Forecasting Carbon Dioxide Price Using a Time-Varying High-Order Moment Hybrid Model of NAGARCHSK and Gated Recurrent Unit Network

The carbon market is recognized as the most effective means for reducing global carbon dioxide emissions. Effective carbon price forecasting can help the carbon market to solve environmental problems at a lower economic cost. However, the existing studies focus on the carbon premium explanation from the perspective of return and volatility spillover under the framework of the mean-variance low-order moment. Specifically, the time-varying, high-order moment shock of market asymmetry and extreme policies on carbon price have been ignored. The innovation of this paper is constructing a new hybrid model, NAGARCHSK-GRU, that is consistent with the special characteristics of the carbon market. In the proposed model, the NAGARCHSK model is designed to extract the time-varying, high-order moment parameter characteristics of carbon price, and the multilayer GRU model is used to train the obtained time-varying parameter and improve the forecasting accuracy. The results conclude that the NAGARCHSK-GRU model has better accuracy and robustness for forecasting carbon price. Moreover, the long-term forecasting performance has been proved. This conclusion proves the rationality of incorporating the time-varying impact of asymmetric information and extreme factors into the forecasting model, and contributes to a powerful reference for investors to formulate investment strategies and assist a reduction in carbon emissions.

Physical study of the non-equilibrium development of a turbulent thermal boundary layer

The direct numerical simulation of a non-equilibrium turbulent heat transfer case is performed in a channel flow, where non-equilibrium is induced by a step change in surface temperature. The domain is thus made of two parts in the streamwise direction. Upstream, the flow is turbulent, homogeneous in temperature and the channel walls are adiabatic. The inflow conditions are extracted from a recycling plane located further downstream, so that a fully developed turbulent adiabatic flow reaches the second part. In the domain located downstream, isothermal boundary conditions are prescribed at the walls. The boundary layer, initially at equilibrium, is perturbed by the abrupt change of boundary conditions, and a non-equilibrium transient phase is observed until, further downstream, the flow reaches a new equilibrium state, presenting a fully developed thermal boundary layer. The work aims at identifying the non-equilibrium effects that are expected to be encountered in comparable flows, while providing the means to understand them. In particular, the study allows for the identification of an inner region of the developing boundary layer where several quantities are at equilibrium. Other quantities, instead, exhibit a behaviour of their own, especially in proximity to the leading edge. The analysis is supported by mean and root-mean-square profiles of temperature and velocity, as well as by budgets of first- and second-order moment balance equations for the enthalpy and momentum turbulent fields.

On Some Approximation Properties for a Sequence of λ-Bernstein Type Operators

In 2010, Long and Zeng introduced a new generalization of the Bernstein polynomials that depends on a parameter and called -Bernstein polynomials. After that, in 2018, Lain and Zhou studied the uniform convergence for these -polynomials and obtained a Voronovaskaja-type asymptotic formula in ordinary approximation. This paper studies the convergence theorem and gives two Voronovaskaja-type asymptotic formulas of the sequence of -Bernstein polynomials in both ordinary and simultaneous approximations. For this purpose, we discuss the possibility of finding the recurrence relations of the -th order moment for these polynomials and evaluate the values of -Bernstein for the functions , is a non-negative integer

Higher-order moment matching based fine-grained adversarial domain adaptation method for intelligent bearing fault diagnosis

Due to the data distribution discrepancy caused by the time-varying working conditions, the intelligent diagnosis methods fail to achieve accurate fault classification in engineering scenarios. To this end, this paper presents a novel higher-order moment matching-based adversarial domain adaptation method (HMMADA) for intelligent bearing fault diagnosis. First, the deep one-dimensional convolution neural network is constructed as the feature extractor to learn the discriminative features of each category through different domains. Then, the distribution discrepancy across domains is significantly reduced by using the joint higher-order moment statistics (HMS) and adversarial learning. In particular, the HMS integrates the first-order and second-order statistics into a unified framework and achieves a fine-grained distribution adaptation between different domains. Finally, the feasibility and effectiveness of the HMMADA are validated by several transfer experiments constructed on two different bearing datasets. The results demonstrate that the HMS is more effective compared with the lower-order statistics.

Reliability Assessment on Pile Foundation Bearing Capacity Based on the First Four Moments in High-Order Moment Method

In this paper, the high-order moment method (HOMM) was developed for estimating pile foundation bearing capacity reliability assessment. Firstly, after the performance function was established, the first four moments (viz. mean, variance, skewness, and kurtosis) were suggested to be determined by a point estimate method based on two-dimensional reduction integrations. Then, the probability distribution of the performance function for the pile foundation bearing capacity was then approximated by a four-parameter cubic normal distribution, in which its distribution parameters are the first four moments. Meanwhile, the quantile of the probability distribution for the performance function and its reliability index was capable to be obtained through this distribution. In order to examine the efficiency of this method in engineering application, four pile foundations with different length-diameter radios were investigated in detail. The results demonstrate that the reliability analysis based on HOMM is greatly improved to the computational efficiency without loss precision compared with Monte Carlo simulation (MCS) and does not require complex partial derivative solving, checking point sought, and large numbers of iteration comparing with first-order reliability method (FORM). Moreover, the probability distribution function (PDF) approximated by the four-parameter cubic normal distribution was found to be consistent with that obtained by MCS. Eventually, the effects of parameter sensitivity for relative soil layer of the certain pile on reliability index were illustrated using the above-mentioned method. It indicated that the HOMM is an effective and simple approach for reliability assessment of the pile foundation bearing capacity.

Statistical Machine Learning Model for Uncertainty Planning of Distributed Renewable Energy Sources in Distribution Networks

New energy power systems with high-permeability photovoltaic and wind power are high-dimensional dynamic large-scale systems with nonlinear, uncertain and complex operating characteristics. The uncertainty of new energies creates challenges in detailed analyses of operating conditions and the efficient planning of distribution networks. Probabilistic power flows (PPFs) are effective tools for uncertainty analyses of distribution networks, and they can be applied in stochastic programming, risk assessment and other fields. We propose different forms of PPFs, which are origin moments rather than means and variances, based on point estimation. We design a stochastic programming model suitable for new energy planning in practice, and the PPF results can be used to improve energy stochastic programming methods by considering the principle of maximum entropy (POME) and quadratic fourth-order moment (QFM) estimation. The origin moments of PPFs are transformed into central moments as inputs of QFM based on probability theory. QFM can efficiently estimate the constraint probability levels of stochastic optimal planning models, and the proposed method is verified based on an IEEE 33-node distribution network.

Multi-temperature generalized Zhdanov closure for scrape-off layer/edge applications

The derivation of the multi-temperature generalized Zhdanov closure is provided starting from the most general form of the left hand side of the moment averaged kinetic equation with the Sonine-Hermite polynomial ansatz for an arbitrary number of moments. The process of arriving at the reduced higher-order moment equations, with its assumptions and approximations, is explicitly outlined. The generalized multi-species, multi-temperature coefficients from the authors' previous article are used to compute values of higher order moments such as heat flux in terms of the lower order moments. Transport coefficients and the friction and thermal forces for magnetic confinement fusion relevant cases with the generalized coefficients are compared to the scheme with the single-temperature coefficients previously provided by Zhdanov et al. It is found that the 21N-moment multi-temperature coefficients are adequate for most cases relevant to fusion. Furthermore, the 21N-moment scheme is also tested against the trace approximation to determine the range of validity of the trace approximation with respect to fusion relevant plasmas. Possible refinements to the closure scheme are illustrated as well, in order to account for quantities which might be significant in certain schemes such as the drift approximation.

Kármán–Howarth solutions of homogeneous isotropic turbulence

The Kármán–Howarth equation (KHEq) is solved using a closure model to obtain solutions of the second-order moment of the velocity increment, $S_2$ , in homogeneous isotropic turbulence (HIT). The results are in good agreement with experimental data for decaying turbulence and are also consistent with calculations based on the three-dimensional energy spectrum for decaying HIT. They differ, however, from those for forced HIT, the difference occurring mainly at large scales. This difference is attributed to the fact that the forcing generates large-scale motions which are not compatible with the KHEq. As the Reynolds number increases, the impact of forcing on the small scales decreases, thus allowing the KHEq and spectrally based solutions to agree well in the range of scales unaffected by forcing. Finally, the results show that the two-thirds law is compatible with the KHEq solutions as the Reynolds number increases to very large, if not infinite, values.

Quasi-Entropy Closure: A Fast and Reliable Approach to Close the Moment Equations of the Chemical Master Equation

MotivationThe Chemical Master Equation is the most comprehensive stochastic approach to describe the evolution of a (bio-)chemical reaction system. Its solution is a time-dependent probability distribution on all possible configurations of the system. As the number of possible configurations is typically very large, the Master Equation is often practically unsolvable. The Method of Moments reduces the system to the evolution of a few moments of this distribution, which are described by a system of ordinary differential equations. Those equations are not closed, since lower order moments generally depend on higher order moments. Various closure schemes have been suggested to solve this problem, with different advantages and limitations. Two major problems with these approaches are first that they are open loop systems, which can diverge from the true solution, and second, some of them are computationally expensive.ResultsHere we introduce Quasi-Entropy Closure, a moment closure scheme for the Method of Moments which estimates higher order moments by reconstructing the distribution that minimizes the distance to a uniform distribution subject to lower order moment constraints. Quasi-Entropy closure is similar to Zero-Information closure, which maximizes the information entropy. Results show that both approaches outperform truncation schemes. Moreover, Quasi-Entropy Closure is computationally much faster than Zero-Information Closure. Finally, our scheme includes a plausibility check for the existence of a distribution satisfying a given set of moments on the feasible set of configurations. Results are evaluated on different benchmark problems.Abstract Figure