The “principal component analysis (PCA)” is one of the analysis techniques in the multivariate analysis, and also is a useful analysis technique for parameter estimations. First, this report shows to applicate the PCA to multicollinearity problems and the equation error method. Next, this report disucusses the “perpendicular error method (PE method)” proposed by this paper, which is one of the three main estimation methods under the concept of the “in-flight wind tunnel test” and corresponds to the maximum likelihood method under the concept of the response time history method. The PE method estimates the aerodynamic regression plane, on which the perpendicular aerodynamic error variance between the data and the regression plane becomes minimum. The PCA is a vital analysis technique for this PE method.
Electronic-speckle-pattern interferometry (ESPI) using a cw Ar-laser, a video system and an image processor was applied to the strain measurements at high temperatures. Applying ESPI, several problems which caused the reduction in visibility of interference fringes were encountered. The problem on the turbulence in the hot air surrounding high temperature objects was solved by using a vacuum chamber. The background radiations from the objects were suppressed considerably by an interference filter. The problem on the oxidation of the object surface couldn't be solved. The spacings of interference fringes were calculated by FFT to avoid human error. The fringes were observable and the strains could be measured up to 1200°C. The results measured in the vacuum chamber were nearly equal to the data which have already been published, up to about 1000°C.
In this paper, effects of configuration, boundary deflection, position, etc. of circular and equilateral triangular membrane elements subject to isotropic tension, upon root-mean-square (rms) surface error in a faceted reflector surface are analyzed. Boundaries of the membranes are assumed to coincide with elliptic or hyperbolic paraboloidal surfaces (including a plane surface), or paraboloidal curves. Exact solutions for the deflection of circular and triangular membranes are obtained based on the linear membrane theory. These solutions are used to calculate the rms errors between the approximate parabolic surface (APS) which approximate the ideal parabolic surface and the membrane surfaces. Different kinds of rms error optimizations according to constraints of parameters which determine the boundary deflections of membrane elements are carried out, from which corresponding optimum membranes are obtained and compared. Rms errors of the optimum membranes calculated reduce as the distance of the membranes from the axis of the reflector becomes large. The rms error of the optimum membrane which gives minimum surface error among others is found to be 0.5 (circular membrane) and 0.46 (equilateral triangular membrane) of that of the membrane whose boundary coincides with the approximate parabolic surface, and 1-0.577 (circular membrane) and 0.28-0.43 (equilateral triangular membrane) of that of the best fit flat membrane. Comparison of the rms errors of a circular and triangular membrane with the same area is also made.
Using a point mass approximation, two and three dimensional minimum time turn problems of a helicopter are formulated as the nonlinear optimal control problems. Optimum solutions are obtained numerically by SCGRA and MQA. The rotor is modeled as an ideal aerodynamic force generator which provide the thrust and the lift as well as control forces of the vehicle without any inertia effect. It is clarified the minimum time turn performances of the helicopter are consisted with bang-bang controls of the angle of attack of the rotor and the engine power and largely dependent on its autorotation capability. It is also revealed that for a rotary wing aircraft such as a helicopter, proper inclusions of the rotor induced power are essential for its maneuverability optimization.