least squares method

Examining the mechanical properties of polymer materials has particular importance due to the increasing usage of these materials. In this paper, the crack development process was identified using the experimental data obtained from the tensile tests of polyvinyl chloride polymer (PVC) to reduce the experimental test number. Some pre-cracks were created on the experimental samples by slotting and broaching methods and the experimental results of force versus displacement were recorded for each sample. In the next step, some mathematical pre-processing operations including equating the sampling intervals using interpolation and integration using trapezoidal methods were performed on the experimental data. In the third stage, by using the pre-processed data and the Least Squares (LS) identification method, the mathematical model of the system, the frequency domain discrete transfer function of the crack development process, was obtained. Finally, after evaluating and verifying the obtained mathematical model with other experimental results, it was proposed to predict the crack development process. The obtained results showed that by identifying the crack development process for limited samples, it is possible to avoid the number of experimental tests that are time-consuming and costly. In addition, the second-order two-stage least squares method with five unknown parameters was promisingly able to estimate crack development dynamics with acceptable accuracy, particularly in the first half of the development process.

This article aims to investigate the stability and estimate the aerodynamic coefficients of an aircraft based on experimental flight data. The least squares method was used to estimate these coefficients by using data from an inertial measurement unit (IMU) and global positioning system (GPS). This research, for the first time, has estimated these coefficients on a high-wing aircraft and during various flight maneuvers, including takeoff, landing and variant turns. It has been conducted utilizing time and frequency response data based on actual flight. In this article, the match between the recorded flight path of the aircraft and the flight path plotted by MATLAB software output was evaluated, and the output of the flight path model confirmed this match. Moreover, to improve the estimation of aerodynamic coefficients, the least squares method was modified using past inputs to estimate a value. The method explained in this article was evaluated in 5 experiments using actual flight data from the aircraft. Finally, the maximum estimation error generated by the modified method is 6.7%, which was related to the pitching moment coefficient.

In this paper, a meshless approach utilizing least-squares error technique and Taylor series was used to numerically solve an inviscid hypersonic flow. Second and fourth order derivatives were used as artificial dissipation terms to stabilize the solution and prevent unwanted oscillations especially around the vicinity of shockwave. In this study, chemical reactions caused by increased temperature were assumed to be in equilibrium condition and derived graphs were used to estimate the specific heat ratio. We used an explicit four-stage Runge–Kutta method for temporal discretization of governing equations, and used local time-stepping and residual smoothing techniques to accelerate the convergence process. The results obtained from meshless approach were compared with those obtained from finite-volume method with identical point distribution, and this comparison showed that using meshless approach provides better convergence and lower computation time. Result also showed that replacing ideal gas model with real gas model and applying the hot gas effects lead to precise identification of shockwave’s location, and provides a more accurate prediction of temperature and pressure distribution behind the shockwave.

With the advent of the satellite altimetry in 1973, new scientific applications become possible in oceanography, marine sciences and Earth-related studies, and it was made possible to monitor the sea level with high accuracy and tidal modeling in a global scale. Advances in the sensors technology and different satellite altimetry missions in the recent years led to a great evolution in geodesy and the gravity field modeling studies. The oceanic tide is a periodic phenomenon of rise and fallen of the sea level that has emerged from the combination of waves with different periods. It is governed by the gravitational action of the solar system bodies essentially the moon and the sun, it translates by a transport of water masses. Tide phenomenon is of particular significance among researchers in different scientific societies such as Geodesy, Geophysics, and Oceanography. Since tide is one of the most effective factors on instantaneous sea level fluctuations, it is necessary to know the status of tidal in all offshore projects. So, we can have wider and more optimal exploitation of marine resources with known of the main components of the tide, and finally, the tide phenomenon and sea levels could be predicted with the exact knowledge of the tidal frequencies. Several methods, including Least squares method, Fourier analysis, and statistical methods, have been developed to determine the tidal frequencies. Fourier analysis is a convenient and efficient mathematical tool for modeling the behavior of a periodic phenomenon. In this study, main constituent frequencies of time-series and finally, tidal frequencies in Caspian Sea are determined using the Fourier analysis method relying on the concept of stationary time-series. In this way, first, for a closer look at the data and better visibility of other fluctuations in time-series, the trend component is removed from the data using the Fourier seriese. Next, the frequencies that make up the time-series were identified by the Fourier analysis and least squares method, and as mentioned, the concept of stationary time-series is used to find the main components of the tide in this study. Data from the altimetry satellite Jason-2 from 2008 to early 2014 is analyzed to form the instantaneous sea level time-series in 7 points in Caspian Sea that indicates large instantaneous sea level fluctuations. For time-series, the suitable model for tide modeling can be determined by the following equ ation: where is amplitude, is frequency, is related phase, and is the number of frequencies contained in the model. A discrete set of frequencies can be achieved by in a time-series with equidistant data, where is the time of the first observation and is related to the last. Nyquist Frequency is calculated as. So, the above equation can be written as: So, the amplitudes related to each frequency can be calculated using a least squares adjustment and much more effective frequencies contained in the signal can be identified based on these amplitudes. This analysis uses the concept of Aliased Frequency to calculate the main tidal components in 7 points in Caspian Sea, including: SSA، SA، S2، M2، MF، MM، S4 and M6 component. Finally, spectral analysis is used to study the effect of Volga River on the Caspian Sea level changes.

Dam break time history have always been the intrest of many researchers. This phenomena can be modeled by Eulerian or Lagrangian approach which each of them have their benefits and disadvantages. In this paper isogeometric method is utilized for modeling flow in dam break analysis by Lagrangian approach. Mass and momentum conservation laws are governing equations of flow which are solved by pressure correction in Lagrangian approach. Least square method is used for discretization of space. Matrix size is notably smaller in isogeometric method in comparison with other methods (finite elements and meshless methods). Also stiffness matrix is symmetric and positive definitive. NURBS (Non - Uniform Rational B - Spline) functions are used as shape functions. Free surface profile and pressure values of isogeometric method in different times are compared with a meshless method. The results indicate the ability of the proposed method in solution of moving fluid with moving boundaries.

Geodetic data processing usually is performed using the least-squares method. To achieve the best linear unbiased estimation، it is necessary to use the proper and realistic stochastic model of the observables. The estimation of the unknown (co) variance components of the observables is referred to as variance component estimation (VCE). In geodetic applications، VCE is also known as the observables weights estimation. In this paper، least-squares variance component estimation is applied in a straightforward manner to GPS observables for determination of the realistic stochastic model. For this purpose، the functional model used in the analysis is the GPS geometry-based observation model (GFOM). The numerical results for two receivers، namely Trimble 4000 SSi and Trimble R7، are presented. The results indicate that the correlation between observation types is significant. A positive correlation of 0. 55 is observed between the code observations on CA and P2 for Trimble 4000 SSi. Also، a significant positive correlation of 0. 64 is observed between the phase observations on L1 and L2 for Trimble R7.