Exponential decay law of acoustic emission and microseismic activities caused by disturbances associated with multilevel loading and mining blast

To investigate decay law of acoustic emission and microseismic activities caused by disturbances associated with multilevel loading and mining blast,a new exponential decay(ED)law was proposed.The results show that the micro-fracture activity decay law after multistage stress loading and blasting disturbance conforms to the ED model,in which the sum of A and n represents the number of initial micro-fracture events,and n represents the level of background micro-fracture events.The ED model can describe the number of initial micro-fracture events with a deviation less than 10%.The ED model outperforms the traditional aftershock models in describing the micro-fracture event decay law in the three cases considered.The ED model can provide a reference for selecting the blasting interval in mines,which is of great significance to maintain the stability of the surrounding rock and ensure safe production in metal mines.

Vibrations of FGM thin cylindrical shells with exponential volume fraction law

In this paper, the influence of an exponential volume fraction law on the vibration frequencies of thin functionally graded cylindrical shells is studied. Material properties in the shell thickness direction are graded in accordance with the exponential law. Expressions for the strain-displacement and curvature-displacement relationships are taken from Love＇s thin shell theory. The Rayleigh-Ritz approach is used to derive the shell eigenfrequency equation. Axial modal dependence is assumed in the characteristic beam functions. Natural frequencies of the shells are observed to be dependent on the constituent volume fractions. The results are compared with those available in the literature for the validity of the present methodology.

Sliding mode control of three-phase AC/DC converters using exponential rate reaching law

Sliding mode control(SMC) becomes a common tool in designing robust nonlinear control systems, due to its inherent characteristics such as insensitivity to system uncertainties and fast dynamic response.Two modes are involved in the SMC operation, namely reaching mode and sliding mode.In the reaching mode, the system state is forced to reach the sliding surface in a finite time.The major drawback of the SMC approach is the occurrence of chattering in the sliding mode, which is undesirable in most applications.Generally, the trade-off between chattering reduction and fast reaching time must be considered in the conventional SMC design.This paper proposes SMC design with a novel reaching law called the exponential rate reaching law(ERRL) to reduce chattering, and the control structure of the converter is designed based on the multiinput SMC that is applied to a three-phase AC/DC power converter.The simulation and experimental results show the effectiveness of the proposed technique.

Integrated Sliding Mode Velocity Control of Linear Permanent Magnet Synchronous Motor with Thrust Ripple Compensation

In this paper,a compound sliding mode velocity control scheme with a new exponential reaching law(NERL)with thrust ripple observation strategy is proposed to obtain a high performance velocity loop of the linear permanent magnet synchronous motor(LPMSM)control system.A sliding mode velocity controller based on NERL is firstly discussed to restrain chattering of the conventional exponential reaching law(CERL).Furthermore,the unavoidable thrust ripple caused by the special structure of linear motor will bring about velocity fluctuation and reduced control performance.Thus,a thrust ripple compensation strategy on the basis of extend Kalman filter(EKF)theory is proposed.The estimated thrust ripple will be introduced into the sliding mode velocity controller to optimize the control accuracy and robustness.The effectiveness of the proposal is validated with experimental results.

Exponential inequalities under the sub-linear expectations with applications to laws of the iterated logarithm

Kolmogorov's exponential inequalities are basic tools for studying the strong limit theorems such as the classical laws of the iterated logarithm for both independent and dependent random variables. This paper establishes the Kolmogorov type exponential inequalities of the partial sums of independent random variables as well as negatively dependent random variables under the sub-linear expectations. As applications of the exponential inequalities, the laws of the iterated logarithm in the sense of non-additive capacities are proved for independent or negatively dependent identically distributed random variables with finite second order moments.For deriving a lower bound of an exponential inequality, a central limit theorem is also proved under the sublinear expectation for random variables with only finite variances.

Discrete-time sliding mode control with power rate exponential reaching law of a pneumatic artificial muscle system

This paper develops a discrete-time sliding mode controller with a power rate exponential reaching law approach to enhance the performance of a pneumatic artificial muscle system in both reaching time and chattering reduction.The proposed method dynamically adapts to the variation of the switching function,which is based on an exponential term and a power rate term of the sliding surface.Thus,the controlled system can achieve high tracking performance while still obtain chattering-free control.Moreover,the effectiveness of the proposed method is validated through multiple experimental tests,focused on a dual pneumatic artificial muscle system.Finally,experimental results show the effectiveness of the proposed approach in this paper.

Sliding mode control of engine-variable pump-variable motor drive system

Engine-variable pump-variable motor drive system is a complex nonlinear system. In order to improve system response speed and stability,a sliding-mode variable-structure control based on a feedback linearization theory is analyzed in this research. A standardized system model is established and linearized by the feedback linearization theory,and the input dimension is reduced through the relationship between variables which has simplified the linearization process. Then the sliding-mode controller using an exponential reaching law is designed and the Lyapunov stability of this algorithm is verified. The simulation results show that the sliding-mode variable-structure controller based on the feedback linearization theory can improve system response speed,reduce overshoot and achieve stronger robustness,so the vehicle speed control requirements can be satisfied well.

A New Nonspherical Oxidation Model of Metal Particles

This paper analyzes the oxidation law of metal particles and proposes a new oxidation reaction rate model,based on measurements of thermogravimetric-mass spectrometer(TG-MS),X-ray diffractometer(XRD)and scanning electron microscope(SEM).The model is named EBM(egg broken model)with a formula of exponential law.According to the model,the aluminum particles do not react in a spherical shape,but crack and the melted metal inside flows out to form a new nonspherical surface and the reaction rate is still determined by the surface area.The model is verified with heating rates of 5℃/min,10℃/min and 25℃/min,and with particle size of 1–2μm,8–9μm and 20–22μm.Many models are based on spherical hypothesis and the new model gives a different physical illustration to explain oxidation progress of metal particles.The new model gives an exponential law,which fits the experimental data well,and it may be useful to understand oxidation mechanism of metal particles.

Effect of solid contents on the controlled shear stress rheological properties of different types of sludge

Controlled shear stress （CSS） test was used to study the effect of solid contents on the corresponding rheological parameters for sludge. Three types of sludge with or without conditioning, including activated sludge （AS）, anaerobic digested sludge （ADS）, and water treatment residuals （WTRs）, were collected for the CSS test. Results showed that the yield stress and the cohesion energy of the sludge networks were improved with increased total suspending solid （TSS） contents in most cases. For the conditioned AS/ADS and the raw WTRs, exponential law was observed in the relationships between cohesion energy of material networks or yield stress and the TSS contents, whereas for the conditioned WTRs, only exponential law dependence was found between the parameters of shear modulus or critical strain and the TSS contents.

Simulation and comparative study of two types of Topographic Index model for a homogeneous mountain catchment

In order to expand the application range of the classic Topographic Index model(TOPMODEL) and develop a more appropriate submodel of hydrological processes for use in the land surface model, two types of TOPMODEL are investigated, one with saturated hydraulic conductivity change with depth obeying exponential law(classical e-TOPMODEL or e-TOPMODEL for short) and the other obeying general power law(general p-TOPMODEL or p-TOPMODEL for short). Using observation date in the Suomo River catchment located in the upper reaches of the Yangtze River, the sensitivity study of the p-TOPMODEL was conducted and the simulated results from the model were examined and evaluated first, and then the results were compared with the results from the e-TOPMODEL to find the similarities and differences between the two types of models. The main conclusions obtained from the above studies are(1) topographic index and its distribution derived from the p-TOPPMODEL for the Suomo Basin are sensitive to changes of parameter n and m;(2) changes of n and m have impacts on the simulation results of various hydrological components(such as daily runoff, monthly averaged runoff, monthly averaged surface runoff and subsurface runoff), but have the weaker impacts on forty-year averaged total runoff; and(3) for the same value of m, the simulated results of e-TOPMODEL display higher surface runoff and lower subsurface runoff than the general p-TOPMODEL does but multi-year averaged total runoffs produced from the two types of TOPMODEL show insignificant difference. The differences between the two types of models indicate that it is necessary to pay close attention to correct selection from different hydrological models for use in land surface model development. The result mentioned above is useful to provide some referential information for the model selection.