[Objective] The aim was to develop a nonlinear model of quantitative analysis of melamine content by infrared spectroscopy and provide theoretical basis for the nondestructive detection of melamine. [Method] According...[Objective] The aim was to develop a nonlinear model of quantitative analysis of melamine content by infrared spectroscopy and provide theoretical basis for the nondestructive detection of melamine. [Method] According to dynamics,mathematical modeling and optimization theory,linear and nonlinear models were respectively set up by taking an absorption peak of 1 550 cm-1 as characteristic absorption peak. [Result] The correlation coefficient of nonlinear model was 0.922 7 and the recovery was 96%,which showed that the nonlinear model was more accurate than linearity model with correlation coefficient of 0.904 9 and recovery of 557%. [Conclusion] It is feasible to determine melamine content by using the nonlinear model quantitatively.展开更多
An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local ...An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.展开更多
Let X be a metric space with an ordering structure,A: X→X is a operator and x≤Ax for any x∈X. In this paper we prove a new fixed point theorem, which generalizes famous caristi fixed point theorem.
The nonlinear finite element method is used to analyze the geometrical nonlinear stability of cable truss domes with different cable distributions. The results indicate that the critical load increases evidently when...The nonlinear finite element method is used to analyze the geometrical nonlinear stability of cable truss domes with different cable distributions. The results indicate that the critical load increases evidently when cables, especially diagonal cables, are distributed in the structure. The critical loads of the structure at different rise span ratios are also discussed in this paper. It was shown that the effect of the tensional cable is more evident at small rise span ratio. The buckling of the structure is characterized by a global collapse at small rise span ratio; that the torsional buckling of the radial truss occurs at big rise span ratio; and that at proper rise span ratio, the global collapse and the lateral buckling of the truss occur nearly simultaneously.展开更多
In this paper, we present a new ear-following model, i.e. comprehensive optimal velocity model （COVM）, whose optimal velocity function not only depends on the following distance of the preceding vehicle, but also de...In this paper, we present a new ear-following model, i.e. comprehensive optimal velocity model （COVM）, whose optimal velocity function not only depends on the following distance of the preceding vehicle, but also depends on the velocity difference with preceding vehicle. Simulation results show that COVM is an improvement over the previous ones theoretically. Then, the stability condition of the model is obtained by the linear stability analysis, which has shown that the model could obtain a bigger stable region than previous models in the phase diagram. Through the nonlinear analysis, the Burgers, Korteweg-de Vries （KdV） and modified KdV （mKdV） equations are derived for the triangular shock wave, the soliton wave, and the kink-antikink soliton wave. At the same time, numerical simulations are also carried out to show that the model could simulate these density waves.展开更多
A nonlinear dynamics model and a mathematical expression were set up to investigatethe mechanism and conditions of vibration creep acceleration.The model showsthat hydraulic spring and nonlinear friction are major fac...A nonlinear dynamics model and a mathematical expression were set up to investigatethe mechanism and conditions of vibration creep acceleration.The model showsthat hydraulic spring and nonlinear friction are major factors that can affect low-speed instability.The mathematic model was established to obtain the change rule of speed andinstantaneous acceleration of the hydraulic motor.Then, Matlab was used to simulate theeffect of nonlinear friction force and hydraulic motor parameters such as coefficient of leakand compression ratio, etc., under low speed.Finally, some measures were proposed toimprove the low-speed stability of the hydraulic motor.展开更多
A method was developed for content determination of Na, Mg, A1, Si, P,S, C1, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, Ga, Nb, Zr, Y, Sr, Rb, Ba, La and Ce etc. covering 26 major, minor, and trace elements in marine sedim...A method was developed for content determination of Na, Mg, A1, Si, P,S, C1, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, Ga, Nb, Zr, Y, Sr, Rb, Ba, La and Ce etc. covering 26 major, minor, and trace elements in marine sediment samples using fused glass disc by X-ray Fluorescence spectrometry. Calibration was made using marine sediment certified reference materials and the synthetic standard samples prepared by mixing several marine sediments with stream sediment and carbonate standard samples in different proportions. The matrix effect was corrected using theoretical alpha coefficients, experience coefficients and the scattered radiation as the internal standard （for the trace elements）. The accuracy of the method was evaluated by analysis of certified reference materials GBW07314, GBW07334 and GSMS6. The results are in good agreement with the certified values of the standards with RSD less than 2.60%, except for Y, Cr, Ga, Ce, La, Nb, Rb, and V with RSD less than 9.0% （n=12）.展开更多
Complex dynamics are studied in the T system, a three-dimensional autonomous nonlinear system. In particular, we perform an extended Hopf bifurcation analysis of the system. The periodic orbit immediately following th...Complex dynamics are studied in the T system, a three-dimensional autonomous nonlinear system. In particular, we perform an extended Hopf bifurcation analysis of the system. The periodic orbit immediately following the Hopf bifurcation is constructed analytically for the T system using the method of multiple scales, and the stability of such orbits is analyzed. Such analytical results complement the numerical results present in the literature. The analytical results in the post-bifurcation regime are verified and extended via numerical simulations, as well as by the use of standard power spectra, autocorrelation functions, and fractal dimensions diagnostics. We find that the T system exhibits interesting behaviors in many parameter regimes.展开更多
The novel quantitative assessment method using transmission line measurement was developed. A new style of stability criterion was suggested which is based on the line measurement. The stability indices for lines, cut...The novel quantitative assessment method using transmission line measurement was developed. A new style of stability criterion was suggested which is based on the line measurement. The stability indices for lines, cutsets and power system according to features of transient energy in the lines were given, which not only provide a reliable and accurate assessment of the transient stability of power system, but also can be used to assess the effect of lines and cutsets on the transient stability and identify the weak transmission segment. Examples were presented by simulation on the IEEE-39 buses test system.展开更多
The stability of natural slope was analyzed on the basis of limit analysis. The sliding model of a kind of natural slope was presented. A new kinematically admissible velocity field for the new sliding model was const...The stability of natural slope was analyzed on the basis of limit analysis. The sliding model of a kind of natural slope was presented. A new kinematically admissible velocity field for the new sliding model was constructed. The stability factor formulation by the upper bound theorem leads to a classical nonlinear programming problem, when the external work rate and internal energy dissipation were solved, and the constraint condition of the programming problem was given. The upper bound optimization problem can be solved efficiently by applying a nonlinear SQP algorithm, and stability factor was obtained, which agrees well with previous achievements.展开更多
The main purpose of this paper is to set up the finite difference scheme with incremental unknowns for the nonlinear differential equation by means of introducing incremental unknowns method and discuss the stability ...The main purpose of this paper is to set up the finite difference scheme with incremental unknowns for the nonlinear differential equation by means of introducing incremental unknowns method and discuss the stability of the scheme.Through the stability analyzing for the scheme,it was shown that the stability of the finite difference scheme with the incremental unknowns is improved when compared with the stability of the corresponding classic difference scheme.展开更多
By simplifying saturatedly magnetized wire-rope to magnetic dipoles of the same magnetic field strength, an equivalent magnetic dipoles model is developed and the measuring principle for recognising damage of broken w...By simplifying saturatedly magnetized wire-rope to magnetic dipoles of the same magnetic field strength, an equivalent magnetic dipoles model is developed and the measuring principle for recognising damage of broken wire was presented. The relevant calculation formulas were also deduced. A composite solution method about nonlinear optimization was given. An example was given to illustrate the use of the equivalent magnetic dipoles method for quantitative damage recognition, and demonstrates that the result of this method is consistent with the real situation, so the method is valid and practical. wire-rope, damage of broken wires, quantitative recognition, equivalent magnetic dipoles, simulate展开更多
The stability analysis of linear multistep (LM) methods is carried out under Kreiss resolvent condition when they are applied to neutral delay differential equations of the form y′(t)=ay(t)+by(t-τ)+ cy′(t- τ) y(t)...The stability analysis of linear multistep (LM) methods is carried out under Kreiss resolvent condition when they are applied to neutral delay differential equations of the form y′(t)=ay(t)+by(t-τ)+ cy′(t- τ) y(t)=g(t) -τ≤t≤0 with τ>0 and a, b and c∈, and it is proved that the ‖B n‖ is suitably bounded, where B is the companion matrix.展开更多
We quantitatively study magnetic anomalies of reinforcement rods in bored insitu concrete piles for the first time and summarized their magnetic anomaly character. Key factors such as measuring borehole orientation, b...We quantitatively study magnetic anomalies of reinforcement rods in bored insitu concrete piles for the first time and summarized their magnetic anomaly character. Key factors such as measuring borehole orientation, borehole-reinforcement distance, and multiple-section reinforcement rods are discussed which contributes valid and quantitative reference for using the magnetic method to detect reinforcement rods. Through tests with model piles, we confirm the accuracy of theoretical computations and then utilize the law discovered in theoretical computations to explain the characteristics of the actual testing curves. The results show that the Za curves of the reinforcement rod reflect important factors regarding the reinforcement rods, such as rod length, change of reinforcement ratio, length of overlap, and etc. This research perfects the magnetic method for detecting reinforcement rods in bored in-situ concrete piles and the method has great importance for preventing building contractor fraud.展开更多
In this paper, we investigate two kinds of second-order consensus algorithms for multiple agents with coupling delay under general fixed directed information topology. Stability analysis is performed based on Lyapunov...In this paper, we investigate two kinds of second-order consensus algorithms for multiple agents with coupling delay under general fixed directed information topology. Stability analysis is performed based on Lyapunov- Krasovskii functional method. Delay-dependent asymptotical stability condition in terms of linear matrix inequalities （LMIs） is derived for the second-order consensus algorithm of delayed dynamical networks. Both delay-independent and delay-dependent asymptotical stability conditions in terms of LMIs are derived for the second-order consensus algorithm with information feedback.展开更多
基金Supported by Promoting Projects of the Industrialization of University Research of Jiangsu Province (JHZD09-35)Natural Science Research Project of Universities in Jiangsu Province (09KJD210001)Research Foundation of Huaiyin Institute of Technology(HGA0908)~~
文摘[Objective] The aim was to develop a nonlinear model of quantitative analysis of melamine content by infrared spectroscopy and provide theoretical basis for the nondestructive detection of melamine. [Method] According to dynamics,mathematical modeling and optimization theory,linear and nonlinear models were respectively set up by taking an absorption peak of 1 550 cm-1 as characteristic absorption peak. [Result] The correlation coefficient of nonlinear model was 0.922 7 and the recovery was 96%,which showed that the nonlinear model was more accurate than linearity model with correlation coefficient of 0.904 9 and recovery of 557%. [Conclusion] It is feasible to determine melamine content by using the nonlinear model quantitatively.
基金Specialized Research Fund for the Doctoral Program of Higher Education ( No. 20090092110051)the Key Project of Chinese Ministry of Education ( No. 108060)the National Natural Science Foundation of China ( No. 51076027, 51036002, 51106024)
文摘An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.
文摘Let X be a metric space with an ordering structure,A: X→X is a operator and x≤Ax for any x∈X. In this paper we prove a new fixed point theorem, which generalizes famous caristi fixed point theorem.
文摘The nonlinear finite element method is used to analyze the geometrical nonlinear stability of cable truss domes with different cable distributions. The results indicate that the critical load increases evidently when cables, especially diagonal cables, are distributed in the structure. The critical loads of the structure at different rise span ratios are also discussed in this paper. It was shown that the effect of the tensional cable is more evident at small rise span ratio. The buckling of the structure is characterized by a global collapse at small rise span ratio; that the torsional buckling of the radial truss occurs at big rise span ratio; and that at proper rise span ratio, the global collapse and the lateral buckling of the truss occur nearly simultaneously.
基金Supported by the National Natural Science Foundation of China under Grant Nos.71071013,71001004,and 71071012Foundation of Beijing Jiaotong University under Grant No.2009JBZ012-2
文摘In this paper, we present a new ear-following model, i.e. comprehensive optimal velocity model （COVM）, whose optimal velocity function not only depends on the following distance of the preceding vehicle, but also depends on the velocity difference with preceding vehicle. Simulation results show that COVM is an improvement over the previous ones theoretically. Then, the stability condition of the model is obtained by the linear stability analysis, which has shown that the model could obtain a bigger stable region than previous models in the phase diagram. Through the nonlinear analysis, the Burgers, Korteweg-de Vries （KdV） and modified KdV （mKdV） equations are derived for the triangular shock wave, the soliton wave, and the kink-antikink soliton wave. At the same time, numerical simulations are also carried out to show that the model could simulate these density waves.
基金Supported by the Natural Science Foundation of Fujian Province of China(2009J01259)Scientific Research Foundation of Department of Education(JB08182)
文摘A nonlinear dynamics model and a mathematical expression were set up to investigatethe mechanism and conditions of vibration creep acceleration.The model showsthat hydraulic spring and nonlinear friction are major factors that can affect low-speed instability.The mathematic model was established to obtain the change rule of speed andinstantaneous acceleration of the hydraulic motor.Then, Matlab was used to simulate theeffect of nonlinear friction force and hydraulic motor parameters such as coefficient of leakand compression ratio, etc., under low speed.Finally, some measures were proposed toimprove the low-speed stability of the hydraulic motor.
基金Supported by China Ministry of Science and Technology (2000DEB20081)China Ocean Mineral Resources R&D Association (COMRA) (No.DY105-05-01-05)+1 种基金China Ministry of Education(No.205089)China National Natural Science Foundation (No.40076015)
文摘A method was developed for content determination of Na, Mg, A1, Si, P,S, C1, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, Ga, Nb, Zr, Y, Sr, Rb, Ba, La and Ce etc. covering 26 major, minor, and trace elements in marine sediment samples using fused glass disc by X-ray Fluorescence spectrometry. Calibration was made using marine sediment certified reference materials and the synthetic standard samples prepared by mixing several marine sediments with stream sediment and carbonate standard samples in different proportions. The matrix effect was corrected using theoretical alpha coefficients, experience coefficients and the scattered radiation as the internal standard （for the trace elements）. The accuracy of the method was evaluated by analysis of certified reference materials GBW07314, GBW07334 and GSMS6. The results are in good agreement with the certified values of the standards with RSD less than 2.60%, except for Y, Cr, Ga, Ce, La, Nb, Rb, and V with RSD less than 9.0% （n=12）.
文摘Complex dynamics are studied in the T system, a three-dimensional autonomous nonlinear system. In particular, we perform an extended Hopf bifurcation analysis of the system. The periodic orbit immediately following the Hopf bifurcation is constructed analytically for the T system using the method of multiple scales, and the stability of such orbits is analyzed. Such analytical results complement the numerical results present in the literature. The analytical results in the post-bifurcation regime are verified and extended via numerical simulations, as well as by the use of standard power spectra, autocorrelation functions, and fractal dimensions diagnostics. We find that the T system exhibits interesting behaviors in many parameter regimes.
基金National Natural Science Foundation ofChina( No.5 99770 0 1)
文摘The novel quantitative assessment method using transmission line measurement was developed. A new style of stability criterion was suggested which is based on the line measurement. The stability indices for lines, cutsets and power system according to features of transient energy in the lines were given, which not only provide a reliable and accurate assessment of the transient stability of power system, but also can be used to assess the effect of lines and cutsets on the transient stability and identify the weak transmission segment. Examples were presented by simulation on the IEEE-39 buses test system.
基金Project(2013CB036004)supported by the National Basic Research Program of ChinaProject(51178468)supported by the National Natural Science Foundation of China
文摘The stability of natural slope was analyzed on the basis of limit analysis. The sliding model of a kind of natural slope was presented. A new kinematically admissible velocity field for the new sliding model was constructed. The stability factor formulation by the upper bound theorem leads to a classical nonlinear programming problem, when the external work rate and internal energy dissipation were solved, and the constraint condition of the programming problem was given. The upper bound optimization problem can be solved efficiently by applying a nonlinear SQP algorithm, and stability factor was obtained, which agrees well with previous achievements.
文摘The main purpose of this paper is to set up the finite difference scheme with incremental unknowns for the nonlinear differential equation by means of introducing incremental unknowns method and discuss the stability of the scheme.Through the stability analyzing for the scheme,it was shown that the stability of the finite difference scheme with the incremental unknowns is improved when compared with the stability of the corresponding classic difference scheme.
基金Supported by the National Natural Science Foundation of China(50475166) and Natural Science Foundation of Shandong Province (Y2002F09) and Qingdao Scientific Bureau(04-3NS-10)
文摘By simplifying saturatedly magnetized wire-rope to magnetic dipoles of the same magnetic field strength, an equivalent magnetic dipoles model is developed and the measuring principle for recognising damage of broken wire was presented. The relevant calculation formulas were also deduced. A composite solution method about nonlinear optimization was given. An example was given to illustrate the use of the equivalent magnetic dipoles method for quantitative damage recognition, and demonstrates that the result of this method is consistent with the real situation, so the method is valid and practical. wire-rope, damage of broken wires, quantitative recognition, equivalent magnetic dipoles, simulate
文摘The stability analysis of linear multistep (LM) methods is carried out under Kreiss resolvent condition when they are applied to neutral delay differential equations of the form y′(t)=ay(t)+by(t-τ)+ cy′(t- τ) y(t)=g(t) -τ≤t≤0 with τ>0 and a, b and c∈, and it is proved that the ‖B n‖ is suitably bounded, where B is the companion matrix.
基金supported by Transportation Research Project of Jiangsu Province (05Y015),China
文摘We quantitatively study magnetic anomalies of reinforcement rods in bored insitu concrete piles for the first time and summarized their magnetic anomaly character. Key factors such as measuring borehole orientation, borehole-reinforcement distance, and multiple-section reinforcement rods are discussed which contributes valid and quantitative reference for using the magnetic method to detect reinforcement rods. Through tests with model piles, we confirm the accuracy of theoretical computations and then utilize the law discovered in theoretical computations to explain the characteristics of the actual testing curves. The results show that the Za curves of the reinforcement rod reflect important factors regarding the reinforcement rods, such as rod length, change of reinforcement ratio, length of overlap, and etc. This research perfects the magnetic method for detecting reinforcement rods in bored in-situ concrete piles and the method has great importance for preventing building contractor fraud.
文摘In this paper, we investigate two kinds of second-order consensus algorithms for multiple agents with coupling delay under general fixed directed information topology. Stability analysis is performed based on Lyapunov- Krasovskii functional method. Delay-dependent asymptotical stability condition in terms of linear matrix inequalities （LMIs） is derived for the second-order consensus algorithm of delayed dynamical networks. Both delay-independent and delay-dependent asymptotical stability conditions in terms of LMIs are derived for the second-order consensus algorithm with information feedback.
