Derivation of Simplified Models of Plan View Pattern Control Function for Plate Mill

The plan view pattern control theoretical models were simplified. Under the condition of constant volume for the plan view pattern compensation, the relation between the thickness and the length can be simplified to the linearity in the segment for the plan view pattern control function. The compensation volume can be dispersed for easy calculation. By comparing the model calculation result with the actual result, it was concluded that the simplified model can be used for the online control process.

A Simplified Model for SO_(2) Generation during Spontaneous Combustion of Coal Gangue

A simplified model for SO_(2) generation during spontaneous combustion of coal gangue was put forward and validated using the measured data.Using the proposed model,the effects of initial temperature inside the gangue and fresh air supply on SO_(2) generation were discussed.The results showed that,higher initial temperature inside the gangue could accelerate the oxidation rate of FeS_(2) and increase the maximum concentration of SO_(2).If initial temperature inside the gangue increased by about 37%,the total SO_(2) generation increased by 166%.Fresh air supply had less significant effect on the oxidation rate of FeS_(2).However,the higher the fresh air supply was,the more FeS_(2) could be oxidized,which ultimately produced more SO_(2).Although the computed results and the measured data concerning the inner locations inside the gangue had a certain degree of error,the proposed model can provide a relatively precise total release of SO_(2) within acceptable accuracy.Besides,this method provides a useful prototype to predict the generation of hazardous materials,such as CO,NO_(x),and chlorine during the spontaneous combustion of coal gangue.

A Simplified Model for Buckling and Post-Buckling Analysis of Cu Nanobeam Under Compression

Both of Buckling and post-buckling are fundamental problems of geometric nonlinearity in solid mechanics.With the rapid development of nanotechnology in recent years,buckling behaviors in nanobeams receive more attention due to its applications in sensors,actuators,transistors,probes,and resonators in nanoelectromechanical systems(NEMS)and biotechnology.In this work,buckling and post-buckling of copper nanobeam under uniaxial compression are investigated with theoretical analysis and atomistic simulations.Different cross sections are explored for the consideration of surface effects.To avoid complicated high order buckling modes,a stressbased simplified model is proposed to analyze the critical strain for buckling,maximum deflection,and nominal failure strain for post-buckling.Surface effects should be considered regarding critical buckling strain and the maximum post-buckling deflection.The critical strain increases with increasing nanobeam cross section,while themaximumdeflection increases with increasing loading strain but stays nearly the same for different cross sections,and the underlying mechanisms are revealed by our model.The maximum deflection is also influenced by surface effects.The nominal failure strains are captured by our simulations,and they are in good agreement with the simplified model.Our results can be used for helping design strain gauge sensors and nanodevices with self-detecting ability.

A Simplified Scheme of the Generalized Layered Radiative Transfer Model

In this paper, firstly, a simplified version （SGRTM） of the generalized layered radiative transfer model （GRTM） within the canopy, developed by us, is presented. It reduces the information requirement of inputted sky diffuse radiation, as well as of canopy morphology, and in turn saves computer resources. Results from the SGRTM agree perfectly with those of the GRTM. Secondly, by applying the linear superposition principle of the optics and by using the basic solutions of the GRTM for radiative transfer within the canopy under the condition of assumed zero soil reflectance, two sets of explicit analytical solutions of radiative transfer within the canopy with any soil reflectance magnitude are derived： one for incident diffuse, and the other for direct beam radiation. The explicit analytical solutions need two sets of basic solutions of canopy reflectance and transmittance under zero soil reflectance, run by the model for both diffuse and direct beam radiation. One set of basic solutions is the canopy reflectance αf （written as α1 for direct beam radiation） and transmittance βf （written as β1 for direction beam radiation） with zero soil reflectance for the downward radiation from above the canopy （i.e. sky）, and the other set is the canopy reflectance （αb） and transmittance βb for the upward radiation from below the canopy （i.e., ground）. Under the condition of the same plant architecture in the vertical layers, and the same leaf adaxial and abaxial optical properties in the canopies for the uniform diffuse radiation, the explicit solutions need only one set of basic solutions, because under this condition the two basic solutions are equal, i.e., αf = αb and βf = βb. Using the explicit analytical solutions, the fractions of any kind of incident solar radiation reflected from （defined as surface albedo, or canopy reflectance）, transmitted through （defined as canopy transmittance）, and absorbed by （defined as canopy absorptance） the canopy and other properties pertinent to the radiative transfer within the canopy can be estimated easily on the ground surface below the canopy （soil or snow surface） with any reflectance magnitudes. The simplified transfer model is proven to have a similar accuracy compared to the detailed model, as well as very efficient computing.

A Simplified Model for Generating 3D Realistic Sound in the Multimedia and Virtual Reality Systems

It is a key feature to embed 3D realistic sound effect in the future multimedia and virtual reality systems. Recent research on acoustics and psychoacoustics reveals the important cues for sound localization and sound perception. One promising approach to generate 3D realistic sound effect uses two earphones by simulating the sound waveforms from sound source to eardrum. This paper summarizes two methods for generating 3D realistic sound and points out their inherent drawbacks. To overcome these drawbacks we propose a simplified model to generate 3D realistic sound at any positions in the horizontal plane based on the results of sound perception and localization. Experimental results show that the model is correct and efficient.

Simplified Prediction Model for Vortex-Induced Vibrations of Top Tensioned Risers

According to the characteristics of deepwater top tensioned risers, a simplified model is presented to predict the multi-modal response of vortex-induced vibration （VIV） in non-uniform flow based on energy equilibrium theory and the exporimental data from VIV self-excited and forced oscillations of rigid cylinders. The response amplitude of each mode is determined by a balance between the energy fed into the riser over the lock-in regions and the energy dissipated by the fluid damping over the remainders. Compared with the previous prediction models, this method can take fully account of the intrinsic nature of VIV for low mass ratio structures on lock-in regions, added mass and nonlinear fluid damping effect, etc. Moreover, it is the first time to propose the accurate calculating procedure for VIV amplitude correction factor by solving energy equilibrium equation and a closed form solution is presented for the case of a riser of uniform mass and cross-section oscillating in a uniform flow. The predicted values show a reasonable agreement with VIV experiments of riser models in stepped and sheared currents.

The Numerical Scheme Development of a Simplified Frozen Soil Model

In almost all frozen soil models used currently, three variables of temperature, ice content and moisture content are used as prognostic variables and the rate term, accounting for the contribution of the phase change between water and ice, is shown explicitly in both the energy and mass balance equations. The models must be solved by a numerical method with an iterative process, and the rate term of the phase change needs to be pre-estimated at the beginning in each iteration step. Since the rate term of the phase change in the energy equation is closely related to the release or absorption of the great amount of fusion heat, a small error in the rate term estimation will introduce greater error in the energy balance, which will amplify the error in the temperature calculation and in turn, cause problems for the numerical solution convergence. In this work, in order to first reduce the trouble, the methodology of the variable transformation is applied to a simplified frozen soil model used currently, which leads to new frozen soil scheme used in this work. In the new scheme, the enthalpy and the total water equivalent are used as predictive variables in the governing equations to replace temperature, volumetric soil moisture and ice content used in many current models. By doing so, the rate terms of the phase change are not shown explicitly in both the mass and energy equations and its pre-estimation is avoided. Secondly, in order to solve this new scheme more functionally, the development of the numerical scheme to the new scheme is described and a numerical algorithm appropriate to the numerical scheme is developed. In order to evaluate the new scheme of the frozen soil model and its relevant algorithm, a series of model evaluations are conducted by comparing numerical results from the new model scheme with three observational data sets. The comparisons show that the results from the model are in good agreement with these data sets in both the change trend of variables and their magnitude values, and the new scheme, together with the algorithm, is more efficient and saves more computer time.

Evaporation Erosion During the Relay Contact Breaking Process Based on a Simplified Arc Model

Evaporation erosion of the contacts is one of the fundamental failure mechanisms for relays. In this paper, the evaporation erosion characteristics are investigated for the copper contact pair breaking a resistive direct current （dc） 30 V/10 A circuit in the air. Molten pool simulation of the contacts is coupled with the gas dynamics to calculate the evaporation rate. A simplified arc model is constructed to obtain the contact voltage and current variations with time for the prediction of the current density and the heat flux distributions flowing from the arc into the contacts. The evaporation rate and mass variations with time during the breaking process are presented. Experiments are carried out to verify the simulation results.

Simplified Thermodynamic Model for Pro-Eutectoid Ferrite Formation in Multicomponent Structural Steel

By introducing aparameter of difference in ferrite formation temperature between binary Fe-C and multicomponent system,and referring to the thermodynamic model for Fe-C binary system,a simplified thermodynamic model for pro-eutectoid ferrite formation in Fe-ΣXiC multicomponent structural steels(Xi=Mn,Si,Mo,Cr,Ni or Ti,etc)was suggested.The comparison of the calculated Ae3 temperatures with the measured data of steels 42 shows that the relative standard deviation and root-mean-square(RMS)error between them are only 0.71% and 8.92 K,respectively.However,the deviations between the same measured data and the values calculated from the superelement model are as high as 1.86% and 23.83 K,respectively.It can be concluded that the simplified thermodynamic model for pro-eutectoid ferrite formation in multicomponent structural steels is acceptable and the calculated Ae3 temperatures are in good agreement with the experimental data.

Optimization for friction damped post-tensioned steel frame based on simplified FE model and GA

The post-tensioned(PT)energy-dissipating connection for steel frames has drawn the attention of many researchers for its good seismic performance.Friction mechanisms,such as friction damped PT steel connections,are the approaches typically used to improve energy-dissipating capacity.The mechanical behavior of PT connections has been extensively investigated.The seismic performance of PT frames should be optimized by employing a suitable design of a friction device.In this study,the influence of f_(max)on the seismic behavior of a PT frame is investigated.The_(max)static frictional force f_(max)is optimized based on a genetic algorithm(GA).Results indicate that the reasonable distribution of f_(max)can evidently improve seismic performance.Consequently,the GA method can be effectively utilized for seeking the optimal combination of f_(max)if the simplified finite element model is adopted.Results derived will provide a foundation for analysis and design of PT frame structures.

A preliminary study on simplified simulation model of spring wheat growth

In the model developed in this paper, taking the characters and requirements of meteorological services into account, some conventional meteorological observations which are easy to be obtained have been ch.osen, and mathematical equations describing micro-growth processes of crops have been established on the basis of the field experiments, laboratorial analysis and computer's modelling tests with time interval of ten-days for several years (1987-1989), in accordance with the known biological and physical rules and corresponding reference literatures. It is a preliminary simplified simulation model of spring wheat growth in optimal water and nutrient conditions. The field experiments show that simulation results of this simplified model are satisfactory. The potential operational application and theoretical sense are significant in the meteorological forecast of yield and in the assessment of influences of climatic change on agriculture.

Numerical Simulation Investigation of the Impact of Simplified Architectural Canopy Models on the Distribution of Flow Filed

A series of simulations of air flow through three kinds of2 D vegetation canopies along with different canopy morphology have been conducted by computational fluid dynamics( CFD). Two different turbulent closure models have been used, including standard k-ε turbulent model and RNG k-ε turbulent model with or without source / sink terms,respectively,for the purpose of wind energy applications. In this study,the complicated morphology of3 D vegetation canopy is simplified to three types of 2D simplified canopy model analyzed by the main parameter leaf area index( LAI). Effects of branches and leaves on airflow are also modelled by introducing circles into the 2D simplified canopy model with or without source / sink terms by adding drag force terms in the momentum and turbulent energy equations in porous sub-domains.The main model parameters of source / sink terms are identified thanks to experimental data obtained by direct wind tunnel measurements of the air flow speeds through a branch of Osmanthus fragrans. Moreover,three different canopy shapes of the vegetation canopy are introduced into the simulation. The predictive skills of single-and two-equation( k-ε) models with or without source / sink to compute profiles of mean velocity( u),turbulent kinetic energy( TKE),TKE dissipation rate( ε) and turbulent intensity( I) are compared against datasets collected from other works and field measurements. In conclusion, it is demonstrated that vegetation canopy model 1 using RNG or standard k-ε turbulent model with source / sink terms proves to be a physically accurate and numerically robust method. The method which is better than other two vegetation canopy models is recommended for future use in simulating turbulent flows within and above the canopy in 3D in more details.

An efficient physics-guided Bayesian framework for predicting ground settlement profile during excavations in clay

Recently,the application of Bayesian updating to predict excavation-induced deformation has proven successful and improved prediction accuracy significantly.However,updating the ground settlement profile,which is crucial for determining potential damage to nearby infrastructures,has received limited attention.To address this,this paper proposes a physics-guided simplified model combined with a Bayesian updating framework to accurately predict the ground settlement profile.The advantage of this model is that it eliminates the need for complex finite element modeling and makes the updating framework user-friendly.Furthermore,the model is physically interpretable,which can provide valuable references for construction adjustments.The effectiveness of the proposed method is demonstrated through two field case studies,showing that it can yield satisfactory predictions for the settlement profile.

Added Mass Effect and an Extended Unsteady Blade Element Model of Insect Hovering

During the insect flight, the force peak at the start of each stroke contributes a lot to the total aerodynamic force. Yet how this force is generated is still controversial. Two current explanations to this are wake capture and Added Mass Effect （AME） mechanisms. To study the AME, we present an extended unsteady blade element model which takes both the added mass of fluid and rotational effect of the wing into account. Simulation results show a high force peak at the start of each stroke and are quite similar to the measured forces on the physical wing model. We found that although the Added Mass Force （AMF） of the medium contributes a lot to this force peak, the wake capture effect further augments this force and may play a more important role in delayed mode. Furthermore, we also found that there might be an unknown mechanism which may augment the AME during acceleration period at the start of each stroke, and diminish the AME during deceleration at the end of each stroke.

A SIMPLIFIED NUMERICAL MODEL OF 3-D GROUNDWATER AND SOLUTE TRANSPORT AT LARGE SCALE AREA

A simplified numerical model of groundwater and solute transport is developed. At large scale area there exists a big spatial scale difference between horizontal and vertical length scales. In the resultant model, the seepage region is particularly divided into several virtual layers along the z direction and vertical 1-D columns covering x-y 2-D area according to stratum properties. The numerical algorithm is replacing the full 3-D water and mass balance analysis as the 2-D Galerkin finite element method in x- and y-directions and 1-D finite differential approach in the z direction. The reasonable method of giving minimum thickness is successfully used to handle transient change of water table, drying cells and problem of rewetting. The solution of the simplified model is preconditioned conjugate gradient and ORTHOMIN method. The validity of the developed 3-D groundwater model is tested with the typical pumping and backwater scenarios. Results of water balance of the computed example reveal the model computation reliability. Based on a representative 3-D pollution case, the solute transport module is tested against computing results using the MT3DMS. The capability and high efficiency to predict non-stationary situations of free groundwater surface and solute plume in regional scale problem is quantitatively investigated. It is shown that the proposed model is computationally effective.

Simplified equivalent models of large-scale wind power and their application on small-signal stability

With the rapid growth of grid-connected wind power penetration level,it is necessary to study the impacts of wind power on power system stability.The small-signal stability of power systems with large-scale wind power is explored using the eigenvalue analysis method.A prototype sample system,the two-synchronous-generator system with a wind farm,is proposed for theoretical analysis.Then,simplified models of wind turbines(WTs)and the corresponding equivalent models of wind farms are analyzed.Three kinds of typical WT models,i.e.,squirrel cage induction generator,doubly-fed induction generator,and permanent magnet synchronous generator are used.Furthermore,based on the simplified equivalent models,effects of large-scale wind farms on the electromechanical oscillation modes(EOMs)of synchronous systems are discussed.Simulation results indicate that wind farms of the three kinds of WTs have positive effects on EOMs.However,long transmission lines connecting wind farmto the systemmay produce negative effects on the small-signal stability of the system.

Investigation of the DBD Plasma Effect on Flat Plate Flow

Particle image velocimetry experiments and simulations were conducted in this study to clarify the influence of the DBD plasma actuator on the flow over a flat plate. The result shows that the actuator not only effectively leads to a local rise in near-wall velocity, but also efficiently causes a decrease in the displacement thickness of the boundary layer. Actuator-induced vorticity is generated to intensify the energy exchange between the main flow and the boundary layer, and dynamic energy is thus added directly to the low-energy fluid by the actuator. Although the increase in fluid velocity also brings a rise in dynamic energy loss, the energy added by the actuator can cover this to provide growth in the energy of the boundary layer. The plasma actuator presents a better performance when the free-stream velocity is lower.

Comparison of capacities at road intersections

In order to research the capacity differences of road intersections,this paper analyzed the influence factors and calculation models of various types of capacity at intersections and then obtained simplified models through reasonable assumption. 2 /2,4 /2,4 /4 intersections at which saturation and forecasted traffic volume were given were taken as examples,and an appropriate type was selected through capacity comparison. This paper can give a predictive estimation of the intersection capacity and provides theoretical data for the type selection of intersections.

Simplified Markov Model for Reliability Analysis of Phased-Mission System Using States Merging Method

This paper presents a simplified Markov model to evaluate the reliability of phased-mission system(PMS). The time cost and storage requirement are very huge for traditional Markov model to analyze the PMS reliability as the number of components increases to a large scale. The states merging method proposed in this paper can account for the PMS with subsystems consisting of identical components, and similar PMSs are common in real-world systems. The simplified Markov model by states merging has smaller number of system states, compared with the traditional one. Furthermore, for the above subsystems, the size of our model increases only linearly as the number of components increases, while the size of the traditional model exponentially increases.Finally, the effectiveness and correctness of our approach are analyzed by comparing with the traditional Markov method.

On-board modeling of gravity fields of elongated asteroids using Hopfield neural networks

To rapidly model the gravity field near elongated asteroids,an intelligent inversion method using Hopfield neural networks(HNNs)is proposed to estimate on-orbit simplified model parameters.First,based on a rotating mass dipole model,the gravitational field of asteroids is characterized using a few parameters.To solve all the parameters of this simplified model,a stepped parameter estimation model is constructed based on different gravity field models.Second,to overcome linearization difficulties caused by the coupling of the parameters to be estimated and the system state,a dynamic parameter linearization technique is proposed such that all terms except the parameter terms are known or available.Moreover,the Lyapunov function of the HNNs is matched to the problem of minimizing parameter estimation errors.Equilibrium values of the Lyapunov function areused as estimated values.The proposed method is applied to natural elongated asteroids 216 Kleopatra,951 Gaspra,and 433 Eros.Simulation results indicate that this method can estimate the simplified model parameters rapidly,and that the estimated simplified model provides a good approximation of the gravity field of elongated asteroids.