Large Eddy Simulation and Dynamic Mode Decomposition of Turbulent Mixing Layers

Turbulent mixing layers are canonical flow in nature and engineering, and deserve comprehensive studies under various conditions using different methods. In this paper, turbulent mixing layers are investigated using large eddy simulation and dynamic mode decomposition. The accuracy of the computations is verified and validated. Standard dynamic mode decomposition is utilized to flow decomposition, reconstruction and prediction. It was found that the dominant-mode selection criterion based on mode amplitude is more suitable for turbulent mixing layer flow compared with the other three criteria based on singular value, modal energy and integral modal amplitude, respectively. For the mixing layer with random disturbance, the standard dynamic mode decomposition method could accurately reconstruct and predict the region before instability happens, but is not qualified in the regions after that, which implies that improved dynamic mode decomposition methods need to be utilized or developed for the future dynamic mode decomposition of turbulent mixing layers.

DDPG-Based Continuous Thickness and Tension Coupling Control for the Unsteady Cold Rolling Process

Cold rolling is an important part of the iron and steel industry, and the unsteady rolling process of cold rolling usually brings significant influences on the stability of product quality. In the unsteady rolling process, various disturbances and uncertainties such as variable lubrication state, variable equipment working conditions lead to difficulties in the establishment of state space model of thickness and tension, which has become a thorny problem in thickness and tension control. In this paper, we present a model-free controller based on Deep Deterministic Policy Gradient(DDPG), which can continuously control the thickness tension of the unsteady rolling process without the mathematical model. We first formulate the thickness and tension control problem to Markov Decision Process(MDP). We apply strategies such as dividing state space variables with mechanism model, defining reward function and state normalization, the random disturbance and complex uncertainties of unsteady cold rolling process are coped with by utilizing the DDPG controller. In addition, these strategies also ensure the learning performance and stability of the DDPG controller under random disturbance. Simulations and experiments show that the proposed the DDPG controller does not require any prior knowledge of uncertain parameters and can operate without knowing unsteady rolling mathematical models, which has better accuracy, stability and rapidity for thickness and tension in the unsteady rolling process than proportional integral(PI) controller. The artificial intelligence-based controller brings both product quality improvement and intelligence to cold rolling.

The Dynamics of a Stochastic SIR Epidemic Model with Nonlinear Incidence and Vertical Transmission

In this study, we build a stochastic SIR epidemic model with vertical infection and nonlinear incidence. The influence of the fluctuation of disease transmission parameters and state variables on the dynamic behaviors of the system is the focus of our study. Through the theoretical analysis, we obtain that there exists a unique global positive solution for any positive initial value. A threshold R 0 s is given. When R 0 s < 1 , the diseases can be extincted with probability one. When R 0 s > 1 , we construct a stochastic Lyapunov function to prove that the system exists an ergodic stationary distribution, which means that the disease will persist. Then, we obtain the conditions that the solution of the stochastic model fluctuates widely near the equilibria of the corresponding deterministic model. Finally, the correctness of the results is verified by numerical simulation. It is further found that the fluctuation of disease transmission parameters and infected individuals with the environment can reduce the threshold of disease outbreak, while the fluctuation of susceptible and recovered individuals has a little effect on the dynamic behavior of the system. Therefore, we can make the disease extinct by adjusting the appropriate random disturbance.

Exponentially fitted multisymplectic scheme for conservative Maxwell equations with oscillary solutions

Aiming at conservative Maxwell equations with periodic oscillatory solutions, we adopt exponentially fitted trapezoidal scheme to approximate the temporal and spatial derivatives. The scheme is a multisymplectic scheme. Under periodic boundary condition, the scheme satisfies two discrete energy conservation laws. The scheme also preserves two discrete divergences. To reduce computation cost, we split the original Maxwell equations into three local one-dimension (LOD) Maxwell equations. Then exponentially fitted trapezoidal scheme, applied to the resulted LOD equations, generates LOD multisymplectic scheme. We prove the unconditional stability and convergence of the LOD multisymplectic scheme. Convergence of numerical dispersion relation is also analyzed. At last, we present two numerical examples with periodic oscillatory solutions to confirm the theoretical analysis. Numerical results indicate that the LOD multisymplectic scheme is efficient, stable and conservative in solving conservative Maxwell equations with oscillatory solutions. In addition, to one-dimension Maxwell equations, we apply least square method and LOD multisymplectic scheme to fit the electric permittivity by using exact solution disturbed with small random errors as measured data. Numerical results of parameter inversion fit well with measured data, which shows that least square method combined with LOD multisymplectic scheme is efficient to estimate the model parameter under small random disturbance.

Optimal Network Defense Strategy Selection Method: A Stochastic Differential Game Model

In a real-world network confrontation process, attack and defense actions change rapidly and continuously. The network environment is complex and dynamically random. Therefore, attack and defense strategies are inevitably subject to random disturbances during their execution, and the transition of the network security state is affected accordingly. In this paper, we construct a network security state transition model by referring to the epidemic evolution process, use Gaussian noise to describe random effects during the strategy execution, and introduce a random disturbance intensity factor to describe the degree of random effects. On this basis, we establish an attack-defense stochastic differential game model, propose a saddle point equilibrium solution method, and provide an algorithm to select the optimal defense strategy. Our method achieves real-time defense decision-making in network attack-defense scenarios with random disturbances and has better real-time performance and practicality than current methods. Results of a simulation experiment show that our model and algorithm are effective and feasible.

Development of Joint Stated-Preference-off-Revealed-Preference Model for Shanghai Commute Mode Choices in Response to Parking Fee Management

Facing challenges in parking demand-and-supply imbalance and severe road traffic congestion during peak periods in Shanghai, in this paper we develop an SP-off-RP (stated-preference-off-revealed-preference) choice model to analyze relations between parking fee and commute mode choices based on survey data collected there. The survey questionnaire collects information about travelers’ daily commute, travel choices in the SP context, and personal socioeconomic and demographic attributes. The road network and public transportation network data are also used for model development. The model includes three main travel modes: car, public transit, and non-motorized mode. Variables that significantly influence mode choice and the reasons behind it are discussed, including the parking fee, the level-of-service (LOS) of the three modes, and socioeconomic and demographic variables. In the process of model development, a random sample of full-mode commute trips in Shanghai is integrated to improve model precision. The study reveals that the new random disturbance in the SP context is relatively large. The direct elasticity of the parking fee is estimated at −0.85, which means that when the parking fee increases by 10%, the average probability of choosing a private car for the commute will decrease by 8.5%. It is also found that transit LOS improvements have potential to reduce auto use in Shanghai. The study provides references on parking pricing as an alternative policy for travel demand management in Shanghai.

A time-varying grey Riccati model based on interval grey numbers for China's clean energy generation predicting

PurposeIn order to accurately predict the uncertain and nonlinear characteristics of China's three clean energy generation, this paper presents a novel time-varying grey Riccati model (TGRM(1,1)) based on interval grey number sequences.Design/methodology/approachBy combining grey Verhulst model and a special kind of Riccati equation and introducing a time-varying parameter and random disturbance term the authors advance a TGRM(1,1) based on interval grey number sequences. Additionally, interval grey number sequences are converted into middle value sequences and trapezoid area sequences by using geometric characteristics. Then the predicted formula is obtained by using differential equation principle. Finally, the proposed model's predictive effect is evaluated by three numerical examples of China's clean energy generation.FindingsBased on the interval grey number sequences, the TGRM(1,1) is applied to predict the development trend of China's wind power generation, China's hydropower generation and China's nuclear power generation, respectively, to verify the effectiveness of the novel model. The results show that the proposed model has better simulated and predicted performance than compared models.Practical implicationsDue to the uncertain information and continuous changing of clean energy generation in the past decade, interval grey number sequences are introduced to characterize full information of the annual clean energy generation data. And the novel TGRM(1,1) is applied to predict upper and lower bound values of China's clean energy generation, which is significant to give directions for energy policy improvements and modifications.Originality/valueThe main contribution of this paper is to propose a novel TGRM(1,1) based on interval grey number sequences, which considers the changes of parameters over time by introducing a time-varying parameter and random disturbance term. In addition, the model introduces the Riccati equation into classic Verhulst, which has higher practicability and prediction accuracy.

On σ-entropy Analysis of Linear Stochastic Systems in State Space

In this paper the problem of random disturbance attenuation capabilities in linear continuous systems is studied. It is supposed that the system operates under random disturbances with bounded σ-entropy level. σ-entropy norm indicates a performance index of the continuous system on the set of the random signals with bounded σ-entropy. This paper presents a time-domain solution to the calculation of σ-entropy norm of the continuous linear time-invariant system. σ-entropy norm is defined after solving coupled matrix equations: one algebraic Riccati equation, one nonlinear equation over log determinant function, and two Lyapunov equations.