Q estimation using multifrequency point average method based on the Taylor series expansion with a different order

The quality factor Q is an important parameter because it can refl ect the reservoir attenuated features and can be used for inverse-Q filtering to compensate for the seismic wave energy.The accuracy of the Q estimation is greatly significant for improving the precision of the reservoir prediction and the resolution of seismic data.In this paper,the Q estimation formulas of the single-frequency point are derived on the basis of a diff erent-order Taylor series expansion of the amplitude attenuated factor.Moreover,the multifrequency point average(MFPA)method is introduced to obtain a stable Q estimation.The model tests demonstrate that the MFPA method is less aff ected by the frequency band,travel time diff erence,time window width,and noise interference than the logical spectrum ratio(LSR)method and the energy ratio(ER)method and has a higher Q estimation accuracy.In addition,the proposed method can be applied to post-stack seismic data and obtain eff ective Q values of complex models.When the MFPA method was applied to real marine seismic data,the Q values estimated by the MFPA method with the 1st–4th order showed good consistency with each other.In contrast,the Q values obtained by the ER method were larger than those of the proposed method,while those estimated by the LSR method signifi cantly deviated from the average values.In conclusion,the MFPA method has superior stability and practicability for the Q estimation.

Accelerating spectral digital image correlation computation with Taylor series image reconstruction

In this paper,we introduce an accelerating algorithm based on the Taylor series for reconstructing target images in the spectral digital image correlation method(SDIC).The Taylor series image reconstruction method is employed instead of the previous direct Fourier transform(DFT)image reconstruction method,which consumes the majority of the computational time for target image reconstruction.The partial derivatives in the Taylor series are computed using the fast Fourier transform(FFT)of the entire image,following the principles of Fourier transform theory.To examine the impact of different orders of Taylor series expansion on accuracy and efficiency,we employ third-and fourth-order Taylor series image reconstruction methods and compare them with the DFT image reconstruction method through simulated experiments.As a result of these enhancements,the computational efficiency using the third-and fourth-order Taylor series improves by factors of 57 and 46,respectively,compared to the previous method.In terms of analysis accuracy,within a strain range of 0–0.1 and without the addition of image noise,the accuracy of the proposed method increases with higher expansion orders,surpassing that of the DFT image reconstruction method when the fourth order is utilized.However,when different levels of Gaussian noise are applied to simulated images individually,the accuracy of the third-or fourth-order Taylor series expansion method is superior to that of the DFT reconstruction method.Finally,we present the analyzed experimental results of a silicone rubber plate specimen with bilateral cracks under uniaxial tension.

LAI scale effect research based on compact airborne spectrographic imager data in the Heihe Oasis

As one of the key parameters for characterizing crop canopy structure, Leaf Area Index(LAI) has great significance in monitoring the crop growth and estimating the yield. However, due to the nonlinearity and spatial heterogeneity of LAI inversion model, there exists scale error in LAI inversion result, which limits the application of LAI product from different remote sensing data. Therefore, it is necessary to conduct studies on scale effect. This study was based on the Heihe Oasis, Zhangye city, Gansu province, China and the following works were carried out: Airborne hyperspectral CASI(Compact Airborne Spectrographic Imager) image and LAI statistic models were adopted in muti-scale LAI inversion. The overall difference of muti-scale LAI inversion was analyzed in an all-round way. This was based on two aspects, "first inversion and then integration" and "first integration and then inversion", and on scale difference characteristics of three scale transformation methods. The generation mechanism of scale effect was refined, and the optimal LAI inversion model was expanded by Taylor expansion. By doing so, it quantitatively analyzed the contribution of various inversion processes to scale effect. It was found that the cubic polynomial regression model based on NDVI(940.7 nm, 712 nm) was the optimal model, where its coefficient of determination R2 and the correlation coefficient of test samples R reached 0.72 and 0.936, respectively. Combined with Taylor expansion, it analyzed the scale error generated by LAI inversion model. After the scale effect correction of one-dimensional and twodimensional variables, the correlation coefficient of CCD-LAI(China Environment Satellite HJ/CCD images) and CASI-LAI products(Compact Airborne Spectro graphic Imager products) increased from 0.793 to 0.875 and 0.901, respectively. The mean value, standard deviation, and relative true value of the two went consistent. Compared with onedimensional variable correction method, the twodimensional method had a better correction result. This research used the effective information in hyperspectral data as sub-pixels and adopted Taylor expansion to correct the scale error in large-scale and low-resolution LAI product, achieving large-scale and high-precision LAI monitoring.

On Simplified Models for Dynamics of Pointlike Objects

Motivation: We study the asymptotic-type dynamics of various real pointlike objects that one models by a variety of differential equations. Their response to an external force one defines solely by the trajectory of a single point. Its velocity eventually stops changing after cessation of the external force. The response of their acceleration to the long-term external force is slow and possibly nonlinear. Objective: Our objective is to present technique for making simplified models for the long-term dynamics of pointlike objects whose motion interacts with the surroundings. In the asymptotic-type long-term dynamics, the time variable t ∈ (tm, +∞) and tm > 0 is large, say ! Method: We apply Taylor series expansion to differential equations to model the acceleration of pointlike object whose response to the long-term external force is not instantaneous and possibly nonlinear. Results: We make simplified models for the long-term dynamics of pointlike objects by Taylor polynomials in time derivatives of the external force. Application: We interpret the relativistic Lorentz-Abraham-Dirac equation as an equation for modeling the long-term dynamics, where t ≥ tm ≫ 0. This interpretation resolves the conceptual and usage controversy surrounding its troublesome application to determine the trajectory of a radiating charged particle, thus contributing to the development of more adequate modeling of physical phenomena.

An Alternative Approach to the Solution of Multi-Objective Geometric Programming Problems

The aim of this study is to present an alternative approach for solving the multi-objective posynomial geometric programming problems. The proposed approach minimizes the weighted objective function comes from multi-objective geometric programming problem subject to constraints which constructed by using Kuhn-Tucker Conditions. A new nonlinear problem formed by this approach is solved iteratively. The solution of this approach gives the Pareto optimal solution for the multi-objective posynomial geometric programming problem. To demonstrate the performance of this approach, a problem which was solved with a weighted mean method by Ojha and Biswal (2010) is used. The comparison of solutions between two methods shows that similar results are obtained. In this manner, the proposed approach can be used as an alternative of weighted mean method.

A Nonlinear Optimal Control Approach for Bacterial Infections Under Antibiotics Resistance

The overuse and misuse of antibiotics has become a major problem for public health.People become resistant to antibiotics and because of this the anticipated therapeutic effect is never reached.In-hospital infections are often aggravated and large amounts of money are spent for treating complications in the patients'condition.In this paper a nonlinear optimal(H-infinity)control method is developed for the dynamic model of bacterial infections exhibiting resistance to antibiotics.First,differential flatness properties are proven for the associated state-space model.Next,the state-space description undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices.The linearization process takes place at each sampling instance around a time-varying operating point which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector.For the approximately linearized model of the system a stabilizing H-infinity feedback controller is designed.To compute the controller's gains an algebraic Riccati equation has to be repetitively solved at each time-step of the control algorithm.The global stability properties of the control scheme are proven through Lyapunov analysis.The proposed method achieves stabilization and remedy for the bacterial infection under moderate use of antibiotics.

A TSE based design for MMSE and QRD of MIMO systems based on ASIP

A Taylor series expansion(TSE) based design for minimum mean-square error(MMSE) and QR decomposition(QRD) of multi-input and multi-output(MIMO) systems is proposed based on application specific instruction set processor(ASIP), which uses TSE algorithm instead of resource-consuming reciprocal and reciprocal square root(RSR) operations.The aim is to give a high performance implementation for MMSE and QRD in one programmable platform simultaneously.Furthermore, instruction set architecture(ISA) and the allocation of data paths in single instruction multiple data-very long instruction word(SIMD-VLIW) architecture are provided, offering more data parallelism and instruction parallelism for different dimension matrices and operation types.Meanwhile, multiple level numerical precision can be achieved with flexible table size and expansion order in TSE ISA.The ASIP has been implemented to a 28 nm CMOS process and frequency reaches 800 MHz.Experimental results show that the proposed design provides perfect numerical precision within the fixed bit-width of the ASIP, higher matrix processing rate better than the requirements of 5G system and more rate-area efficiency comparable with ASIC implementations.

Power system transient stability simulation under uncertainty based on Taylor model arithmetic

The Taylor model arithmetic is introduced to deal with uncertainty.The uncertainty of model parameters is described by Taylor models and each variable in functions is replaced with the Taylor model(TM).Thus,time domain simulation under uncertainty is transformed to the integration of TM-based differential equations.In this paper,the Taylor series method is employed to compute differential equations;moreover,power system time domain simulation under uncertainty based on Taylor model method is presented.This method allows a rigorous estimation of the influence of either form of uncertainty and only needs one simulation.It is computationally fast compared with the Monte Carlo method,which is another technique for uncertainty analysis.The proposed method has been tested on the 39-bus New England system.The test results illustrate the effectiveness and practical value of the approach by comparing with the results of Monte Carlo simulation and traditional time domain simulation.

A collocation interval analysis method for interval structural parameters and stochastic excitation

Uncertainty propagation, one of the structural engineering problems, is receiving increasing attention owing to the fact that most significant loads are random in nature and structural parameters are typically subject to variation. In the study, the collocation interval analysis method based on the first class Chebyshev polynomial approximation is presented to investigate the least favorable responses and the most favorable responses of interval-parameter structures under random excitations. Compared with the interval analysis method based on the first order Taylor expansion, in which only information including the function value and derivative at midpoint is used, the collocation interval analysis method is a non-gradient algorithm using several collocation points which improve the precision of results owing to better approximation of a response function. The pseudo excitation method is introduced to the solving procedure to transform the random problem into a deterministic problem. To validate the procedure, we present numerical results concerning a building under seismic ground motion and aerofoil under continuous atmosphere turbulence to show the effectiveness of the collocation interval analysis method.

A Nonlinear Optimal Control Approach for Tracked Mobile Robots

The article proposes a nonlinear optimal(H-infinity)control approach for the model of a tracked robotic vehicle.The kinematic model of such a tracked vehicle takes into account slippage effects due to the contact of the tracks with the ground.To solve the related control problem,the dynamic model of the vehicle undergoes first approximate linearization around a temporary operating point which is updated at each iteration of the control algorithm.The linearization process relies on first-order Taylor series expansion and on the computation of the Jacobian matrices of the state-space model of the vehicle.For the approximately linearized description of the tracked vehicle a stabilizing H-infinity feedback controller is designed.To compute the controller’s feedback gains an algebraic Riccati equation is solved at each time-step of the control method.The stability properties of the control scheme are proven through Lyapunov analysis.It is also demonstrated that the control method retains the advantages of linear optimal control,that is fast and accurate tracking of reference setpoints under moderate variations of the control inputs.

A Nonlinear Optimal Control Method for Attitude Stabilization of Micro-Satellites

Attitude control and stabilization of micro-satellites is a nontrivial problem due to the highly nonlinear and multivariable structure of the satellites'state-space model.In this paper,a novel nonlinear optimal(H-infinity)control approach is developed for this control problem.The dynamic model of the satellite's attitude dynamics undergoesfirst approximate linearization around a temporary operating point which is updated at each iteration of the control algorithm.The linearization process relies on first-order Taylor series expansion and on the computation of the Jacobian matrices of the state-space model of the satellite's attitude dynamics.For the approximately linearized description of the satellite's attitude a stabilizing H-infinity feedback controller is designed.To compute the controller's feedback gains,an algebraic Riccati equation is solved at each time-step of the control method.The stability properties of the control scheme are proven through Lyapunov analysis.It is also demonstrated that the control method retains the advantages of linear optimal control that is fast and accurate tracking of the reference setpoints under moderate variations of the control inputs.

Approximate Solutions to the Hamilton-Jacobi Equations for Generating Functions

For a nonlinear finite time optimal control problem,a systematic numerical algorithm to solve the Hamilton-Jacobi equation for a generating function is proposed in this paper.This algorithm allows one to obtain the Taylor series expansion of the generating function up to any prescribed order by solving a sequence of first order ordinary differential equations recursively.Furthermore,the coefficients of the Taylor series expansion of the generating function can be computed exactly under a certain technical condition.Once a generating function is found,it can be used to generate a family of optimal control for different boundary conditions.Since the generating function is computed off-line,the on-demand computational effort for different boundary conditions decreases a lot compared with the conventional method.It is useful to online optimal trajectory generation problems.Numerical examples illustrate the effectiveness of the proposed algorithm.