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Because of the three-dimensional (3D) imaging scene’s sparsity, compressed sensing (CS) algorithms can be used for linear array synthetic aperture radar (LASAR) 3D sparse imaging. CS algorithms usually achieve high-quality sparse imaging at the expense of computational efficiency. To solve this problem, a fast Bayesian compressed sensing algorithm via relevance vector machine (FBCS–RVM) is proposed in this paper. The proposed method calculates the maximum marginal likelihood function under the framework of the RVM to obtain the optimal hyper-parameters; the scattering units corresponding to the non-zero optimal hyper-parameters are extracted as the target-areas in the imaging scene. Then, based on the target-areas, we simplify the measurement matrix and conduct sparse imaging. In addition, under low signal to noise ratio (SNR), low sampling rate, or high sparsity, the target-areas cannot always be extracted accurately, which probably contain several elements whose scattering coefficients are too small and closer to 0 compared to other elements. Those elements probably make the diagonal matrix singular and irreversible; the scattering coefficients cannot be estimated correctly. To solve this problem, the inverse matrix of the singular matrix is replaced with the generalized inverse matrix obtained by the truncated singular value decomposition (TSVD) algorithm to estimate the scattering coefficients correctly. Based on the rank of the singular matrix, those elements with small scattering coefficients are extracted and eliminated to obtain more accurate target-areas. Both simulation and experimental results show that the proposed method can improve the computational efficiency and imaging quality of LASAR 3D imaging compared with the state-of-the-art CS-based methods.

Discovering governing physical laws from noisy data is a grand challenge in many science and engineering research areas. We present a new approach to data-driven discovery of ordinary differential equations (ODEs) and partial differential equations (PDEs), in explicit or implicit form. We demonstrate our approach on a wide range of problems, including shallow water equations and Navier–Stokes equations. The key idea is to select candidate terms for the underlying equations using dimensional analysis, and to approximate the weights of the terms with error bars using our threshold sparse Bayesian regression. This new algorithm employs Bayesian inference to tune the hyperparameters automatically. Our approach is effective, robust and able to quantify uncertainties by providing an error bar for each discovered candidate equation. The effectiveness of our algorithm is demonstrated through a collection of classical ODEs and PDEs. Numerical experiments demonstrate the robustness of our algorithm with respect to noisy data and its ability to discover various candidate equations with error bars that represent the quantified uncertainties. Detailed comparisons with the sequential threshold least-squares algorithm and the lasso algorithm are studied from noisy time-series measurements and indicate that the proposed method provides more robust and accurate results. In addition, the data-driven prediction of dynamics with error bars using discovered governing physical laws is more accurate and robust than classical polynomial regressions.

This study investigates the feasibility of a relevance vector machine tuned with improved Manta-Ray foraging optimization (RVM-IMRFO) in predicting monthly pan evaporation using limited climatic input data (e.g. temperature). The accuracy of the RVM-IMRFO was evaluated by comparing it with RVM tuned by gray wolf optimization, RVM tuned with a whale optimization algorithm, and RVM tuned with Manta Ray foraging optimization concerning root mean square errors (RMSE), mean absolute errors (MAE), determination coefficient (R 2 ) and Nash-Sutcliffe Efficiency (NSE) and new graphical inspection methods. The models were assessed using data acquired from two stations in China and data were divided into three equal parts. The models were tested using each data set. The application outcomes revealed that the proposed algorithm considerably improved the accuracy of a single RVM in monthly pan evaporation prediction by an average improvement in RMSE, MAE, R 2 , and NSE as 27.65%, 27.53%, 8.40% and 8.63%, respectively. It is also found that the proposed algorithm showed significant dominance over others models with respect to improvement in overall mean values of RMSE, MAE, R 2 , and NSE statistics from 34.7-38.2 to 18.2-19.5, 36.2-36.4 to 19.1-18.5, 12.5-13.8 to 3.6-3.7, and 12.4-14.6 to 3.6-3.9%, for both climatic stations, respectively. Importing extraterrestrial radiation and periodicity component (month number of the data) into the model inputs improved the prediction accuracy of the implemented models. The outcomes revealed that the RVM-IMRFO performed superior to the other methods in predicting monthly pan evaporation using only temperature data which is essential, especially in developing countries where other climatic data are missing or unavailable. The RVM model was also compared with standard multi-layer perceptron neural networks (MLPNN) and found that the first acts better than the latter in monthly pan evaporation prediction.

The ground vibration caused by rock blasting is an extremely hazardous outcome of the blasting operation. Blasting activity has detrimental effects on both the ecology and the human population living in proximity to the area. Evaluating the magnitude of blasting vibrations requires careful evaluation of the peak particle velocity (PPV) as a fundamental and essential parameter for quantifying vibration velocity. Therefore, this study employs models using the relevance vector machine (RVM) approach for predicting the PPV resulting from quarry blasting. This investigation utilized the conventional and optimized RVM models for the first time in ground vibration prediction. This work compares thirty-three RVM models to choose the most efficient performance model. The following conclusions have been mapped from the outcomes of the several analyses. The performance evaluation of each RVM model demonstrates each model achieved a performance of more than 0.85 during the testing phase, there was a strong correlation observed between the actual ground vibrations and the predicted ones. The analysis of performance metrics (RMSE = 21.2999 mm/s, 16.2272 mm/s, R = 0.9175, PI = 1.59, IOA = 0.8239, IOS = 0.2541), score analysis (= 93), REC curve (= 6.85E−03, close to the actual, i.e., 0), curve fitting (= 1.05 close to best fit, i.e., 1), AD test (= 11.607 close to the actual, i.e., 9.790), Wilcoxon test (= 95%), Uncertainty analysis (WCB = 0.0134), and computational cost (= 0.0180) demonstrate that PSO_DRVM model MD29 outperformed better than other RVM models in the testing phase. This study will help mining and civil engineers and blasting experts to select the best kernel function and its hyperparameters in estimating ground vibration during rock blasting project. In the context of the mining and civil industry, the application of this study offers significant potential for enhancing safety protocols and optimizing operational efficiency.

Modeling potential evapotranspiration (ET0) is an important issue for water resources planning and management projects involving droughts and flood hazards. Evapotranspiration, one of the main components of the hydrological cycle, is highly effective in drought monitoring. This study investigates the efficiency of two machine-learning methods, random vector functional link (RVFL) and relevance vector machine (RVM), improved with new metaheuristic algorithms, quantum-based avian navigation optimizer algorithm (QANA), and artificial hummingbird algorithm (AHA) in modeling ET0 using limited climatic data, minimum temperature, maximum temperature, and extraterrestrial radiation. The outcomes of the hybrid RVFL-AHA, RVFL-QANA, RVM-AHA, and RVM-QANA models compared with single RVFL and RVM models. Various input combinations and three data split scenarios were employed. The results revealed that the AHA and QANA considerably improved the efficiency of RVFL and RVM methods in modeling ET0. Considering the periodicity component and extraterrestrial radiation as inputs improved the prediction accuracy of the applied methods.

Cancer in Liver is the one among all other types of cancer which causes death of carcinogenic victim people throughout the world. GLOBOCAN12 was an initiative for simultaneously generating the expected dominance and mortality incidence that raised out of the cancer over the whole globe. It reported that about 782,000 new cases in the population were reported to have liver cancer, in which around 745,000 people loosed their lives from these kind of diseases worldwide. Some traditional algorithms were found to be widely used in liver segmentation processes. However, it had some limitations such as less effective outcomes in terms of proceeded segmentation operations and also it was very difficult to apply tumor segmentation especially for larger severity intensities of tumor region, which usually gave rise to high computational cost. It was also required to improve the performance of those algorithms for diagnosing even the tiniest parts of liver along with the improvisation needed when there was misclassification of the tumors near the liver boundaries. Along this way as an improvising methodology, an efficient method is proposed in order to overcome all the above discussed issues one by one through our work. The novelty/major contribution of this proposed method is being contributed in three stages namely, preprocessing, segmentation and classification. In preprocessing, the noises of image will be removed and then, the input image edge will be sharpened by using a frequency-based edge sharpening technique which aids in taking the pixels in the images into consideration for proceeding with the next operation of segmentation. The segmentation process gets the appropriated preprocessed images as input and the Outline Preservation Based Segmentation (OPBS) algorithm is used to segment the images in the segmentation phase. The algorithms involving features extraction were preferably deployed to extract the corresponding features from an image. So, the features present in the segmented image serves as the necessary information for the classification purposes. Next, the features were classified in the classification phase by using novel similarity search based hybrid classification technique. The Outline Preservation Based Segmentation and Search Based Hybrid Classification (OPBS-SSHC) used the 3D IR CAD dataset. It was used to analyze with various parameters such as accuracy, precision, recall, and F-measures. Volumetric Overlap Error (VOE), Jaccard, Dice, and Kappa will be determined later on to predict the errors in the segmentation process undertaken. The proposed method of OPBS-SSHC performance was found to be better than other classification techniques of Relevance Vector Machine (RVM), Probabilistic Neural Network (PNN), and Support Vector Machine (SVM), which were considered for comparison by taking the above metrics and coefficients as and when required throughout this extensive comparative study.

This research aims at proposing a new artificial intelligence approach (namely RVM-ICA) which is based on the Relevance Vector Machine (RVM) and the Imperialist Competitive Algorithm (ICA) optimization for landslide susceptibility modeling. A Geographic Information System (GIS) spatial database was generated from Lang Son city in Lang Son province (Vietnam). This GIS database includes a landslide inventory map and fourteen landslide conditioning factors. The suitability of these factors for landslide susceptibility modeling in the study area was verified by the Information Gain Ratio (IGR) technique. A landslide susceptibility prediction model based on RVM-ICA and the GIS database was established by training and prediction phases. The predictive capability of the new approach was evaluated by calculations of sensitivity, specificity, accuracy, and the area under the Receiver Operating Characteristic curve (AUC). In addition, to assess the applicability of the proposed model, two state-of-the-art soft computing techniques including the support vector machine (SVM) and logistic regression (LR) were used as benchmark methods. The results of this study show that RVM-ICA with AUC = 0.92 achieved a high goodness-of-fit based on both the training and testing datasets. The predictive capability of RVM-ICA outperformed those of SVM with AUC = 0.91 and LR with AUC = 0.87. The experimental results confirm that the newly proposed model is a very promising alternative to assist planners and decision makers in the task of managing landslide prone areas.

The observation data of dam displacement can reflect the dam’s actual service behavior intuitively. Therefore, the establishment of a precise data-driven model to realize accurate and reliable safety monitoring of dam deformation is necessary. This study proposes a novel probabilistic prediction approach for concrete dam displacement based on optimized relevance vector machine (ORVM). A practical optimization framework for parameters estimation using the parallel Jaya algorithm (PJA) is developed, and various simple kernel/multi-kernel functions of relevance vector machine (RVM) are tested to obtain the optimal selection. The proposed model is tested on radial displacement measurements of a concrete arch dam to mine the effect of hydrostatic, seasonal and irreversible time components on dam deformation. Four algorithms, including support vector regression (SVR), radial basis function neural network (RBF-NN), extreme learning machine (ELM) and the HST-based multiple linear regression (HST-MLR), are used for comparison with the ORVM model. The simulation results demonstrate that the proposed multi-kernel ORVM model has the best performance for predicting the displacement out of range of the used measurements dataset. Meanwhile, the ORVM model has the advantages of probabilistic output and can provide reasonable confidence interval (CI) for dam safety monitoring. This study lays the foundation for the application of RVM in the field of dam health monitoring.

This work introduces an optimal performance model for predicting the unconfined compressive strength (UCS) of lime-stabilized soil using the machine (ensemble tree (ET), Gaussian process regression (GPR), and decision tree (DT), support vector machine (SVM)), and hybrid (relevance vector machine (RVM)) learning computational techniques. The conventional (non-optimized) and hybrid (genetic (GA) and particle swarm algorithm optimized (PSO)) RVM models have been developed and compared with machine learning models. For the first time, UCS of virgin cohesive soil has been used as input variable to predict the UCS of lime-stabilized soil. A database of 371 results of lime-stabilized soil has been compiled from the literature and used to create training, testing, and validation databases. Furthermore, the multicollinearity levels for each input variable, i.e., lime content, UCS of cohesive soil, and curing period, have been determined as weak for the overall database. The performance of built-in models has been measured by three new index performance metrics: the a20-index, the index of scatter (IOS), and the index of agreement (IOA). This research concludes that the weak multicollinearity of input variables affects the performance of the non-optimized RVM models. Also, the ensemble tree has performed better than SVM, DT, and GPR because it consists of the number of trees. The overall performance comparison concludes that the PSO-optimized Laplacian kernel–based RVM model UCS16 outperformed all models with higher a20-index (testing = 67.30, validation = 55.95), IOA (testing = 0.8634, validation = 0.7795), and IOS (testing = 0.2799, validation = 0.3506) and has been recognized as the optimal performance model. ANOVA, Z , and Anderson-darling tests reject the null hypothesis for the present research. The lime content influences the prediction of UCS of lime-stabilized soil. The computational cost and external validation results show the robustness of model UCS16.

Many hydrologic phenomena and applications such as drought, flood, irrigation management and scheduling needs high resolution satellite soil moisture data at a local/regional scale. Downscaling is a very important process to convert a coarse domain satellite data to a finer spatial resolution. Three artificial intelligence techniques along with the generalized linear model (GLM) are used to improve the spatial resolution of Soil Moisture and Ocean Salinity (SMOS) derived soil moisture, which is currently available at a very coarse scale of ~40 Km. Artificial neural network (ANN), support vector machine, relevance vector machine and generalized linear models are chosen for this study to integrate the Moderate Resolution Imaging Spectroradiometer (MODIS) Land Surface Temperature (LST) with the SMOS derived soil moisture. Soil moisture deficit (SMD) derived from a hydrological model called PDM (Probability Distribution Model) is used for the downscaling performance evaluation. The statistical evaluation has also been made with the day-time and night-time MODIS LST differences with the mean day and night-time PDM SMD data for the selection of effective MODIS products. The accuracy and robustness of all the downscaling algorithms are discussed in terms of their assumptions and applicability. The statistical performance indices such as R 2 , %Bias and RMSE indicates that the ANN ( R 2   = 0.751 , %Bias = −0.628 and RMSE = 0.011 ), RVM ( R 2   = 0.691 , %Bias = 1.009 and RMSE = 0.013 ), SVM ( R 2   = 0.698 , %Bias = 2.370 and RMSE = 0.013 ) and GLM ( R 2   = 0.698 , %Bias = 1.009 and RMSE = 0.013 ) algorithms on the whole are relatively more skillful to downscale the variability of the soil moisture in comparison to the non-downscaled data ( R 2   = 0.418 and RMSE = 0.017 ) with the outperformance of ANN algorithm. The other attempts related to growing and non-growing seasons have been used in this study to reveal that season based downscaling is even better than continuous time series with fairly high performance statistics.