Conventional reliability-based design optimization （RBDO） requires to use the most probable point （MPP） method for a probabilistic analysis of the reliability constraints. A new approach is presented, called as th...Conventional reliability-based design optimization （RBDO） requires to use the most probable point （MPP） method for a probabilistic analysis of the reliability constraints. A new approach is presented, called as the minimum error point （MEP） method or the MEP based method, for reliability-based design optimization, whose idea is to minimize the error produced by approximating performance functions. The MEP based method uses the first order Taylor＇s expansion at MEP instead of MPP. Examples demonstrate that the MEP based design optimization can ensure product reliability at the required level, which is very imperative for many important engineering systems. The MEP based reliability design optimization method is feasible and is considered as an alternative for solving reliability design optimization problems. The MEP based method is more robust than the commonly used MPP based method for some irregular performance functions.展开更多
In this paper, a class of generalized strongly nonlinear quasivariational inclusions are studied. By using the properties of the resolvent operator associated with a maximal monotone; mapping in Hilbert space, an exis...In this paper, a class of generalized strongly nonlinear quasivariational inclusions are studied. By using the properties of the resolvent operator associated with a maximal monotone; mapping in Hilbert space, an existence theorem of solutions for generalized strongly nonlinear quasivariational inclusion is established and a new proximal point algorithm with errors is suggested for finding approximate solutions which strongly converge to the exact solution of the generalized strongly, nonlinear quasivariational inclusion. As special cases, some known results in this field are also discussed.展开更多
A phased array radar seeker（PARS） must be able to effectively decouple body motion and accurately extract the line-of-sight（LOS） rate for target missile tracking.In this study,the realtime two-channel beam pointin...A phased array radar seeker（PARS） must be able to effectively decouple body motion and accurately extract the line-of-sight（LOS） rate for target missile tracking.In this study,the realtime two-channel beam pointing error（BPE） compensation method of PARS for LOS rate extraction is designed.The PARS discrete beam motion principium is analyzed,and the mathematical model of beam scanning control is finished.According to the principle of the antenna element shift phase,both the antenna element shift phase law and the causes of beam-pointing error under phantom-bit conditions are analyzed,and the effect of BPE caused by phantom-bit technology（PBT） on the extraction accuracy of the LOS rate is examined.A compensation method is given,which includes coordinate transforms,beam angle margin compensation,and detector dislocation angle calculation.When the method is used,the beam angle margin in the pitch and yaw directions is calculated to reduce the effect of the missile body disturbance and to improve LOS rate extraction precision by compensating for the detector dislocation angle.The simulation results validate the proposed method.展开更多
The purpose is to conduct a research in the energy variation of echo wave and the imaging effect caused by the aero bistatic SAR pointing errors. Based on the moving geometry configuration of aero bistatic SAR, a mode...The purpose is to conduct a research in the energy variation of echo wave and the imaging effect caused by the aero bistatic SAR pointing errors. Based on the moving geometry configuration of aero bistatic SAR, a model of beam pointing errors is built. Based on this, the azimuth Doppler frequency center estimation caused by these errors and the limitation to the beam pointing synchronization error are studied, and then the imaging result of different errors are analyzed. The computer＇s simulations are provided to prove the validity of the above analysis.展开更多
Traditional cubature Kalman filter(CKF)is a preferable tool for the inertial navigation system(INS)/global positioning system(GPS)integration under Gaussian noises.The CKF,however,may provide a significantly biased es...Traditional cubature Kalman filter(CKF)is a preferable tool for the inertial navigation system(INS)/global positioning system(GPS)integration under Gaussian noises.The CKF,however,may provide a significantly biased estimate when the INS/GPS system suffers from complex non-Gaussian disturbances.To address this issue,a robust nonlinear Kalman filter referred to as cubature Kalman filter under minimum error entropy with fiducial points(MEEF-CKF)is proposed.The MEEF-CKF behaves a strong robustness against complex nonGaussian noises by operating several major steps,i.e.,regression model construction,robust state estimation and free parameters optimization.More concretely,a regression model is constructed with the consideration of residual error caused by linearizing a nonlinear function at the first step.The MEEF-CKF is then developed by solving an optimization problem based on minimum error entropy with fiducial points(MEEF)under the framework of the regression model.In the MEEF-CKF,a novel optimization approach is provided for the purpose of determining free parameters adaptively.In addition,the computational complexity and convergence analyses of the MEEF-CKF are conducted for demonstrating the calculational burden and convergence characteristic.The enhanced robustness of the MEEF-CKF is demonstrated by Monte Carlo simulations on the application of a target tracking with INS/GPS integration under complex nonGaussian noises.展开更多
Aiming at the deficiency of the robustness of thermal error compensation models of CNC machine tools, the mechanism of improving the models＇ robustness is studied by regarding the Leaderway-V450 machining center as t...Aiming at the deficiency of the robustness of thermal error compensation models of CNC machine tools, the mechanism of improving the models＇ robustness is studied by regarding the Leaderway-V450 machining center as the object. Through the analysis of actual spindle air cutting experimental data on Leaderway-V450 machine, it is found that the temperature-sensitive points used for modeling is volatility, and this volatility directly leads to large changes on the collinear degree among modeling independent variables. Thus, the forecasting accuracy of multivariate regression model is severely affected, and the forecasting robustness becomes poor too. To overcome this effect, a modeling method of establishing thermal error models by using single temperature variable under the jamming of temperature-sensitive points＇ volatility is put forward. According to the actual data of thermal error measured in different seasons, it is proved that the single temperature variable model can reduce the loss of fore- casting accuracy resulted from the volatility of tempera- ture-sensitive points, especially for the prediction of cross quarter data, the improvement of forecasting accuracy is about 5 μm or more. The purpose that improving the robustness of the thermal error models is realized, which can provide a reference for selecting the modelingindependent variable in the application of thermal error compensation of CNC machine tools.展开更多
Joint clearances in antenna pointing mechanisms lead to uncertainty in function deviation. Current studies mainly focus on radial clearance of revolute joints, while axial clearance has rarely been taken into consider...Joint clearances in antenna pointing mechanisms lead to uncertainty in function deviation. Current studies mainly focus on radial clearance of revolute joints, while axial clearance has rarely been taken into consideration. In fact, own?ing to errors from machining and assembly, thermal deformation and so forth, practically, axial clearance is inevitable in the joint. In this study, an error equivalent model(EEM) of revolute joints is proposed with considering both radial and axial clearances. Compared to the planar model of revolute joints only considering radial clearance, the journal motion inside the bearing is more abundant and matches the reality better in the EEM. The model is also extended for analyzing the error distribution of a spatial dual?axis("X–Y" type) antenna pointing mechanism of Spot?beam antennas which especially demand a high pointing accuracy. Three case studies are performed which illustrates the internal relation between radial clearance and axial clearance. It is found that when the axial clearance is big enough, the physical journal can freely realize both translational motion and rotational motion. While if the axial clearance is limited, the motion of the physical journal will be restricted. Analysis results indicate that the consideration of both radial and axial clearances in the revolute joint describes the journal motion inside the bearing more precise. To further validate the proposed model, a model of the EEM is designed and fabricated. Some suggestions on the design of revolute joints are also provided.展开更多
For the unsorted database quantum search with the unknown fraction λ of target items, there are mainly two kinds of methods, i.e., fixed-point and trail-and-error.(i) In terms of the fixed-point method, Yoder et al. ...For the unsorted database quantum search with the unknown fraction λ of target items, there are mainly two kinds of methods, i.e., fixed-point and trail-and-error.(i) In terms of the fixed-point method, Yoder et al. [Phys. Rev. Lett.113 210501(2014)] claimed that the quadratic speedup over classical algorithms has been achieved. However, in this paper, we point out that this is not the case, because the query complexity of Yoder’s algorithm is actually in O(1/λ01/2)rather than O(1/λ1/2), where λ0 is a known lower bound of λ.(ii) In terms of the trail-and-error method, currently the algorithm without randomness has to take more than 1 times queries or iterations than the algorithm with randomly selected parameters. For the above problems, we provide the first hybrid quantum search algorithm based on the fixed-point and trail-and-error methods, where the matched multiphase Grover operations are trialed multiple times and the number of iterations increases exponentially along with the number of trials. The upper bound of expected queries as well as the optimal parameters are derived. Compared with Yoder’s algorithm, the query complexity of our algorithm indeed achieves the optimal scaling in λ for quantum search, which reconfirms the practicality of the fixed-point method. In addition, our algorithm also does not contain randomness, and compared with the existing deterministic algorithm, the query complexity can be reduced by about 1/3. Our work provides a new idea for the research on fixed-point and trial-and-error quantum search.展开更多
Through the analysis of roundness error separation technique of three-point method and based on the invariability and periodicity of the geometrical characteristic of measured round contour, a new matrix algorithm, wh...Through the analysis of roundness error separation technique of three-point method and based on the invariability and periodicity of the geometrical characteristic of measured round contour, a new matrix algorithm, which can be used to solve directly the roundness of the measured round contour without Fourier transform, is presented. On the basis of the research and analysis of the rotation error movement which is separated by using the three-point method, a mathematical equation is derived, which can be used to separate the eccentric motion of least square center of measured round contour and the pure rotation motion error of spindle in rotation motion. The correctness of this method is validated by means of simulation.展开更多
In this paper, we consider the following problem:The quadratic spline collocation, with uniform mesh and the mid-knot points are taken as the collocation points for this problem is considered. With some assumptions, w...In this paper, we consider the following problem:The quadratic spline collocation, with uniform mesh and the mid-knot points are taken as the collocation points for this problem is considered. With some assumptions, we have proved that the solution of the quadratic spline collocation for the nonlinear problem can be written as a series expansions in integer powers of the mesh-size parameter. This gives us a construction method for using Richardson’s extrapolation. When we have a set of approximate solution with different mesh-size parameter a solution with high accuracy can he obtained by Richardson’s extrapolation.展开更多
As a new remote sensing technology, the global navigation satellite system（GNSS） reflection signals can be used to collect the information of ocean surface wind, surface roughness and sea surface height. Ocean altim...As a new remote sensing technology, the global navigation satellite system（GNSS） reflection signals can be used to collect the information of ocean surface wind, surface roughness and sea surface height. Ocean altimetry based on GNSS reflection technique is of low cost and it is easy to obtain large amounts of data thanks to the global navigation satellite constellation. We can estimate the sea surface height as well as the position of the specular reflection point. This paper focuses on the study of the algorithm to determine the specular reflection point and altimetry equations to estimate the sea surface height over the reflection region. We derive the error equation of sea surface height based on the error propagation theory. Effects of the Doppler shift and the size of the glistening zone on the altimetry are discussed and analyzed at the same time. Finally, we calculate the sea surface height based on the simulated GNSS data within the whole day and verify the sea surface height errors according to the satellite elevation angles. The results show that the sea surface height can reach the precision of 6 cm for elevation angles of 55° to 90°, and the theoretical error and the calculated error are in good agreement.展开更多
基金This project is supported by National Natural Science Foundation of China(No.50575072)Outstanding Youth Fund of Hunan Education Department, China (No.04B007).
文摘Conventional reliability-based design optimization （RBDO） requires to use the most probable point （MPP） method for a probabilistic analysis of the reliability constraints. A new approach is presented, called as the minimum error point （MEP） method or the MEP based method, for reliability-based design optimization, whose idea is to minimize the error produced by approximating performance functions. The MEP based method uses the first order Taylor＇s expansion at MEP instead of MPP. Examples demonstrate that the MEP based design optimization can ensure product reliability at the required level, which is very imperative for many important engineering systems. The MEP based reliability design optimization method is feasible and is considered as an alternative for solving reliability design optimization problems. The MEP based method is more robust than the commonly used MPP based method for some irregular performance functions.
文摘In this paper, a class of generalized strongly nonlinear quasivariational inclusions are studied. By using the properties of the resolvent operator associated with a maximal monotone; mapping in Hilbert space, an existence theorem of solutions for generalized strongly nonlinear quasivariational inclusion is established and a new proximal point algorithm with errors is suggested for finding approximate solutions which strongly converge to the exact solution of the generalized strongly, nonlinear quasivariational inclusion. As special cases, some known results in this field are also discussed.
文摘A phased array radar seeker（PARS） must be able to effectively decouple body motion and accurately extract the line-of-sight（LOS） rate for target missile tracking.In this study,the realtime two-channel beam pointing error（BPE） compensation method of PARS for LOS rate extraction is designed.The PARS discrete beam motion principium is analyzed,and the mathematical model of beam scanning control is finished.According to the principle of the antenna element shift phase,both the antenna element shift phase law and the causes of beam-pointing error under phantom-bit conditions are analyzed,and the effect of BPE caused by phantom-bit technology（PBT） on the extraction accuracy of the LOS rate is examined.A compensation method is given,which includes coordinate transforms,beam angle margin compensation,and detector dislocation angle calculation.When the method is used,the beam angle margin in the pitch and yaw directions is calculated to reduce the effect of the missile body disturbance and to improve LOS rate extraction precision by compensating for the detector dislocation angle.The simulation results validate the proposed method.
文摘The purpose is to conduct a research in the energy variation of echo wave and the imaging effect caused by the aero bistatic SAR pointing errors. Based on the moving geometry configuration of aero bistatic SAR, a model of beam pointing errors is built. Based on this, the azimuth Doppler frequency center estimation caused by these errors and the limitation to the beam pointing synchronization error are studied, and then the imaging result of different errors are analyzed. The computer＇s simulations are provided to prove the validity of the above analysis.
基金supported by the Fundamental Research Funds for the Central Universities(xzy022020045)the National Natural Science Foundation of China(61976175)。
文摘Traditional cubature Kalman filter(CKF)is a preferable tool for the inertial navigation system(INS)/global positioning system(GPS)integration under Gaussian noises.The CKF,however,may provide a significantly biased estimate when the INS/GPS system suffers from complex non-Gaussian disturbances.To address this issue,a robust nonlinear Kalman filter referred to as cubature Kalman filter under minimum error entropy with fiducial points(MEEF-CKF)is proposed.The MEEF-CKF behaves a strong robustness against complex nonGaussian noises by operating several major steps,i.e.,regression model construction,robust state estimation and free parameters optimization.More concretely,a regression model is constructed with the consideration of residual error caused by linearizing a nonlinear function at the first step.The MEEF-CKF is then developed by solving an optimization problem based on minimum error entropy with fiducial points(MEEF)under the framework of the regression model.In the MEEF-CKF,a novel optimization approach is provided for the purpose of determining free parameters adaptively.In addition,the computational complexity and convergence analyses of the MEEF-CKF are conducted for demonstrating the calculational burden and convergence characteristic.The enhanced robustness of the MEEF-CKF is demonstrated by Monte Carlo simulations on the application of a target tracking with INS/GPS integration under complex nonGaussian noises.
基金Supported by Key Project of National Natural Science Fund of China(Grant No.51490660/51490661)National Natural Science Foundation of China(Grant No.51175142)
文摘Aiming at the deficiency of the robustness of thermal error compensation models of CNC machine tools, the mechanism of improving the models＇ robustness is studied by regarding the Leaderway-V450 machining center as the object. Through the analysis of actual spindle air cutting experimental data on Leaderway-V450 machine, it is found that the temperature-sensitive points used for modeling is volatility, and this volatility directly leads to large changes on the collinear degree among modeling independent variables. Thus, the forecasting accuracy of multivariate regression model is severely affected, and the forecasting robustness becomes poor too. To overcome this effect, a modeling method of establishing thermal error models by using single temperature variable under the jamming of temperature-sensitive points＇ volatility is put forward. According to the actual data of thermal error measured in different seasons, it is proved that the single temperature variable model can reduce the loss of fore- casting accuracy resulted from the volatility of tempera- ture-sensitive points, especially for the prediction of cross quarter data, the improvement of forecasting accuracy is about 5 μm or more. The purpose that improving the robustness of the thermal error models is realized, which can provide a reference for selecting the modelingindependent variable in the application of thermal error compensation of CNC machine tools.
基金Supported by National Natural Science Foundation of China(Grant Nos.51635002(Key Program),51605011,51275015)
文摘Joint clearances in antenna pointing mechanisms lead to uncertainty in function deviation. Current studies mainly focus on radial clearance of revolute joints, while axial clearance has rarely been taken into consideration. In fact, own?ing to errors from machining and assembly, thermal deformation and so forth, practically, axial clearance is inevitable in the joint. In this study, an error equivalent model(EEM) of revolute joints is proposed with considering both radial and axial clearances. Compared to the planar model of revolute joints only considering radial clearance, the journal motion inside the bearing is more abundant and matches the reality better in the EEM. The model is also extended for analyzing the error distribution of a spatial dual?axis("X–Y" type) antenna pointing mechanism of Spot?beam antennas which especially demand a high pointing accuracy. Three case studies are performed which illustrates the internal relation between radial clearance and axial clearance. It is found that when the axial clearance is big enough, the physical journal can freely realize both translational motion and rotational motion. While if the axial clearance is limited, the motion of the physical journal will be restricted. Analysis results indicate that the consideration of both radial and axial clearances in the revolute joint describes the journal motion inside the bearing more precise. To further validate the proposed model, a model of the EEM is designed and fabricated. Some suggestions on the design of revolute joints are also provided.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11504430 and 61502526)the National Basic Research Program of China(Grant No.2013CB338002)
文摘For the unsorted database quantum search with the unknown fraction λ of target items, there are mainly two kinds of methods, i.e., fixed-point and trail-and-error.(i) In terms of the fixed-point method, Yoder et al. [Phys. Rev. Lett.113 210501(2014)] claimed that the quadratic speedup over classical algorithms has been achieved. However, in this paper, we point out that this is not the case, because the query complexity of Yoder’s algorithm is actually in O(1/λ01/2)rather than O(1/λ1/2), where λ0 is a known lower bound of λ.(ii) In terms of the trail-and-error method, currently the algorithm without randomness has to take more than 1 times queries or iterations than the algorithm with randomly selected parameters. For the above problems, we provide the first hybrid quantum search algorithm based on the fixed-point and trail-and-error methods, where the matched multiphase Grover operations are trialed multiple times and the number of iterations increases exponentially along with the number of trials. The upper bound of expected queries as well as the optimal parameters are derived. Compared with Yoder’s algorithm, the query complexity of our algorithm indeed achieves the optimal scaling in λ for quantum search, which reconfirms the practicality of the fixed-point method. In addition, our algorithm also does not contain randomness, and compared with the existing deterministic algorithm, the query complexity can be reduced by about 1/3. Our work provides a new idea for the research on fixed-point and trial-and-error quantum search.
基金Henan Innovation Project for University Prominent Research Talents (2004KYCX006)Ph.D.Inital Foundation of Henan University of Science &Techonologythe Natural Science Foundation of Henan Education Agency (2008A460007)
文摘Through the analysis of roundness error separation technique of three-point method and based on the invariability and periodicity of the geometrical characteristic of measured round contour, a new matrix algorithm, which can be used to solve directly the roundness of the measured round contour without Fourier transform, is presented. On the basis of the research and analysis of the rotation error movement which is separated by using the three-point method, a mathematical equation is derived, which can be used to separate the eccentric motion of least square center of measured round contour and the pure rotation motion error of spindle in rotation motion. The correctness of this method is validated by means of simulation.
基金The Project was supported by National Natural Science Foundation of China
文摘In this paper, we consider the following problem:The quadratic spline collocation, with uniform mesh and the mid-knot points are taken as the collocation points for this problem is considered. With some assumptions, we have proved that the solution of the quadratic spline collocation for the nonlinear problem can be written as a series expansions in integer powers of the mesh-size parameter. This gives us a construction method for using Richardson’s extrapolation. When we have a set of approximate solution with different mesh-size parameter a solution with high accuracy can he obtained by Richardson’s extrapolation.
基金financially supported by the National Natural Science Foundation of China(Grant No.41374009)the Shandong Natural Science Foundation of China(Grant No.ZR2013DM009)+3 种基金the National Basic Research Program of China(973 ProgramGrant No.2013CB733302)the Public Benefit Scientific Research Project of China(Grant No.201412001)the SDUST Research Fund(Grant No.2014TDJH101)
文摘As a new remote sensing technology, the global navigation satellite system（GNSS） reflection signals can be used to collect the information of ocean surface wind, surface roughness and sea surface height. Ocean altimetry based on GNSS reflection technique is of low cost and it is easy to obtain large amounts of data thanks to the global navigation satellite constellation. We can estimate the sea surface height as well as the position of the specular reflection point. This paper focuses on the study of the algorithm to determine the specular reflection point and altimetry equations to estimate the sea surface height over the reflection region. We derive the error equation of sea surface height based on the error propagation theory. Effects of the Doppler shift and the size of the glistening zone on the altimetry are discussed and analyzed at the same time. Finally, we calculate the sea surface height based on the simulated GNSS data within the whole day and verify the sea surface height errors according to the satellite elevation angles. The results show that the sea surface height can reach the precision of 6 cm for elevation angles of 55° to 90°, and the theoretical error and the calculated error are in good agreement.
