Reliability mesh convergence analysis by introducing expanded control variates

The safety evaluation of engineering systems whose performance evaluation requires finite element analysis is a challenge in reliability theory.Recently,Adjusted Control Variates Technique(ACVAT)has proposed by the authors to solve this issue.ACVAT uses the results of a finite element method(FEM)model with coarse mesh density as the control variates of the model with fine mesh and efficiently solves FEM-based reliability problems.ACVAT however does not provide any results about the reliability-based mesh convergence of the problem,which is an important tool in FEM.Mesh-refinement analysis allows checking whether the numerical solution is sufficiently accurate,even though the exact solution is unknown.In this study,by introducing expanded control variates(ECV)formulation,ACVAT is improved and the capabilities of the method are also extended for efficient reliability mesh convergence analysis ofFEM-based reliability problems.In the present study,the FEM-based reliability analyses of four practical engineering problems are investigated by this method and the corresponding results are compared with accurate results obtained by analytical solutions for two problems.The results confirm that the proposed approach not only handles the mesh refinement progress with the required accuracy,but it also reduces considerably the computational cost of FEM-based reliability problems.

Reservoir-induced landslides and risk control in Three Gorges Project on Yangtze River,China

The Three Gorges region in China was basically a geohazard-prone area prior to construction of the Three Gorges Reservoir （TGR）. After construction of the TGR, the water level was raised from 70 m to 175 m above sea level （ASL）, and annual reservoir regulation has caused a 30-m water level difference after impoundment of the TGR since September 2008. This paper first presents the spatiotemporal distribution of landslides in six periods of 175 m ASL trial impoundments from 2008 to 2014. The results show that the number of landslides sharply decreased from 273 at the initial stage to less than ten at the second stage of impoundment. Based on this, the reservoir-induced landslides in the TGR region can be roughly classified into five failure patterns, i.e. accumulation landslide, dip-slope landslide, reversed bedding landslide, rockfall, and karst breccia landslide. The accumulation landslides and dip-slope landslides account for more than 90%. Taking the Shuping accumulation landslide （a sliding mass volume of 20.7 × 106 m^3） in Zigui County and the Outang dip-slope landslide （a sliding mass volume of about 90 × 106 m^3） in Fengjie County as two typical cases, the mechanisms of reactivation of the two landslides are analyzed. The monitoring data and factor of safety （FOS） calculation show that the accumulation landslide is dominated by water level variation in the reservoir as most part of the mass body is under 175 m ASL, and the dip-slope landslide is controlled by the coupling effect of reservoir water level variation and precipitation as an extensive recharge area of rainfall from the rear and the front mass is below 175 m ASL. The characteristics of landslide-induced impulsive wave hazards after and before reservoir impoundment are studied, and the probability of occurrence of a landslide-induced impulsive wave hazard has increased in the reservoir region. Simulation results of the Ganjingzi landslide in Wushan County indicate the strong relationship between landslide-induced surge and water variation with high potential risk to shipping and residential areas. Regarding reservoir regulation in TGR when using a single index, i.e. 1-d water level variation, water resources are not well utilized, and there is also potential risk of disasters since 2008. In addition, various indices such as 1-d, 5-d, and 10-d water level variations are proposed for reservoir regulation. Finally, taking reservoir-induced landslides in June 2015 for example, the feasibility of the optimizing indices of water level variations is verified.

Variational Quality Control of Non-Gaussian Innovations in the GRAPES m3DVAR System: Mass Field Evaluation of Assimilation Experiments

The existence of outliers can seriously influence the analysis of variational data assimilation.Quality control allows us to effectively eliminate or absorb these outliers to produce better analysis fields.In particular,variational quality control(VarQC) can process gray zone outliers and is thus broadly used in variational data assimilation systems.In this study,governing equations are derived for two VarQC algorithms that utilize different contaminated Gaussian distributions(CGDs): Gaussian plus flat distribution and Huber norm distribution.As such,these VarQC algorithms can handle outliers that have non-Gaussian innovations.Then,these VarQC algorithms are implemented in the Global/Regional Assimilation and PrEdiction System(GRAPES) model-level three-dimensional variational data assimilation(m3 DVAR) system.Tests using artificial observations indicate that the VarQC method using the Huber distribution has stronger robustness for including outliers to improve posterior analysis than the VarQC method using the Gaussian plus flat distribution.Furthermore,real observation experiments show that the distribution of observation analysis weights conform well with theory,indicating that the application of VarQC is effective in the GRAPES m3 DVAR system.Subsequent case study and longperiod data assimilation experiments show that the spatial distribution and amplitude of the observation analysis weights are related to the analysis increments of the mass field(geopotential height and temperature).Compared to the control experiment,VarQC experiments have noticeably better posterior mass fields.Finally,the VarQC method using the Huber distribution is superior to the VarQC method using the Gaussian plus flat distribution,especially at the middle and lower levels.

Diurnal and Seasonal Variations of CO2Fluxes and Their Climate Controlling Factors for a Subtropical Forest in Ningxiang

In this study, the diurnal and seasonal variations of CO2 fluxes in a subtropical mixed evergreen forest in Ningxiang of Hunan Province, part of the East Asian monsoon region, were quantified for the first time. The fluxes were based on eddy covariance measurements from a newly initiated flux tower. The relationship between the CO2 fluxes and climate factors was also analyzed. The results showed that the target ecosystem appeared to be a clear carbon sink in 2013, with integrated net ecosystem CO2exchange（NEE）, ecosystem respiration（RE）, and gross ecosystem productivity（GEP） of-428.8, 1534.8 and1963.6 g C m^-2yr^-1, respectively. The net carbon uptake（i.e. the-NEE）, RE and GEP showed obvious seasonal variability,and were lower in winter and under drought conditions and higher in the growing season. The minimum NEE occurred on12 June（-7.4 g C m^-2d^-1）, due mainly to strong radiation, adequate moisture, and moderate temperature; while a very low net CO2 uptake occurred in August（9 g C m^-2month^-1）, attributable to extreme summer drought. In addition, the NEE and GEP showed obvious diurnal variability that changed with the seasons. In winter, solar radiation and temperature were the main controlling factors for GEP, while the soil water content and vapor pressure deficit were the controlling factors in summer. Furthermore, the daytime NEE was mainly limited by the water-stress effect under dry and warm atmospheric conditions, rather than by the direct temperature-stress effect.

Start-up phase plasma discharge design of a tokamak via control parameterization method

The tokamak start-up is a very important phase during the process to obtain a suitable equalizing plasma, and its governing model can be described as a set of nonlinear ordinary differential equations（ODEs）. In this paper, we first estimate the parameters in the original model and set up an accurate model to express how the variables change during the start-up phase, especially how the plasma current changes with respect to time and the loop voltage. Then, we apply the control parameterization method to obtain an approximate optimal parameters selection problem for the loop voltage design to achieve a desired plasma current target. Computational optimal control techniques such as the variational method and the costate method are employed to solve the problem, respectively. Finally, numerical simulations are performed and the results obtained via different methods are compared. Our numerical parameterization method and optimization procedure turn out to be effective.

Atmospheric Pollution Control Effect of Key Cities in Inner Mongolia in 2014

APEC conference was held in Beijing during November 3- 12,2014. Hohhot City and Baotou City fall into the peripheral key air pollution control cities in the ＂ Beijing- Tianjin- Hebei＂ region. Inner Mongolia government adopted powerful pollution control measures in the period of the conference. According to pollutant concentration data and meteorological data etc. in the course of the event and the same period of last year,the atmospheric pollution variations and control effect were discussed in this study. The results showed that during October 1- 25,2014,there were 16 days with air pollution in Hohhot City and 15 days with air pollution in Baotou City,respectively increasing by 8% and 34% compared with the same period of 2013,and the concentration of particulate matter was also higher than that of last year. During October 22- 24,2014,Hohhot and Baotou cities were polluted persistently. The variation features of hourly concentration of main pollutants PM（10） and PM2. 5were similar to those in the same period of 2013. That is,the pollutant concentration reached the maximum from 21：00 to 23：00,and the minimum appeared from 15： 00 to 19： 00 in the next day. In the course of the event,the concentration of particulate matter in the two cities stared to reduce greatly on October 26. From October 26 to November 13,there were no days with air pollution in Hohhot City,decreasing by 100% compared with the same period of 2013; there were five days with air pollution in Baotou City,and the numbers of days with slight,moderate and severe pollution reduced by 37%,100% and67% respectively compared with the same period of last year. The persistent air pollution from October 22 to the first 10 days of November was related to unfavorable meteorological conditions,and the meteorological condition in the same period of 2014 was even worse. In the course of the event,the Inner Mongolia Government adopted air pollution control measures around October 25 and began to adopt some powerful pollution control measures on November 1. As a result,air pollution in key cities has been controlled effectively. This event showed that urban atmospheric pollution problem can be resolved,and we should take an optimistic attitude towards this matter.

Variational quality control of non-Gaussian innovations and its parametric optimizations for the GRAPES m3DVAR system

The magnitude and distribution of observation innovations,which have an important impact on the analyzed accuracy,are critical variables in data assimilation.Variational quality control(VarQC)based on the contaminated Gaussian distribution(CGD)of observation innovations is now widely used in data assimilation,owing to the more reasonable representation of the probability density function of innovations that can sufficiently absorb observations by assigning different weights iteratively.However,the inaccurate parameters prevent VarQC from showing the advantages it should have in the GRAPES(Global/Regional Assimilation and PrEdiction System)m3DVAR system.Consequently,the parameter optimization methods are considerable critical studies to improve VarQC.In this paper,we describe two probable CGDs to include the non-Gaussian distribution of actual observation errors,Gaussian plus flat distribution and Huber norm distribution.The potential optimization methods of the parameters are introduced in detail for different VarQCs.With different parameter configurations,the optimization analysis shows that the Gaussian plus flat distribution and the Huber norm distribution are more consistent with the long-tail distribution of actual innovations compared to the Gaussian distribution.The VarQC’s cost and gradient functions with Huber norm distribution are more reasonable,while the VarQC’s cost function with Gaussian plus flat distribution may converge on different minimums due to its nonconcave properties.The weight functions of two VarQCs gradually decrease with the increase of innovation but show different shapes,and the VarQC with Huber norm distribution shows more elasticity to assimilate the observations with a high contamination rate.Moreover,we reveal a general derivation relationship between the CGDs and VarQCs.A novel schematic interpretation that classifies the assimilated data into three categories in VarQC is presented.They are conducive to the development of a new VarQC method in the future.

Common Fixed Point Theorems and Q-property for Quasi-contractive Mappings under c-distance on TVS-valued Cone Metric Spaces without the Normality

In this paper, we derive the stochastic maximum principle for optimal control problems of the forward-backward Markovian regime-switching system. The control system is described by an anticipated forward-backward stochastic pantograph equation and modulated by a continuous-time finite-state Markov chain. By virtue of classical variational approach, duality method, and convex analysis, we obtain a stochastic maximum principle for the optimal control.

Machining Error Control by Integrating Multivariate Statistical Process Control and Stream of Variations Methodology

For aircraft manufacturing industries, the analyses and prediction of part machining error during machining process are very important to control and improve part machining quality. In order to effectively control machining error, the method of integrating multivariate statistical process control （MSPC） and stream of variations （SoV） is proposed. Firstly, machining error is modeled by multi-operation approaches for part machining process. SoV is adopted to establish the mathematic model of the relationship between the error of upstream operations and the error of downstream operations. Here error sources not only include the influence of upstream operations but also include many of other error sources. The standard model and the predicted model about SoV are built respectively by whether the operation is done or not to satisfy different requests during part machining process. Secondly, the method of one-step ahead forecast error （OSFE） is used to eliminate autocorrelativity of the sample data from the SoV model, and the T2 control chart in MSPC is built to realize machining error detection according to the data characteristics of the above error model, which can judge whether the operation is out of control or not. If it is, then feedback is sent to the operations. The error model is modified by adjusting the operation out of control, and continually it is used to monitor operations. Finally, a machining instance containing two operations demonstrates the effectiveness of the machining error control method presented in this paper.

Optimal Control of a Frictional Contact Problem

We consider a mathematical model which describes a contact between a deformable body and a foundation. The contact is bilateral and modelled with Tresca＇s friction law. The goal of this paper is to study an optimal control problem which consists of leading the stress tensor as close as possible to a given target, by acting with a control on the boundary of the body. We state an optimal control problem which admits at least one solution. We also introduce the regularized control problem for which we study the convergence when the regularization parameter tends to zero. Finally, an optimally condition is established for this problem.

Efficient Simulations of Option Pricing and Greeks Under Three-Factor Model by Conditional Monte Carlo Method

This paper proposes a hybrid Monte Carlo simulation method for pricing European options under the stochastic volatility model and three-factor model.First,the European options are expressed as a conditional expectation formula,which can be used not only for reducing variance of simulations,but also for calculating the value of Greeks easily,due to the elimination of the weak singularity for the payoff of the option.Then,in order to reduce variance further,the authors also construct a new explicit regression based control variate under Heston model and three-factor model respectively.Numerical results of experiments show that the proposed method can greatly reduce the variance of simulation for pricing European option,and is easy to complement for the calculation of Greeks.