Considering three longitudinal displacement functions and uniform axial displacement functions for shear lag effect and uniform axial deformation of thin-walled box girder with varying depths,a simple and efficient me...Considering three longitudinal displacement functions and uniform axial displacement functions for shear lag effect and uniform axial deformation of thin-walled box girder with varying depths,a simple and efficient method with high precision to analyze the shear lag effect of thin-walled box girders was proposed.The governing differential equations and boundary conditions of the box girder under lateral loading were derived based on the energy-variational method,and closed-form solutions to stress and deflection corresponding to lateral loading were obtained.Analysis and calculations were carried out with respect to a trapezoidal box girder under concentrated loading or uniform loading and a rectangular box girder under concentrated loading.The analytical results were compared with numerical solutions derived according to the high order finite strip element method and the experimental results.The investigation shows that the closed-form solution is in good agreement with the numerical solutions derived according to the high order finite strip method and the experimental results,and has good stability.Because of the shear lag effect,the stress in cross-section centroid is no longer zero,thus it is not reasonable enough to assume that the strain in cross-section centroid is zero without considering uniform axial deformation.展开更多
This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement res...This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement residual and stress residual along the boundaries. Numerical results show that there are notable differences for response amplitudes between a semi-circular cavity and a whole-circular cavity in a half-space.展开更多
Based on the consideration of longitudinal warp caused by shear lag effects on concrete slabs and bottom plates of steel beams,shear deformation of steel beams and interface slip between steel beams and concrete slabs...Based on the consideration of longitudinal warp caused by shear lag effects on concrete slabs and bottom plates of steel beams,shear deformation of steel beams and interface slip between steel beams and concrete slabs,the governing differential equations and boundary conditions of the steel-concrete composite box beams under lateral loading were derived using energy-variational method.The closed-form solutions for stress,deflection and slip of box beams under lateral loading were obtained,and the comparison of the analytical results and the experimental results for steel-concrete composite box beams under concentrated loading or uniform loading verifies the closed-form solution.The investigation of the parameters of load effects on composite box beams shows that:1) Slip stiffness has considerable impact on mid-span deflection and end slip when it is comparatively small;the mid-span deflection and end slip decrease significantly with the increase of slip stiffness,but when the slip stiffness reaches a certain value,its impact on mid-span deflection and end slip decreases to be negligible.2) The shear deformation has certain influence on mid-span deflection,and the larger the load is,the greater the influence is.3) The impact of shear deformation on end slip can be neglected.4) The strain of bottom plate of steel beam decreases with the increase of slip stiffness,while the shear lag effect becomes more significant.展开更多
The prediction of liquefaction-induced lateral spreading/displacement(Dh)is a challenging task for civil/geotechnical engineers.In this study,a new approach is proposed to predict Dh using gene expression programming(...The prediction of liquefaction-induced lateral spreading/displacement(Dh)is a challenging task for civil/geotechnical engineers.In this study,a new approach is proposed to predict Dh using gene expression programming(GEP).Based on statistical reasoning,individual models were developed for two topographies:free-face and gently sloping ground.Along with a comparison with conventional approaches for predicting the Dh,four additional regression-based soft computing models,i.e.Gaussian process regression(GPR),relevance vector machine(RVM),sequential minimal optimization regression(SMOR),and M5-tree,were developed and compared with the GEP model.The results indicate that the GEP models predict Dh with less bias,as evidenced by the root mean square error(RMSE)and mean absolute error(MAE)for training(i.e.1.092 and 0.815;and 0.643 and 0.526)and for testing(i.e.0.89 and 0.705;and 0.773 and 0.573)in free-face and gently sloping ground topographies,respectively.The overall performance for the free-face topology was ranked as follows:GEP>RVM>M5-tree>GPR>SMOR,with a total score of 40,32,24,15,and 10,respectively.For the gently sloping condition,the performance was ranked as follows:GEP>RVM>GPR>M5-tree>SMOR with a total score of 40,32,21,19,and 8,respectively.Finally,the results of the sensitivity analysis showed that for both free-face and gently sloping ground,the liquefiable layer thickness(T_(15))was the major parameter with percentage deterioration(%D)value of 99.15 and 90.72,respectively.展开更多
The direct separation of variables is used to obtain the closed-form solutions for the free vibrations of rectangular Mindlin plates. Three different characteristic equations are derived by using three different metho...The direct separation of variables is used to obtain the closed-form solutions for the free vibrations of rectangular Mindlin plates. Three different characteristic equations are derived by using three different methods. It is found that the deflection can be expressed by means of the four characteristic roots and the two rotations should be expressed by all the six characteristic roots,which is the particularity of Mindlin plate theory. And the closed-form solutions,which satisfy two of the three governing equations and all boundary conditions and are accurate for rectangular plates with moderate thickness,are derived for any combinations of simply supported and clamped edges. The free edges can also be dealt with if the other pair of opposite edges is simply supported. The present results agree well with results published previously by other methods for different aspect ratios and relative thickness.展开更多
Dynamic programming(DP)is frequently used to obtain the optimal solution to the hybrid electric vehicle(HEV)energy management.The trade-off between the accuracy and the computational effort is the biggest problem for ...Dynamic programming(DP)is frequently used to obtain the optimal solution to the hybrid electric vehicle(HEV)energy management.The trade-off between the accuracy and the computational effort is the biggest problem for the DP method.The closed-form solution to the DP is proposed to solve this problem.Firstly,the affine linear model of the engine fuel rate is obtained based on engine test data.The piecewise linear approximation of the motor power demand is obtained considering the different energy flows in the charging and discharging stages of the battery.Then,the second-order Taylor expansion for the cost matrix at each time and state grid point is introduced to get the closed-form solution of the optimal torque split.The results show that this method can greatly reduce the computing burden by 93%while ensuring near-optimal fuel economy compared with the conventional DP method.展开更多
Classical localization methods use Cartesian or Polar coordinates, which require a priori range information to determine whether to estimate position or to only find bearings. The modified polar representation (MPR) u...Classical localization methods use Cartesian or Polar coordinates, which require a priori range information to determine whether to estimate position or to only find bearings. The modified polar representation (MPR) unifies near-field and farfield models, alleviating the thresholding effect. Current localization methods in MPR based on the angle of arrival (AOA) and time difference of arrival (TDOA) measurements resort to semidefinite relaxation (SDR) and Gauss-Newton iteration, which are computationally complex and face the possible diverge problem. This paper formulates a pseudo linear equation between the measurements and the unknown MPR position,which leads to a closed-form solution for the hybrid TDOA-AOA localization problem, namely hybrid constrained optimization(HCO). HCO attains Cramér-Rao bound (CRB)-level accuracy for mild Gaussian noise. Compared with the existing closed-form solutions for the hybrid TDOA-AOA case, HCO provides comparable performance to the hybrid generalized trust region subproblem (HGTRS) solution and is better than the hybrid successive unconstrained minimization (HSUM) solution in large noise region. Its computational complexity is lower than that of HGTRS. Simulations validate the performance of HCO achieves the CRB that the maximum likelihood estimator (MLE) attains if the noise is small, but the MLE deviates from CRB earlier.展开更多
When concentrated forces are applied at any points of the outer region of an ellipse in an infinite plate, the complex potentials are determined using the conformal mapping method and Cauchy＇s integral formula. And t...When concentrated forces are applied at any points of the outer region of an ellipse in an infinite plate, the complex potentials are determined using the conformal mapping method and Cauchy＇s integral formula. And then, based on the superposition principle, the analyt- ical solutions for stress around an elliptical hole in an infinite plate subjected to a uniform far-field stress and concentrated forces, are obtained. Tangential stress concentration will occur on the hole boundary when only far-field uniform loads are applied. When concen- trated forces are applied in the reversed directions of the uniform loads, tangential stress concentration on the hole boundary can be released significantly. In order to minimize the tangential stress concentration, we need to determine the optimum positions and values of the concentrated forces. Three different optimization methods are applied to achieve this aim. The results show that the tangential stress can be released significantly when the op- timized concentrated forces are applied.展开更多
Highly accurate closed-form eigensolutions for flutter of three-dimensional(3D)panel with arbitrary combinations of simply supported(S),glide(G),clamped(C)and free(F)boundary conditions(BCs),such as cantilever panels,...Highly accurate closed-form eigensolutions for flutter of three-dimensional(3D)panel with arbitrary combinations of simply supported(S),glide(G),clamped(C)and free(F)boundary conditions(BCs),such as cantilever panels,are achieved according to the linear thin plate theory and the first-order piston theory as well as the complex modal analysis,and all solutions are in a simple and explicit form.The iterative Separation-of-Variable(iSOV)method proposed by the pre-sent authors is employed to obtain the highly accurate eigensolutions.The flutter mechanism is studied with the benefit of eigenvalue properties from mathematical senses.The effects of boundary conditions,chord-thickness ratios,aerodynamic damping,aspect ratios and in-plane loads on flut-ter properties are examined.The results are compared with those of Kantorovich method and Galerkin method,and also coincide well with analytical solutions in literature,verifying the accu-racy of the present closed-form results.It is revealed that,(A)the flutter characteristics are domi-nated by the cross section properties of panels in the direction of stream flow;(B)two types of flutter,called coupled-mode flutter and zero-frequency flutter which includes zero-frequency single-mode flutter and buckling,are observed;(C)boundary conditions and in-plane loads can affect both flutter boundary and flutter type;(D)the flutter behavior of 3D panel is similar to that of the two-dimensional(2D)panel if the aspect ratio is up to a certain value;(E)four to six modes should be used in the Galerkin method for accurate eigensolutions,and the results converge to that of Kantorovich method which uses the same mode functions in the direction perpendicular to the stream flow.The present analysis method can be used as a reference for other stability issues characterized by complex eigenvalues,and the highly closed-form solutions are useful in parameter designs and can also be taken as benchmarks for the validation of numerical methods.展开更多
The forward kinematics analysis of a special 6-SPS Stewart platform is presented, in which both the base and the mobile platforms are hexagon and similar to each other. The forward kinematics of the parallel mechanism...The forward kinematics analysis of a special 6-SPS Stewart platform is presented, in which both the base and the mobile platforms are hexagon and similar to each other. The forward kinematics of the parallel mechanism is a complicated nonlinear problem, however. there exists a class of parallel kinematics platforms that have the simplest forward kinematics. By introducing quaternion to represent the rotary transformation matrix and applying dual space method to eliminate the high degree polynomials, the forward kinematics can be expressed by a set of quadratic algebra equations, which decouple the position and the orientation of the mobile platform. The approach only requires solving one-variable quadratic equations. Besides, spurious complex roots are automatically avoided. Eight possible solutions are obtained from the approach. It discovers the inner symmetry relationship between the solutions of the forward kinematics.展开更多
Nonlinear evolution equations(NLEEs)are frequently employed to determine the fundamental principles of natural phenomena.Nonlinear equations are studied extensively in nonlinear sciences,ocean physics,fluid dynamics,p...Nonlinear evolution equations(NLEEs)are frequently employed to determine the fundamental principles of natural phenomena.Nonlinear equations are studied extensively in nonlinear sciences,ocean physics,fluid dynamics,plasma physics,scientific applications,and marine engineering.The generalized exponen-tial rational function(GERF)technique is used in this article to seek several closed-form wave solutions and the evolving dynamics of different wave profiles to the generalized nonlinear wave equation in(3+1)dimensions,which explains several more nonlinear phenomena in liquids,including gas bubbles.A large number of closed-form wave solutions are generated,including trigonometric function solutions,hyper-bolic trigonometric function solutions,and exponential rational functional solutions.In the dynamics of distinct solitary waves,a variety of soliton solutions are obtained,including single soliton,multi-wave structure soliton,kink-type soliton,combo singular soliton,and singularity-form wave profiles.These de-termined solutions have never previously been published.The dynamical wave structures of some analyt-ical solutions are graphically demonstrated using three-dimensional graphics by providing suitable values to free parameters.This technique can also be used to obtain the soliton solutions of other well-known equations in engineering physics,fluid dynamics,and other fields of nonlinear sciences.展开更多
This study proposed an analytical model for the tunnel supported with a tangentially yielding liner in viscoelastic ground.The efficiency of the developed analytical model was verified by comparing the calculated resu...This study proposed an analytical model for the tunnel supported with a tangentially yielding liner in viscoelastic ground.The efficiency of the developed analytical model was verified by comparing the calculated results with associated numerical simulation results.Using the analytical model,a comprehensive parameter sensitivity analysis was performed to examine the effects of the rate of tunnel face advancement,concrete liner thickness,installation time of liner,and strength and thickness of yielding elements on the tunnel responses.The results highlight the significant benefit of the tangentially yielding liner to relieve overstress in the tunnel liner and improve the stability of the tunnel.The yield efficiency of the tangentially yielding liner depends highly on the yielding strength and deformable capacity of the yielding elements and less on the installation time.展开更多
Reliable,nondestructive fish freshness evaluation applicable during fish commercialization has been continuously pursued by scientists and industry.Taking into account that fish texture is primarily affected even at ...Reliable,nondestructive fish freshness evaluation applicable during fish commercialization has been continuously pursued by scientists and industry.Taking into account that fish texture is primarily affected even at early stages of post-mortem storage,a relevant nondestructive testing framework for rapid textural assessment of fish freshness was developed in the past.Herein,an algorithm operating within the aforementioned framework and optimized for use in industrial environments is proposed.Sea bass(Dicentrarchus labrax)both freshly killed and stored on ice for 6 days have been used for comparative testing.The fish is part of a system,which is vibrationtested via a new testing protocol designed for easy implementation and robustness to noise.At the same time,a new closed-form analytical expression for the system response to the specific testing is computed and used along with experimental data,for obtaining specific mechanical(thus muscle-structural)characteristics of fish flesh.This computation is designed to only require readily available routines found in most relevant software.The algorithmic operational framework has been used in two different test setups(a custom-built test rig and a prototype device),with results following remarkably similar trends,clearly discriminating different textural(thus freshness)characteristics,and consequently validating the proposed approach.展开更多
We propose a novel stochastic modeling framework for coal production and logistics using option pricing theory.The problem of valuing the inherent real optionality a coal producer has when mining and processing therma...We propose a novel stochastic modeling framework for coal production and logistics using option pricing theory.The problem of valuing the inherent real optionality a coal producer has when mining and processing thermal coal is modelled as pricing spread options of three assets under the stochastic volatility model.We derive a three-dimensional Fast Fourier Transform(“FFT”)lower bound approximation to value the inherent real optionality and for robustness check,we compare the semi-analytical pricing accuracy with the Monte Carlo simulation.Model parameters are estimated from the historical monthly data,and stochastic volatility parameters are obtained by matching the Kurtosis of the low-ash diff data to the Kurtosis of the stochastic volatility process which is assumed to follow Cox–Ingersoll–Ross(“CIR”)model.展开更多
Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for ...Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.展开更多
In the fields of oceanography,hydrodynamics,and marine engineering,many mathematicians and physi-cists are interested in Burgers-type equations to show the different dynamics of nonlinear wave phenom-ena,one of which ...In the fields of oceanography,hydrodynamics,and marine engineering,many mathematicians and physi-cists are interested in Burgers-type equations to show the different dynamics of nonlinear wave phenom-ena,one of which is a(3+1)-dimensional Burgers system that is currently being studied.In this paper,we apply two different analytical methods,namely the generalized Kudryashov(GK)method,and the generalized exponential rational function method,to derive abundant novel analytic exact solitary wave solutions,including multi-wave solitons,multi-wave peakon solitons,kink-wave profiles,stripe solitons,wave-wave interaction profiles,and periodic oscillating wave profiles for a(3+1)-dimensional Burgers sys-tem with the assistance of symbolic computation.By employing the generalized Kudryashov method,we obtain some new families of exact solitary wave solutions for the Burgers system.Further,we applied the generalized exponential rational function method to obtain a large number of soliton solutions in the forms of trigonometric and hyperbolic function solutions,exponential rational function solutions,peri-odic breather-wave soliton solutions,dark and bright solitons,singular periodic oscillating wave soliton solutions,and complex multi-wave solutions under various family cases.Based on soft computing via Wolfram Mathematica,all the newly established solutions are verified by back substituting them into the considered Burgers system.Eventually,the dynamical behaviors of some established results are exhibited graphically through three-and two-dimensional wave profiles via numerical simulation.展开更多
The elastoplastic pure bending problem of a curved beam with material inhomo- geneity is investigated based on Tresca＇s yield criterion and its associated flow rule. Suppose that the material is elastically isotropic...The elastoplastic pure bending problem of a curved beam with material inhomo- geneity is investigated based on Tresca＇s yield criterion and its associated flow rule. Suppose that the material is elastically isotropic, ideally elastic-plastic and its elastic modulus and yield limit vary radially according to exponential functions. Closed-form solutions to the stresses and radial displacement in both purely elastic stress state and partially plastic stress state are presented. Numerical examples reveal the distinct characteristics of elastoplastic bending of a curved beam composed of inhomogeneous materials. Due to the inhomogeneity of materials, the bearing capac- ity of the curved beam can be improved greatly and the initial yield mode can also be dominated. Closed-form solutions presented here can serve as benchmark results for evaluating numerical solutions.展开更多
基金Projects(51078355,50938008) supported by the National Natural Science Foundation of ChinaProject(CX2011B093) supported by the Doctoral Candidate Research Innovation Program of Hunan Province, ChinaProject(20117Q008) supported by the Basic Scientific Research Funds for Central Universities of China
文摘Considering three longitudinal displacement functions and uniform axial displacement functions for shear lag effect and uniform axial deformation of thin-walled box girder with varying depths,a simple and efficient method with high precision to analyze the shear lag effect of thin-walled box girders was proposed.The governing differential equations and boundary conditions of the box girder under lateral loading were derived based on the energy-variational method,and closed-form solutions to stress and deflection corresponding to lateral loading were obtained.Analysis and calculations were carried out with respect to a trapezoidal box girder under concentrated loading or uniform loading and a rectangular box girder under concentrated loading.The analytical results were compared with numerical solutions derived according to the high order finite strip element method and the experimental results.The investigation shows that the closed-form solution is in good agreement with the numerical solutions derived according to the high order finite strip method and the experimental results,and has good stability.Because of the shear lag effect,the stress in cross-section centroid is no longer zero,thus it is not reasonable enough to assume that the strain in cross-section centroid is zero without considering uniform axial deformation.
基金supported by National Natural Science Foundation of China (No. 50978183)Tianjin Natural Science Foundation (No. 07JCZDJC10100)
文摘This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement residual and stress residual along the boundaries. Numerical results show that there are notable differences for response amplitudes between a semi-circular cavity and a whole-circular cavity in a half-space.
基金Projects(51078355,50938008) supported by the National Natural Science Foundation of ChinaProject(094801020) supported by the Academic Scholarship for Doctoral Candidates of the Ministry of Education,China+1 种基金Project(CX2011B093) supported by the Doctoral Candidate Research Innovation Project of Hunan Province, ChinaProject(20117Q008) supported by the Central University Basic Scientific Research Business Expenses Special Fund of China
文摘Based on the consideration of longitudinal warp caused by shear lag effects on concrete slabs and bottom plates of steel beams,shear deformation of steel beams and interface slip between steel beams and concrete slabs,the governing differential equations and boundary conditions of the steel-concrete composite box beams under lateral loading were derived using energy-variational method.The closed-form solutions for stress,deflection and slip of box beams under lateral loading were obtained,and the comparison of the analytical results and the experimental results for steel-concrete composite box beams under concentrated loading or uniform loading verifies the closed-form solution.The investigation of the parameters of load effects on composite box beams shows that:1) Slip stiffness has considerable impact on mid-span deflection and end slip when it is comparatively small;the mid-span deflection and end slip decrease significantly with the increase of slip stiffness,but when the slip stiffness reaches a certain value,its impact on mid-span deflection and end slip decreases to be negligible.2) The shear deformation has certain influence on mid-span deflection,and the larger the load is,the greater the influence is.3) The impact of shear deformation on end slip can be neglected.4) The strain of bottom plate of steel beam decreases with the increase of slip stiffness,while the shear lag effect becomes more significant.
文摘The prediction of liquefaction-induced lateral spreading/displacement(Dh)is a challenging task for civil/geotechnical engineers.In this study,a new approach is proposed to predict Dh using gene expression programming(GEP).Based on statistical reasoning,individual models were developed for two topographies:free-face and gently sloping ground.Along with a comparison with conventional approaches for predicting the Dh,four additional regression-based soft computing models,i.e.Gaussian process regression(GPR),relevance vector machine(RVM),sequential minimal optimization regression(SMOR),and M5-tree,were developed and compared with the GEP model.The results indicate that the GEP models predict Dh with less bias,as evidenced by the root mean square error(RMSE)and mean absolute error(MAE)for training(i.e.1.092 and 0.815;and 0.643 and 0.526)and for testing(i.e.0.89 and 0.705;and 0.773 and 0.573)in free-face and gently sloping ground topographies,respectively.The overall performance for the free-face topology was ranked as follows:GEP>RVM>M5-tree>GPR>SMOR,with a total score of 40,32,24,15,and 10,respectively.For the gently sloping condition,the performance was ranked as follows:GEP>RVM>GPR>M5-tree>SMOR with a total score of 40,32,21,19,and 8,respectively.Finally,the results of the sensitivity analysis showed that for both free-face and gently sloping ground,the liquefiable layer thickness(T_(15))was the major parameter with percentage deterioration(%D)value of 99.15 and 90.72,respectively.
基金supported by the National Natural Science Foundation of China (No. 10772014)
文摘The direct separation of variables is used to obtain the closed-form solutions for the free vibrations of rectangular Mindlin plates. Three different characteristic equations are derived by using three different methods. It is found that the deflection can be expressed by means of the four characteristic roots and the two rotations should be expressed by all the six characteristic roots,which is the particularity of Mindlin plate theory. And the closed-form solutions,which satisfy two of the three governing equations and all boundary conditions and are accurate for rectangular plates with moderate thickness,are derived for any combinations of simply supported and clamped edges. The free edges can also be dealt with if the other pair of opposite edges is simply supported. The present results agree well with results published previously by other methods for different aspect ratios and relative thickness.
基金National Natural Science Foundation of China:[Grant Number 52077217].
文摘Dynamic programming(DP)is frequently used to obtain the optimal solution to the hybrid electric vehicle(HEV)energy management.The trade-off between the accuracy and the computational effort is the biggest problem for the DP method.The closed-form solution to the DP is proposed to solve this problem.Firstly,the affine linear model of the engine fuel rate is obtained based on engine test data.The piecewise linear approximation of the motor power demand is obtained considering the different energy flows in the charging and discharging stages of the battery.Then,the second-order Taylor expansion for the cost matrix at each time and state grid point is introduced to get the closed-form solution of the optimal torque split.The results show that this method can greatly reduce the computing burden by 93%while ensuring near-optimal fuel economy compared with the conventional DP method.
基金supported by the National Natural Science Foundation of China (62101359)Sichuan University and Yibin Municipal People’s Government University and City Strategic Cooperation Special Fund Project (2020CDYB-29)+1 种基金the Science and Technology Plan Transfer Payment Project of Sichuan Province (2021ZYSF007)the Key Research and Development Program of Science and Technology Department of Sichuan Province (2020YFS0575,2021KJT0012-2 021YFS-0067)。
文摘Classical localization methods use Cartesian or Polar coordinates, which require a priori range information to determine whether to estimate position or to only find bearings. The modified polar representation (MPR) unifies near-field and farfield models, alleviating the thresholding effect. Current localization methods in MPR based on the angle of arrival (AOA) and time difference of arrival (TDOA) measurements resort to semidefinite relaxation (SDR) and Gauss-Newton iteration, which are computationally complex and face the possible diverge problem. This paper formulates a pseudo linear equation between the measurements and the unknown MPR position,which leads to a closed-form solution for the hybrid TDOA-AOA localization problem, namely hybrid constrained optimization(HCO). HCO attains Cramér-Rao bound (CRB)-level accuracy for mild Gaussian noise. Compared with the existing closed-form solutions for the hybrid TDOA-AOA case, HCO provides comparable performance to the hybrid generalized trust region subproblem (HGTRS) solution and is better than the hybrid successive unconstrained minimization (HSUM) solution in large noise region. Its computational complexity is lower than that of HGTRS. Simulations validate the performance of HCO achieves the CRB that the maximum likelihood estimator (MLE) attains if the noise is small, but the MLE deviates from CRB earlier.
基金supported by the National Natural Science Foundation of China [grant numbers 11172101, 11572126]
文摘When concentrated forces are applied at any points of the outer region of an ellipse in an infinite plate, the complex potentials are determined using the conformal mapping method and Cauchy＇s integral formula. And then, based on the superposition principle, the analyt- ical solutions for stress around an elliptical hole in an infinite plate subjected to a uniform far-field stress and concentrated forces, are obtained. Tangential stress concentration will occur on the hole boundary when only far-field uniform loads are applied. When concen- trated forces are applied in the reversed directions of the uniform loads, tangential stress concentration on the hole boundary can be released significantly. In order to minimize the tangential stress concentration, we need to determine the optimum positions and values of the concentrated forces. Three different optimization methods are applied to achieve this aim. The results show that the tangential stress can be released significantly when the op- timized concentrated forces are applied.
基金supported by the National Natural Science Foundation of China(Nos.11872090,11672019,11472035)。
文摘Highly accurate closed-form eigensolutions for flutter of three-dimensional(3D)panel with arbitrary combinations of simply supported(S),glide(G),clamped(C)and free(F)boundary conditions(BCs),such as cantilever panels,are achieved according to the linear thin plate theory and the first-order piston theory as well as the complex modal analysis,and all solutions are in a simple and explicit form.The iterative Separation-of-Variable(iSOV)method proposed by the pre-sent authors is employed to obtain the highly accurate eigensolutions.The flutter mechanism is studied with the benefit of eigenvalue properties from mathematical senses.The effects of boundary conditions,chord-thickness ratios,aerodynamic damping,aspect ratios and in-plane loads on flut-ter properties are examined.The results are compared with those of Kantorovich method and Galerkin method,and also coincide well with analytical solutions in literature,verifying the accu-racy of the present closed-form results.It is revealed that,(A)the flutter characteristics are domi-nated by the cross section properties of panels in the direction of stream flow;(B)two types of flutter,called coupled-mode flutter and zero-frequency flutter which includes zero-frequency single-mode flutter and buckling,are observed;(C)boundary conditions and in-plane loads can affect both flutter boundary and flutter type;(D)the flutter behavior of 3D panel is similar to that of the two-dimensional(2D)panel if the aspect ratio is up to a certain value;(E)four to six modes should be used in the Galerkin method for accurate eigensolutions,and the results converge to that of Kantorovich method which uses the same mode functions in the direction perpendicular to the stream flow.The present analysis method can be used as a reference for other stability issues characterized by complex eigenvalues,and the highly closed-form solutions are useful in parameter designs and can also be taken as benchmarks for the validation of numerical methods.
文摘The forward kinematics analysis of a special 6-SPS Stewart platform is presented, in which both the base and the mobile platforms are hexagon and similar to each other. The forward kinematics of the parallel mechanism is a complicated nonlinear problem, however. there exists a class of parallel kinematics platforms that have the simplest forward kinematics. By introducing quaternion to represent the rotary transformation matrix and applying dual space method to eliminate the high degree polynomials, the forward kinematics can be expressed by a set of quadratic algebra equations, which decouple the position and the orientation of the mobile platform. The approach only requires solving one-variable quadratic equations. Besides, spurious complex roots are automatically avoided. Eight possible solutions are obtained from the approach. It discovers the inner symmetry relationship between the solutions of the forward kinematics.
基金the Institution of Emi-nence,University of Delhi,India,for providing financial assistance for this research through the IoE scheme under Faculty Research Programme(FRP)with Ref.No./IoE/2021/12/FRP.
文摘Nonlinear evolution equations(NLEEs)are frequently employed to determine the fundamental principles of natural phenomena.Nonlinear equations are studied extensively in nonlinear sciences,ocean physics,fluid dynamics,plasma physics,scientific applications,and marine engineering.The generalized exponen-tial rational function(GERF)technique is used in this article to seek several closed-form wave solutions and the evolving dynamics of different wave profiles to the generalized nonlinear wave equation in(3+1)dimensions,which explains several more nonlinear phenomena in liquids,including gas bubbles.A large number of closed-form wave solutions are generated,including trigonometric function solutions,hyper-bolic trigonometric function solutions,and exponential rational functional solutions.In the dynamics of distinct solitary waves,a variety of soliton solutions are obtained,including single soliton,multi-wave structure soliton,kink-type soliton,combo singular soliton,and singularity-form wave profiles.These de-termined solutions have never previously been published.The dynamical wave structures of some analyt-ical solutions are graphically demonstrated using three-dimensional graphics by providing suitable values to free parameters.This technique can also be used to obtain the soliton solutions of other well-known equations in engineering physics,fluid dynamics,and other fields of nonlinear sciences.
基金We acknowledge the funding support from the University Transportation Center for Underground Transportation Infrastructure(UTC-UTI)at the Colorado School of Mines and the U.S.Department of Transportation(DOT)(Grant No.69A3551747118).
文摘This study proposed an analytical model for the tunnel supported with a tangentially yielding liner in viscoelastic ground.The efficiency of the developed analytical model was verified by comparing the calculated results with associated numerical simulation results.Using the analytical model,a comprehensive parameter sensitivity analysis was performed to examine the effects of the rate of tunnel face advancement,concrete liner thickness,installation time of liner,and strength and thickness of yielding elements on the tunnel responses.The results highlight the significant benefit of the tangentially yielding liner to relieve overstress in the tunnel liner and improve the stability of the tunnel.The yield efficiency of the tangentially yielding liner depends highly on the yielding strength and deformable capacity of the yielding elements and less on the installation time.
基金FutureEUAqua project(Future growth in sustainable,resilient and climate friendly organic and conventional European aquaculture)funded by European Union’s Horizon 2020 research and innovation program under grant agreement No 817737The authors are particularly grateful to associates Mr.Emmanuel Tzevelekakis MSc who has been in charge for designing and building the Texture Evaluation device used for part of testing in this work and Dr.Panagiotis Christofilogiannis(AQUARK)for coordinating and providing the means for the Texture Evaluation device development.
文摘Reliable,nondestructive fish freshness evaluation applicable during fish commercialization has been continuously pursued by scientists and industry.Taking into account that fish texture is primarily affected even at early stages of post-mortem storage,a relevant nondestructive testing framework for rapid textural assessment of fish freshness was developed in the past.Herein,an algorithm operating within the aforementioned framework and optimized for use in industrial environments is proposed.Sea bass(Dicentrarchus labrax)both freshly killed and stored on ice for 6 days have been used for comparative testing.The fish is part of a system,which is vibrationtested via a new testing protocol designed for easy implementation and robustness to noise.At the same time,a new closed-form analytical expression for the system response to the specific testing is computed and used along with experimental data,for obtaining specific mechanical(thus muscle-structural)characteristics of fish flesh.This computation is designed to only require readily available routines found in most relevant software.The algorithmic operational framework has been used in two different test setups(a custom-built test rig and a prototype device),with results following remarkably similar trends,clearly discriminating different textural(thus freshness)characteristics,and consequently validating the proposed approach.
文摘We propose a novel stochastic modeling framework for coal production and logistics using option pricing theory.The problem of valuing the inherent real optionality a coal producer has when mining and processing thermal coal is modelled as pricing spread options of three assets under the stochastic volatility model.We derive a three-dimensional Fast Fourier Transform(“FFT”)lower bound approximation to value the inherent real optionality and for robustness check,we compare the semi-analytical pricing accuracy with the Monte Carlo simulation.Model parameters are estimated from the historical monthly data,and stochastic volatility parameters are obtained by matching the Kurtosis of the low-ash diff data to the Kurtosis of the stochastic volatility process which is assumed to follow Cox–Ingersoll–Ross(“CIR”)model.
基金Project supported by the National Natural Science Foundation of China (No. 12272323)。
文摘Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.
基金supported and funded by SERB-DST,India,under project scheme EEQ/2020/000238.
文摘In the fields of oceanography,hydrodynamics,and marine engineering,many mathematicians and physi-cists are interested in Burgers-type equations to show the different dynamics of nonlinear wave phenom-ena,one of which is a(3+1)-dimensional Burgers system that is currently being studied.In this paper,we apply two different analytical methods,namely the generalized Kudryashov(GK)method,and the generalized exponential rational function method,to derive abundant novel analytic exact solitary wave solutions,including multi-wave solitons,multi-wave peakon solitons,kink-wave profiles,stripe solitons,wave-wave interaction profiles,and periodic oscillating wave profiles for a(3+1)-dimensional Burgers sys-tem with the assistance of symbolic computation.By employing the generalized Kudryashov method,we obtain some new families of exact solitary wave solutions for the Burgers system.Further,we applied the generalized exponential rational function method to obtain a large number of soliton solutions in the forms of trigonometric and hyperbolic function solutions,exponential rational function solutions,peri-odic breather-wave soliton solutions,dark and bright solitons,singular periodic oscillating wave soliton solutions,and complex multi-wave solutions under various family cases.Based on soft computing via Wolfram Mathematica,all the newly established solutions are verified by back substituting them into the considered Burgers system.Eventually,the dynamical behaviors of some established results are exhibited graphically through three-and two-dimensional wave profiles via numerical simulation.
基金supported by the Disaster Prevention and Engineering Safety Laboratory in Guangxi and the National NaturalScience Foundation of China(Nos.11072177 and 10872150)the Scientific Research Foundation for the ReturnedOverseas Chinese Scholars,State Education Ministry
文摘The elastoplastic pure bending problem of a curved beam with material inhomo- geneity is investigated based on Tresca＇s yield criterion and its associated flow rule. Suppose that the material is elastically isotropic, ideally elastic-plastic and its elastic modulus and yield limit vary radially according to exponential functions. Closed-form solutions to the stresses and radial displacement in both purely elastic stress state and partially plastic stress state are presented. Numerical examples reveal the distinct characteristics of elastoplastic bending of a curved beam composed of inhomogeneous materials. Due to the inhomogeneity of materials, the bearing capac- ity of the curved beam can be improved greatly and the initial yield mode can also be dominated. Closed-form solutions presented here can serve as benchmark results for evaluating numerical solutions.
