Radial Basis Function Network Method Research Articles

A modified radial basis function network integrating Mahalanobis distance and LASSO for soil mapping

In recent decades, machine learning (ML) has replaced geostatistics in soil mapping to overcome the lack of regional soil data. The radial basis function network (RBFN) is a classical ML method for spatial interpolation, but it has limitations in terms of anisotropy and flexibility in soil science. To overcome these shortcomings, we proposed a new model called RBFN-S by incorporating the Mahalanobis distance and the least absolute shrinkage and selection operator (LASSO) into the conventional RFBN, which are new developments in spatial interpolation. One simulated and two real cases were used for validation and investigation. The results showed that RFBN-S performed well in interpolating both Gaussian fields and non-stationary and non-Gaussian fields. In addition, the two introduced elements also played a significant role in improving the interpolation. The comparisons between RBFN-S and conventional RBFN, LASSO, and geostatistical methods demonstrate the advantage of RBFN-S in capturing correlations between soil properties and their location. Further development of the RBFN-S can be performed from the perspective of uncertainty quantification, optimization of meta-parameter tuning, and incorporation of environmental covariates.

Predicting Auger Energy Consumption for Olive Orchards Using the Artificial Neural Networks

The present work aims to study the development and application of Radial Basis Function (RBF) networks for predicting auger energy consumption based on input energy. The study utilized RBF networks and explored the input energy with treatments 2 (Soil moisture content), 2 (Rotary speeds), 2 (Hole depths) and 4 (Replication) based on field operations. As indicated by the results, energy input differed between the treatments but was not significant. The highest input value in transaction soil moisture content was 14.75 %, rotary speeds of 235 rpm, and hole depths of 40 cm. In comparison, the lower input energy at transaction soil moisture content was 7.9%, rotary speeds of 235 rpm, and hole depths of 20 cm. Input energy in treatment (14.75 %, 235 rpm, and 40 cm) and treatment (7.9 %,235 rpm, and 20 cm) were 100.204 and 57.135 MJ. ha-1, respectively. The highest input energy shares were recorded for diesel fuel at all treatments. Furthermore, the RBF network with one hidden layer had good convergence. The output results showed 10 and five hidden neurons in a hidden layer with high accuracy for treatment (14.75 %, 235 rpm, and 40 cm) and treatment (7.9%, 235 rpm, and 20 cm). In the treatment (14.75 %, 235 rpm, and 40 cm), the MSE for the training and testing sets was 0.0001 % and 0.01 % for data points with Ordinary RBF (ORBF type). The performance of the 3-10-1 architecture was better than other architectures. Finally, this research concluded that the RBF network method can forecast the input energy and energy expenditures related to the types of treatments.

Analytical Assessment of the Structural Behavior of a Specific Composite Floor System at Elevated Temperatures Using a Newly Developed Hybrid Intelligence Method

The aim of this paper is to study the performance of a composite floor system at different heat stages using artificial intelligence to derive a sustainable design and to select the most critical factors for a sustainable floor system at elevated temperatures. In a composite floor system, load bearing is due to composite action between steel and concrete materials which is achieved by using shear connectors. Although shear connectors play an important role in the performance of a composite floor system by transferring shear force from the concrete to the steel profile, if the composite floor system is exposed to high temperature conditions excessive deformations may reduce the shear-bearing capacity of the composite floor system. Therefore, in this paper, the slip response of angle shear connectors is evaluated by using artificial intelligence techniques to determine the performance of a composite floor system during high temperatures. Accordingly, authenticated experimental data on monotonic loading of a composite steel-concrete floor system in different heat stages were employed for analytical assessment. Moreover, an artificial neural network was developed with a fuzzy system (ANFIS) optimized by using a genetic algorithm (GA) and particle swarm optimization (PSO), namely the ANFIS-PSO-GA (ANPG) method. In addition, the results of the ANPG method were compared with those of an extreme learning machine (ELM) method and a radial basis function network (RBFN) method. The mechanical and geometrical properties of the shear connectors and the temperatures were included in the dataset. Based on the results, although the behavior of the composite floor system was accurately predicted by the three methods, the RBFN and ANPG methods represented the most accurate values for split-tensile load and slip prediction, respectively. Based on the numerical results, since the slip response had a rational relationship with the load and geometrical parameters, it was dramatically predictable. In addition, slip response and temperature were determined as the most critical factors affecting the shear-bearing capacity of the composite floor system at elevated temperatures.

Groundwater contamination sources identification based on the Long-Short Term Memory network

When simulation–optimization (S/O) is used for groundwater contamination source identification (GCSI), to reduce the calculation load and time generated by calling the simulation model, a surrogate model is often used instead of the simulation model. However, when the conversion relationship between the simulation model inputs and outputs is complex and the model is highly nonlinear, the commonly used approach of building a surrogate model may lose its advantage. This study use and check a deep learning method with the long-short term memory (LSTM) network which has great potential for characterizing the input–output conversion relationship of complex nonlinear numerical simulations, to a surrogate model of the simulation model. The accuracy of the surrogate model developed by the LSTM method was compared with that of commonly used surrogate models developed by the Kriging method, the radial basis function network method, and the kernel extreme learning machine method. The surrogate model with the highest accuracy was linked to the optimization model, and the optimization model was solved to identify the contamination source information. Results show that compared with the other three methods, the surrogate model constructed by the LSTM method had the best accuracy and generalization performance. LSTM is therefore an effective method of building a surrogate model. Linking the LSTM surrogate model to an optimization model and then solving the optimization model can save approximately 99% of the computing load and time otherwise required.

Diffuseness effect and radial basis function network for optimizing α decay calculations * *Supported by the National Natural Science Foundation of China (11947229, 11675223, 11675066), the China Postdoctoral Science Foundation (2019M663853), the Fundamental Research Funds for the Central Universities (lzujbky-2017-ot04) and Feitian Scholar Project of Gansu province

A radial basis function network (RBFN) approach is adopted for the first time to optimize the calculation of decay half-life in the generalized liquid drop model (GLDM), while concurrently incorporating the surface diffuseness effect. The calculations presented herein agree closely with the experimental half-lives for 68 superheavy nuclei (SHN), achieving a remarkable reduction of 40% in the root-mean-square (rms) deviations of half-lives. Furthermore, using the RBFN method, the half-lives for four SHN isotopes, 252-288Rf, 272-310Fl, 286-316119, and 292-318120, are predicted using the improved GLDM with the diffuseness correction and the decay energies from WS4 and FRDM as inputs. Therefore, we conclude that the diffuseness effect should be embodied in the proximity energy. Moreover, increased application of neural network methods in nuclear reaction studies is encouraged.

Numerical solution of a highly nonlinear and non-integrable equation using integrated radial basis function network method.

In this paper, we investigate a wide range of dynamical regimes produced by the nonlinearly excited phase (NEP) equation (a single sixth-order nonlinear partial differential equation) using a more advanced numerical method, namely, the integrated radial basis function network method. Previously, we obtained single-step spinning solutions of the equation using the Galerkin method. First, we verify the numerical solver through an exact solution of a forced version of the equation. Doing so, we compare the numerical results obtained for different space and time steps with the exact solution. Then, we apply the method to solve the NEP equation and reproduce the previously obtained spinning regimes. In the new series of numerical experiments, we find regimes in the form of spinning trains of steps/kinks comprising one, two, or three kinks. The evolution of the distance between the kinks is analyzed. Two different kinds of boundary conditions are considered: homogeneous and periodic. The dependence of the dynamics on the size of the domain is explored showing how larger domains accommodate multiple spinning fronts. We determine the critical domain size (bifurcation size) above which non-trivial settled regimes become possible. The initial condition determines the direction of motion of the kinks but not their sizes and velocities.

Lateral control strategy based on head movement responses for motion sickness mitigation in autonomous vehicle

Passengers are more susceptible to motion sickness (MS) than the drivers because during cornering, they tilt their heads according to lateral acceleration direction, while the drivers tilt their heads against it. During slalom driving, high lateral acceleration that resulted from inappropriate wheel’s turning will increase the severity level of MS as it contributes to a larger passenger’s head roll angle towards the lateral acceleration direction. Thus, for an autonomous vehicle, it is necessary to design a smooth lateral control to obtain appropriate wheel angle to prevent high lateral acceleration. This study proposes an inner-loop lateral control strategy which utilized head roll angle as the controlled variable to generate corrective wheel angle to reduce the lateral acceleration. Firstly, an estimation model of driver’s and passenger’s head roll angle is developed by radial basis function network method based on the correlation between lateral acceleration and occupant’s head roll angle. The driver’s and passenger’s models are considered as the reference and the controlled subject, respectively. Secondly, a fuzzy logic controller is adopted to generate corrective wheel angle based on the head roll angle responses. The reduction of the lateral acceleration caused by the corrective wheel angle minimized the passenger’s head roll angle and hence mitigated their MS level. Simulation results show 3.25% and 10.86% reduction of motion sickness incidence in a single lap and ten laps after the proposed control strategy is applied. It is expected that the proposed control strategy will contribute to the MS mitigation study in autonomous vehicle field.

Non-parametric machine learning methods for interpolation of spatially varying non-stationary and non-Gaussian geotechnical properties

Spatial interpolation has been frequently encountered in earth sciences and engineering. A reasonable appraisal of subsurface heterogeneity plays a significant role in planning, risk assessment and decision making for geotechnical practice. Geostatistics is commonly used to interpolate spatially varying properties at un-sampled locations from scatter measurements. However, successful application of classic geostatistical models requires prior characterization of spatial auto-correlation structures, which poses a great challenge for unexperienced engineers, particularly when only limited measurements are available. Data-driven machine learning methods, such as radial basis function network (RBFN), require minimal human intervention and provide effective alternatives for spatial interpolation of non-stationary and non-Gaussian data, particularly when measurements are sparse. Conventional RBFN, however, is direction independent (i.e. isotropic) and cannot quantify prediction uncertainty in spatial interpolation. In this study, an ensemble RBFN method is proposed that not only allows geotechnical anisotropy to be properly incorporated, but also quantifies uncertainty in spatial interpolation. The proposed method is illustrated using numerical examples of cone penetration test (CPT) data, which involve interpolation of a 2D CPT cross-section from limited continuous 1D CPT soundings in the vertical direction. In addition, a comparative study is performed to benchmark the proposed ensemble RBFN with two other non-parametric data-driven approaches, namely, Multiple Point Statistics (MPS) and Bayesian Compressive Sensing (BCS). The results reveal that the proposed ensemble RBFN provides a better estimation of spatial patterns and associated prediction uncertainty at un-sampled locations when a reasonable amount of data is available as input. Moreover, the prediction accuracy of all the three methods improves as the number of measurements increases, and vice versa. It is also found that BCS prediction is less sensitive to the number of measurement data and outperforms RBFN and MPS when only limited point observations are available.

RBFN 과 강화학습을 활용한 관성항법장치의 자이로 바이어스 추정 기법

In this paper, a new gyro bias estimation method is proposed by using reinforcement learning and RBFN (Radial Basis Function Network). A set of lattices for better navigation performance is investigated using reinforcement learning. A function of estimating gyro bias is constructed by connecting the set lattices using RBFN. The performance of the proposed method is evaluated by comparing with various methods such as 3rd order function method, 3rd order function with a temperature rate method (TRM), classic RBFN method, and MLR (Multiple Linear Regression) method. The results of experiment show that the proposed gyro bias estimation method has better navigation performance than other methods.

Parameters and Branching Auto-Pulses in a Fluid Channel with Active Walls

We present numerical solutions of the semi-phenomenological model of self-propagating fluid pulses (auto-pulses) in the channel branching into two thinner channels, which simulates branching of a hypothetical artificial artery. The model is based on the lubrication theory coupled with elasticity and has the form of a single nonlinear partial differential equation with respect to the displacement of the elastic wall as a function of the distance along the channel and time. The equation is solved numerically using the 1D integrated radial basis function network method. Using homogeneous boundary conditions on the edges of space domain and continuity condition at the branching point, we obtained and analyzed solutions in the form of auto-pulses penetrating through the branching point from the thick channel into the thin channels. We evaluated magnitudes of the phenomenological coefficients responsible for the active motion of the walls in the model.

Characterization of the displacement response in chromatic confocal microscopy with a hybrid radial basis function network.

Characterization of the displacement response is critical for accurate chromatic confocal measurement. Current characterization methods usually provide a linear or polynomial relationship between the extracted peak wavelengths of the spectral signal and displacement. However, these methods are susceptible to errors in the peak extraction algorithms and errors in the selected model. In this paper, we propose a hybrid radial basis function network method to characterise the displacement response. With this method, the peak wavelength of the spectral signal is firstly extracted with a state-of-art peak extraction algorithm, following which, a higher-accuracy chromatic dispersion model is applied to determine the displacement-wavelength relationship. Lastly, a radial basis function network is optimized to provide a mapping between the spectral signals and the residual fitting errors of the chromatic dispersion model. Using experimental tests, we show that the hybrid radial basis function network method significantly improves the measurement accuracy, when compared to the existing characterizing methods.

Learning Solutions for Electromagnetic Problems Using RBF Network-Based FE-LSSVM

Solutions to most electromagnetic problems use numerical methods, such as the finite element method (FEM), element free method (EFM), and soft computing method. To decrease the computational complexities of these methods, this paper presents an approach for solving electromagnetic problems, called radial basis function (RBF) network-based finite element least square support vector machine (FE-LSSVM). First, the expansion of approximate solutions by the proposed method uses the same structure as the RBF network method. Second, governing equations of electromagnetic problems are transformed to weak integral forms and variational formulations of FEM. Finally, Dirichlet boundary conditions are handled in the LS-SVM framework, which are considered as constraints of an optimization problem. By the Lagrange multiplier method, the quadratic programming problem can be transformed to a problem requiring the solution of a system of equations. The advantages of the proposed method are to directly satisfy the natural boundary conditions of the electromagnetic equations and remarkably improve the calculation accuracy. To verify the efficiency of the method, four categories of electromagnetic problems are investigated by using the proposed method. An analytical method and FEM are also carried out as comparisons to prove the advantages of the method proposed in this paper.

Experimental investigation and radial basis function network modeling of direct evaporative cooling systems

Radial basis function network method is used for modeling a direct evaporative cooling system. Air dry exit temperature, air pressure drop across the cooler and cooler efficiency are predicted using these models. The inputs are pad thickness, air inlet speed, air dry inlet temperature, relative humidity at the inlet and feed water temperature. The data for the models are taken from the experiments performed specifically for this purpose. Model validation is performed using twofold cross validation method. A grid search is used to determine optimal network parameters, such as, optimum number of radial basis elements and spread parameter. Validated models are tested against ordinary least squares models for the output variables. The results indicate that it is feasible to apply radial basis function networks to model direct evaporative coolers.

Reconstruction of Daily Sea Surface Temperature Based on Radial Basis Function Networks

A radial basis function network (RBFN) method is proposed to reconstruct daily Sea surface temperatures (SSTs) with limited SST samples. For the purpose of evaluating the SSTs using this method, non-biased SST samples in the Pacific Ocean (10°N–30°N, 115°E–135°E) are selected when the tropical storm Hagibis arrived in June 2014, and these SST samples are obtained from the Reynolds optimum interpolation (OI) v2 daily 0.25° SST (OISST) products according to the distribution of AVHRR L2p SST and in-situ SST data. Furthermore, an improved nearest neighbor cluster (INNC) algorithm is designed to search for the optimal hidden knots for RBFNs from both the SST samples and the background fields. Then, the reconstructed SSTs from the RBFN method are compared with the results from the OI method. The statistical results show that the RBFN method has a better performance of reconstructing SST than the OI method in the study, and that the average RMSE is 0.48 °C for the RBFN method, which is quite smaller than the value of 0.69 °C for the OI method. Additionally, the RBFN methods with different basis functions and clustering algorithms are tested, and we discover that the INNC algorithm with multi-quadric function is quite suitable for the RBFN method to reconstruct SSTs when the SST samples are sparsely distributed.

New radial basis function network method based on decision trees to predict flow variables in a curved channel

Open channel bends have fascinated engineers and scientists for decades while providing water for domestic, irrigation and industrial consumption. The presence of curvature in a channel impacts the flow pattern, velocity and water surface profile. Simulating flow variables such as velocity and water surface depth is one of the most important matters in the design and application of open channel bends. This study investigates a new neural network method using the radial basis function (RBF) based on decision trees (DT-RBF) to predict velocity and free-surface water profiles in a 90° open channel bend. In this study, 506 flow depth and 520 depth-averaged velocity field data obtained at 5 different discharges (5, 7.8, 13.6, 19.1 and 25.3 l/s) in a 90° sharp bend were used for training and testing purposes. The obtained results showed that the proposed DT-RBF models were more accurate than RBF models in estimating flow depth and depth-averaged velocity in the bend. The RBF root-mean-square error (RMSE), mean absolute error (MAE) and relative error (δ) were reduced by 20, 24 and 23.5%, respectively, when using the hybrid DT-RBF model to estimate the depth-averaged velocity. For water surface prediction, the RMSE, MAE and δ decreased by 33, 27.5 and 37%, respectively, when using the proposed DT-RBF hybrid model. For the longitudinal profiles of water surface profile prediction at the outer edge, MAE (0.018) improved to MAE (0.0084) with DT-RBF. It was found that the hybrid decision tree-based method significantly improved RBF neural network performance in forecasting the velocity and free-surface water profiles in a 90° open channel sharp bend.

Numerical solution for the fluid flow between active elastic walls

We analyse a model of the fluid flow between elastic walls simulating arteries actively interacting with the blood. The lubrication theory for the flow is coupled with the pressure and shear stress from the walls. The resulting nonlinear partial differential equation describes the displacement of the walls as a function of the distance along the flow and time. The equation is solved numerically using the one-dimensional integrated radial basis function network method. A solution in the form of a self-sustained train of pulses is obtained. Numerical experiments demonstrate the process of formation of the train from randomly chosen initial conditions. Dependence of the pulses on the boundary conditions is explored. References S. J. Sherwin, L. Formaggia, J. Peiro and V. Franke. Computational modelling of 1D blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system. Int. J. Numer. Meth. Fluids, 43:673–700, 2003. doi:10.1002/fld.543 C. Kleinstreuer. Biofluid Dynamics. Taylor and Francis, 2006. M. S. Olufsen, C. S. Peskin, W. Y. Kim, E. M. Pedersen, A. Nadim and J. Larsen. Numerical simulation and experimental validation of blood flow in arteries with structured-tree outflow conditions. Ann. Biomed. Eng., 28:1281–1299, 2000. doi:10.1114/1.1326031 K. S. Matthys, J. Alastruey, J. Peiro, A. W. Khir, P. Segers, P. R. Verdonck, K. H. Parker and S. J. Sherwin. Pulse wave propagation in a model human arterial network: Assessment of 1-D numerical simulations against in vitro measurements. J. Biomech., 40:3476–3486, 2007. doi:10.1016/j.jbiomech.2007.05.027 A. J. Roberts. A One-dimensional Introduction to Continuum Mechanics. World Scientific. Singapore, 1994. doi:10.1142/2496 D. V. Strunin, Fluid flow between active elastic plates. ANZIAM J., 50:C871–C883, 2009. doi:10.21914/anziamj.v50i0.1452 D. V. Strunin, Autosoliton model of the spinning fronts of reaction. IMA J. Appl. Math., 63:163–177, 1999. doi:10.1093/imamat/63.2.163 R. Huang and Z. Suo. Wrinkling of a compressed elastic film on a viscous layer. J. Appl. Phys., 91:1135–1142, 2002. doi:10.1063/1.1427407 J. King. The isolation oxidation of silicon: The reaction-controlled case. SIAM J. Appl. Math. 49:1064–1080, 1989. doi:10.1137/0149064 D. Ngo-Cong, N. Mai-Duy, W. Karunasena and T. Tran-Cong. Local moving least square-one-dimensional integrated radial basis function networks technique for incompressible viscous flows. Int. J. Numer. Meth. Fluids, 70:1443–1474, 2012. doi:10.1002/fld.3640 P. Le, N. Mai-Duy, T. Tran-Cong and G. Baker. A meshless modeling of dynamic strain localization in quasi-brittle materials using radial basis function networks, CMES–Comp. Model. Eng., 25:43–66, 2008. doi:10.3970/cmes.2008.025.043 N. Mai-Duy and T. Tran-Cong. Numerical solution of differential equations using multiquadric radial basis function networks, Neural Networks, 14:185–199, 2001. doi:10.1016/S0893-6080(00)00095-2

A BLOCK BY BLOCK METHOD FOR SOLVING SYSTEM OF VOLTERRA INTEGRAL EQUATIONS WITH CONTINUOUS AND ABEL KERNELS

Abstract The aim of the present paper is to introduce a block by block method for solving system of nonlinear Volterra integral equations with continuous kernels and system of Abel integral equations. We prove convergence of the method and show that its convergence order is at least six. To illustrate performance of the method, numerical experiments are presented and they are compared with HPM (Homotopy Perturbation Method) and RBFN (Radial Basis Function Network) method. The given results demonstrate remarkable ability of the proposed method.

Incompressible smoothed particle hydrodynamics-moving IRBFN method for viscous flow problems

We propose a novel numerical approach based on incompressible smoothed particle hydrodynamics and moving integrated radial basis function networks method, namely ISPH-MIRBFN, for solving incompressible viscous flow problems. In the ISPH method, the pressure is acquired from solving Poisson equation. In the present approach, the pressure Poisson equation is solved on a set of MIRBFN nodal points and the obtained results are then transferred to the SPH particles. The performance of the present method is investigated through several numerical examples including spin-down vortex, flows in a lid-driven closed-cavity and a lid-driven open-cavity with a prescribed bottom wall motion. Numerical results show that the proposed method reduces the spurious pressure fluctuations, yields a smoother pressure-field solution and maintains the computational efficiency when compared to the ISPH.

Higher-order approximation of contaminant transport equation for turbulent channel flows based on centre manifolds and its numerical solution

• We accurately reduce the 2D contaminant transport equation to its 1D approximation. • The analytical derivation is based on the centre manifold theory. • Two types of the velocity profile are considered: logarithmic and power profiles. • We develop a high-order numerical approximation for solving high-order PDEs. • The comparison of the 1D and 2D models shows good agreement. The contaminant transport process governed by the advection–diffusion equation plays an important role in modelling industrial and environmental flows. In this article, our aim is to accurately reduce the 2-D advection–diffusion equation governing the dispersion of a contaminant in a turbulent open channel flow to its 1-D approximation. The 1-D model helps to quickly estimate the horizontal size of contaminant clouds based on the values of the model coefficients. We derive these coefficients analytically and investigate numerically the model convergence. The derivation is based on the centre manifold theory to obtain successively more accurate approximations in a consistent manner. Two types of the average velocity profile are considered: the classical logarithmic profile and the power profile. We further develop the one-dimensional integrated radial basis function network method as a numerical approach to obtain the numerical solutions to both the original 2-D equation and the approximate 1-D equations. We compare the solutions of the original models with their centre-manifold approximations at very large Reynolds numbers. The numerical results obtained from the approximate 1-D models are in good agreement with those of the original 2-D model for both the logarithmic and power velocity profiles.

An Adaptive Wavelet Frame Neural Network Method for Efficient Reliability Analysis

AbstractArtificial neural networks (ANNs) method is widely used in reliability analysis. However, the performance of ANNs cannot be guaranteed due to the fitting problems because there is no efficient constructive method for choosing the structure and the learning parameters of the network. To mitigate these difficulties, this article presents a new adaptive wavelet frame neural network method for reliability analysis of structures. The new method uses the single‐scaling multidimensional wavelet frame as the activation function in the network to deal with the multidimensional problems in reliability analysis. Because the wavelet frame is highly redundant, the time–frequency localization and matching pursuit algorithm are respectively utilized to eliminate the superfluous wavelets, thus the obtained wavelet frame neural network can be implemented efficiently. Five examples are given to demonstrate the application and effectiveness of the proposed method. Comparisons of the new method and the classical radial basis function network method are made.