Nonlinear Mathematical Modeling and Sensitivity Analysis of Hydraulic Drive Unit

The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity indexes values of four measurable parameters, such as supply pressure, proportional gain, initial position of servo cylinder piston and load force, are verified experimentally on test platform of hydraulic drive unit, and the experimental research shows that the sensitivity analysis results obtained through simulation are approximate to the test results. This research indicates each parameter sensitivity characteristics of hydraulic drive unit, the performance-affected main parameters and secondary parameters are got under different working conditions, which will provide the theoretical foundation for the control compensation and structure optimization of hydraulic drive unit.

COMPLEX NONLINEAR MATHEMATICAL MODEL FOR A KIND OF VEHICLE SHOCK ABSORBORS

A nonlinear mathematical model for the shock absorber in TJ7100 is developed. The oil compressibility and the entrapped gas in the oil are considered in the model. As a result, the hysteresis in the force velocity diagram is included. The results of computer simulation and the experiment are basically identical. The MATLAB/SIMULINK is used for the development of the simulation software. It is found that the pressure inside the cylinder is high if the inputs of velocity or displacement are big by simulation. This is certainly one of the main reasons for which the leak is appeared between the rod and the seal of the shock absorbers for a relatively short time in China.

Mathematical Constraints in Multiscale Subgrid-Scale Modeling of Nonlinear Systems

To shed light on the subgrid-seale （SGS） modeling methodology of nonlinear systems such as the Navier-Stokes turbulence, we define the concepts of assumption and restriction in the modeling procedure, which are shown by generalized derivation of three general mathematical constraints for different combinations of restrictions. These constraints are verified numerically in a one-dimensional nonlinear advection equation. This study is expected to inspire future research on the SGS modeling methodology of nonlinear systems.

Stochastic Investigations for the Fractional Vector-Host Diseased Based Saturated Function of Treatment Model

The goal of this research is to introduce the simulation studies of the vector-host disease nonlinear system(VHDNS)along with the numerical treatment of artificial neural networks(ANNs)techniques supported by Levenberg-Marquardt backpropagation(LMQBP),known as ANNs-LMQBP.This mechanism is physically appropriate,where the number of infected people is increasing along with the limited health services.Furthermore,the biological effects have fadingmemories and exhibit transition behavior.Initially,the model is developed by considering the two and three categories for the humans and the vector species.The VHDNS is constructed with five classes,susceptible humans Sh(t),infected humans Ih(t),recovered humans Rh(t),infected vectors Iv(t),and susceptible vector Sv(t)based system of the fractional-order nonlinear ordinary differential equations.To solve the number of variations of the VHDNS,the numerical simulations are performed using the stochastic ANNs-LMQBP.The achieved numerical solutions for solving the VHDNS using the stochastic ANNs-LMQBP have been described for training,verifying,and testing data to decrease the mean square error(MSE).An extensive analysis is provided using the correlation studies,MSE,error histograms(EHs),state transitions(STs),and regression to observe the accuracy,efficiency,expertise,and aptitude of the computing ANNs-LMQBP.

Research on Maneuver Decision-Making of Multi-Agent Adversarial Game in a Random Interference Environment

The strategy evolution process of game players is highly uncertain due to random emergent situations and other external disturbances.This paper investigates the issue of strategy interaction and behavioral decision-making among game players in simulated confrontation scenarios within a random interference environment.It considers the possible risks that random disturbances may pose to the autonomous decision-making of game players,as well as the impact of participants’manipulative behaviors on the state changes of the players.A nonlinear mathematical model is established to describe the strategy decision-making process of the participants in this scenario.Subsequently,the strategy selection interaction relationship,strategy evolution stability,and dynamic decision-making process of the game players are investigated and verified by simulation experiments.The results show that maneuver-related parameters and random environmental interference factors have different effects on the selection and evolutionary speed of the agent’s strategies.Especially in a highly uncertain environment,even small information asymmetry or miscalculation may have a significant impact on decision-making.This also confirms the feasibility and effectiveness of the method proposed in the paper,which can better explain the behavioral decision-making process of the agent in the interaction process.This study provides feasibility analysis ideas and theoretical references for improving multi-agent interactive decision-making and the interpretability of the game system model.

Nonlinear stability of timber column strengthened with fiber reinforced polymer

By taking into account the effect of the bi-modulus for tension and compression of the fiber reinforced polymer （FRP） sheet in the reinforcement layer, a general mathematical model for the nonlinear bending of a slender timber beam strengthened with the FRP sheet is established under the hypothesis of the large deflection deformation of the beam. Nonlinear governing equations of the second order effect of the beam bending are derived. The nonlinear stability of a simply-supported slender timber column strengthened with the FRP sheet is then investigated. An expression of the critical load of the simply-supported FRP-strengthened timber beam is obtained. The existence of postbuckling solution of the timber column is proved theoretically, and an asymptotic analytical solution of the postbuckling state in the vicinity of the critical load is obtained using the perturbation method. Parameters are studied showing that the FRP reinforcement layer has great influence on the critical load of the timber column, and has little influence on the dimensionless postbuckling state.

ANALYSIS OF THERMAL POST-BUCKLING OF HEATED ELASTIC RODS

Based on the nonlinear geometric theory of extensible rods, an exact mathematical model of thermal post_buckling behavior of uniformly heated elastic rods with axially immovable ends is developed, in which the arc length s(x) of axial line and the longitudinal displacement u(x) are taken as the basic unknown functions. This is a two point boundary value problem of first order ordinary differential equations with strong non_linearity. By using shooting method and analytical continuation, the nonlinear boundary value problems are numerically solved. The thermal post_buckled states of the rods with transversely simply supported and clamped ends are obtained respectively and the corresponding numerical data tables and characteristic curves are also given.

Transient Analysis of Steam Generator in PWR Nuclear Power Plant

The water level control system of steam generator in a pressurized water reactor of nuchear power plant plays an important role which effects the water level control of the steam generator are due the reverse dynamics behavior,so the transient analysis of the steam generator should firstly solve their mathematical models.For determination of dynamic behavior and design and testing of the control system, a nonlinear math model is developed using one dimensional conservation equations of mass,momentum and energy of primary and secondary sides of the steam generator. The nonlinear model is verified with standard power plant data available in the references, then the steady states and transient calculations are performed for full power to 5% power reactor operation of the steam generator of Chinese Qinshan Nuclear Power Plant.

Effects of simulated on-fire processing conditions on the microstructure and mechanical performance of Q345R steel

A series of simulated on-fire processing experiments on Q345R steel plates was conducted, and the plates＇ Brinell hardness, ten- sile strength, and impact energy were tested. Microstructure morphologies were systematically analyzed using a scanning electron micro- scope with the aim of investigating the effect of the steel＇s microstructure on its performance. All examined performance parameters exhib- ited a substantial decrease in the cases of samples heat-treated at temperatures near 700℃. However, although the banded structure decreased with increasing treatment temperature and holding time, it had little effect on the performance decline in fact. Further analysis revealed that pearlite degeneration near 700℃, which was induced by the interaction of both subcritical annealing and conventional spherical annealing, was the primary reason for the degradation behavior. Consequently, some nonlinear mathematical models of different mechanical perform- ances were established to facilitate processing adjustments.

Rumen liquor from slaughtered cattle as inoculum for feed evaluation

Use of nonlinear mathematical models has been majorly based on in vitro gas production(GP) data generated when substrates are incubated with rumen liquor from fistulated steers. However,existing evidence suggests that rumen liquor from slaughtered cattle of unknown dietary history also generates quantifiable in vitro GP data. Fitting and description of GP data obtained from 4 diets incubated with rumen liquor from slaughtered cattle was evaluated using single-pool exponential model with discrete lag time(EXPL), logistic(LOG), Groot's(GRTS) and Gompertz(GOMP) models. Diets were formulated by varying proportions of Rhodes grass(Chloris gayana) hay and a concentrate mixed on dry matter basis to be: 1,000 g/kg Rhodes grass hay(RGH) and 0 of the concentrate(D1), 900 g/kg RGH and 100 g/kg concentrate(D2), 800 g/kg RGH and 200 g/kg concentrate(D3), 700 g/kg RGH and 300 g/kg concentrate(D4). Dietary kinetics for the models were determined by measuring GP at 2,4.8,10.18,24.36,48.72,96 and 120 h. Model comparison was based on derived GP kinetics, graphical analysis of observed versus predicted GP profiles plus residual distribution and goodness-of-fit from analysis of root mean square error(RMSE), adjusted coefficient of determination(Adj-R^2) and Akaike's information criterion(AIC). Asymptotic GP, half-life and fractional rate of GP differed(P < 0.001) among the 4 models. The RMSE, Adj-R^2 and AIC ranged from 1.555 to 4.429,0.906 to0.984 and 2.452 to 15.874, respectively, forall diets compared across the 4 models. Based on the goodness-of-fit statistical criterion, GP profiles of D1 were more appropriately fitted and described by GRTS and GOMP than the EXPLand LOG models. The GRTS model had the lowest AIC value for D2(2.452). Although GRTS model had the most homogenous residual dispersion for the 4 diets, all the 4 models exhibited a sigmoidal behavior.Therefore, rumen liquor from slaughtered cattle of unknown dietary history can be used to derive nutritionally important feed parameters, but choice of the most appropriate model should be made based on fitting criteria and dietary substrates incubated.

Dynamic interaction between clustered liquid propellant rocket engines under their asynchronous start-ups

A nonlinear mathematical model of the low-frequency dynamics of the clustered multi-engine rocket propulsion system has been developed and the computations of the engine transient processes during the start-ups of the four-engine propulsion system with a shared feed system have been made applied.Based on propulsion system start-up modeling the influence of the connectivity of engines in a cluster on the starting characteristics of individual engines is shown.In particular,an advanced nonlinear mathematical model of the pump cavitation phenomena is a distinctive feature of the mathematical model.The computation results showed that the asynchronous engines start-ups during rocket lift-off lead to severely nonlinear engine transients and clustered engine thrust misbalance.The influence of the rocket engines asynchronous start-ups on the clustered feed system transients depends on many factors,mainly on from the clustered feed system low-frequency dynamics,the magnitude of the disturbance and the phase difference between disturbances acting on different branches of the feed system.The deep lingering dips in the flow rate and pressure transients are possible due to the nonlinear dynamic interaction of the engines.In case of great pressure dips at the pump inlet(up to the pressure of saturated vapors during significant periods of start-up time)the cavitation breakdowns of the pumps of one or more engines from the cluster are possible.This can disrupt the operation of the entire propulsion system and leads to the failure of the launch vehicle mission.