Applied Mathematical Modelling最新文献

The nonlinear terms resulting from temperature dependence of thermal conductivity and relaxation time must be considered when studying systems undergoing very short thermal pulses with non-negligible amplitude of the temperature perturbation. Two nonlinear formulations of the Maxwell-Cattaneo-Vernotte equation for thermal transport with relaxation effects are introduced. A comparison of the consequences of these two different nonlinear Cattaneo type equations on thermal pulse propagation is obtained and discussed. The differences in the corresponding velocities and in the corresponding heights of the perturbation peaks turn out to be significant and could be experimentally detected.

Condition monitoring technology plays a crucial role in ensuring the reliable operation of gas turbines. Digital twin has propelled condition monitoring research into a new phase. This paper established a surrogate model of gas turbines for condition monitoring based on Markov-projection approximation subspace tracking. Furthermore, it explores the application of surrogate model in developing digital twin for gas turbines. The study initially establishes a Markov matrix and acquires an observation vector, utilizing the framework of the linear model. Utilizing real-time measurement data of gas turbine, the signal subspace of the observation vector autocorrelation matrix is updated through the projection approximation subspace tracking. By aligning this signal subspace with the generalized observability matrix, the identification results of the surrogate model parameters are obtained online. Furthermore, a variable weight projection approximation subspace tracking method has been proposed to enhance the algorithm robustness. Simulation and real experiment demonstrate that the surrogate model output effectively tracks the real-time changes in gas turbine measurement data. When faults and degradation arise, condition monitoring can be achieved by analyzing the evolution of model parameters to obtain feedback information from the gas turbine. The proposed method maintains its robustness in the presence of impulsive noise. These features offer a novel approach for the development of gas turbine digital twin.

We introduce the class of inflated Kumaraswamy autoregressive and moving average models for modeling and forecasting hydro-environmental time series that assume values in $[0,1)$ or $(0,1]$. The main goal of our proposal is to handle doubly-bounded times series in the presence of inflated data. Conditioned on past observations, the response variable is assumed to follow an inflated Kumaraswamy (IK) distribution, a composite of continuous and discrete distributions. The Kumaraswamy distribution family is particularly useful for modeling hydro-environmental and related data. In the proposed model, the random component follows the IK distribution, while the systematic component comprises two dynamic structures, one for the conditional median and one for the mixture parameter, the latter being simple and parsimonious. The dynamic structure used for the conditional median encompasses autoregressive and moving average dynamics and allows for the inclusion of regressors. Statistical inference based on conditional maximum likelihood is presented. Results from Monte Carlo simulations based on synthetic hydro-environmental series are used to evaluate the accuracy of inferences in finite sample sizes. Finally, three empirical applications using hydro-environmental data are presented and discussed. They showcase the applicability of the proposed model in the context of data-driven water and environmental management.

Fluid-structure interaction (FSI), as a two-phase flow problem, is widely encountered in engineering, which often involves large deformation and moving boundaries and interfaces. The finite particle method (FPM) originated from smoothed particle hydrodynamics (SPH) is one of the most common meshfree particle methods, and is more accurate than conventional SPH. In this paper, based on the virtual work principle, a unified updated Lagrangian FPM framework is proposed by which both fluid and solid are discretized simultaneously. A gradient-free form of artificial pressure dissipation is used in fluid models for pressure oscillation problems. An additional artificial stiffness is introduced to control the numerical instability due to rank-deficiency in solid models. Considering FSI problem, the solid particles regarded as dummy particles are introduced into the governing equations of fluid. This technique can avoid arrangement and updating of dummy particles, and allows a convenient handling of the FSI problems with a complex moving interface. The interface force is formed by a force-pair to ensure momentum conservation. Finally, four FSI numerical tests from different degrees of tracking interface are performed to demonstrate that the method in this work can effectively handle the FSI problem with complex geometrical and moving interfaces. In particular, it is effective in the FSI cases with low and medium Reynolds number.

This study aims to provide a comprehensive exploration of the nonlinear vortex-induced vibration (VIV) characteristics of the wind turbines in parked conditions. Considering the influences of the aero-damping and structure of the wind turbine, a vibration mitigation strategy for VIV is proposed to avoid the potential harm caused by VIV in practical projects. The finite element method (FEM) is used to analyze the mode of the wind turbine, and the aerodynamic performance of the wind turbine is analyzed by employing the blade element theory. Using the van der Pol equation for modeling fluid-structure coupling, a nonlinear equation for simulating the VIV of the tower, accounting for the aero-damping of the wind turbine, is established through the application of Hamilton's principle and the assumed mode method, and is solved by the method of multiple scales. The results show that the VIV in fore-aft bending mode direction of the wind turbine tower should be considered. The VIV of the wind turbine can be mitigated by changing azimuth angles and pitch angles. Furthermore, the effectiveness of the proposed vibration mitigation strategy is validated by the on-site vibration experiment.

This study presents a method to predict the stochastic response of subsystems of interest in multi-degree-of-freedom quasi-integrable Hamiltonian systems under Gaussian white noises. It bypasses the challenges of addressing high-dimensional partial differential equations and evaluating multiple integrals. The proposed method consists of three main steps: (1) first dimensionality reduction–derive the averaged Itô stochastic differential equations for subsystem energies by applying the stochastic averaging method, then the associated reduced Fokker-Planck-Kolmogorov equations; (2) second dimensionality reduction–simplify the reduced Fokker-Planck-Kolmogorov equation to an approximated ordinary differential one by using the subspace method; (3) neural network approximations–train neural network approximations of first and second derivative moments for the approximated Fokker-Planck-Kolmogorov equation from a prespecified data set. Furthermore, approximate theoretical stationary probability density functions of states of interest are obtained easily using the transformation between system states and the subsystem energy. A 10-degree-of-freedom quasi-integrable Hamiltonian system is given as an example to highlight the procedure and accuracy of the proposed method. Results show that, based on the proposed method, fewer samples (only 1/10000 of compared ones) can predict the stochastic responses of subsystems of interest in multi-degree-of-freedom quasi-integrable Hamiltonian systems well.

In response to the limitations of the traditional grey forecasting model in terms of structure and parameters, an unbiased non-homogeneous grey forecasting model containing a nonlinear time term is proposed. First, the background value is improved based on the integral median theorem, which in turn gives a new unbiased parameter estimation method. Second, the optimization effect of the model is further enhanced by better selection of initial value through relative error sum of squares minimization. It not only has the number multiplication transformation consistency, but also can be compatible with many existing grey forecasting models by adjusting its own structural parameters. Third, the unbiasedness and effectiveness of this model are verified with the help of matrix theory and three practical cases, respectively, and the results show that its performance is more advantageous compared with other grey models as well as various time series forecasting models. Finally, the model is applied to the forecasts for consumer expenditure and food production, with in-sample errors of 0.722% and 0.471%, and out-of-sample errors of 1.341% and 0.827%, respectively. Forecasts show that the per capita consumption expenditure of rural residents in Sichuan Province will reach about 23,000 yuan, and grain production in Jiangsu Province will reach about 39.9 million tons in 2027.

Saltstone is an ideal medium for storing fossil energy and highly radioactive nuclear waste. Studying the creep mechanical properties of salt rock is important for the safe operation of underground salt rock reservoirs. An intrinsic model of salt rock creep considering the time effect is established based on the element combination model and combined with the fractal-order calculus theory. The model can describe the viscoelastic–plastic creep mechanical behavior of rocks. The 1D and 3D creep equations of salt rock considering the time effect are deduced based on the theory of combined model. The long-term strength values of salt rocks are determined by analyzing the characteristics of isochronous stress–strain curves of existing uni- and triaxial creep tests of the rocks. The parameters in the model are identified by combining the isochronous stress–strain curves and creep test data. Results show that the established creep constitutive model effectively describes the creep mechanical properties of salt rock under different stress states. The model also compensates for the shortcomings of the traditional model that cannot describe the accelerated creep deformation law. It can provide a certain theoretical basis for predicting the creep deformation characteristics of salt rock.

Information dissemination driven by the epidemic may intensify individuals' awareness to change their behavior, as we observe that aware ones often pursue more resources to resist the epidemic. Particularly, the co-effects of herd awareness to individuals and resource allocation between locations on the spatial spreading of the epidemic has not further uncovered. Therefore, to deeply investigate the co-effects of herd awareness and resource allocation on the spatial spreading of the epidemic, a three-layer metapopulation networks model is proposed to characterize the complex interplay among information diffusion, resource allocation, and epidemic spreading. The results indicate enhancing self-awareness apparently promotes the information dissemination and validly suppresses the epidemic spreading. Intensifying herd awareness can remarkably suppress the epidemic spreading. Besides, pursuing resources excessively has few impacts on curbing the epidemic when individuals suffer from panics, and reducing the infection rate of susceptible individuals via investing resources can properly reduce the final infection scale.

It is well known that, during replication, RNA viruses spontaneously generate defective viral genomes (DVGs). DVGs are unable to complete an infectious cycle autonomously and depend on coinfection with a wild-type helper virus (HV) for their replication and/or transmission. The study of the dynamics arising from a HV and its DVGs has been a longstanding question in virology. It has been shown that DVGs can modulate HV replication and, depending on the strength of interference, result in HV extinctions or self-sustained persistent fluctuations. Extensive experimental work has provided mechanistic explanations for DVG generation and compelling evidences of HV-DVGs virus coevolution. Some of these observations have been captured by mathematical models. Here, we develop and investigate an epidemiological-like mathematical model specifically designed to study the dynamics of betacoronavirus in cell culture experiments. The dynamics of the model is governed by several degenerate normally hyperbolic invariant manifolds given by quasineutral planes - i.e., filled by equilibrium points. Three different quasineutral planes have been identified depending on parameters and involving: (i) persistence of HV and DVGs; (ii) persistence of non-infected cells and DVG-infected cells; and (iii) persistence of DVG-infected cells and DVGs. Key parameters involved in these scenarios are the maximum burst size (B), the fraction of DVGs produced during HV replication (β), and the replication advantage of DVGs (δ). More precisely, in the case $0<B<1+\beta$ the system displays tristability, where all three scenarios are present. In the case $1+\beta <B<1+\beta +\delta$ this tristability persists but attracting scenario (ii) is reduced to a well-defined half-plane. For $B>1+\beta +\delta$, the scenario (i) becomes globally attractor. Scenarios (ii) and (iii) are compatible with the so-called self-curing since the HV is removed from the population. Sensitivity analyses indicate that model dynamics largely depend on DVGs production rate (β) and their replicative advantage (δ), and on both the infection rates and virus-induced cell deaths. Finally, the model has been fitted to single-passage experimental data using an artificial intelligence methodology based on genetic algorithms and key virological parameters have been estimated.