This work presents the application of the recently developed “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5<sup>th</sup>-CASAM-N)” to a simplified Bernoulli ...This work presents the application of the recently developed “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5<sup>th</sup>-CASAM-N)” to a simplified Bernoulli model. The 5<sup>th</sup>-CASAM-N builds upon and incorporates all of the lower-order (i.e., the first-, second-, third-, and fourth-order) adjoint sensitivities analysis methodologies. The Bernoulli model comprises a nonlinear model response, uncertain model parameters, uncertain model domain boundaries and uncertain model boundary conditions, admitting closed-form explicit expressions for the response sensitivities of all orders. Illustrating the specific mechanisms and advantages of applying the 5<sup>th</sup>-CASAM-N for the computation of the response sensitivities with respect to the uncertain parameters and boundaries reveals that the 5<sup>th</sup>-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.展开更多
This study considers a nonlinear grey Bernoulli forecasting model with conformable fractionalorder accumulation,abbreviated as CFNGBM(1,1,λ),to study the gross regional product in the ChengYu area.The new model conta...This study considers a nonlinear grey Bernoulli forecasting model with conformable fractionalorder accumulation,abbreviated as CFNGBM(1,1,λ),to study the gross regional product in the ChengYu area.The new model contains three nonlinear parameters,the power exponentγ,the conformable fractional-orderαand the background valueλ,which increase the adjustability and flexibility of the CFNGBM(1,1,λ)model.Nonlinear parameters are determined by the moth flame optimization algorithm,which minimizes the mean absolute prediction percentage error.The CFNGBM(1,1,λ)model is applied to the gross regional product of 16 cities in the Cheng-Yu area,which are Chongqing,Chengdu,Mianyang,Leshan,Zigong,Deyang,Meishan,Luzhou,Suining,Neijiang,Nanchong,Guang’an,Yibin,Ya’an,Dazhou and Ziyang.With data from 2013 to 2021,several grey models are established and results show that the new model has higher accuracy in most cases.展开更多
In this article, we study the generalized Bernoulli learning model based on the probability of success pi = ai /n where i = 1,2,...n 0a1a2ann and n is positive integer. This gives the previous results given by Abdulna...In this article, we study the generalized Bernoulli learning model based on the probability of success pi = ai /n where i = 1,2,...n 0a1a2ann and n is positive integer. This gives the previous results given by Abdulnasser and Khidr [1], Rashad [2] and EL-Desouky and Mahfouz [3] as special cases, where pi = i/n pi = i2/n2 and pi = ip/np respectively. The probability function P(Wn = k) of this model is derived, some properties of the model are obtained and the limiting distribution of the model is given.展开更多
In several instances of statistical practice, it is not uncommon to use the same data for both model selection and inference, without taking account of the variability induced by model selection step. This is usually ...In several instances of statistical practice, it is not uncommon to use the same data for both model selection and inference, without taking account of the variability induced by model selection step. This is usually referred to as post-model selection inference. The shortcomings of such practice are widely recognized, finding a general solution is extremely challenging. We propose a model averaging alternative consisting on taking into account model selection probability and the like-lihood in assigning the weights. The approach is applied to Bernoulli trials and outperforms Akaike weights model averaging and post-model selection estimators.展开更多
Model based control schemes use the inverse dynamics of the robot arm to produce the main torque component necessary for trajectory tracking. For model-based controller one is required to know the model parameters acc...Model based control schemes use the inverse dynamics of the robot arm to produce the main torque component necessary for trajectory tracking. For model-based controller one is required to know the model parameters accurately. This is a very difficult task especially if the manipulator is flexible. So a reduced model based controller has been developed, which requires only the information of space robot base velocity and link parameters. The flexible link is modeled as Euler Bernoulli beam. To simplify the analysis we have considered Jacobian of rigid manipulator. Bond graph modeling is used to model the dynamics of the system and to devise the control strategy. The scheme has been verified using simulation for two links flexible space manipulator.展开更多
Air flow in nose and sinuses is studied by means of a simple model based on the steady-state ideal fluid flow assumption and repeated use of Bernoulli’s equation. In particular, by describing flow of air drawn in thr...Air flow in nose and sinuses is studied by means of a simple model based on the steady-state ideal fluid flow assumption and repeated use of Bernoulli’s equation. In particular, by describing flow of air drawn in through the vestibulumnasi during inspiration, we investigate how ventilation of the maxillary sinus is affected by surgical removal of part of the lateral walls of the nasal cavity close to the ostiummeatal complex. We find that, according to the model proposed, removal of tissues from this inner part of the nasal cavity may cause a decrease of the flux rate from the maxillary sinus.展开更多
Based on the Timoshenko beam theory and Bernoulli-Fourier method, a single-elastic beam model is developed for transverse vibrations of single-walled carbon nanotubes under additional axial load, which includes the ef...Based on the Timoshenko beam theory and Bernoulli-Fourier method, a single-elastic beam model is developed for transverse vibrations of single-walled carbon nanotubes under additional axial load, which includes the effects of the elastic medium around them. Explicit expressions are derived for the natural frequencies and transversal responses of simply supported single-walled carbon nanotubes. The influence of addition axial load and the properties of elastic medium on the vibrations are discussed. The results showed that the effects of addition axial load on the lower natural frequencies of single-walled carbon nanotubes are sensitive to the lower vibration modes and the stiff elastic medium. The lower natural frequencies depend on the axial load;they become smaller with increasing axial load and vary with the vibration modes. In addition, except for the first mode, the effects of the axial load on the stiff elastic medium are considerably greater than those on the flexible one. However, the constants of the elastic medium have little effect on the first mode. The critical axial buckling stress and strain for simply-supported single-walled carbon nanotubes are also obtained.展开更多
文摘This work presents the application of the recently developed “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5<sup>th</sup>-CASAM-N)” to a simplified Bernoulli model. The 5<sup>th</sup>-CASAM-N builds upon and incorporates all of the lower-order (i.e., the first-, second-, third-, and fourth-order) adjoint sensitivities analysis methodologies. The Bernoulli model comprises a nonlinear model response, uncertain model parameters, uncertain model domain boundaries and uncertain model boundary conditions, admitting closed-form explicit expressions for the response sensitivities of all orders. Illustrating the specific mechanisms and advantages of applying the 5<sup>th</sup>-CASAM-N for the computation of the response sensitivities with respect to the uncertain parameters and boundaries reveals that the 5<sup>th</sup>-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.
基金Supported by the National Natural Science Foundation of China(72001181,71901184)the Sichuan Federation of Social Science Associations(SC20B122)。
文摘This study considers a nonlinear grey Bernoulli forecasting model with conformable fractionalorder accumulation,abbreviated as CFNGBM(1,1,λ),to study the gross regional product in the ChengYu area.The new model contains three nonlinear parameters,the power exponentγ,the conformable fractional-orderαand the background valueλ,which increase the adjustability and flexibility of the CFNGBM(1,1,λ)model.Nonlinear parameters are determined by the moth flame optimization algorithm,which minimizes the mean absolute prediction percentage error.The CFNGBM(1,1,λ)model is applied to the gross regional product of 16 cities in the Cheng-Yu area,which are Chongqing,Chengdu,Mianyang,Leshan,Zigong,Deyang,Meishan,Luzhou,Suining,Neijiang,Nanchong,Guang’an,Yibin,Ya’an,Dazhou and Ziyang.With data from 2013 to 2021,several grey models are established and results show that the new model has higher accuracy in most cases.
文摘In this article, we study the generalized Bernoulli learning model based on the probability of success pi = ai /n where i = 1,2,...n 0a1a2ann and n is positive integer. This gives the previous results given by Abdulnasser and Khidr [1], Rashad [2] and EL-Desouky and Mahfouz [3] as special cases, where pi = i/n pi = i2/n2 and pi = ip/np respectively. The probability function P(Wn = k) of this model is derived, some properties of the model are obtained and the limiting distribution of the model is given.
文摘In several instances of statistical practice, it is not uncommon to use the same data for both model selection and inference, without taking account of the variability induced by model selection step. This is usually referred to as post-model selection inference. The shortcomings of such practice are widely recognized, finding a general solution is extremely challenging. We propose a model averaging alternative consisting on taking into account model selection probability and the like-lihood in assigning the weights. The approach is applied to Bernoulli trials and outperforms Akaike weights model averaging and post-model selection estimators.
文摘Model based control schemes use the inverse dynamics of the robot arm to produce the main torque component necessary for trajectory tracking. For model-based controller one is required to know the model parameters accurately. This is a very difficult task especially if the manipulator is flexible. So a reduced model based controller has been developed, which requires only the information of space robot base velocity and link parameters. The flexible link is modeled as Euler Bernoulli beam. To simplify the analysis we have considered Jacobian of rigid manipulator. Bond graph modeling is used to model the dynamics of the system and to devise the control strategy. The scheme has been verified using simulation for two links flexible space manipulator.
文摘Air flow in nose and sinuses is studied by means of a simple model based on the steady-state ideal fluid flow assumption and repeated use of Bernoulli’s equation. In particular, by describing flow of air drawn in through the vestibulumnasi during inspiration, we investigate how ventilation of the maxillary sinus is affected by surgical removal of part of the lateral walls of the nasal cavity close to the ostiummeatal complex. We find that, according to the model proposed, removal of tissues from this inner part of the nasal cavity may cause a decrease of the flux rate from the maxillary sinus.
文摘Based on the Timoshenko beam theory and Bernoulli-Fourier method, a single-elastic beam model is developed for transverse vibrations of single-walled carbon nanotubes under additional axial load, which includes the effects of the elastic medium around them. Explicit expressions are derived for the natural frequencies and transversal responses of simply supported single-walled carbon nanotubes. The influence of addition axial load and the properties of elastic medium on the vibrations are discussed. The results showed that the effects of addition axial load on the lower natural frequencies of single-walled carbon nanotubes are sensitive to the lower vibration modes and the stiff elastic medium. The lower natural frequencies depend on the axial load;they become smaller with increasing axial load and vary with the vibration modes. In addition, except for the first mode, the effects of the axial load on the stiff elastic medium are considerably greater than those on the flexible one. However, the constants of the elastic medium have little effect on the first mode. The critical axial buckling stress and strain for simply-supported single-walled carbon nanotubes are also obtained.
