Uplift capacity prediction of suction caisson in clay using a hybrid intelligence method (GMDH-HS)

Oilseeds have been the backbone of India’s agricultural economy since long. Oilseed crops play the second most important role in Indian agricultural economy, next to food grains, in terms of area and production. Oilseeds production in India has increased with time, however, the increasing demand for edible oils necessitated the imports in large quantities, leading to a substantial drain of foreign exchange. The need for addressing this deficit motivated a systematic study of the oilseeds economy to formulate appropriate strategies to bridge the demand-supply gap. In this study, an effort is made to forecast oilseeds production by using Autoregressive Integrated Moving Average (ARIMA) model, which is the most widely used model for forecasting time series. One of the main drawbacks of this model is the presumption of linearity. The Group Method of Data Handling (GMDH) model has also been applied for forecasting the oilseeds production because it contains nonlinear patterns. Both ARIMA and GMDH are mathematical models well-known for time series forecasting. The results obtained by the GMDH are compared with the results of ARIMA model. The comparison of modeling results shows that the GMDH model perform better than the ARIMA model in terms of mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE). The experimental results of both models indicate that the GMDH model is a powerful tool to handle the time series data and it provides a promising technique in time series forecasting methods.

The main purpose of this paper is to propose the use of Group Method of Data Handling (GMDH) to predict software reliability. The GMDH algorithm presented in this paper is a heuristic self-organization method. It establishes the input-output relationship of a complex system using multilayered perception type structure that is similar to a feed forward multilayer neural network. The effectiveness of GMDH is demonstrated on a dataset taken from literature. Its performance is compared with that of multiple linear regression (MLR), back propagation trained neural networks (BPNN), threshold accepting trained neural network (TANN), general regression neural network (GRNN), pi-sigma network (PSN), dynamic evolving neuro-fuzzy inference system (DENFIS), TreeNet, multivariate adaptive regression splines (MARS) and wavelet neural network (WNN) in terms of normalized root mean square error (NRMSE). Based on experiments conducted, it is found that GMDH predicted reliability with least error compared to other techniques. Hence, GMDH can be used a sound alternative to the existing techniques for software reliability prediction.KeywordsSoftware reliability forecastingGroup method of Data handlingIntelligent Techniques

Literature review revealed that scour modeling using artificial intelligence (AI) lacks majorly in two aspects - one is the Input variable selection (IVS) and secondly, the relative ranking of scour models based on their performance. In this study, state-of-the-art AI algorithms, including artificial neural network (ANN), artificial neuro-fuzzy interface system (ANFIS), support vector machine (SVM), model tree (M5P), gene expression programming (GEP), and group method of data handling (GMDH) were employed to compute the Local Scour Depth (LSD) and to address identified lacunas. A total of 378 data set consisting of laboratory and field data was used for modeling. Evaluation criteria such as the index of agreement (IOA), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), Skill Score (SS), Correlation (Correl), and Taylor diagram were employed to check the goodness-of-fit of the proposed models. IVS was performed using partial mutual information (PMI). The findings of the study showed that velocity (V), the diameter of the pier (b), Reynolds pier number (Rp), and particle densimetric Froude number (Frd) were highly sensitive parameters to the scour. Quantitative and qualitative results indicated that SVM performed better with RMSE (0.06), MAPE (0.04) and SS (0.9). Tayler diagram also confirmed the above findings.

Summary Many methods have been developed to determine the solution gas/oil ratio (Rs), starting with experiments, followed by empirical correlations establishments, and recently with machine learning applications receiving much interest due to their ability to produce precise results compared with empirical correlations. In this paper, the group method of data handling (GMDH) and the enhanced GMDH based on discrete differential evolution (GMDH-DDE) are used for the first time to estimate the Rs and to provide a correlation to the laboratory measured Rs from bubblepoint pressure (Pb), oil API gravity (API), gas-specific gravity (γg), and reservoir temperature (T) without crude oil properties. These two methods are compared with backpropagation neural networks (BPNN). The reason for using the hybrid GMDH (GMDH-DDE) is to overcome the drawbacks of the GMDH, such as the method used to calculate neuron weights (i.e., quadratic polynomial transfer function), which seems to have inaccuracies. Also, in selecting model inputs, the GMDH tends to choose the most appropriate inputs for the model; however, the selection criteria are not straightforward and may affect the final results. Furthermore, the GMDH has a multicollinearity problem, affecting model coefficient stability and overfitting problems, etc. A total of 420 data sets from the Mpyo oil field were used, with 70% used for training and 30% used for testing. According to the findings, the GMDH-DDE outperformed both the GMDH and BPNN. In comparison with the GMDH and BPNN, the GMDH-DDE has a higher correlation coefficient (R), lower root-mean-square error (RMSE), and lower mean absolute error (MAE). During training, R, RMSE, and MAE were 0.9849, 0.090, and 0.010, respectively, and during testing, R = 0.9603, RMSE = 0.290, and MAE = 0.017. The second-best technique (GMDH) produces R, RMSE, and MAE values of 0.9611, 0.122, and 0.032 in training, and R = 0.9438, RMSE = 0.349, and MAE = 0.055 in testing. Furthermore, the GMDH-DDE used less computational time (1.32 seconds) compared with the GMDH (2.01 seconds) and BPNN (4.96 seconds), proving that the GMDH-DDE has accurate and fast convergence compared with the GMDH and BPNN. These findings show that the GMDH-DDE and GMDH can be adopted as alternative methods for predicting the Rs.

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 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.

The study uses the comparison of Group Method of Data Handling (GMDH)-type neural network algorithm with Vector error correction model to predict the value of FDI on the basis of accuracy of prediction and to model the determinants of FDI in Pakistan. It was estimated in the times series data during the time period 1971-2013 and the time period 2014-2018 has been utilized to predict FDI. The Augmented Dickey-Fuller (ADF) test suggests that all variables data are of I (1) and Johansen co-integration test proved nexus of the variables FDI and its determinants in the long run. Nonetheless, the error correction-term of the vector error correction model (VECM) indicates that around 3 % of cumulative disequilibrium was expunged in every year in Pakistan. This paper compares two new methods Group Method of Data Handling (GMDH) Neural Network Algorithm and Vector Error Correction Model (VECM) in an attempt to obtain the more useful one based on accuracy of analysis when making predictions. Whereas, the effectiveness of VECM is then compared with a non parametric GMDH-like type neural network. An evaluation of forecasting model accuracies in terms of FDI was done using Root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and Diebold Mariano (DM) test. The empirical outcomes are a clear indication that Group Method of Data Handling GMDH-type of neural network algorithm did very well in comparison with the vector error correction model based on forecasting.

PurposeThe purpose of this paper is to use Group Method of Data Handling (GMDH)-type artificial neural network to model the affecting factors of housing price in Isfahan city housing market.Design/methodology/approachThis paper presents an accurate model based on GMDH approach to describing connection between housing price and considered affecting factors in case study of Isfahan city based on trusted data that have been collected from 1995 to 2017 for every six months. The accuracy of the model has been evaluated by mean absolute percentage error (MAPE), root mean square error (RMSE) and mean absolute error (MAE) in this case.FindingsDue to the obtained value of MAPE, RMSE and MAE and also their interpretation, accuracy of modelling the factors affecting housing price in Isfahan city housing market using GMDH-type artificial neural network that has been conducted in this paper, is acceptable.Research limitations/implicationsDue to limitation of reliable data availability about affecting factors, selected period is from 1995 to 2017. Accessing to longer periods of reliable data can improve the accuracy of the model.Originality/valueThe key point of this research is reaching to a mathematical formula that accurately shows the relationships between housing price in Isfahan city and effective factors. The simplified formula can help users to use it easily for analysing and describing the status of housing market in Isfahan city of Iran.

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.

The potential of several predictive models including multiple model-artificial neural network (MM-ANN), multivariate adaptive regression spline (MARS), support vector machine (SVM), multi-gene genetic programming (MGGP), and ‘M5Tree’ were assessed to simulate the pan evaporation in monthly scale (EPm) at two stations (e.g. Ranichauri and Pantnagar) in India. Monthly climatological information were used for simulating the pan evaporation. The utmost effective input-variables for the MM-ANN, MGGP, MARS, SVM, and M5Tree were determined using the Gamma test (GT). The predictive models were compared to each other using several statistical criteria (e.g. mean absolute percentage error (MAPE), Willmott's Index of agreement (WI), root mean squared error (RMSE), Nash-Sutcliffe efficiency (NSE), and Legate and McCabe’s Index (LM)) and visual inspection. The results showed that the MM-ANN-1 and MGGP-1 models (NSE, WI, LM, RMSE, MAPE are 0.954, 0.988, 0.801, 0.536 mm/month, 9.988% at Pantnagar station, and 0.911, 0.975, 0.724, and 0.364 mm/month, 12.297% at Ranichauri station, respectively) with input variables equal to six were more successful than the other techniques during testing period to simulate the monthly pan evaporation at both Ranichauri and Pantnagar stations. Thus, the results of proposed MM-ANN-1 and MGGP-1 models will help to the local stakeholders in terms of water resources management.

Risk and reliability are important aspects of geotechnical structures. Soil is highly variable. Pile tests are extremely expensive and labor-intensive. The paper proposes a reliable method to predict the bearing capacity of the pile using AI-based models like Multivariate Adaptive Regression Splines (MARS), Group method of data handling (GMDH) and Genetic programming (GP) using data of pile dynamic tests conducted on various sites in Indonesia. The performance of the model is ascertained using various performance parameters and are compared among themselves using Rank analysis and Taylor diagrams. The reliability indices of each model are calculated and compared. GP and MARS are concluded as robust models for estimating bearing capacity while performance of GMDH is not exciting.KeywordsReliabilityPilesMARSGMDHGP

BackgroundFractional vegetation coverage (FVC) is a crucial parameter in determining vegetation structure. Automatic measurement of FVC using digital images captured by mobile smart devices is a potential direction for future research on field survey methods in plant ecology, and this algorithm is crucial for accurate FVC measurement. However, there is a lack of insight into the influence of illumination on the accuracy of FVC measurements. Therefore, the main objective of this research is to assess the adaptiveness and performance of different algorithms under varying light conditions for FVC measurements and to deepen our understanding of the influence of illumination on FVC measurement.Methods and resultsBased on a literature survey, we selected four algorithms that have been reported to have high accuracy in automatic FVC measurements. The first algorithm (Fun01) identifies green plants based on the combination of R/G, B/G, and ExG (R, G, and B are the actual pixel digital numbers from the images based on each RGB channel, ExG is the abbreviation of the Excess Green index), the second algorithm (Fun02) is a decision tree that uses color properties to discriminate plants from the background, the third algorithm (Fun03) uses ExG-ExR (ExR is the abbreviation of the Excess Red index) to recognize plants in the image, and the fourth algorithm (Fun04) uses ExG and O{text{tsu}} to separate the plants from the background. Otsu is an algorithm used to determine a threshold to transform the image into a binary image for the vegetation and background. We measured the FVC of several surveyed quadrats using these four algorithms under three scenarios, namely overcast sky, solar forenoon, and solar noon. FVC values obtained using the Photoshop-assisted manual identification method were used as a reference to assess the accuracy of the four algorithms selected. Results indicate that under the overcast sky scenario, Fun01 was more accurate than the other algorithms and the MAPE (mean absolute percentage error), BIAS, relBIAS (relative BIAS), RMSE (root mean square error), and relRMSE (relative RMSE) are 8.68%, 1.3, 3.97, 3.13, and 12.33%, respectively. Under the scenario of the solar forenoon, Fun02 (decision tree) was more accurate than other algorithms, and the MAPE, BIAS, relBIAS, RMSE, and relRMSE are 22.70%, − 2.86, − 7.70, 5.00, and 41.23%. Under the solar noon scenario, Fun02 was also more accurate than the other algorithms, and the MAPE, BIAS, relBIAS, RMSE, and relRMSE are 20.60%, − 6.39, − 20.67, 7.30, and 24.49%, respectively.ConclusionsGiven that each algorithm has its own optimal application scenario, among the four algorithms selected, Fun01 (the combination of R/G, B/G, and ExG) can be recommended for measuring FVC on cloudy days. Fun02 (decision tree) is more suitable for measuring the FVC on sunny days. However, it considerably underestimates the FVC in most cases. We expect the findings of this study to serve as a useful reference for automatic vegetation cover measurements.

Background: Myocardial perfusion scintigraphy (MPS) is an important tool for evaluating ischemia in diabetic populations. However, applications of advanced predictive models like multivariate adaptive regression splines (MARS) to estimate summed stress scores (SSS) are lacking. Methods: In this study, 1028 diabetic women undergoing Thallium-201 MPS were analyzed. The dataset was split into training (80%) and testing (20%) subsets. MARS and multiple linear regression (MLR) models were constructed to predict SSS, and their performance was evaluated using root mean square error (RMSE), relative absolute error (RAE), root relative squared error (RRSE), Mean Absolute Percentage Error (MAPE), and Symmetric Mean Absolute Percentage Error (SMAPE). Results: On the testing dataset, the MARS model outperformed the MLR model across all metrics, with an RMSE of 3.25 compared to 3.89 for MLR, an RAE of 0.52 vs. 0.64, and an RRSE of 0.53 vs. 0.67. Similar trends were observed in MAPE (18.7% vs. 22.1%) and SMAPE (17.3% vs. 20.5%). Conclusions: The superior predictive accuracy of the MARS model suggests its potential to enhance non-invasive myocardial risk stratification in diabetic women.

Predicting discharge coefficient of triangular labyrinth weir using Support Vector Regression, Support Vector Regression-firefly, Response Surface Methodology and Principal Component Analysis

Knowledge of the stage-discharge rating curve is useful in designing and planning flood warnings; thus, developing a reliable stage-discharge rating curve is a fundamental and crucial component of water resource system engineering. Since the continuous measurement is often impossible, the stage-discharge relationship is generally used in natural streams to estimate discharge. This paper aims to optimize the rating curve using a generalized reduced gradient (GRG) solver and the test the accuracy and applicability of the hybridized linear regression (LR) with other machine learning techniques, namely, linear regression-random subspace (LR-RSS), linear regression-reduced error pruning tree (LR-REPTree), linear regression-support vector machine (LR-SVM) and linear regression-M5 pruned (LR-M5P) models. An application of these hybrid models was performed and test to modeling the Gaula Barrage stage-discharge problem. For this, 12-year historical stage-discharge data were collected and analyzed. The 12-year historical daily flow data (m3/s) and stage (m) from during the monsoon season, i.e., June to October only from 03/06/2007 to 31/10/2018, were used for discharge simulation. The best suitable combination of input variables for LR, LR-RSS, LR-REPTree, LR-SVM, and LR-M5P models was identified and decided using the gamma test. GRG-based rating curve equations were found to be as effective and more accurate as conventional rating curve equations. The outcomes from GRG, LR, LR-RSS, LR-REPTree, LR-SVM, and LR-M5P models were compared to observed values of daily discharge based on Nash Sutcliffe model efficiency coefficient (NSE), Willmott Index of Agreement (d), Kling-Gupta efficiency (KGE), mean absolute error (MAE), mean bias error (MBE), relative bias in percent (RE), root mean square error (RMSE) Pearson correlation coefficient (PCC) and coefficient of determination (R2). The LR-REPTree model (combination 1: NSE = 0.993, d = 0.998, KGE = 0.987, PCC(r) = 0.997, and R2 = 0.994 and minimum value of RMSE = 0.109, MAE = 0.041, MBE = −0.010 and RE = −0.1%; combination 2; NSE = 0.941, d = 0.984, KGE = 0. 923, PCC(r) = 0. 973, and R2 = 0. 947 and minimum value of RMSE = 0. 331, MAE = 0.143, MBE = −0.089 and RE = −0.9%) performed superior to the GRG, LR, LR-RSS, LR-SVM, and LR-M5P models in all input combinations during the testing period. It was also noticed that the performance of the alone LR and its hybrid models (i.e., LR-RSS, LR-REPTree, LR-SVM, and LR-M5P) was better than the conventional stage-discharge rating curve, including the GRG method.