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Spatial autocorrelation in regression residuals is a major issue for the modeller because it disturbs parameter estimates and invalidates the reliability of conclusions drawn from models. The purpose of this paper is to develop an approach which generates new spatial predictors that can be mapped and qualitatively analysed while controlling for spatial autocorrelation among residuals.

This paper explores an alternate approach using a Fourier polynomial function based on geographical coordinates to construct an additional spatial predictor that allows to capture the latent spatial pattern hidden among residuals. An empirical validation based on hedonic modelling of sale prices variation using a large dataset of house transactions is provided.

Results show that the spatial autocorrelation problem is under control as shown by low Moran's I indexes. Moreover, this geo‐statistical approach provides coefficients on environmental amenities that are still highly significant by capturing only the remaining spatial autocorrelation.

The originality of this paper relies on the development of a new model that allows considering, simultaneously spatial and time dimension while measuring the marginal impact of environmental amenities on house prices avoiding competition with the weight matrix needed in most spatial econometric models.

To provide an explicit representation for wide‐sense stationary stochastic fields which can be used in stochastic finite element modelling to describe random material properties.

This method represents wide‐sense stationary stochastic fields in terms of multiple Fourier series and a vector of mutually uncorrelated random variables, which are obtained by minimizing the mean‐squared error of a characteristic equation and solving a standard algebraic eigenvalue problem. The result can be treated as a semi‐analytic solution of the Karhunen‐Loève expansion.

According to the Karhunen‐Loève theorem, a second‐order stochastic field can be decomposed into a random part and a deterministic part. Owing to the harmonic essence of wide‐sense stationary stochastic fields, the decomposition can be effectively obtained with the assistance of multiple Fourier series.

The proposed explicit representation of wide‐sense stationary stochastic fields is accurate, efficient and independent of the real shape of the random structure in consideration. Therefore, it can be readily applied in a variety of stochastic finite element formulations to describe random material properties.

This paper discloses the connection between the spectral representation theory of wide‐sense stationary stochastic fields and the Karhunen‐Loève theorem of general second‐order stochastic fields, and obtains a Fourier‐Karhunen‐Loève representation for the former stochastic fields.

The purpose of this study is to build a high accuracy thrust model under various small turbojet engine shaft speeds by using robust, ordinary, linear and nonlinear least squares estimation methods for target drone applications.

The dynamic shaft speeds from the test experiment of a target drone engine is conducted. Then, thrust values are calculated. Based on these, the engine thrust is modeled by robust linear and nonlinear equations. The models are benefited from quadratic, power and various series expansion functions with several coefficients to optimize the model parameters.

The error terms and accuracy of the model are given using sum of squared errors, root mean square error (RMSE) and R-squared (R²) error definitions. Based on the multiple analyses, it is seen that the RMSE values are no more than 17.7539 and the best obtained result for robust least squares estimation is 15.0086 for linear at all cases. Furthermore, the R² value is found to be 0.9996 as the highest with the nonlinear Fourier series expansion model.

The motivation behind this paper is to propose robust nonlinear thrust models based on power, Fourier and various series expansion functions for dynamic shaft speeds from the test experiments.

In this paper, the authors take the first step in the study of constructive methods by using Sobolev polynomials.

To do that, the authors use the connection formulas between Sobolev polynomials and classical Laguerre polynomials, as well as the well-known Fourier coefficients for these latter.

Then, the authors compute explicit formulas for the Fourier coefficients of some families of Laguerre–Sobolev type orthogonal polynomials over a finite interval. The authors also describe an oscillatory region in each case as a reasonable choice for approximation purposes.

In order to take the first step in the study of constructive methods by using Sobolev polynomials, this paper deals with Fourier coefficients for certain families of polynomials orthogonal with respect to the Sobolev type inner product. As far as the authors know, this particular problem has not been addressed in the existing literature.

This paper aims to present a new method, named as augmented polynomial dimensional decomposition (PDD) method, for robust design optimization (RDO) and reliability-based design optimization (RBDO) subject to mixed design variables comprising both distributional and structural design variables.

The method involves a new augmented PDD of a high-dimensional stochastic response for statistical moments and reliability analyses; an integration of the augmented PDD, score functions, and finite-difference approximation for calculating the sensitivities of the first two moments and the failure probability with respect to distributional and structural design variables; and standard gradient-based optimization algorithms.

New closed-form formulae are presented for the design sensitivities of moments that are simultaneously determined along with the moments. A finite-difference approximation integrated with the embedded Monte Carlo simulation of the augmented PDD is put forward for design sensitivities of the failure probability.

In conjunction with the multi-point, single-step design process, the new method provides an efficient means to solve a general stochastic design problem entailing mixed design variables with a large design space. Numerical results, including a three-hole bracket design, indicate that the proposed methods provide accurate and computationally efficient sensitivity estimates and optimal solutions for RDO and RBDO problems.

Teaches by example the application of finite element templates in constructing high performance elements. The example discusses the improvement of the mass and geometric stiffness matrices of a Bernoulli‐Euler plane beam. This process interweaves classical techniques (Fourier analysis and weighted orthogonal polynomials) with newer tools (finite element templates and computer algebra systems). Templates are parameterized algebraic forms that uniquely characterize an element population by a “genetic signature” defined by the set of free parameters. Specific elements are obtained by assigning numeric values to the parameters. This freedom of choice can be used to design “custom” elements. For this example weighted orthogonal polynomials are used to construct templates for the beam material stiffness, geometric stiffness and mass matrices. Fourier analysis carried out through symbolic computation searches for template signatures of mass and geometric stiffness that deliver matrices with desirable properties when used in conjunction with the well‐known Hermitian beam material stiffness. For mass‐stiffness combinations, three objectives are noted: high accuracy for vibration analysis, wide separation of acoustic and optical branches, and low sensitivity to mesh distortion and boundary conditions. Only the first objective is examined in detail.

This paper aims to provide a comprehensive review of uncertainty quantification methods supported by evidence-based comparison studies. Uncertainties are widely encountered in engineering practice, arising from such diverse sources as heterogeneity of materials, variability in measurement, lack of data and ambiguity in knowledge. Academia and industries have long been researching for uncertainty quantification (UQ) methods to quantitatively account for the effects of various input uncertainties on the system response. Despite the rich literature of relevant research, UQ is not an easy subject for novice researchers/practitioners, where many different methods and techniques coexist with inconsistent input/output requirements and analysis schemes.

This confusing status significantly hampers the research progress and practical application of UQ methods in engineering. In the context of engineering analysis, the research efforts of UQ are most focused in two largely separate research fields: structural reliability analysis (SRA) and stochastic finite element method (SFEM). This paper provides a state-of-the-art review of SRA and SFEM, covering both technology and application aspects. Moreover, unlike standard survey papers that focus primarily on description and explanation, a thorough and rigorous comparative study is performed to test all UQ methods reviewed in the paper on a common set of reprehensive examples.

Over 20 uncertainty quantification methods in the fields of structural reliability analysis and stochastic finite element methods are reviewed and rigorously tested on carefully designed numerical examples. They include FORM/SORM, importance sampling, subset simulation, response surface method, surrogate methods, polynomial chaos expansion, perturbation method, stochastic collocation method, etc. The review and comparison tests comment and conclude not only on accuracy and efficiency of each method but also their applicability in different types of uncertainty propagation problems.

The research fields of structural reliability analysis and stochastic finite element methods have largely been developed separately, although both tackle uncertainty quantification in engineering problems. For the first time, all major uncertainty quantification methods in both fields are reviewed and rigorously tested on a common set of examples. Critical opinions and concluding remarks are drawn from the rigorous comparative study, providing objective evidence-based information for further research and practical applications.

Accurate numerical differentiation of approximate data by methods based on Green's second identity often involves singular or nearly singular integrals over domains or their boundaries. This paper applies the finite part integration concept to evaluate such integrals and to generate suitable quadrature formulae. The weak singularity involved in first derivatives is removable; the strong singularities encountered in computing higher derivatives can be reduced. To find derivatives on or near the edge of the integration region, special treatment of boundary integrals is required. Values of normal derivative at points on the edge are obtainable by the method described. Example results are given for derivatives of analytically known functions, as well as results from finite element analysis.

The purpose of this paper is to propose a Chebyshev collocation method (CCM) for Hallén’s equation of thin wire antennas.

Since the current induced on the thin wire antennas behaves like the square root of the distance from the end, a smoothed current is used to annihilate this end effect. Then the CCM adopts Chebyshev polynomials to approximate the smoothed current from which the actual current can be quickly recovered. To handle the difficulty of the kernel singularity and to realize fast computation, a decomposition is adopted by separating the singularity from the exact kernel. The integrals including the singularity in the linear system can be given in an explicit formula while the others can be evaluated efficiently by the fast cosine transform or the fast Fourier transform.

The CCM convergence rate is fast and this method is more efficient than the other existing methods. Specially, it can attain less than 1 percent relative errors by using 32 basis functions when a/h is bigger than 2×10−5 where h is the half length of wire antenna and a is the radius of antenna. Besides, a new efficient scheme to evaluate the exact kernel has been proposed by comparing with most of the literature methods.

Since the kernel evaluation is vital to the solution of Hallén’s and Pocklington’s equations, the proposed scheme to evaluate the exact kernel may be helpful in improving the efficiency of existing methods in the study of wire antennas. Due to the good convergence and efficiency, the CCM may be a competitive method in the analysis of radiation properties of thin wire antennas. Several numerical experiments are presented to validate the proposed method.