The present study introduces a novel and simple matrix method for the solution of longitudinal vibration of rods in terms of Taylor polynomials. The proposed method converts the governing partial differential equation of the system into a matrix equa...
The most popular method for computing the matrix logarithm is a combination of the inverse scaling and squaring method in conjunction with a Padé approximation, sometimes accompanied by the Schur decomposition. In this work, we present a Taylor serie...
The RLC circuit is a basic building block of the more complicated electrical circuits and networks. The present study introduces a novel and simple numerical method for the solution this problem in terms of Taylor polynomials in the matrix form. Part...
Recently, two general methods for evaluating matrix polynomials requiring one matrix product less than the Paterson–Stockmeyer method were proposed, where the cost of evaluating a matrix polynomial is given asymptotically by the total number of matri...
A new way to compute the Taylor polynomial of a matrix exponential is presented which reduces the number of matrix multiplications in comparison with the de-facto standard Paterson-Stockmeyer method for polynomial evaluation. Combined with the scalin...
In this paper, we introduce two approaches to compute the matrix hyperbolic tangent. While one of them is based on its own definition and uses the matrix exponential, the other one is focused on the expansion of its Taylor series. For this second app...
In this paper, we have developed a new method called Generalized Taylor collocation method (GTCM), which is based on the Taylor collocation method, to give approximate solution of linear fractional differential equations with variable coefficients. U...
In this article, we propose a numerical method based on the fractional Taylor vector for solving multi-term fractional differential equations. The main idea of this method is to reduce the given problems to a set of algebraic equations by utilizing t...
The interference of background noise leads to the extremely high spatial complexity of hyperspectral data. Sensitive band selecting is an important task to minimize or eliminate the influence of non-target elements. In this study, Taylor expansion is...
This paper delves into the problem of direct position determination (DPD) for non-Gaussian sources. Existing DPD algorithms are hindered by their high computational complexity from exhaustive grid searches and a disregard for the received signal char...
In this paper, a new approximate method has been presented to solve the linear Fredholm integral equations system (FIEs). The technique is based on, first, differentiating both sides of integral equations n times and then substituting the Taylor ser...
A method for the computation of the
Aiming to solve the problem of dense-frequency signals in the power system caused by the growing proportion of new energy, this paper proposes a dense-frequency signal-detection method based on the primal–dual splitting method. After establishi...
We present a target localization method using an approximated error covariance matrix based weighted least squares (WLS) solution, which integrates received signal strength (RSS) and angle of arrival (AOA) data for wireless sensor networks. We approx...
We show that using Dunford-Taylor’s integral, a classical tool of functional analysis, it is possible to derive an expression for the inverse of a general non-singular complex-valued tridiagonal matrix. The special cases of Jacobi’s symmetric and Toe...
When applying the sequential quadratic programming (SQP) algorithm to topology optimization, using the quasi-Newton methods or calculating the Hessian matrix directly will result in a considerable amount of calculation, making it computationally infe...
This paper presents a methodology to obtain the Fourier coefficients (FCs) and the derivative Fourier coefficients (DFCs) from an input signal. Based on the Taylor series that approximates the input signal into a trigonometric signal model through th...
Machine learning-based models have been widely used in the early drug-design pipeline. To validate these models, cross-validation strategies have been employed, including those using clustering of molecules in terms of their chemical structures. Howe...
Solving the Euler equations often requires expensive computations of complex, high-order time derivatives. Although Taylor Discontinuous Galerkin (TDG) schemes are renowned for their accuracy and stability, directly evaluating third-order tensor deri...
To address the problem of low accuracy for the regular filter algorithm in SINS/DVL integrated navigation, a square-root unscented information filter (SR-UIF) is presented in this paper. The proposed method: (1) adopts the state probability approxima...
In this paper, we propose a degree-of-freedom-based adaptive reduction method that ensures accuracy over a wide band. In the conventional dynamic condensation method, a single reduced model consisting of low-order modes is used throughout the analysi...
The popularization of electricity-gas systems leads to increasing demand for state management of systems. However, the existence of neglected measurement correlations brings uncertainties to the electricity-gas systems state estimation. In this paper...
Currently, there are various calibration methods available to reduce the errors caused by the polarizing section of a dual-rotating-retarder polarimeter. Although these methods have high measurement accuracy, their robustness must be improved and the...
In this paper, we consider numerical solutions for a general form of fractional delay differential equations (FDDEs) with fractional derivatives defined in the Caputo sense. A fractional integration operational matrix, created using a fractional Tayl...
The paper introduces an algorithm to generate a three-variate four-dimensional wind turbulence field suited for yawed wind dynamic load simulation. At large yaw angles, a relaxation of Taylor’s hypothesis of frozen turbulence becomes relevant a...
An adaptive beamformer is sensitive to model mismatch, especially when the desired signal exists in the training samples. Focusing on the problem, this paper proposed a novel adaptive beamformer based on the interference-plus-noise covariance (INC) m...
Traditional interval analysis methods for interior vibro-acoustic system with uncertain-but-bounded parameters are based on interval perturbation theory. However, the solution sets by traditional interval finite-element methods are intrinsically not...
A spacecraft is a typical rigid–flexible–thermal coupled multibody system, and the study of such rigid–flexible–thermal coupled systems has important engineering significance. The dissipation effect of material damping has a s...
The problem of robust fault-tolerant control for actuators of nonlinear systems with uncertain parameters is studied in this paper. Takagi–Sugeno (T-S) fuzzy model is used to describe the wind energy conversion system (WECS). Fuzzy dedicated ob...
In this paper, an easy-to-implement domain-type meshless method—the generalized finite difference method (GFDM)—is applied to simulate the bending behavior of functionally graded (FG) plates. Based on the first-order shear deformation the...
An efficient numerical approach utilizing a variational weak form, grounded in 2D elastic theory and variational principles, is proposed for analyzing the in-plane vibrational behavior of rectangular plates resting on elastically restrained boundarie...
The development of efficient and accurate numerical methods forms a crucial foundation for revealing complex dynamic evolution in nonlinear dynamical systems. Focusing on nonlinear inertia-coupled systems, this paper constructs a semi-analytical meth...
In this study, theorems and proofs related to spherical and focal curves are presented in the BCV-Sasakian space. An approximate solution to the differential equation characterizing spherical curves in the BCV-Sasakian manifold
High-energy ball milling is a process suitable for producing composite powders whose achieved microstructure can be controlled by the processing parameters. Through this technique, it is possible to obtain a homogeneous distribution of reinforced mat...
This paper shows that using the Padé–Laplace (PL) method for deconvolution of multi-exponential functions (stress relaxation of polymers) can produce ill-conditioned systems of equations. Analysis of different sets of generated data points from known...
Shale is typically studied as a transversely isotropic medium with a vertical axis of symmetry (VTI). This model can be extended to vertical fractures in transversely isotropic (VFTI) media when the shale background contains a set of vertical fractur...
The fault detection and isolation are very important for the driving safety of autonomous vehicles. At present, scholars have conducted extensive research on model-based fault detection and isolation algorithms in vehicle systems, but few of them hav...
The Absolute Nodal Coordinate Formulation (ANCF) is extensively utilized in the field of flexible multibody dynamics because it offers a constant mass matrix and inherently eliminates Coriolis forces. However, ANCF requires the computation of complex...
Automated optical inspection is a very important technique. For this reason, this study proposes an optical non-contact slanting surface measuring system. The essential features of the measurement system are obtained through simulations using the opt...
Existing 3D printing techniques are still facing the challenge of low resolution for fabricating polymer matrix composites, inhibiting the wide engineering applications for the biomedical engineering (biomimetic scaffolds), micro fuel cells, and micr...
This study designs and characterizes a novel precise measurement system for simultaneously measuring six-degree-of-freedom geometric motion errors of a long linear stage of a machine tool. The proposed measurement system is based on a method combined...
In the environment of unknown mutual coupling, many works on direction-of-arrival (DOA) estimation with sensor array are prone to performance degradation or even failure. Moreover, there are few literatures on off-grid direction finding using regular...
In this paper, a new Takagi–Sugeno Fuzzy Logic controller (TS-FLC) is presented and applied for modeling and controlling the nonlinear power systems even in the presence of disturbances. Firstly, a nonlinear mathematical model for the electrica...
This study applies the space–time generalized finite difference scheme to solve nonlinear dispersive shallow water waves described by the modified Camassa–Holm equation, the modified Degasperis–Procesi equation, the Fornberg–W...
Structural design often includes geometrically nonlinear analysis to reduce structural weight and increase energy efficiency. The full-order finite element model can perform the geometrically nonlinear analysis, but its computational cost is expensiv...
Modern power systems are high-dimensional, strongly coupled nonlinear systems with complex and diverse dynamic characteristics. The polynomial model of the power system is a key focus in stability research. Therefore, this paper presents a study on t...
In this study, a discrete-time incremental backstepping (DTIBS) controller with an extended Kalman filter (EKF) is proposed for unmanned aerial vehicles (UAVs) with unknown actuator dynamics. The Taylor series and an approximate discrete method are e...
A third-order weak stochastic Taylor expansion (WSTE) is derived for systems driven by additive Gaussian noise with an invertible noise-coupling matrix. In contrast to the classical Kloeden–Platen construction, the present expansion employs a s...
A direction of arrival (DOA) estimator for two-dimensional (2D) incoherently distributed (ID) sources is presented under proposed double cross arrays, satisfying both the small interval of parallel linear arrays and the aperture equalization in the e...
The Kalman filter variants extended Kalman filter (EKF) and error-state Kalman filter (ESKF) are widely used in underwater multi-sensor fusion applications for localization and navigation. Since these filters are designed by employing first-order Tay...
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