Modeling Significant Wave Heights for Multiple Time Horizons Using Metaheuristic Regression Methods

Using spectral indices and terrain attribute datasets and their combination in the prediction of cadmium content in agricultural soil

In this study, six machine learning (ML) models, namely, random forest (RF), Gaussian process regression (GPR), support vector regression (SVR), decision tree (DT), least squares support vector machine (LSSVM), and multivariate adaptive regression spline (MARS) models, were employed to reconstruct the missing daily‐averaged discharge in a mega‐delta from 1980 to 2015 using upstream‐downstream multi‐station data. The performance and accuracy of each ML model were assessed and compared with the stage‐discharge rating curves (RCs) using four statistical indicators, Taylor diagrams, violin plots, scatter plots, time‐series plots, and heatmaps. Model input selection was performed using mutual information and correlation coefficient methods after three data pre‐processing steps: normalization, Fourier series fitting, and first‐order differencing. The results showed that the ML models are superior to their RC counterparts, and MARS and RF are the most reliable algorithms, although MARS achieves marginally better performance than RF. Compared to RC, MARS and RF reduced the root mean square error (RMSE) by 135% and 141% and the mean absolute error by 194% and 179%, respectively, using year‐round data. However, the performance of MARS and RF developed for the climbing (wet season) and recession (dry season) limbs separately worsened slightly compared to that developed using the year‐round data. Specifically, the RMSE of MARS and RF in the falling limb was 856 and 1,040 m3/s, respectively, while that obtained using the year‐round data was 768 and 789 m3/s, respectively. In this study, the DT model is not recommended, while the GPR and SVR models provide acceptable results.

The technology known as cemented paste backfill (CPB) has gained considerable popularity worldwide. Yield stress (YS) is a significant factor considered in the assessment of CPB’s flowability or transportability. The minimal shear stress necessary to start the flow is known as Yield stress (YS), and it serves as an excellent measure of the strength of the particle-particle interaction. The traditional evaluation and measurement of YS performed by experimental tests are time-consuming and costly, which induces delays in construction projects. Moreover, the YS of CPB depends on numerous factors such as cement/tailing ratio, solid content and oxide content of tailing. Therefore, in order to simplify YS estimation and evaluation, the Artificial Intelligence (AI) approaches including eight Machine Learning techniques such as the Extreme Gradient Boosting algorithm, Gradient Boosting algorithm, Random Forest algorithm, Decision Trees, K-Nearest Neighbor, Support Vector Machine, Multivariate Adaptive Regression Splines and Gaussian Process are used to build the soft-computing model in predicting the YS of CPB. The performance of these models is evaluated by three metrics coefficient of determination (R2), Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). The 3 best models were found to predict the Yield Stress of CPB (Gradient Boosting (GB), Extreme Gradient Boosting (XGB) and Random Forest (RF), respectively) with the 3 metrics of the three models, respectively, GB {R2 = 0.9811, RMSE = 0.1327 MPa, MAE = 0.0896 MPa}, XGB {R2 = 0.9034, RMSE = 0.3004 MPa, MAE = 0.1696 MPa} and RF {R2 = 0.8534, RMSE = 0.3700 MPa, MAE = 0.1786 MPa}, for the testing dataset. Based on the best performance model including GB, XG and RF, the other AI techniques such as SHapley Additive exPlanations (SHAP), Permutation Importance, and Individual Conditional Expectation (ICE) are also used for evaluating the factor effect on the YS of CPB. The results of this investigation can help the engineers to accelerate the mixed design of CPB.

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.

The concept of orthometric heights system determination plays a major key role in geodesy, and it has broad applications in various fields and activities. In geodesy, one significant quantity is the orthometric height, the height above or below the geoid along the gravity plumbline. Conventionally, the orthometric height is determined by gravimetry and levelling techniques. However, the aforementioned techniques has its own demerits. Thus, the error is accumulated with the increase of the propagation measurement line, it is difficult to convert two separated points which is located in two continents or islands separated by sea. These techniques are tedious, time consuming and expensive. In order to resolve this challenge, many researchers resort to various techniques and approaches of obtaining orthometric heights for an area using various mathematical models. It is in this quest that, this study seek to estimate orthometric heights of a mine by utilizing plausible alternative techniques based on artificial neural networks (ANN), multivariate adaptive regression splines (MARS), polynomial regression models and multiple linear regression (MLR). The working efficiency and performance of each model has been assessed based on statistical indicators of Mean (M), Mean Square Error (MSE), Root Mean Square Error (RMSE), Mean Bias Error (MBE), Mean Absolute Error (MAE), Standard Deviation (SD), Correlation coefficient (R), Correction of determination (R2), and Signal to Noise Ratio (SNR). The statistical findings reveal that all the models produce satisfactory results in estimating the orthometric heights in the mine. MARS and ANN models compare to the MLR and polynomial models achieved higher results in terms of accuracy with mean and standard deviation of -0.000001888 m, +2.24736 m, and +0.005835 m and 0.095063 m respectively. This study will create the opportunity for geospatial practitioners to recognize the significant of ANN, MARS, MLR, and Polynomial model in solving some of the problems in geoscientific community.

Su kaynaklarının planlanması ve tarımsal su yönetimi için referans bitki su tüketiminin (ET0) doğru tahmin edilmesi oldukça önemlidir. Bu çalışmada üç farklı makine öğrenimi yönteminin, yapay sinir ağları (YSA), rassal ağaç (RT) ve gauss süreç regresyonu (GPR), yarı nemli iklim koşullarına sahip bir bölgeden alınan iklim verileri kullanılarak günlük ET0’ı tahmin etme performansları araştırılmıştır. Modelleri eğitmek ve test etmek için Bafra’da 2018–2020 döneminde toplanan günlük meteorolojik verilerin beş girdi kombinasyonu [günlük ortalama (Tort), maksimum (Tmax) ve minimum sıcaklık (Tmin), rüzgar hızı (u2), bağıl nem (RHort) ve güneşlenme şiddeti (Rs) hem tam hem de eksik kombinasyonları dahil] kullanılmıştır. Makine öğrenimi modellerinin performansı ise FAO-56 Penman Monteith (FAO-56 PM) standart denklemi ile karşılaştırılmıştır. Modellerin doğruluğunu değerlendirmek için dört farklı istatistiksel performans indeksi kullanılmıştır [belirleme katsayısı (R2), ortalama mutlak hata (MAE), hata kareleri toplamının karekökü (RMSE) ve Nash–Sutcliffe etkinlik katsayısı (NSE)]. Sonuçlar, her beş senaryoda da YSA modellerinin RT ve GPR modellerinden daha iyi performans gösterdiğini ortaya koymuştur. Tüm verilerin girdi olarak kullanıldığı beşinci senaryo için YSA modelleri tarafından tahmin edilen ET0 değerlerinin FAO-56 PM değerleri ile iyi bir uyum içinde olduğu belirlenmiştir (R2=0.988, MAE=0.166, RMSE=0.205, NSE=0.984). Bununla birlikte meteorolojik veriler tam olmadığında bile sadece Tort, RHort ve Rs ile oldukça yüksek günlük ET0 tahminleri elde edilmiştir. Genel olarak, radyasyona dayalı makine öğrenimi modelleri, sıcaklığa dayalı makine öğrenimi modellerinden daha iyi performans göstermiştir. Sonuçlar, yarı nemli iklim özelliklerine sahip bir bölgede YSA modelinin ET0'ı oldukça verimli ve doğru bir şekilde modellemek için etkili bir şekilde kullanılabileceğini göstermektedir.

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

Near-infrared reflectance spectroscopy (NIRS) was used to determine the total starch and amylose contents in various kinds of cereals namely wheat, waxy rice, non-waxy rice, millet, sorghum, waxy maize, buckwheat, barley, and hulless oat. The partial least-squares (PLS) analysis and principal component regression (PCR) were used to establish the calibration models. PLS model achieved a better effect than PCR at 1100 - 2500 nm, and the coefficient of determination (R2) of the calibration and prediction sets were both higher than 0.9 after the best pre-treatment method, first derivative plus Savitzky-Golay. Additionally, the root mean square error (RMSE) was lower than 2.50, and the root mean square error of cross-validation (RMSECV) was less than 3.50 for starch. By comparing PLS models at different waveband regions, the optimal determination results for starch and amylose were obtained at 1923 - 1961 and 1724 - 1818 nm, respectively. NIRS was found to be a successful method to determine of the starch and amylose contents in various cereals.

&amp;lt;p&amp;gt;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.&amp;amp;#160; 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 &amp;amp;#8216;future data&amp;amp;#8217; 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.&amp;amp;#160;&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;For Lakes Michigan and Ontario, 1212 monthly WL (m) records (spanning Jan 1918&amp;amp;#8211;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.&amp;amp;#160; 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).&amp;amp;#160; For each method (SVR, RF, and CNN-LSTM), mother wavelet, and decomposition level a model was generated.&amp;amp;#160; 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.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;The datasets were partitioned into calibration and validation subsets. After calibrating the models, various performance evaluation metrics, e.g., coefficient of determination (R&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;), 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.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;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.&amp;lt;/p&amp;gt;

A stock price index measures the change in several share prices, which can describe the market and assist investors in deciding on a specific investment. Thus, foreseeing the stock price index benefits investors in creating a better investment strategy. However, forecasting the stock price index can be challenging due to its non-linearity, non-stationary and high uncertainty. Gaussian process regression (GPR) is an attractive and powerful approach for prediction, especially when the data fluctuates over time with fewer restrictions. Besides, the GPR gains advantages over other forecasting techniques as it can offer predictions with uncertainty to provide margin errors. In this study, we evaluate the use of GPR to predict the stock price of Thailand (SET). The SET data are divided into 2 datasets; the data in the year 2015 - 2020 and the data in the year 2020 due to the massive change during the COVID-19 pandemic. The prediction results from the GPR are then compared to the machine learning approaches, artificial neural network (ANN) and recurrent neural network (RNN) using evaluation scores; the root mean square error (RMSE), the mean absolute error (MAE), the mean absolute percentage error (MAPE) and the Nash-Sutcliffe efficiency (NSE). The results indicate that the GPR is superior to the ANN and RNN for both datasets as it provides a high prediction accuracy. Moreover, the results suggest that the GPR is less sensitive to the number of input lags in the model. Therefore, the GPR is more favorable for the prediction of SET than the ANN and RNN.&#x0D; HIGHLIGHTS&#x0D; &#x0D; The Gaussian process regression (GPR) was applied to predict the stock price index of Thailand (SET)&#x0D; The predictive performance of the GPR was compared to artificial neural networks (ANNs) and recurrent neural networks (RNNs)&#x0D; The results indicate that GPR outperformed the other methods as it provided a high prediction accuracy along with prediction intervals&#x0D; &#x0D; GRAPHICAL ABSTRACT

Project cost prediction is one of the key elements in the civil engineering activities development. Project cost is a highly sensitive component to diverse parameters and hence it is associated with complex trends that make it difficult to be predicted and fully understood. Due to the massive advancement of soft computing (SC) and Internet of things (IoT), the main research objective of the current study was initiative. Several machine learning (ML) models including extreme learning machine (ELM), multivariate adaptive regression spline (MARS), and partial least square regression (PLS) were adopted to predict field canal cost. Several essential predictors were used to develop the prediction network “the learning process” including the total length of the PVC pipeline, served area, geographical zone, construction year, and cost and duration of field canal improvement projects (FCIP) construction. Data were collected from the open source published literature. The modeling results evidenced the potential of the applied SC models in predicting the FCIP cost. In numerical magnitude evaluation, MARS model indicated the least value for the root mean square error (RMSE = 27422.7), mean absolute error (MAE = 19761.8), and mean absolute percentage error (MAPE = 0.05454) with Nash–Sutcliffe efficiency (NSE = 0.94), agreement index (MD = 0.89), and coefficient of determination (R2 = 0.94), with best precision of prediction using all predictors, except geographical zone parameter in which less influence on the cost construction is presented. In general, the research outcome gave an informative primary cost initiative for cost civil engineering project.

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

Accurate forest biomass estimation serves as the foundation of forest management and holds critical significance for a comprehensive understanding of forest carbon storage and balance. This study aimed to integrate Landsat 8 OLI and Sentinel-1A SAR satellite image data and selected a portion of the Shanxia Experimental Forest in Jiangxi Province as the study area to establish a biomass estimation model by screening influencing factors. Firstly, we extracted spectral information, vegetation indices, principal component features, and texture features within 3 × 3-pixel neighborhoods from Landsat 8 OLI. Moreover, we incorporated Sentinel-1’s VV (vertical transmit–vertical receive) and VH (vertical transmit–horizontal receive) polarizations. We proposed an ensemble AGB (aboveground biomass) model based on a neural network. In addition to the neural network model, namely the tent mapping atom search optimized BP neural network (Tent_ASO_BP) model, partial least squares regression (PLSR), support vector machine (SVR), and random forest (RF) regression prediction techniques were also employed to establish the relationship between multisource remote sensing data and forest biomass. Optical variables (Landsat 8 OLI), SAR variables (Sentinel-1A), and their combinations were input into the four prediction models. The results indicate that Tent_ ASO_ BP model can better estimate forest biomass. Compared to pure optical or single microwave data, the Tent_ASO_BP model with the optimal combination of optical and microwave input features achieved the highest accuracy. Its R2 was 0.74, root mean square error (RMSE) was 11.54 Mg/ha, and mean absolute error (MAE) was 9.06 Mg/ha. Following this, the RF model (R2 = 0.54, RMSE = 21.33 Mg/ha, MAE = 17.35 Mg/ha), SVR (R2 = 0.52, RMSE = 17.66 Mg/ha, MAE = 15.11 Mg/ha), and PLSR (R2 = 0.50, RMSE = 16.52 Mg/ha, MAE = 12.15 Mg/ha) models were employed. In conclusion, the BP neural network model improved by tent mapping atom search optimization algorithm significantly enhanced the accuracy of AGB estimation in biomass studies. This will provide a new avenue for large-scale forest resource surveys.

This study predicts the strength of rotary brace damper by analyzing a new set of probabilistic models using the usual method of multiple linear regressions (MLR) and advanced machine-learning methods of multivariate adaptive regression splines (MARS), Rotary brace damper can be easily assembled with high energy-dissipation capability. To investigate the behavior of this damper in structures, a steel frame is modeled with this device subjected to monotonic and cyclic loading. Several response parameters are considered, and the performance of damper in reducing each response is evaluated. MLR and MARS methods were used to predict the strength of this damper. Displacement was determined to be the most effective parameter of damper strength, whereas the thickness did not exhibit any effect. Adding thickness parameter as inputs to MARS and MLR models did not increase the accuracies of the models in predicting the strength of this damper. The MARS model with a root mean square error (RMSE) of 0.127 and mean absolute error (MAE) of 0.090 performed better than the MLR model with an RMSE of 0.221 and MAE of 0.181.

Application of robust principal component analysis–multivariate adaptive regression splines for the determination of °API gravity in crude oil samples using ATR-FTIR spectroscopy