We obtained a number of inequalities and laws of large numbers for two parameter vector valued martingales.In the other direction we characterized p smoothness and q convexity of Banach spaces by using the...We obtained a number of inequalities and laws of large numbers for two parameter vector valued martingales.In the other direction we characterized p smoothness and q convexity of Banach spaces by using these inequalities and laws of large numbers for two parameter vector valued martingales.展开更多
Let {Y (t);t= (t 1,t 2)≥0}={X k(t 1,t 2);t 1≥0,t 2≥0} ∞ k=1 be a sequence of two parameter Ornstein Uhlenbeck processes (OUP 2) with coefficients α k>0,β k>0 . A Fernique type in...Let {Y (t);t= (t 1,t 2)≥0}={X k(t 1,t 2);t 1≥0,t 2≥0} ∞ k=1 be a sequence of two parameter Ornstein Uhlenbeck processes (OUP 2) with coefficients α k>0,β k>0 . A Fernique type inequality is established and the sufficient condition for a.s. l 2 continuity of Y(·) is studied by means of the inequality.展开更多
A method for simultaneous determination of mixed model parameters,which have different physical dimensions or different responses to data,is presented.Mixed parameter estimation from observed data within a single mode...A method for simultaneous determination of mixed model parameters,which have different physical dimensions or different responses to data,is presented.Mixed parameter estimation from observed data within a single model space shows instabilities and trade-offs of the solutions. We separate the model space into N-subspaces based on their physical properties or computational convenience and solve the N-subspaces systems by damped least-squares and singular-value decomposition. Since the condition number of each subsystem is smaller than that of the single global system,the approach can greatly increase the stability of the inversion. We also introduce different damping factors into the subsystems to reduce the tradeoffs between the different parameters. The damping factors depend on the conditioning of the subsystems and may be adequately chosen in a range from 0.1 % to 10 % of the largest singular value. We illustrate the method with an example of simultaneous determination of source history,source geometry,and hypocentral location from regional seismograms,although it is applicable to any geophysical inversion.展开更多
This paper focuses on synthesizing a mixed robust H_2/H_∞ linear parameter varying(LPV) controller for the longitudinal motion of an air-breathing hypersonic vehicle via a high order singular value decomposition(H...This paper focuses on synthesizing a mixed robust H_2/H_∞ linear parameter varying(LPV) controller for the longitudinal motion of an air-breathing hypersonic vehicle via a high order singular value decomposition(HOSVD) approach.The design of hypersonic flight control systems is highly challenging due to the enormous complexity of the vehicle dynamics and the presence of significant uncertainties.Motivated by recent results on both LPV control and tensor-product(TP) model transformation approach,the velocity and altitude tracking control problems for the air-breathing hypersonic vehicle is reduced to that of a state feedback stabilizing controller design for a polytopic LPV system with guaranteed performances.The controller implementation is converted into a convex optimization problem with parameterdependent linear matrix inequalities(LMIs) constraints,which is intuitively tractable using LMI control toolbox.Finally,numerical simulation results demonstrate the effectiveness of the proposed approach.展开更多
A cosmological model was developed using the equation of state of photon gas, as well as cosmic time. The primary objective of this model is to see if determining the observed rotation speed of galactic matter is poss...A cosmological model was developed using the equation of state of photon gas, as well as cosmic time. The primary objective of this model is to see if determining the observed rotation speed of galactic matter is possible, without using dark matter (halo) as a parameter. To do so, a numerical application of the evolution of variables in accordance with cosmic time and a new state equation was developed to determine precise, realistic values for a number of cosmological parameters, such as the energy of the universe <i>U</i>, cosmological constant Λ, the curvature of space <i>k</i>, energy density <i>ρ</i><sub>Λe</sub>, age of the universe <i>t</i><sub>Ω</sub> etc. The development of the state equation highlights the importance of not neglecting any of the differential terms given the very large amounts in play that can counterbalance the infinitesimals. Some assumptions were put forth in order to solve these equations. The current version of the model partially explains several of the observed phenomena that raise questions. Numerical application of the model has yielded the following results, among others: Initially, during the Planck era, at the very beginning of Planck time, <i>t<sub>p</sub></i>, the universe contained a single photon at Planck temperature <i>T<sub>P</sub></i>, almost Planck energy <i>E<sub>P</sub></i> in the Planck volume. During the photon inflation phase (before characteristic time ~10<sup>-9</sup> [s]), the number of original photons (alphatons) increased at each unit of Planck time <i>t<sub>p</sub></i> and geometrical progression~<i>n</i><sup>3</sup>, where n is the quotient of cosmic time over Planck time <i>t</i>/<i>t<sub>p</sub></i>. Then, the primordial number of photons reached a maximum of <i>N</i>~10<sup>89</sup>, where it remained constant. These primordial photons (alphatons) are still present today and represent the essential of the energy contained in the universe via the cosmological constant expressed in the form of energy <i>E</i><sub>Λ</sub>. Such geometric growth in the number of photons can bring a solution to the horizon problem through <i>γγ</i> exchange and a photon energy volume that is in phase with that of the volume energy of the universe. The predicted total mass (p, n, e, and <i>ν</i>), based on the Maxwell-Juttner relativistic statistical distribution, is ~7 × 10<sup>50</sup> [kg]. The predicted cosmic neutrino mass is ≤8.69 × 10<sup>-32</sup> [kg] (≤48.7 [keV·<i>c</i><sup>-2</sup>]) if based on observations of SN1987A. The temperature variation of the cosmic microwave background (CMB), as measured by Planck, can be said to be partially due to energy variations in the universe (Δ<i>U</i>/<i>U</i>) during the primordial baryon synthesis (energy jump from the creation of protons and neutrons).展开更多
The horizontal diffusion coefficients of the operational model (T42L9) in numerical weather prediction are optimized by the steepest descent search of multi-dimensional optimization. In order to improve prediction acc...The horizontal diffusion coefficients of the operational model (T42L9) in numerical weather prediction are optimized by the steepest descent search of multi-dimensional optimization. In order to improve prediction accuracy in low latitudes, the optimum horizontal diffusion coefficients are chosen, with changing variation of the basic diffusion coefficient with the passage of time, and later forecasts are also made better. In view of the averages of forecast verifications of 9 cases, the forecasts with optimum diffusion coefficients are an improvement on operational forecasts. It means that the forecasts are got much better with optimum values of some important parameters by optimization in numerical weather prediction.展开更多
We propose a novel parameter value selection strategy for the Lüsystem to construct a chaotic robot to accomplish the complete coverage path planning(CCPP)task.The algorithm can meet the requirements of high rand...We propose a novel parameter value selection strategy for the Lüsystem to construct a chaotic robot to accomplish the complete coverage path planning(CCPP)task.The algorithm can meet the requirements of high randomness and coverage rate to perform specific types of missions.First,we roughly determine the value range of the parameter of the Lüsystem to meet the requirement of being a dissipative system.Second,we calculate the Lyapunov exponents to narrow the value range further.Next,we draw the phase planes of the system to approximately judge the topological distribution characteristics of its trajectories.Furthermore,we calculate the Pearson correlation coefficient of the variable for those good ones to judge its random characteristics.Finally,we construct a chaotic robot using variables with the determined parameter values and simulate and test the coverage rate to study the relationship between the coverage rate and the random characteristics of the variables.The above selection strategy gradually narrows the value range of the system parameter according to the randomness requirement of the coverage trajectory.Using the proposed strategy,proper variables can be chosen with a larger Lyapunov exponent to construct a chaotic robot with a higher coverage rate.Another chaotic system,the Lorenz system,is used to verify the feasibility and effectiveness of the designed strategy.The proposed strategy for enhancing the coverage rate of the mobile robot can improve the efficiency of accomplishing CCPP tasks under specific types of missions.展开更多
A cosmological model was developed using the equation of state of photon gas, as well as cosmic time. The primary objective of this model is to see if determining the observed rotation speed of galactic matter is poss...A cosmological model was developed using the equation of state of photon gas, as well as cosmic time. The primary objective of this model is to see if determining the observed rotation speed of galactic matter is possible, without using dark matter (halo) as a parameter. To do so, a numerical application of the evolution of variables in accordance with cosmic time and a new state equation was developed to determine precise, realistic values for a number of cosmological parameters, such as the energy of the universe <i>U</i>, cosmological constant Λ, the curvature of space <i>k</i>, energy density <i>ρ</i><sub>Λe</sub> (part 1). The age of the universe in cosmic time that is in line with positive energy conservation (in terms of conventional thermodynamics) and the creation of proton, neutron, electron, and neutrino masses, is ~76 [Gy] (observed <img src="Edit_6d0b63d7-3b06-4a39-97c8-a0004319d14d.png" width="15" height="15" alt="" /> ~ 70 [km · s<sup>-1</sup> · Mpc<sup>-1</sup>]). In this model, what is usually referred to as dark energy actually corresponds to the energy of the universe that has not been converted to mass, and which acts on the mass created by the energy-mass equivalence principle and the cosmological gravity field, F<sub>Λ</sub>, associated with the cosmological constant, which is high during the primordial formation of the galaxies (<1 [Gy]). A look at the Casimir effect makes it possible to estimate a minimum Casimir pressure <i>P<sub>c</sub></i><sup>0</sup> and thus determine our possible relative position in the universe at cosmic time 0.1813 (<i>t</i><sub>0</sub>/<i>t</i><sub>Ω</sub> = 13.8[Gy]/76.1[Gy]). Therefore, from the observed age of 13.8 [Gy], we can derive a possible cosmic age of ~76.1 [Gy]. That energy of the universe, when taken into consideration during the formation of the first galaxies (<1 [Gy]), provides a relatively adequate explanation of the non-Keplerian rotation of galactic masses.展开更多
Aeroengines,as the sole power source for aircraft,play a vital role in ensuring flight safety.The gas path,which represents the fundamental pathway for airflow within an aeroengine,directly impacts the aeroengine'...Aeroengines,as the sole power source for aircraft,play a vital role in ensuring flight safety.The gas path,which represents the fundamental pathway for airflow within an aeroengine,directly impacts the aeroengine's performance,fuel efficiency,and safety.Therefore,timely and accurate evaluation of gas path performance is of paramount importance.This paper proposes a knowledge and data jointly driven aeroengine gas path performance assessment method,combining Fingerprint and gas path parameter deviation values.Firstly,Fingerprint is used to correct gas path parameter deviation values,eliminating parameter shifts caused by non-component performance degradation.Secondly,coarse errors are removed using the Romanovsky criterion for short-term data divided by an equal-length overlapping sliding window.Thirdly,an Ensemble Empirical Mode Decomposition and Non-Local Means(EEMD-NLM)filtering method is designed to“clean”data noise,completing the preprocessing for gas path parameter deviation values.Afterward,based on the characteristics of gas path parameter deviation values,a Dynamic Temporary Blended Network(DTBN)model is built to extract its temporal features,cascaded with Multi-Layer Perceptron(MLP),and combined with Fingerprint to construct a Dynamic Temporary Blended AutoEncoder(DTB-AutoEncoder).Eventually,by training this improved autoencoder,the aeroengine gas path multi-component performance assessment model is formed,which can sufficiently decouple the nonlinear mapping relationship between aeroengine gas path multi-component performance degradation and gas path parameter deviation values,thereby achieving the performance assessment of engine gas path components.Through practical application cases,the effectiveness of this model in assessing the aeroengine gas path multi-component performance is verified.展开更多
文摘We obtained a number of inequalities and laws of large numbers for two parameter vector valued martingales.In the other direction we characterized p smoothness and q convexity of Banach spaces by using these inequalities and laws of large numbers for two parameter vector valued martingales.
基金Research supported by National Natural Science Foundation of China(1 0 0 71 0 2 7)
文摘Let {Y (t);t= (t 1,t 2)≥0}={X k(t 1,t 2);t 1≥0,t 2≥0} ∞ k=1 be a sequence of two parameter Ornstein Uhlenbeck processes (OUP 2) with coefficients α k>0,β k>0 . A Fernique type inequality is established and the sufficient condition for a.s. l 2 continuity of Y(·) is studied by means of the inequality.
基金supported by Innovation Project of Chinese Academy of Sciences
文摘A method for simultaneous determination of mixed model parameters,which have different physical dimensions or different responses to data,is presented.Mixed parameter estimation from observed data within a single model space shows instabilities and trade-offs of the solutions. We separate the model space into N-subspaces based on their physical properties or computational convenience and solve the N-subspaces systems by damped least-squares and singular-value decomposition. Since the condition number of each subsystem is smaller than that of the single global system,the approach can greatly increase the stability of the inversion. We also introduce different damping factors into the subsystems to reduce the tradeoffs between the different parameters. The damping factors depend on the conditioning of the subsystems and may be adequately chosen in a range from 0.1 % to 10 % of the largest singular value. We illustrate the method with an example of simultaneous determination of source history,source geometry,and hypocentral location from regional seismograms,although it is applicable to any geophysical inversion.
基金supported by the National Natural Science Foundation of China(6120300761304239+1 种基金61503392)the Natural Science Foundation of Shaanxi Province(2015JQ6213)
文摘This paper focuses on synthesizing a mixed robust H_2/H_∞ linear parameter varying(LPV) controller for the longitudinal motion of an air-breathing hypersonic vehicle via a high order singular value decomposition(HOSVD) approach.The design of hypersonic flight control systems is highly challenging due to the enormous complexity of the vehicle dynamics and the presence of significant uncertainties.Motivated by recent results on both LPV control and tensor-product(TP) model transformation approach,the velocity and altitude tracking control problems for the air-breathing hypersonic vehicle is reduced to that of a state feedback stabilizing controller design for a polytopic LPV system with guaranteed performances.The controller implementation is converted into a convex optimization problem with parameterdependent linear matrix inequalities(LMIs) constraints,which is intuitively tractable using LMI control toolbox.Finally,numerical simulation results demonstrate the effectiveness of the proposed approach.
文摘A cosmological model was developed using the equation of state of photon gas, as well as cosmic time. The primary objective of this model is to see if determining the observed rotation speed of galactic matter is possible, without using dark matter (halo) as a parameter. To do so, a numerical application of the evolution of variables in accordance with cosmic time and a new state equation was developed to determine precise, realistic values for a number of cosmological parameters, such as the energy of the universe <i>U</i>, cosmological constant Λ, the curvature of space <i>k</i>, energy density <i>ρ</i><sub>Λe</sub>, age of the universe <i>t</i><sub>Ω</sub> etc. The development of the state equation highlights the importance of not neglecting any of the differential terms given the very large amounts in play that can counterbalance the infinitesimals. Some assumptions were put forth in order to solve these equations. The current version of the model partially explains several of the observed phenomena that raise questions. Numerical application of the model has yielded the following results, among others: Initially, during the Planck era, at the very beginning of Planck time, <i>t<sub>p</sub></i>, the universe contained a single photon at Planck temperature <i>T<sub>P</sub></i>, almost Planck energy <i>E<sub>P</sub></i> in the Planck volume. During the photon inflation phase (before characteristic time ~10<sup>-9</sup> [s]), the number of original photons (alphatons) increased at each unit of Planck time <i>t<sub>p</sub></i> and geometrical progression~<i>n</i><sup>3</sup>, where n is the quotient of cosmic time over Planck time <i>t</i>/<i>t<sub>p</sub></i>. Then, the primordial number of photons reached a maximum of <i>N</i>~10<sup>89</sup>, where it remained constant. These primordial photons (alphatons) are still present today and represent the essential of the energy contained in the universe via the cosmological constant expressed in the form of energy <i>E</i><sub>Λ</sub>. Such geometric growth in the number of photons can bring a solution to the horizon problem through <i>γγ</i> exchange and a photon energy volume that is in phase with that of the volume energy of the universe. The predicted total mass (p, n, e, and <i>ν</i>), based on the Maxwell-Juttner relativistic statistical distribution, is ~7 × 10<sup>50</sup> [kg]. The predicted cosmic neutrino mass is ≤8.69 × 10<sup>-32</sup> [kg] (≤48.7 [keV·<i>c</i><sup>-2</sup>]) if based on observations of SN1987A. The temperature variation of the cosmic microwave background (CMB), as measured by Planck, can be said to be partially due to energy variations in the universe (Δ<i>U</i>/<i>U</i>) during the primordial baryon synthesis (energy jump from the creation of protons and neutrons).
文摘The horizontal diffusion coefficients of the operational model (T42L9) in numerical weather prediction are optimized by the steepest descent search of multi-dimensional optimization. In order to improve prediction accuracy in low latitudes, the optimum horizontal diffusion coefficients are chosen, with changing variation of the basic diffusion coefficient with the passage of time, and later forecasts are also made better. In view of the averages of forecast verifications of 9 cases, the forecasts with optimum diffusion coefficients are an improvement on operational forecasts. It means that the forecasts are got much better with optimum values of some important parameters by optimization in numerical weather prediction.
基金Project supported by the National Natural Science Foundation of China(Nos.61973184 and 61473179)the Natural Science Foundation of Shandong Province,China(No.ZR2021MF072)。
文摘We propose a novel parameter value selection strategy for the Lüsystem to construct a chaotic robot to accomplish the complete coverage path planning(CCPP)task.The algorithm can meet the requirements of high randomness and coverage rate to perform specific types of missions.First,we roughly determine the value range of the parameter of the Lüsystem to meet the requirement of being a dissipative system.Second,we calculate the Lyapunov exponents to narrow the value range further.Next,we draw the phase planes of the system to approximately judge the topological distribution characteristics of its trajectories.Furthermore,we calculate the Pearson correlation coefficient of the variable for those good ones to judge its random characteristics.Finally,we construct a chaotic robot using variables with the determined parameter values and simulate and test the coverage rate to study the relationship between the coverage rate and the random characteristics of the variables.The above selection strategy gradually narrows the value range of the system parameter according to the randomness requirement of the coverage trajectory.Using the proposed strategy,proper variables can be chosen with a larger Lyapunov exponent to construct a chaotic robot with a higher coverage rate.Another chaotic system,the Lorenz system,is used to verify the feasibility and effectiveness of the designed strategy.The proposed strategy for enhancing the coverage rate of the mobile robot can improve the efficiency of accomplishing CCPP tasks under specific types of missions.
文摘A cosmological model was developed using the equation of state of photon gas, as well as cosmic time. The primary objective of this model is to see if determining the observed rotation speed of galactic matter is possible, without using dark matter (halo) as a parameter. To do so, a numerical application of the evolution of variables in accordance with cosmic time and a new state equation was developed to determine precise, realistic values for a number of cosmological parameters, such as the energy of the universe <i>U</i>, cosmological constant Λ, the curvature of space <i>k</i>, energy density <i>ρ</i><sub>Λe</sub> (part 1). The age of the universe in cosmic time that is in line with positive energy conservation (in terms of conventional thermodynamics) and the creation of proton, neutron, electron, and neutrino masses, is ~76 [Gy] (observed <img src="Edit_6d0b63d7-3b06-4a39-97c8-a0004319d14d.png" width="15" height="15" alt="" /> ~ 70 [km · s<sup>-1</sup> · Mpc<sup>-1</sup>]). In this model, what is usually referred to as dark energy actually corresponds to the energy of the universe that has not been converted to mass, and which acts on the mass created by the energy-mass equivalence principle and the cosmological gravity field, F<sub>Λ</sub>, associated with the cosmological constant, which is high during the primordial formation of the galaxies (<1 [Gy]). A look at the Casimir effect makes it possible to estimate a minimum Casimir pressure <i>P<sub>c</sub></i><sup>0</sup> and thus determine our possible relative position in the universe at cosmic time 0.1813 (<i>t</i><sub>0</sub>/<i>t</i><sub>Ω</sub> = 13.8[Gy]/76.1[Gy]). Therefore, from the observed age of 13.8 [Gy], we can derive a possible cosmic age of ~76.1 [Gy]. That energy of the universe, when taken into consideration during the formation of the first galaxies (<1 [Gy]), provides a relatively adequate explanation of the non-Keplerian rotation of galactic masses.
基金This study was co-supported by the National Key Research and Development Program of China(No.2020YFB1709800)the National Science and Technology Major Project(No.J2019-I-0001-0001).
文摘Aeroengines,as the sole power source for aircraft,play a vital role in ensuring flight safety.The gas path,which represents the fundamental pathway for airflow within an aeroengine,directly impacts the aeroengine's performance,fuel efficiency,and safety.Therefore,timely and accurate evaluation of gas path performance is of paramount importance.This paper proposes a knowledge and data jointly driven aeroengine gas path performance assessment method,combining Fingerprint and gas path parameter deviation values.Firstly,Fingerprint is used to correct gas path parameter deviation values,eliminating parameter shifts caused by non-component performance degradation.Secondly,coarse errors are removed using the Romanovsky criterion for short-term data divided by an equal-length overlapping sliding window.Thirdly,an Ensemble Empirical Mode Decomposition and Non-Local Means(EEMD-NLM)filtering method is designed to“clean”data noise,completing the preprocessing for gas path parameter deviation values.Afterward,based on the characteristics of gas path parameter deviation values,a Dynamic Temporary Blended Network(DTBN)model is built to extract its temporal features,cascaded with Multi-Layer Perceptron(MLP),and combined with Fingerprint to construct a Dynamic Temporary Blended AutoEncoder(DTB-AutoEncoder).Eventually,by training this improved autoencoder,the aeroengine gas path multi-component performance assessment model is formed,which can sufficiently decouple the nonlinear mapping relationship between aeroengine gas path multi-component performance degradation and gas path parameter deviation values,thereby achieving the performance assessment of engine gas path components.Through practical application cases,the effectiveness of this model in assessing the aeroengine gas path multi-component performance is verified.