiratory exchange ratio at anaerobic threshold; HRAT, heart rate at anaerobic threshold; VEAT, pulmonary ventilation at anaerobic threshold; power at anaerobic threshold relative to body mass; LAAT, blood lactate concentration at anaerobic threshold; rVO2RCP, oxygen uptake at respiratory compensation point relative to body mass; RERRCP, respiratory exchange ratio at respiratory compensation point; HRRCP, heart rate at respiratory compensation point; VERCP, pulmonary ventilation at respiratory compensation point; LARCP, blood lactate concentration at respiratory compensation point; power at respiratory compensation point relative to body mass; rVO2max, maximal oxygen uptake relative to body mass. selection variables were in the further only selected parameters were into multiple linear regression The data for MLR model building were randomly into that is testing, validation and of the a only significant were in the Derived are by the of mean and mean analysis was used to the model’s precision and accuracy during validation and tests to the fulfilment of MLR test the of in MLR test assessment between and test of Each model was examined the and any have not been 2 package in RStudio (R Core Team, Vienna, Austria; version version for and software version were used in was considered as the Results Somatic measurements and CPET results data of the runners models for testing, and validation are in Table while cyclists are in Table The runners of and for testing, and validation the cyclists and differences between of runners and cyclists were in BMI and between testing in all between validation only in CPET results for runners models are in Table 3 and for cyclists in Table Runners in the cohort achieved relative to body mass VO2max of in testing group and in validation group cyclists mean was and for testing, and validation to body mass oxygen uptake at anaerobic threshold in runners for ± ± and ± of in testing, and validation it was ± ± and ± of rVO2max, relative to body mass oxygen uptake at respiratory compensation point in runners for ± ± and ± of for testing, and validation while in cyclists for ± ± and ± of rVO2max, There were no significant differences in values between testing, and validation the runners and cyclists between runners and cyclists results were all significant Prediction models based on AT and RCP Full of MLR prediction models for cyclists are in Table for runners in Table The models prediction performance is as with and for cyclists from for somatic parameters to for RCP equations. For runners from for to for AT and equations. for cyclists models was the for RCP and the highest for For from for AT and to for equation. observed for cyclists was the for RCP in the validation group and the highest for while in runners the for AT and and the highest for The performance of prediction is in Figure Figure 2 Download asset Open asset of prediction for Abbreviations: maximal oxygen anaerobic threshold; RCP, respiratory compensation point; All values are in performance for running while the performance for cycling equations. performance of the prediction model for for for AT and for somatic-only equation. Table 5 VO2max prediction for cyclists. linear regression group group = = = = based on anaerobic threshold; RCP, based on respiratory compensation point; based on somatic variables mean mean maximal oxygen uptake relative to body mass rVO2AT, oxygen uptake at anaerobic threshold relative to body mass power at anaerobic threshold relative to body mass rVO2RCP, oxygen uptake at respiratory compensation point relative to body mass VERCP, pulmonary ventilation at respiratory compensation point BF, body fat BM, body mass Table VO2max prediction for runners. linear regression group group = = = = based on anaerobic threshold; RCP, based on respiratory compensation point; based on somatic variables mean mean maximal oxygen uptake relative to body mass rVO2AT, oxygen uptake at anaerobic threshold relative to body mass SPEEDAT, velocity at anaerobic threshold FFM, fat mass VEAT, pulmonary ventilation at anaerobic threshold HRAT, heart rate at anaerobic threshold BF, body fat rVO2RCP, oxygen uptake at respiratory compensation point relative to body mass SPEEDRCP, velocity at respiratory compensation point Models validation of each model for cyclists is in Table while for runners in Table the performance of our prediction was to that observed in the

Improving forecasts, particularly the accuracy, efficiency, and precision of time-series forecasts, is becoming critical for authorities to predict, monitor, and prevent the spread of the Coronavirus disease. However, the results obtained from the predictive models are imprecise and inefficient because the dataset contains linear and non-linear patterns, respectively. Linear models such as autoregressive integrated moving average cannot be used effectively to predict complex time series, so nonlinear approaches are better suited for such a purpose. Therefore, to achieve a more accurate and efficient predictive value of COVID-19 that is closer to the true value of COVID-19, a hybrid approach was implemented. Therefore, the objectives of this study are twofold. The first objective is to propose intelligence-based prediction methods to achieve better prediction results called autoregressive integrated moving average-least-squares support vector machine. The second objective is to investigate the performance of these proposed models by comparing them with the autoregressive integrated moving average, support vector machine, least-squares support vector machine, and autoregressive integrated moving average-support vector machine. Our investigation is based on three COVID-19 real datasets, i.e., daily new cases data, daily new death cases data, and daily new recovered cases data. Then, statistical measures such as mean square error, root mean square error, mean absolute error, and mean absolute percentage error were performed to verify that the proposed models are better than the autoregressive integrated moving average, support vector machine model, least-squares support vector machine, and autoregressive integrated moving average-support vector machine. Empirical results using three recent datasets of known the Coronavirus Disease-19 cases in Malaysia show that the proposed model generates the smallest mean square error, root mean square error, mean absolute error, and mean absolute percentage error values for training and testing datasets compared to the autoregressive integrated moving average, support vector machine, least-squares support vector machine, and autoregressive integrated moving average-support vector machine models. This means that the predicted value of the proposed model is closer to the true value. These results demonstrate that the proposed model can generate estimates more accurately and efficiently. Compared to the autoregressive integrated moving average, support vector machine, least-squares support vector machine, and autoregressive integrated moving average-support vector machine models, our proposed models perform much better in terms of percent error reduction for both training and testing all datasets. Therefore, the proposed model is possibly the most efficient and effective way to improve prediction for future pandemic performance with a higher level of accuracy and efficiency.

Miami-Dade County, FL, has complex hydrological and water management conditions, creating challenges for predicting groundwater levels. Due to the potential impacts of increasing sea level and changes in rain patterns on flooding and saltwater intrusion, it is essential to be able to accurately predict groundwater levels and to understand the drivers of groundwater levels. The method traditionally used to predict groundwater levels in south Florida and elsewhere is through the implementation of a numerical model. This research looks at machine learning techniques as an alternative method to provide improved predictions of groundwater levels. Extreme gradient boosting is one of the machine learning techniques that uses algorithms to train a model by identifying hidden patterns and relationships between groundwater level drivers and groundwater levels. The accuracies of the extreme gradient boosting model and a numerical model were compared by computing the root mean square error as a model performance measure. Comparing these two methods showed that the extreme gradient boosting model had better accuracy in predicting groundwater levels at the majority of groundwater monitoring sites. Furthermore, comparison of these two models helped us to identify problematic areas where both models performed poorly and narrow down the factors that could cause this poor model performance. Finally, the extreme gradient boosting method gave the importance of each feature included among the potential groundwater level drivers, including the ranked importance of a particular factor and its lag time, at each of the considered groundwater level monitoring sites.

Hybrid random forest-based models for predicting shear strength of structural surfaces based on surface morphology parameters and metaheuristic algorithms

This paper presents a data-driven approach to determine the load and flexural capacities of reinforced concrete (RC) beams strengthened with fabric reinforced cementitious matrix (FRCM) composites in flexure. A total of seven machine learning (ML) models such as kernel ridge regression, K-nearest neighbors, support vector regression, classification and regression trees, random forest, gradient boosted trees, and extreme gradient boosting (xgBoost) are evaluated to propose the best predictive model for FRCM-strengthened beams. Beam geometry, internal steel reinforcement area, FRCM reinforcement area, and mechanical characteristics of concrete, steel, and FRCM are the main input parameters included in the database. Among the studied ML models, the xgBoost model is the most accurate model with the highest coefficient of determination (R2=99.3%) and least root mean square (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). A comparative study of the performance of the proposed and existing analytical models revealed the superior predictive capability and robustness of the proposed model. The predicted flexural and load capacities of the beams based on the existing analytical models are highly scattered and either over-conservative or unsafe. A unified SHapley Additive exPlanations approach is employed to explain the output of the best ML model and identify the most significant input features and interactions that influence the capacity of FRCM-strengthened RC beams in flexure. Furthermore, a reliability analysis is performed to calibrate the resistance reduction factor (ϕ) to achieve a specified target reliability index (βT=3.5).

Globally, wind energy if properly harnessed, could serve as a source of energy generation in Africa. This study compared the performance of two Machine Learning (ML) algorithms (Linear regression and Random Forest) in predicting wind speed in five major cities in Africa (Yaoundé, Pretoria, Nairobi, Cairo and Abuja). Wind data were collected between January 1, 2000, and December 31, 2022, using the Solar Radiation Data Archive. The data preprocessing was carried out with 80% of the data used for training and 20% for validation. The performance of these ML algorithms was evaluated using Mean Square Error (MSE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) and coefficient of determination (R2). The result shows that Nairobi (3.814795 m/s) closely followed by Cairo (3.606453 m/s) has the highest mean wind speed while Yaoundé (1.090512 m/s) has the lowest. Based on the performance metrics used, the two Machine Learning algorithms were competitive. Still, the Linear Regression (LR) algorithm outperformed the Random Forest Algorithm in predicting wind speed in all the selected major African cities. In Yaoundé (RMSE = 0.3892, MAE= 0.3001, MAPE =0.5030), Pretoria (RMSE=1.2339, MAE=0.9480, MAPE=0.7450) Nairobi (RMSE= 0.4223, MAE =0.6499, MAPE =0.1872), Nairobi (RMSE=0.6499, MAE=0.5171, MAPE =0.1872), Cairo (RMSE =1.0909, MAE =0.8544, MAPE =0.3541) and Abuja (RMSE = 0.70245, MAE =0.5441, MAPE= 0.4515) the Linear regression algorithms was found to outperformed Random Forest Regression. Therefore, the Linear regression algorithm is more reliable in predicting wind speed compared with the Random Forest regression.

Recently, the quality of fresh water resources is threatened by numerous pollutants. Prediction of water quality is an important tool for controlling and reducing water pollution. By employing superior big data processing ability of deep learning it is possible to improve the accuracy of prediction. This paper proposes a method for predicting water quality based on the deep belief network (DBN) model. First, the particle swarm optimization (PSO) algorithm is used to optimize the network parameters of the deep belief network, which is to extract feature vectors of water quality time series data at multiple scales. Then, combined with the least squares support vector regression (LSSVR) machine which is taken as the top prediction layer of the model, a new water quality prediction model referred to as PSO-DBN-LSSVR is put forward. The developed model is valued in terms of the mean absolute error (MAE), the mean absolute percentage error (MAPE), the root mean square error (RMSE), and the coefficient of determination ( R 2 ). Results illustrate that the model proposed in this paper can accurately predict water quality parameters and better robustness of water quality parameters compared with the traditional back propagation (BP) neural network, LSSVR, the DBN neural network, and the DBN-LSSVR combined model.

Compressive strength is an important mechanical property of high-strength concrete (HSC), but testing methods are usually uneconomical, time-consuming, and labor-intensive. To this end, in this paper, a long short-term memory (LSTM) model was proposed to predict the HSC compressive strength using 324 data sets with five input independent variables, namely water, cement, fine aggregate, coarse aggregate, and superplasticizer. The prediction results were compared with those of the conventional support vector regression (SVR) model using four metrics, root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and correlation coefficient (R2). The results showed that the prediction accuracy and reliability of LSTM were higher with R2 = 0.997, RMSE = 0.508, MAE = 0.08, and MAPE = 0.653 compared to the evaluation metrics R2 = 0.973, RMSE = 1.595, MAE = 0.312, MAPE = 2.469 of the SVR model. The LSTM model is recommended for the pre-estimation of HSC compressive strength under a given mix ratio before the laboratory compression test. Additionally, the Shapley additive explanations (SHAP)-based approach was performed to analyze the relative importance and contribution of the input variables to the output compressive strength.

Machine learning modeling integrating experimental analysis for predicting the properties of sugarcane bagasse ash concrete

Nowadays , nonlinear time series and artificial neural networks (ANN) models are used for forecasting in the field of business, agriculture and soon. Recent studies have shown, ANN have been successfully used for forecasting of financial and agriculture data series The classical methods used for time series prediction like Box-Jenkins or ARIMA assumes that there is a linear relationship between inputs and outputs. ANN have more advantages that can approximate to model both linear and nonlinear structures in time series, they are not able to handling both structures equally well. The autoregressive integrated moving average (ARIMA) model and two ANN models namely, Radial basis function neural networks (RBFNN), and Elman recurrent neural networks (ERNN) methods were applied to Hyderabad airport traffic data. The data obtained for 15 years from 2002–2003 to 2016–2017 about domestic and international passenger of International Airport of Hyderabad, India. In this research paper, we compared the performances of ARIMA, RBFNN and ERNN were based on three measures: mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE). The results showed that RBFNN obtained the smallest MAE, MAPE and RMSE in both the modeling and forecasting processes. The performances of the three models ranked in ascending order were: ARIMA, ERNN and the RBFNN model. Keywords: T ime series, forecasting, artificial neural networks, ARIMA models, radial basis function neural networks, and Elman recurrent neural networks Cite this Article R. Ramakrishna, Berhe Aregay, Tewodros Gebregergs. The Comparison in Time Series Forecasting of Air Traffic Data by Autoregressive Integrated Moving Average Model, Radial Basis Function and Elman Recurrent Neural Networks. Research & Reviews: Journal of Statistics . 2018; 7(3): 75–90p.

Accurate and efficient prediction of oilfield productivity is very important for the formulation of development and adjustment plans. Machine learning (ML) productivity prediction model can quickly obtain the productivity of oilfield development. In this paper, an oilfield development productivity prediction model based on five ML algorithms including multivariable linear regression (LR), extreme gradient boosting (XGBoost), light gradient boosting machine (LightGBM), back propagation (BP) neural network and long short term memory (LSTM) neural network is established. Through the evaluation of model performance indicators (include the root mean square error (RMSE), the coefficient of determination (R2), the mean absolute error (MAE) and mean absolute percentage error (MAPE)), the best performance prediction model is selected. The research results show that the prediction results of LR model are greatly affected by the data of high productivity oil wells, XGBoost model are easily affected by fitting, and BP neural network model is far less effective than other models. Through comprehensive comparison of prediction results, LightGBM model has better stability and generalization performance. The difference between the prediction results of each model is mainly caused by the characteristics of the algorithm and the size of the data sets. At the same time, LSTM can predict the future oil well production based on the oil well time series observation data. The research results of this paper have guiding significance for the selection of productivity prediction model for oilfield development based on data-driven.

Water level prediction is an essential factor for the safe operation of pumping stations. However, due to the complex nonlinear relationship between the water level of the front pool of the pumping station and the influencing factors, the prediction of the water level is still inaccurate and untimely. Backpropagation (BP) neural network, improved particle swarm optimization-BP neural network (PSO-BP), support vector machine regression (SVR), and improved PSO-SVR were used to construct 4-h and 8-h ahead prediction models for pumping station prestation water levels. Mean absolute error, mean squared error (MSE), root mean square error (RMSE), mean absolute percentage error (MAPE), and R correlation coefficient were used as prediction evaluation metrics. This method is applied in the Baliwan Pumping Station, the highest pumping station in the South-to-North Water Diversion Eastern Route Project (SNWDERP). The results showed that the MSE, RMSE, and MAPE of the improved PSO-BP model were smaller than other models, whereas the R correlation coefficient was larger, confirming its high prediction accuracy. All models had higher prediction accuracy 4 h ahead than 8 h ahead. Combining the time-phased water level prediction method and hybrid machine learning can enhance the water level prediction accuracy of a pumping station pre-station.

Traffic speed prediction is an emerging paradigm for achieving a better transportation system in smart cities and improving the heavy traffic management in the intelligent transportation system (ITS). The accurate traffic speed prediction is affected by many contextual factors such as abnormal traffic conditions, traffic incidents, lane closures due to construction or events, and traffic congestion. To overcome these problems, we propose a new method named fuzzy optimized long short‐term memory (FOLSTM) neural network for long‐term traffic speed prediction. FOLSTM technique is a hybrid method composed of computational intelligence (CI), machine learning (ML), and metaheuristic techniques, capable of predicting the speed for macroscopic traffic key parameters. First, the proposed hybrid unsupervised learning method, agglomerated hierarchical K‐means (AHK) clustering, divides the input samples into a group of clusters. Second, based on parameters the Gaussian bell‐shaped fuzzy membership function calculates the degree of membership (high, low, and medium) for each cluster using Takagi‐Sugeno fuzzy rules. Finally, the whale optimization algorithm (WOA) is used in LSTM to optimize the parameters obtained by fuzzy rules and calculate the optimal weight value. FOLSTM evaluates the accurate traffic speed from the abnormal traffic data to overcome the nonlinear characteristics. Experimental results demonstrated that our proposed method outperforms the state‐of‐the‐art approaches in terms of metrics such as mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE).