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The purpose of this paper is to assess the feasibility of analytical models, specifically the radial basis function method, Akbari–Ganji method and Gaussian method, in conjunction with the finite element method. The aim is to examine the impact of processing parameters on temperature history.

Through analytical investigation and finite element simulation, this research examines the influence of processing parameters on temperature history. Simufact software with a thermomechanical approach was used for finite element simulation, while radial basis function, Akbari–Ganji and Gaussian methods were used for analytical modeling to solve the heat transfer differential equation.

The accuracy of both finite element and analytical methods was validated with about 90%. The findings revealed direct relationships between thermal conductivity (from 100 to 200), laser power (from 400 to 800 W), heat source depth (from 0.35 to 0.75) and power absorption coefficient (from 0.4 to 0.8). Increasing the values of these parameters led to higher temperature history. On the other hand, density (from 7,600 to 8,200), emission coefficient (from 0.5 to 0.7) and convective heat transfer (from 35 to 90) exhibited an inverse relationship with temperature history.

The application of analytical modeling, particularly the utilization of the Akbari–Ganji, radial basis functions and Gaussian methods, showcases an innovative approach to studying directed energy deposition. This analytical investigation offers an alternative to relying solely on experimental procedures, potentially saving time and resources in the optimization of DED processes.

In the process of building the “Belt and Road” and “Bright Road” community of interests between China and Kazakhstan, this paper proposes the construction of an inland nuclear power plant in Kazakhstan. Considering the uncertainty of investment in nuclear power generation, the authors propose the MGT (Monte-Carlo and Gaussian Radial Basis with Tensor factorization) utility evaluation model to evaluate the risk of investment in nuclear power in Kazakhstan and provide a relevant reference for decision making on inland nuclear investment in Kazakhstan.

Based on real options portfolio combined with a weighted utility function, this study takes into account the uncertainties associated with nuclear power investments through a minimum variance Monte Carlo approach, proposes a noise-enhancing process combined with geometric Brownian motion in solving complex conditions, and incorporates a measure of investment flexibility and strategic value in the investment, and then uses a deep noise reduction encoder to learn the initial values for potential features of cost and investment effectiveness. A Gaussian radial basis function used to construct a weighted utility function for each uncertainty, generate a minimization of the objective function for the tensor decomposition, and then optimize the objective loss function for the tensor decomposition, find the corresponding weights, and perform noise reduction to generalize the nonlinear problem to evaluate the effectiveness of nuclear power investment. Finally, the two dimensions of cost and risk (estimation of investment value and measurement of investment risk) are applied and simulated through actual data in Kazakhstan.

The authors assess the core indicators of Kazakhstan's nuclear power plants throughout their construction and operating cycles, based on data relating to a cluster of nuclear power plants of 10 different technologies. The authors compared it with several popular methods for evaluating the benefits of nuclear power generation and conducted subsequent sensitivity analyses of key indicators. Experimental results on the dataset show that the MGT method outperforms the other four methods and that changes in nuclear investment returns are more sensitive to changes in costs while operating cash flows from nuclear power are certainly an effective way to drive investment reform in inland nuclear power generation in Kazakhstan at current levels of investment costs.

Future research could consider exploring other excellent methods to improve the accuracy of the investment prediction further using sparseness and noise interference. Also consider collecting some expert advice and providing more appropriate specific suggestions, which will facilitate the application in practice.

The Novel Coronavirus epidemic has plunged the global economy into a deep recession, the tension between China and the US has made the energy cooperation road unusually tortuous, Kazakhstan in Central Asia has natural geographical and resource advantages, so China–Kazakhstan energy cooperation as a new era of opportunity, providing a strong guarantee for China's political and economic stability. The basic idea of building large-scale nuclear power plants in Balkhash and Aktau is put forward, considering the development strategy of building Kazakhstan into a regional international energy base. This work will be a good inspiration for the investment of nuclear generation.

This study solves the problem of increasing noise by combining Monte Carlo simulation with geometric Brownian motion under complex conditions, adds the measure of investment flexibility and strategic value, constructs the utility function of noise reduction weight based on Gaussian radial basis function and extends the nonlinear problem to the evaluation of nuclear power investment benefit.

The purpose of this paper is to provide an effective and simple technique to structural damage identification, particularly to identify a crack in a structure. Artificial neural networks approach is an alternative to identify the extent and location of the damage over the classical methods. Radial basis function (RBF) networks are good at function mapping and generalization ability among the various neural network approaches. RBF neural networks are chosen for the present study of crack identification.

Analyzing the vibration response of a structure is an effective way to monitor its health and even to detect the damage. A novel two‐stage improved radial basis function (IRBF) neural network methodology with conventional RBF in the first stage and a reduced search space moving technique in the second stage is proposed to identify the crack in a cantilever beam structure in the frequency domain. Latin hypercube sampling (LHS) technique is used in both stages to sample the frequency modal patterns to train the proposed network. Study is also conducted with and without addition of 5% white noise to the input patterns to simulate the experimental errors.

The results show a significant improvement in identifying the location and magnitude of a crack by the proposed IRBF method, in comparison with conventional RBF method and other classical methods. In case of crack location in a beam, the average identification error over 12 test cases was 0.69 per cent by IRBF network compared to 4.88 per cent by conventional RBF. Similar improvements are reported when compared to hybrid CPN BPN networks. It also requires much less computational effort as compared to other hybrid neural network approaches and classical methods.

The proposed novel IRBF crack identification technique is unique in originality and not reported elsewhere. It can identify the crack location and crack depth with very good accuracy, less computational effort and ease of implementation.

This paper presents an investigation into the classical problem using an experimental apparatus and applying an artificial neural network (NN) optimisation approach for determining the pressure distribution in a journal bearing at elasto‐hydrodynamic state of lubrication. The experimental system is employed at different working speeds with different surface roughness of shafts for getting pressure distribution. A NN is employed to predict the real data of the system as an optimisation technique. The NN is a radial basis function back propagation network. The NN has a superior performance to follow the desired results of the system and is employed to analyse such systems parameters in practical applications.

The purpose of this paper is to both determine the effects of the nonlinearity on the wave dynamics and assess the temporal and spatial accuracy of five finite difference methods for the solution of the inviscid generalized regularized long-wave (GRLW) equation subject to initial Gaussian conditions.

Two implicit second- and fourth-order accurate finite difference methods and three Runge-Kutta procedures are introduced. The methods employ a new dependent variable which contains the wave amplitude and its second-order spatial derivative. Numerical experiments are reported for several temporal and spatial step sizes in order to assess their accuracy and the preservation of the first two invariants of the inviscid GRLW equation as functions of the spatial and temporal orders of accuracy, and thus determine the conditions under which grid-independent results are obtained.

It has been found that the steepening of the wave increase as the nonlinearity exponent is increased and that the accuracy of the fourth-order Runge-Kutta method is comparable to that of a second-order implicit procedure for time steps smaller than 100th, and that only the fourth-order compact method is almost grid-independent if the time step is on the order of 1,000th and more than 5,000 grid points are used, because of the initial steepening of the initial profile, wave breakup and solitary wave propagation.

This is the first study where an accuracy assessment of wave breakup of the inviscid GRLW equation subject to initial Gaussian conditions is reported.

The paper aims to develop an efficient data-driven modeling approach for the hydroelastic analysis of a semi-circular pipe conveying fluid with elastic end supports. Besides the structural displacement-dependent unsteady fluid force, the steady one related to structural initial configuration and the variable structural parameters (i.e. the variable support stiffness) are considered in the modeling.

The steady fluid force is treated as a pipe preload, and the elastically supported pipe-fluid model is dealt with as a prestressed hydroelastic system with variable parameters. To avoid repeated numerical simulations caused by parameter variation, structural and hydrodynamic reduced-order models (ROMs) instead of conventional computational structural dynamics (CSD) and computational fluid dynamics (CFD) solvers are utilized to produce data for the update of the structural, hydrodynamic and hydroelastic state-space equations. Radial basis function neural network (RBFNN), autoregressive with exogenous input (ARX) model as well as proper orthogonal decomposition (POD) algorithm are applied to modeling these two ROMs, and a hybrid framework is proposed to incorporate them.

The proposed approach is validated by comparing its predictions with theoretical solutions. When the steady fluid force is absent, the predictions agree well with the “inextensible theory”. The pipe always loses its stability via out-of-plane divergence first, regardless of the support stiffness. However, when steady fluid force is considered, the pipe remains stable throughout as flow speed increases, consistent with the “extensible theory”. These results not only verify the accuracy of the present modeling method but also indicate that the steady fluid force, rather than the extensibility of the pipe, is the leading factor for the differences between the in- and extensible theories.

The steady fluid force and the variable structural parameters are considered in the data-driven modeling of a hydroelastic system. Since there are no special restrictions on structural configuration, steady flow pattern and variable structural parameters, the proposed approach has strong portability and great potential application for other hydroelastic problems.

This paper aims to design a neural controller based on radial basis function networks (RBFN) for electrically driven robots subjected to constrained inputs.

It is assumed that the electrical motors have limitations on the applied voltages from the controller. Due to the universal approximation property of RBFN, uncertainties including un-modeled dynamics and external disturbances are represented with this powerful neural network. Then, the lumped uncertainty including the nonlinearities imposed by actuator saturation is introduced and a mathematical model suitable for model-free control is presented. Based on the closed-loop equation, a Lyapunove function is defined and the stability analysis is performed. It is assumed that the electrical motors have limitations on the applied voltages from the controller.

A comparison with a similar controller shows the superiority of the proposed controller in reducing the tracking error. Experimental results on a SCARA manipulator actuated by permanent magnet DC motors have been presented to guarantee its successful practical implementation.

The novelty of this paper in comparison with previous related works is improving the stability analysis by involving the actuator saturation in the design procedure. It is assumed that the electrical motors have limitations on the applied voltages from the controller. Thus, a comprehensive approach is adopted to include the saturated and unsaturated areas, while in previous related works these areas are considered separately. Moreover, a performance evaluation has been carried out to verify satisfactory performance of transient response of the controller.

In this article, a practical design methodology is proposed for discrete sizing optimization of high-rise concrete buildings with a focus on large-scale and real-life structures.

This framework relies on a computationally efficient approximation of the constraint and objective functions using a radial basis function model with a linear tail, also called the combined response surface methodology (RSM) in this article. Considering both the code-stipulated constraints and other construction requirements, three sub-optimization problems were constructed based on the relaxation model of the original problem, and then the structural weight could be automatically minimized under multiple constraints and loading scenarios. After modulization, the obtained results could meet the discretization requirements. By integrating the commercially available ETABS, a dedicated optimization software program with an independent interface was developed and details for practical software development were also presented in this paper.

The proposed framework was used to optimize different high-rise concrete buildings, and case studies showed that material usage could be saved by up to 12.8% compared to the conventional design, and the over-limit constraints could be adjusted, which proved the feasibility and effectiveness.

This methodology can therefore be applied by engineers to explore the optimal distribution of dimensions for high-rise buildings and to reduce material usage for a more sustainable design.

This article offered two meshfree algorithms, namely the local radial basis functions-finite difference (LRBF-FD) approximation and local radial basis functions-differential quadrature method (LRBF-DQM) to simulate the multidimensional hyperbolic wave models and work is an extension of Jiwari (2015).

In the evolvement of the first algorithm, the time derivative is discretized by the forward FD scheme and the Crank-Nicolson scheme is used for the rest of the terms. After that, the LRBF-FD approximation is used for spatial discretization and quasi-linearization process for linearization of the problem. Finally, the obtained linear system is solved by the LU decomposition method. In the development of the second algorithm, semi-discretization in space is done via LRBF-DQM and then an explicit RK4 is used for fully discretization in time.

For simulation purposes, some 1D and 2D wave models are pondered to instigate the chastity and competence of the developed algorithms.

The developed algorithms are novel for the multidimensional hyperbolic wave models. Also, the stability analysis of the second algorithm is a new work for these types of model.

The Motz problem can be considered as a benchmark problem for testing the performance of numerical methods in the solution of elliptic problems with boundary singularities. The purpose of this paper is to address the solution of the Motz problem using the radial basis function (RBF) method, which is a truly meshfree scheme.

Both the global RBF collocation method (also known as Kansa's method) and the recently proposed local RBF‐based differential quadrature (LRBFDQ) method are considered. In both cases, it is shown that the accuracy of the solution can be significantly increased by using special functions which capture the behavior of the singularity. In the case of global collocation, the functional space spanned by the RBF is enlarged by adding singular functions which capture the behavior of the local singular solution. In the case of local collocation, the problem is modified appropriately in order to eliminate the singularities from the formulation.

The paper shows that the exponential convergence both with increasing resolution and increasing shape parameter, which is typical of the RBF method, is lost in problems containing singularities. The accuracy of the solution can be increased by collocation of the partial differential equation (PDE) at boundary nodes. However, in order to restore the exponential convergence of the RBF method, it is necessary to use special functions which capture the behavior of the solution near the discontinuity.

The paper uses Motz's problem as a prototype for problems described by elliptic partial differential equations with boundary singularities. However, the results obtained in the paper are applicable to a wide range of problems containing boundaries with conditions which change from Dirichlet to Neumann, thus leading to singularities in the first derivatives.

The paper shows that both the global RBF collocation method and the LRBFDQ method, are truly meshless methods which can be very useful for the solution of elliptic problems with boundary singularities. In particular, when complemented with special functions that capture the behavior of the solution near the discontinuity, the method exhibits exponential convergence both with resolution and with shape parameter.