Computation of the stability derivatives via CFD and the sensitivity equations

The method to calculate the aerodynamic stability derivates of aircrafts by using the sensitivity equations is ex- tended to flows with shock waves in this paper. Using the newly developed second-order cell-centered finite volume scheme on the unstructured-grid, the unsteady Euler equations and sensitivity equations are solved simultaneously in a non-inertial frame of reference, so that the aerodynamic stability derivatives can be calculated for aircrafts with complex geometries. Based on the numerical results, behavior of the aerodynamic sensitivity parameters near the shock wave is discussed. Furthermore, the stability derivatives are analyzed for supersonic and hypersonic flows. The numerical results of the stability derivatives are found in good agree- ment with theoretical results for supersonic flows, and variations of the aerodynamic force and moment predicted by the stability derivatives are very close to those obtained by CFD simulation for both supersonic and hypersonic flows.

The computation of the pitch damping stability derivatives of supersonic blunt cones using unsteady sensitivity equations

The numerical methods for computing the stability derivatives of the aircraft by solving unsteady sensitivity equations which was proposed in our previous papers was extended to solve three-dimensional problems in this paper.Both the static and dynamic derivatives of the hypersonic blunt cone undergoing pitching oscillation around a fixed point were computed using the new methods.The predicted static derivative and dynamic derivative were found to be in reasonable agreement with the experimental data.For the present method,it is possible to distinguish the components of dynamic derivatives caused by different state parameters.It is found that C_(m_α) and C_(mq) are usually of opposite signs and tend to eliminate each other,which makes C_(m_α)+C_(mq) being much smaller than its individual components.Another feature of this method is that the moment of pressure derivatives proposed in the present paper can be used to predict the contribution of each part of the blunt cone to the overall stability quantitatively.It is found that the head region is crucial for the static stability and the body region contributes most to the dynamic stability.

Finite element model updating for structural damage detection using transmissibility data

This paper presents a new finite element model updating method for estimating structural parameters and detecting structural damage location and severity based on the structural responses(output-only data).The method uses the sensitivity relation of transmissibility data through a least-squares algorithm and appropriate normalization of the extracted equations.The proposed transmissibility-based sensitivity equation produces a more significant number of equations than the sensitivity equations based on the frequency response function(FRF),which can estimate the structural parameters with higher accuracy.The abilities of the proposed method are assessed by using numerical data of a two-story two-bay frame model and a plate structure model.In evaluating different damage cases,the number,location,and stiffness reduction of the damaged elements and the severity of the simulated damage have been accurately identified.The reliability and stability of the presented method against measurement and modeling errors are examined using error-contaminated data.The parameter estimation results prove the method’s capabilities as an accurate model updating algorithm.

Numerical simulation based on two-directional freeze and thaw algorithm for thermal diffusion model

Freeze-thaw processes significantly modulate hydraulic and thermal char- acteristics of soil. The changes in the frost and thaw fronts （FTFs） affect the water and energy cycles between the land surface and the atmosphere. Thus, the frozen soil com- prising permafrost and seasonally frozen soil has important effects on the land surface hydrology in cold regions. In this study, a two-directional freeze and thaw algorithm is incorporated into a thermal diffusion equation for simulating FTFs. A local adaptive variable-grid method is used to discretize the model. Sensitivity tests demonstrate that the method is stable and FTFs can be tracked continuously. The FTFs and soil tempera- ture at the Qinghai-Tibet Plateau D66 site are simulated hourly from September 1, 1997 to September 22, 1998. The results show that the incorporated model performs much better in the soil temperature simulation than the original thermal diffusion equation, showing potential applications of the method in land-surface process modeling.

An inverse problem to estimate an unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes' first problem for a heated generalized second grade fluid

In this paper,we propose a numerical method to estimate the unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes＇ first problem for a heated generalized second grade fluid.The implicit numerical method is employed to solve the direct problem.For the inverse problem,we first obtain the fractional sensitivity equation by means of the digamma function,and then we propose an efficient numerical method,that is,the Levenberg-Marquardt algorithm based on a fractional derivative,to estimate the unknown order of a Riemann-Liouville fractional derivative.In order to demonstrate the effectiveness of the proposed numerical method,two cases in which the measurement values contain random measurement error or not are considered.The computational results demonstrate that the proposed numerical method could efficiently obtain the optimal estimation of the unknown order of a RiemannLiouville fractional derivative for a fractional Stokes＇ first problem for a heated generalized second grade fluid.

IMPROVED CALIBRATION METHOD FOR AIRBORNE ATI-SAR BASELINE

Airborne Along-Track Interferometric Synthetic Aperture Radar (ATI-SAR) baseline error is a main error resource affecting the precision of velocity measurement of moving objects and therefore should be calibrated externally. The Jet Propulsion Laboratory (JPL) has proposed a calibration scheme for tasks of PacRim98 and PacRim2000 based on several static objects on the ground. In this paper, the influence of phase center uncertainty on baseline determination by using PacRim method proposed by JPL is analyzed. According to the analysis, the phase center uncertainty can cause a constant part of error to the result of baseline calibration. In order to deal with this problem, an improved calibration method on the basis of sensitivity equations and some ground moving targets, whose velocities are already known, is proposed in this paper. The simulation results show that our proposed calibration method has improved the accuracy of baseline calibration and has obviously prohibited the effect of antennas' phase center uncertainty.

COMPUTATIONAL ISSUES IN SENSITIVITY ANALYSIS FOR 1-D INTERFACE PROBLEMS

This paper is concerned with the construction of accurate and efficient computational algorithms for the numerical approximation of sensitivities with respect to a parameter dependent interface location. Motivated by sensitivity analysis with respect to piezoelectric actuator placement on an Euler-Bernonlli beam, this work illustrates the key concepts related to sensitivity equation formulation for interface problems where the parameter of interest determines the location of the interface. A fourth order model problem is considered, and a homogenization procedure for sensitivity computation is constructed using standard finite clement methods. Numerical results show that proper formulation and approximation of the sensitivity interface conditions is critical to obtaining convergent numerical sensitivity approximations. A second order elliptic interface model problem is also mentioned, and the homogenization procedure is outlined briefly for this model.