MULTIPLE SOLUTIONS FOR HAMILTONIAN SYSTEMS WITH PERIODIC NONLINEARITY AND STRONG RESONANCE

I. Introduction In this paper we are looking for solutions of the following Hamiltonian system of second order: where x= （x1, x2） and V satisfies （V. 1） V: R×R2→R is a C1-function, 1-periodic In t, （V.2） V is periodic in x1 with the period T>0, （V. 3） V→O, Vx→O as |x2|→∞, uniformly in （t, x1）.

Constitutive equations of 1060 pure aluminum based on modified double multiple nonlinear regression model

In order to study the work-ability and establish the optimum hot formation processing parameters for industrial 1060 pure aluminum, the compressive deformation behavior of pure aluminum was investigated at temperatures of 523?823 K and strain rates of 0.005?10 s?1 on a Gleeble?1500 thermo-simulation machine. The influence rule of processing parameters (strain, strain rate and temperature) on flow stress of pure aluminum was investigated. Nine analysis factors consisting of material parameters and according weights were optimized. Then, the constitutive equations of multilevel series rules, multilevel parallel rules and multilevel series &parallel rules were established. The correlation coefficients (R) are 0.992, 0.988 and 0.990, respectively, and the average absolute relative errors (AAREs) are 6.77%, 8.70% and 7.63%, respectively, which proves that the constitutive equations of multilevel series rules can predict the flow stress of pure aluminum with good correlation and precision.

Rheological Behaviour for Polymer Melts and Concentrated Solutions Part Ⅰ:A New Multiple Reptation Model to Predict the Nonlinear Visco-elasticity with Nagai Chain Constraints in Entangled Polymer Melts

An approach of stochastically statistical mechanics and a unified molecular theory of nonlinear viscoelasticity with constraints of Nagai chain entanglement for polymer melts have been proposed. A multimode model structure for a single polymer chain with n tail segments and N reversible entanglement sites on the test polymer chain is developed. Based on the above model structure and the mechanism of molecular flow by the dynamical reorganization of entanglement sites, the probability distribution function of the end-to-end vectr for a single polymer chain at entangled state and the viscoelastic free energy of deformation for polymer melts are calculated by using the method of the stochastically statistical mechanics. The four types of stress-strain relation and the memory function are derived from this thery. The above theoretical relations are verified by the experimentaf data for various polymer melts. These relations are found to be in good agreement with the experimental results

UNITIVE ANALYSIS SCHEMES ON PROBLEMS OF MULTIPLE MOVING BOUNDARIES WITH 3-D LIQUID-SOLID MULTIPLE NONLINEAR COUPLING FOR UPLIFT OF ANCHOREDLIQUID STORAGE TANKS

In the paper, 3-D analysis method with unitive schemes is set up, which is used to resolve the uplift with multiple moving boundaries and multiple nonlinear coupling for anchored liquid storage tanks. hi it, an algorithm of quasi-harmonious finite elements for arbitrary quadrilateral of thin plates and shells is built up to analyze the multiple coupling problems of general thin plates and shells structures with three dimensions, the complementary equations for analyzing uplifting moving boundary problems are deduced. The axial symmetry and presumption of beam type mode are not used. In it, an algorithm is put forward for analyzing the Navier-Stokes problems of unsteady, three-dimensional, and viscous liquid with sloshing of moving boundary surfaces in large amplitude under ALE frame by scheme of time-split-steps to which linear potential theory is not applied. The algorithms can be used to analyze the solid-liquid multiple nonlinear coupling problems with 3-D moving boundary with friction in multiple places.

On the Multiple Equilibrium of the Development of Tropical Cyclone in Nonlinear CISK Model

By using non-static atmosphere equations including basic current, heating force and friction, we discuss the balance amplitude of vertical motion in the conditions of constant heating force, linear and non-linear interaction between large-scale ascending motion and diabatic heating force. In the non-linear condition, the multiple equilibrium feature of the tropical cyclone development is discussed and the reason of the sudden varying of tropical cyclone intensity is studied preliminarily.

CONVEX CONTROLLER DESIGN APPLIED TO AC INDUCTION MOTOR TO SATISFY MULTIPLE SIMULTANEOUS SPECIFICATIONS

The application of a closed-loop specification oriented feedback control design method, which addresses the design of controllers to satisfy multiple simultaneous conflicting closed-loop performance specifications is presented. The proposed approach is well suited to the design of controllers which must meet a set of conflicting performance specifications. Gain tuning is central to the design process, however, the tuning process is greatly simplified over that presented by the problem of tuning a PID controller for example. The proposed control method is applied to an AC induction motor, with an inner-loop flux vector controller applied to design a position control system. Experimental results verify the effectiveness of this method.

Unconfined compressive strength and failure behaviour of completely weathered granite from a fault zone

Understanding the strength characteristics and deformation behaviour of the tunnel surrounding rock in a fault zone is significant for tunnel stability evaluation.In this study,a series of unconfined compression tests were conducted to investigate the mechanical characteristics and failure behaviour of completely weathered granite(CWG)from a fault zone,considering with height-diameter(h/d)ratio,dry densities(ρd)and moisture contents(ω).Based on the experimental results,a regression mathematical model of unconfined compressive strength(UCS)for CWG was developed using the Multiple Nonlinear Regression method(MNLR).The research results indicated that the UCS of the specimen with a h/d ratio of 0.6 decreased with the increase ofω.When the h/d ratio increased to 1.0,the UCS increasedωwith up to 10.5%and then decreased.Increasingρd is conducive to the improvement of the UCS at anyω.The deformation and rupture process as well as final failure modes of the specimen are controlled by h/d ratio,ρd andω,and the h/d ratio is the dominant factor affecting the final failure mode,followed byωandρd.The specimens with different h/d ratio exhibited completely different fracture mode,i.e.,typical splitting failure(h/d=0.6)and shear failure(h/d=1.0).By comparing the experimental results,this regression model for predicting UCS is accurate and reliable,and the h/d ratio is the dominant factor affecting the UCS of CWG,followed byρd and thenω.These findings provide important references for maintenance of the tunnel crossing other fault fractured zones,especially at low confining pressure or unconfined condition.

Support pressure assessment for deep buried railway tunnels using BQ-index

Estimation of support pressure is extremely important to the support system design and the construction safety of tunnels.At present,there are many methods for the estimation of support pressure based on different rock mass classification systems,such as Q system,GSI system and RMR system.However,various rock mass classification systems are based on different tunnel geologic conditions in various regions.Therefore,each rock mass classification system has a certain regionality.In China,the BQ-Inex(BQ system)has been widely used in the field of rock engineering ever since its development.Unfortunately,there is still no estimation method of support pressure with BQ-index as parameters.Based on the field test data from 54 tunnels in China,a new empirical method considering BQ-Inex,tunnel span and rock weight is proposed to estimate the support pressure using multiple nonlinear regression analysis methods.And then the significance and necessity of support pressure estimation method for the safety of tunnel construction in China is explained through the comparison and analysis with the existing internationally widely used support pressure estimation methods of RMR system,Q system and GSI system.Finally,the empirical method of estimating the support pressure based on BQ-index was applied to designing the support system in the China’s high-speed railway tunnel—Zhengwan high-speed railway and the rationality of this method has been verified through the data of field test.

BLIND ADAPTIVE MULTIUSER DETECTOR FOR NONLINEARLY MODULATED SATELLITE MOBILE CDMA SYSTEMS

This paper presents a novel blind adaptive noncoherent decorrelative multiuser detector for nonlinearly modulated satellite mobile Code Division Multiple Access (CDMA) systems. By using the known signature waveforms of the counterpart earth station in the blind adaptive multiuser detector, the system performance has been improved obviously. The computation results about the convergence properties of the new detector and the previous detectors demonstrate that the proposed multiuser detector has better performance than previous multiuser detectors for nonlinearly modulated CDMA systems.

Approximate and numerical analysis of nonlinear forced vibration of axially moving viscoelastic beams

Steady-state periodical response is investigated for an axially moving viscoelastic beam with hybrid supports via approximate analysis with numerical confirmation. It is assumed that the excitation is spatially uniform and temporally harmonic. The transverse motion of axially moving beams is governed by a nonlinear partial-differential equation and a nonlinear integro-partial-differential equation. The material time derivative is used in the viscoelastic constitutive relation. The method of multiple scales is applied to the governing equations to investigate primary resonances under general boundary conditions. It is demonstrated that the mode uninvolved in the resonance has no effect on the steady-state response. Numerical examples are presented to demonstrate the effects of the boundary constraint stiffness on the amplitude and the stability of the steady-state response. The results derived for two governing equations are qualitatively the same,but quantitatively different. The differential quadrature schemes are developed to verify those results via the method of multiple scales.

Predicting Surface Roughness and Moisture of Bare Soils Using Multi- band Spectral Reflectance Under Field Conditions

Soil surface roughness, denoted by the root mean square height(RMSH), and soil moisture(SM) are critical factors that affect the accuracy of quantitative remote sensing research due to their combined influence on spectral reflectance(SR). In regards to this issue, three SM levels and four RMSH levels were artificially designed in this study; a total of 12 plots was used, each plot had a size of 3 m × 3 m. Eight spectral observations were conducted from 14 to 30 October 2017 to investigate the correlation between RMSH, SM, and SR. On this basis, 6 commonly used bands of optical satellite sensors were selected in this study, which are red(675 nm), green(555 nm), blue(485 nm), near infrared(845 nm), shortwave infrared 1(1600 nm), and shortwave infrared 2(2200 nm). A negative correlation was found between SR and RMSH, and between SR and SM. The bands with higher coefficient of determination R^2 values were selected for stepwise multiple nonlinear regression analysis. Four characterized bands(i.e., blue, green, near infrared, and shortwave infrared 2) were chosen as the independent variables to estimate SM with R^2 and root mean square error(RMSE) values equal to 0.62 and 2.6%, respectively. Similarly, the four bands(green, red, near infrared, and shortwave infrared 1) were used to estimate RMSH with R^2 and RMSE values equal to 0.48 and 0.69 cm, respectively. These results indicate that the method used is not only suitable for estimating SM but can also be extended to the prediction of RMSH. Finally, the evaluation approach presented in this paper highly restores the real situation of the natural farmland surface on the one hand, and obtains high precision values of SM and RMSH on the other. The method can be further applied to the prediction of farmland SM and RMSH based on satellite and unmanned aerial vehicle(UAV) optical imagery.

An Adaptive Design for Six Sigma(ADFSS): a Simulated Annealing and Regression Analysis Embedded Approach

Design for six sigma （DFSS） is a powerful approach of designing products, processes, and services with the objective of meeting the needs of customers in a cost-effective maimer. DFSS activities are classified into four major phases viz. identify, design, optimize, and validate （IDOV）. And an adaptive design for six sigma （ADFSS） incorporating the traits of artifidai intelligence and statistical techniques is presented. In the identify phase of the ADFSS, fuzzy relation measures between customer attributes （CAs） and engineering characteristics （ECs） as well as fuzzy correlation measures among ECs are determined with the aid of two fuzzy logic controllers （FLCs）. These two measures are then used to establish the cumulative impact factor for ECs. In the next phase （ i. e. design phase）, a transfer function is developed with the aid of robust multiple nonlinear regression analysis. Furthermore, 1this transfer function is optimized with the simulated annealing （ SA ） algorithm in the optimize phase. In the validate phase, t-test is conducted for the validation of the design resulted in earlier phase. Finally, a case study of a hypothetical writing instrument is simulated to test the efficacy of the proposed ADFSS.

A smart data-driven rapid method to recognize the strawberry maturity

In recent years,there have been many studies on the recognition of strawberry maturity,but there are still problems such as low recognition accuracy and expensive experimental instruments.These factors make their methods difficult for farmers to use.To solve these problems,we developed a fast,non-destructive,accurate and convenient method for strawberry maturity identification using smartphones.In this paper,strawberry maturity is divided into three levels:mature,nearly-mature and immature.Considering the actual strawberry harvest process and postharvest handling,we focus on the differentiation between the mature and the nearly-mature ones to help farmers reduce possible damage in transit and improve profitability.We obtained the images of strawberries with different maturities at 535 nm and 670 nm wavelengths through a smartphone and got absorbance data by image processing based on the region of interest.The absorbance data were used to establish three maturity recognition models—i.e.,multivariate linear,multivariate nonlinear and SoftMax regression classifier.The results showed that the multivariate nonlinear model had the highest identification accuracy(which is over 94%)in the greenhouse.Therefore,this method has considerable potential as a means for rapid recognition of strawberry maturity.

Global Disturbance Rejection of Switched Nonlinear Systems with Switched Internal Model

This paper investigates the problem of global disturbance rejection for a class of switched nonlinear systems where the solvability of the disturbance rejection problem for subsystems is not assumed. The disturbances are assumed to be sinusoidal with completely unknown frequencies, phases and amplitudes. First, as an extension of the classic concept of internal model for non-switched systems, a switched internal model is proposed. Second, in order to solve the problem under study, an adaptive control method is established on the basis of the multiple Lyapunov functions method. Also,adaptive state-feedback controllers of subsystems are designed and incorporated with a switching law to asymptotically reject the unknown disturbances. Finally, an example is provided to demonstrate the effectiveness of the proposed design method.