In this article, the propagating effect of uncertainties in nonlinear structural systems is investigated. Via considering uncertain‐but‐bounded parameters as interval variables, a Newton ...iteration‐based interval analysis method (NI‐IAM) is proposed to quantify the uncertainty of the nonlinear structural response, namely predicting the upper and lower bounds of the response. In the proposed method, a nonlinear structural system with uncertain interval parameters is described as a series of interval nonlinear equations. With Taylor series expansion, an interval iteration scheme is established to successively approximate the upper and lower bounds of the response based on the Newton method. The structural response bounds in every iteration step are updated by solving linear interval increment determination equations via the Lagrangian multiplier method. Thereout, an uncertain nonlinear problem is simplified to a series of uncertain linear issues. The convergence of the proposed method is further discussed in this article. Numerical examples are provided to demonstrate the effectiveness and applicability of the proposed method by contrast with several existing methods. Moreover, the compatibility between numerical results of the perturbation‐based probabilistic method and the proposed method is then studied and verified.
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BFBNIB, FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
In order to improve the performance and prolong the life of the equipment, it is usually necessary to maintain the equipment in practice. Remaining useful life prediction with imperfect maintenance ...activities is of great importance to prognostics and health management. In this paper, a multi-phase Wiener process-based degradation model is constructed to characterize the degradation process subjected to imperfect maintenance activities. The beta distribution is introduced to describe the residual degradation coefficient caused by the imperfect maintenance activity. The hyper-parameters of residual degradation coefficient are estimated through the maximum likelihood estimation and Newton iteration method. To reflect the unit heterogeneity, the drift coefficient and diffusion coefficient of each phase are synchronously defined as random variables. Furthermore, the analytical forms of remaining useful life are obtained by the convolution operator. The approximate expression of probability density function is derived by the Monte Carlo simulation approach. In the end, a numerical study and a practical study of gyroscopes are provided to demonstrate the practicality and effectiveness of the proposed method.
•A multi-phase Wiener propose-based degradation model is improved.•Drift and diffusion coefficients are synchronously reviewed as random variables.•The approximate expressions of PDF for RUL are derived.•The method is accurate and superior based on a numerical study and gyro datasets.•The model realizes accurate RUL prediction under imperfect maintenance activities.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Signal modeling is an important technique in many engineering applications. This paper is concerned about signal modeling problem for the sine multi-frequency signals or periodic signals. In terms of ...different characteristics between the signal output and the signal parameters, a separable modeling scheme is presented for estimating the signal parameters. In order to seize the real-time information of the signals to be modeled, a sliding measurement window is designed for using the observations dynamically and implementing accurate parameter estimates. Because the amplitude parameters are linear with respect to the signal output and the angular frequency parameters are nonlinear with respect to the signal output, the signal parameters are separated into a linear parameter set and a nonlinear parameter set. Based on these separable parameter sets, a nonlinear optimization problem is converted into a combination of the optimization quadric and the nonlinear optimization. Then, a separable multi-innovation Newton iterative signal modeling method is derived and implemented to estimate sine multi-frequency signals and periodic signals. The simulation results are found to be effective of modeling dynamic signals. For the reason that the proposed method is based on dynamic sliding measurement window, it can be used for online estimation applications.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Currently, massive multiple-input multiple-output (MIMO) is one of the most promising wireless transmission technologies for 5G. Massive MIMO requires handling with large-scale matrix computation, ...especially for matrix inversion. In this letter, we find that matrix inversion based on Newton iteration (NI) is suitable for data detection in massive MIMO system. In contrast with recently proposed polynomial expansion (PE) method for matrix inversion, we analyze both the algorithm complexity and precision in detail, and propose a diagonal band Newton iteration (DBNI) method, which is an approximate method for NI. Compared with PE method, DBNI can obtain higher precision and approximately equal complexity, and we give an explanation of how to select the bandwidth of DBNI.
This paper uses the Newton iteration to study new identification methods for determining the parameters of dynamical systems from step responses. On the basis of the step response analysis, we ...present the Newton iterative algorithms. Moreover, in order to test the accuracy of the estimated parameters, the frequency and step response experiment are applied to the dynamical systems between the estimated and true models. The simulation results show that the obtained models can capture the dynamics of the systems, i.e., the estimated model's outputs are close to the outputs of the actual systems. This confirms the effectiveness of the proposed Newton iterative identification methods.
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We consider nonlinear solvers for the incompressible, steady (or at a fixed time step for unsteady) Navier–Stokes equations in the setting where partial measurement data of the solution is available. ...The measurement data is incorporated/assimilated into the solution through a nudging term addition to the Picard iteration that penalized the difference between the coarse mesh interpolants of the true solution and solver solution, analogous to how continuous data assimilation (CDA) is implemented for time dependent PDEs. This was considered in the paper (Li et al. 2023), and we extend the methodology by improving the analysis to be in the L2 norm instead of a weighted H1 norm where the weight depended on the coarse mesh width, and to the case of noisy measurement data. For noisy measurement data, we prove that the CDA-Picard method is stable and convergent, up to the size of the noise. Numerical tests illustrate the results, and show that a very good strategy when using noisy data is to use CDA-Picard to generate an initial guess for the classical Newton iteration.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
To achieve low-carbon goals, long-distance district heating (LDH) systems are widely applied, which utilize the waste heats from renewable energy power plants and waste incineration plants. The ...hydraulic oscillations induced by pump-stopping in LDH systems may give rise to critical incidents, such as pipeline ruptures and heating disruptions. The systematic analysis of hydraulic oscillations induced by pump-stopping and the subsequent revelation of critical factors that mitigate their intensity are fundamental prerequisites for ensuring the safety and reliability of LDH system. In this paper, firstly, a pump-stopping hydraulic transient model of the LDH system is established based on the distributed parameter method. Then, combining the method of characteristics (MOC) and the Newton iteration method, the numerical solution scheme for this model is proposed. Finally, taking a 20 km LDH system as an example, the characteristics of hydraulic oscillations induced by pump-stopping is analyzed, and the key factors influencing the intensity of these hydraulic oscillations are investigated. In addition, the differences between hydraulic oscillations induced by pump-stopping and those induced by sudden faults on pipelines are also analyzed. The results indicate that an optimal pump inertia moment value and a properly sized bypass pipe at the pump significantly mitigate hydraulic oscillations, while the influence of constant pressure at the heat source inlet on hydraulic oscillations can be negligible. Our study has important reference value for improving the safe and reliable operation of LDH systems.
•1.A pump-stopping hydraulic transient model of the LDH system is established.•A numerical solution scheme combined MOC and Newton iteration method is proposed.•Too small pump inertia moments intensify pump-stopping-induced hydraulic oscillation.•Bypass pipe reduces the pressure oscillation at the outlet of the heat source.
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In this paper, a new Newton iterative identification method is presented for estimating the parameters of a second-order dynamic system utilizing the obtained data from the step response. In order to ...obtain the desired dynamic performance, a controller design method based on the root locus is presented to meet the requirement of the dynamic performance of the overshoot. The simulation results indicate that the proposed Newton iterative identification method is effective and the system response can meet the requirement of system dynamic performances.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
In this paper, we provide a theoretical analysis for an iteration solver to implement a finite difference numerical scheme for the Poisson-Nernst–Planck (PNP) system, based on the Energetic ...Variational Approach (EnVarA), in which a non-constant mobility H−1 gradient flow is formulated. In particular, the nonlinear and singular nature of the logarithmic energy potentials has always been the essential difficulty. In the numerical design, the mobility function is explicitly updated, for the sake of unique solvability analysis. The logarithmic and the electric potential diffusion terms, which come from the gradient of convex energy functional parts, are implicitly computed. The positivity-preserving property for all the concentrations, an unconditional energy stability, and the optimal rate error estimate have been established in a recent work. A modified Newton iteration for the nonlinear and logarithmic part, combined with a linear iteration for the electric potential part, is proposed to implement the given numerical scheme, in which a non-constant linear elliptic equation needs to be solved at each iteration stage. A theoretical analysis is presented in this article, and a linear convergence is proved for such an iteration, with an asymptotic error constant in the same order of the time step size. A numerical test is also presented in this article, which demonstrates the linear convergence rate of the proposed iteration solver.
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In this paper we propose a mesh-free method for parabolic nonlocal problem. The proposed method comprises web-splines, Euler scheme and Newton's method. We give existence and uniqueness results for ...the weak formulation at continuous level and prove a priori error bounds for the fully-discrete solution. Finally, we show some numerical results based on web-spline method to confirm our theoretical findings.
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