Adaptive Basis Function Research Articles

Adaptive Visual Control for Robotic Manipulators with Consideration of Rigid-Body Dynamics and Joint-Motor Dynamics

A novel cascade visual control scheme is proposed to tailor for electrically driven robotic manipulators that operate under kinematic and dynamic uncertainties, utilizing an uncalibrated stationary camera. The proposed control approach incorporates adaptive weight radial basis function neural networks (RBFNNs) to learn the behaviors of the uncertain dynamics of the robot and the joint actuators. The controllers are designed to nullify the approximation error and mitigate unknown disturbances through an integrated robust adaptive mechanism. A major advantage of the proposed approach is that prior knowledge of the dynamics of the robotic manipulator and its actuator is no longer required. The controller autonomously assimilates the robot and actuator dynamics online, thereby obviating the need for fussy regression matrix derivation and advance dynamic measurement to establish the adaptive dynamic parameter update algorithm. The proposed scheme ensures closed-loop system stability, bounded system states, and the convergence of tracking errors to zero. Simulation results, employing a PUMA manipulator as a testbed, substantiate the viability of the proposed control policy.

Efficient augmented radial basis function for reliability analysis with dynamic importance sampling

Conducting reliability analysis on complex systems, particularly those characterized by minimal failure probabilities and computationally intensive models, presents significant challenges. This article introduces a reliability analysis method combining the adaptive augmented radial basis function and the dynamic importance sampling (ARBF-DIS) algorithm. This method improves the generalization capacity of the augmented radial basis function at both local and global scales through the application of an anisotropic technique and orthogonal conditions. By using efficient cross-validation, the methodology facilitates the training of the metamodel, enabling it to provide predictive variance essential for constructing an adaptive sampling learning function. A key aspect of this approach is its capability to address the issue of low failure probabilities through dynamic importance sampling, which involves calculating an optimal importance sampling function derived from the current metamodel. The effectiveness and precision of the ARBF-DIS method are demonstrated through two analytical examples and a solid rocket motor reliability problem.

A bivariational, stable, and convergent hierarchy for time-dependent coupled cluster with adaptive basis sets.

We propose a new formulation of time-dependent coupled cluster with adaptive basis functions and division of the one-particle space into active and secondary subspaces. The formalism is fully bivariational in the sense of a real-valued time-dependent bivariational principle and converges to the complete-active-space solution, a property that is obtained by the use of biorthogonal basis functions. A key and distinguishing feature of the theory is that the active bra and ket functions span the same space by construction. This ensures numerical stability and is achieved by employing a split unitary/non-unitary basis set transformation: the unitary part changes the active space itself, while the non-unitary part transforms the active basis. The formulation covers vibrational as well as electron dynamics. Detailed equations of motion are derived and implemented in the context of vibrational dynamics, and the numerical behavior is studied and compared to related methods.

Adaptive Orthogonal Basis Function Detection Method for Unknown Magnetic Target Motion State

Traditional methods of orthogonal basis function decomposition have been extensively used to detect magnetic anomaly signals. However, the determination of the relative velocity between the detection platform and the magnetic target remains elusive in practical detection. And, the non-ideal uniform motion of the magnetic target further complicates the process and adversely impacts the detector’s performance. To address this challenge, this paper introduces an adaptive scale factor method based on orthogonal basis function decomposition. This new method can be used to adjust the relative velocity between the detection platform and the magnetic target and to refine the characteristic time in the basis functions. In this paper, a mathematical relationship between the scale factor and the relative velocity is established, which is subsequently fitted into a Gauss function curve. The optimal scale factor, denoted as β, is adaptively chosen from the fitting curve when the magnetic target moves at a non-ideal uniform velocity with an unknown motion state. The results of simulations indicate that the scale factor improves the signal-to-noise ratio of the magnetic anomaly signals in a non-ideal state. And, this method can improve the energy value of OBF decomposition by 17.7%. Simultaneously, this method ensures that the moment the magnetic target passes the CPA coincides with the energy peak of the orthogonal basis detection, which improves the accuracy by 54.1% compared with the traditional method. The effectiveness and precision of the proposed method are verified using simulations and practical experiments.

Adaptive Basis Function Method for the Detection of an Undersurface Magnetic Anomaly Target

The orthogonal basis functions (OBFs) method is a prevailing choice for the detection of undersurface magnetic anomaly targets. However, it requires the detecting platform or target to move uniformly along a straight path. To circumvent the restrictions, a new adaptive basis functions (ABFs) approach is proposed in this article. It permits the detection platform to search for a possible target at different speeds along any course. The ABFs are constructed using the real-time data of the onboard triaxial fluxgate, GPS module, and attitude gyro. Based on the pseudo-energy of an apparent target signal, the constant false alarm rate (CFAR) method is employed to judge whether a target is present. Moreover, by defining the pixel as a relative possibility for a target at a geographic location, a magnetic anomaly target imaging scheme is introduced by displaying the pixels onto the searching area. On-site experimental data are utilized to demonstrate the proposed approach. Compared with the traditional OBFs method, the present ABFs approach can substantially improve the detection possibility and reduce false alarms.

Time-dependent coupled cluster with orthogonal adaptive basis functions: General formalism and application to the vibrational problem.

We derive equations of motion for bivariational wave functions with orthogonal adaptive basis sets and specialize the formalism to the coupled cluster Ansatz. The equations are related to the biorthogonal case in a transparent way, and similarities and differences are analyzed. We show that the amplitude equations are identical in the orthogonal and biorthogonal formalisms, while the linear equations that determine the basis set time evolution differ by symmetrization. Applying the orthogonal framework to the nuclear dynamics problem, we introduce and implement the orthogonal time-dependent modal vibrational coupled cluster (oTDMVCC) method and benchmark it against exact reference results for four triatomic molecules as well as a reduced-dimensional (5D) trans-bithiophene model. We confirm numerically that the biorthogonal TDMVCC hierarchy converges to the exact solution, while oTDMVCC does not. The differences between TDMVCC and oTDMVCC are found to be small for three of the five cases, but we also identify one case where the formal deficiency of the oTDMVCC approach results in clear and visible errors relative to the exact result. For the remaining example, oTDMVCC exhibits rather modest but visible errors.

Surrogate Modelling of Field Performance Analysis and Optimization via Hierarchical Proper Orthogonal Decomposition and Adaptive Sampling Radial Basis Function

Surrogate Modelling of Field Performance Analysis and Optimization via Hierarchical Proper Orthogonal Decomposition and Adaptive Sampling Radial Basis Function

Adaptive Block-based Krylov Subspace Basis Functions for Solving Bistatic Scattering Problems

Adaptive Block-based Krylov Subspace Basis Functions for Solving Bistatic Scattering Problems

Robust Temperature and Gas Concentration Imaging by LAS Tomography With Adaptive Basis Function Fitting and Artifact Removal

Robust Temperature and Gas Concentration Imaging by LAS Tomography With Adaptive Basis Function Fitting and Artifact Removal

Adaptive Basis Function Selection for Computationally Efficient Predictions

Adaptive Basis Function Selection for Computationally Efficient Predictions

Robust adaptive backstepping neural networks fault tolerant control for mobile manipulator UAV with multiple uncertainties

The present study outlines the development of an Adaptive Backstepping Radial Basis Function Neural Networks Fault Tolerant Control (ABRBFNNFTC) methodology. The aforementioned methodology is employed to address the challenge of achieving trajectory following in the context of a Mobile Manipulator Unmanned Aerial Vehicle (MMUAV) when subjected to the effects of actuator faults and parametric uncertainties. The utilization of an adaptive radial basis function neural networks (RBFNNs) controller is employed for the purpose of approximating an unidentified nonlinear backstepping controller that relies on the precise model of the MMUAV. The Lyapunov direct method is utilized to establish the stability analysis of the entire system. The closed-loop system guarantees the Uniformly Ultimately Bounded (UUB) stability of all signals. The control methodology put forth ensures the achievement of a prescribed trajectory, and mitigates the impact of uncertainties and actuator faults. The efficiency of the proposed ABRBFNNFTC scheme is demonstrated through the presentation of extensive simulation studies.

Adaptive Multioutput Gradient RBF Tracker for Nonlinear and Nonstationary Regression.

Multioutput regression of nonlinear and nonstationary data is largely understudied in both machine learning and control communities. This article develops an adaptive multioutput gradient radial basis function (MGRBF) tracker for online modeling of multioutput nonlinear and nonstationary processes. Specifically, a compact MGRBF network is first constructed with a new two-step training procedure to produce excellent predictive capacity. To improve its tracking ability in fast time-varying scenarios, an adaptive MGRBF (AMGRBF) tracker is proposed, which updates the MGRBF network structure online by replacing the worst performing node with a new node that automatically encodes the newly emerging system state and acts as a perfect local multioutput predictor for the current system state. Extensive experimental results confirm that the proposed AMGRBF tracker significantly outperforms existing state-of-the-art online multioutput regression methods as well as deep-learning-based models, in terms of adaptive modeling accuracy and online computational complexity.

Learning adaptive coarse basis functions of FETI-DP

Domain decomposition methods are successful and highly parallel scalable iterative solution methods for discretized partial differential equations. Nevertheless, for many classes of problems, for example, elliptic partial differential equations with arbitrary coefficient distributions, adaptive coarse spaces are necessary to obtain robustness or, in other words, to guarantee a reliable and fast convergence. Adaptive coarse spaces are usually computed by solving many localized eigenvalue problems related to edges or faces of the domain decomposition. This results in a computationally expensive setup of the domain decomposition preconditioner or system operator. In earlier work, to which the authors have contributed, a deep learning based classification model was used to classify the critical edges or faces where eigenvalue problems have to be solved. In the present paper, we suggest to directly learn the adaptive constraints using a deep feedforward neural network regression model and thus completely skip the computationally most expensive part of the setup, i.e., the solution of local eigenvalue problems. We consider a specific adaptive FETI-DP (Finite Tearing and Interconnecting – Dual Primal) approach and concentrate on stationary diffusion problems in two dimensions with arbitrary coefficient functions with large jumps. As an input for the neural network, we use an image representation of the coefficient function which resolves the structure of the coefficient distribution but is not necessarily identical to the discretization of the partial differential equation. Therefore, our approach is independent of the finite element mesh and can, in principle, be easily extended to other adaptive coarse spaces, problems, and domain decomposition methods. We show the robustness of our method for different problems and the generalization property of our trained neural networks by considering different coefficient distributions not contained in the training set. We also combine the learned constraints with computationally cheap frugal constraints to further improve our approach.

An atom-in-molecule adaptive polarized valence single-ζ atomic orbital basis for electronic structure calculations.

Many low-cost or semiempirical quantum mechanical-based electronic structure methods suffer from the use of unpolarized minimal atomic orbital (AO) basis sets. In this work, we overcome this limitation by a fully DFT variationally optimized, adaptive minimal basis set consistently available for the elements up to radon (Z = 86). The new key feature is to make the linear coefficients of the primitive Gaussians in a contracted AO dependent on the effective atomic charge of the atom in the molecule, i.e., each symmetry-unique atom obtains its "own" specifically adapted basis functions. In this way, the physically important "breathing" of the AOs in a molecule with (a) atomic charge (expansion/contraction for anionic/cationic states) and (b) the number of close-lying bonded neighbor atoms is accounted for. The required atomic charges are obtained from a specially developed extended Hückel type Hamiltonian and the coordination numbers from the molecule geometry. Proper analytical derivatives of the resulting adaptive basis functions can easily be derived. Moreover, the basis functions are electric field-dependent, thus improving the description of, e.g., dipole moments and polarizabilities. The new basis set termed q-vSZP (charge dependent valence single-ζ, polarized) is thoroughly benchmarked for atomic/molecular and thermochemical properties compared to standard minimal and double-ζ basis sets at the DFT level with the accurate ωB97X-D4 functional. It is shown that q-vSZP is clearly superior to existing minimal basis sets, often reaching double-ζ quality or even better results. We expect it to be the optimal choice in future semiempirical quantum mechanical methods.

Adaptive Basis Function Selection Enhanced Multisurrogate-Assisted Evolutionary Algorithm for Production Optimization

Summary Surrogate-assisted evolutionary algorithms (SAEAs) have become a popular approach for solving reservoir production optimization problems. The radial-basis-function network (RBFN) is a robust surrogate model technology suitable for reservoir development with numerous wells and a long production lifetime. There are several types of basis functions for constructing RBFN models. However, existing research shows that selecting the basis function with competitive performance for the current optimization problem is challenging without prior knowledge. In conventional SAEAs, the basis function is often predetermined, but its prediction accuracy for the problem at hand cannot be guaranteed. Furthermore, canonical SAEAs usually employ only one surrogate model for the entire optimization process. However, relying on a single surrogate model for optimization increases the probability of search direction misdirection due to prediction deviations. In this paper, a novel method named adaptive basis function selection enhanced multisurrogate-assisted evolutionary algorithm (ABMSEA) is introduced for production optimization. This method mainly includes two innovations. First, by training and testing different types of basis functions, the one with the best prediction performance is adaptively selected. Second, the ensemble model is constructed using the bootstrap sampling method, comprising multiple global surrogate models based on the selected best basis function. To search for a set of solutions that perform well on multiple surrogates, we employ an efficient multiobjective optimization (MOO) algorithm called nondominated sorting genetic algorithm II (NSGA-II). This algorithm uses the surrogates themselves as objective functions, aiming to find solutions that yield favorable results across multiple surrogates. The proposed method improves the efficiency of production optimization while enhancing global search capabilities. To evaluate the effectiveness of ABMSEA, we conduct tests on four 100D benchmark functions, a three-channel model, and an egg model. The obtained results are compared with those obtained from differential evolution (DE) and three other surrogate-model-based methods. The experimental results demonstrate that ABMSEA exhibits an accurate selection of competitive basis functions for the current optimization period while maintaining high optimization efficiency and avoiding local optima. Consequently, our method enables optimal well control, leading to the attainment of the highest net present value (NPV).

Event-triggered adaptive sliding mode control for steer-by-wire systems with actuator fault

The event-triggered tracking control is studied for the steer-by-wire (SbW) system with actuator fault, inaccurate dynamic model, and external disturbance. First, an adaptive sliding mode control based on event-triggering mechanism is proposed. The lumped nonlinearity, including friction torque and self-aligning torque of SbW systems, is approximated by an adaptive robust radial basis function neural network (RBFNN). Robust terms of sliding mode control attenuate the negative effects of the actuator fault, modeling error, external disturbance, and event-triggering error on control performance. More importantly, the sliding-mode high-frequency switching control appears in the high-order derivative of sliding variable without increasing the input–output relative degree, thereby eliminating chattering. Furthermore, the designed method can achieve the practical finite-time stability. The proposed event-triggering mechanism can strictly exclude Zeno behavior and economize the communication resources. Finally, simulations and experiments show the effectiveness of the proposed algorithm.

NOx Emissions Prediction With a Brain-Inspired Modular Neural Network in Municipal Solid Waste Incineration Processes

The timely and accurate measurement of nitrogen oxide (NOx) emissions is important for efficient pollution controlling of municipal solid waste incineratio plants. To design an efficient and effective prediction model for NOx concentrations, a brain-inspired modular neural network (BIMNN) is developed in this study. First, a biologically-inspired modularization technique is proposed, in which the topological modularity gives rise to functional modularity. Consequently, different modules correspond to different tasks, improving the network efficiency by performing task decomposition. Subsequently, an adaptive task-oriented radial basis function (ATO-RBF) neural network is applied to construct each module. The ATO-RBF neural network is comprised of a structure self-organizing mechanism and an adaptive second-order learning algorithm, providing basis for generalization ability of BIMNN. Finally, during the testing or application stages, a competitive strategy is utilized to integrate the modules. The proposed prediction methodology is verified using industrial data, and the experimental results demonstrate its outperformance.

Adaptive one-pass passive-aggressive radial basis function for classification problems

This paper presents a novel adaptive one-pass Passive-Aggressive Radial Basis Function (APARBF) for classification problems. The APARBF uses elliptic Gaussian neurons followed by a Softmax layer and cross-entropy loss function. This network tries to overcome the elasticity-plasticity dilemma by using the Passive-Aggressive (PA) algorithm and adapting the hidden layer structure. The weight updates have to be plastic to acquire the most information from each sample and at the same time need to be elastic to retrain the information from the past instances. Inspired by PA, a novel update formula for cross-entropy loss minimization has been derived. The adaptive design of the network lets it start with zero hidden neurons and grow or shrink according to the data. For kernel parameters, the adaptive structure determines the correct number of hidden neurons and updates recursively each neuron’s center and covariance matrix. To evaluate our network, we perform two series of experiments. The first experiments compare the proposed APARBF with other recently developed one-pass algorithms (i.e., OVIG, OBHT, SCW, AROW, OGD, and PA). The subsequent experiments include comparing the proposed algorithm with some online adaptive structures such as FGAP-RBF, C-Mantec, McNN, and PBL-McNN, based on their mean classification error and the number of hidden neurons. Wilcoxon sign rank test and Friedman test clearly show the superiority of the proposed network’s results compared with its competitors in one-pass classification problems.

Comparing multi-index stochastic collocation and multi-fidelity stochastic radial basis functions for forward uncertainty quantification of ship resistance

This paper presents a comparison of two multi-fidelity methods for the forward uncertainty quantification of a naval engineering problem. Specifically, we consider the problem of quantifying the uncertainty of the hydrodynamic resistance of a roll-on/roll-off passenger ferry advancing in calm water and subject to two operational uncertainties (ship speed and payload). The first four statistical moments (mean, variance, skewness, and kurtosis), and the probability density function for such quantity of interest (QoI) are computed with two multi-fidelity methods, i.e., the Multi-Index Stochastic Collocation (MISC) and an adaptive multi-fidelity Stochastic Radial Basis Functions (SRBF). The QoI is evaluated via computational fluid dynamics simulations, which are performed with the in-house unsteady Reynolds-Averaged Navier–Stokes (RANS) multi-grid solver chinavis. The different fidelities employed by both methods are obtained by stopping the RANS solver at different grid levels of the multi-grid cycle. The performance of both methods are presented and discussed: in a nutshell, the findings suggest that, at least for the current implementation of both methods, MISC could be preferred whenever a limited computational budget is available, whereas for a larger computational budget SRBF seems to be preferable, thanks to its robustness to the numerical noise in the evaluations of the QoI.

Forecasting of Trend-Cycle Time Series Using Hybrid Model Linear Regression

Forecasting for a time series signal carrying single pattern characteristics can be done properly using function mapping-based principle by a well-designed artificial neural network model. But the performances degraded very much when time series carried the mixture of different patterns characteristics. The level of difficulty increases further when there is a need to predict far time samples. Among several possible mixtures of patterns, the trend-cycle time series is having its importance because of its occurrence in many real-life applications like in electric power generation, fuel consumption and automobile sales. Over the mixed characteristics of patterns, a neural model, suffered heavily in getting generalized learning, in result poor performances appeared over test data. To overcome this issue in this work, a decomposition-based approach has been applied to separate the component patterns of trend and cyclic patterns, and a dedicated model has been developed for predicting the individual data patterns. The linear characteristic of the trend data pattern has been modeled through a linear regression model while the nonlinearity behavior of cyclic pattern has been model by an adaptive radial basis function neural network. The final predicted outcome has been considered as the linear combination of individual model outcomes. The Gaussian function has been considered as the kernel function in the radial basis function neural network because of its wider and efficient applicability in function mapping. The performance of the neural model has been improved very much by providing the adaptive value of spreads and centers of basis function along with weights values. In this paper, two different applications of forecasting in the area of electric power demand by the individual house and month-wise annual power generation have been considered. Based on house characteristics parameters, the power demanded by a house have been considered which carried a moderate complexity of function mapping problem while in another case, total power generation needed to be predicted on the monthly basis for a year from just the previous year observation, which carried the mixed behavior of trend and cyclic pattern. For house power demand forecasting the adaptive kernel-based radial basis function has shown very satisfactory performances and much better against static kernel radial basis function and multilayer perceptron neural network. The integrated approach of neural model and linear regression has shown very efficient outcomes for the mixture pattern while individual neural models were failed to do so. The coefficient of determination (R2) has been applied to estimate the quality of predicted outcomes and comparison.