Regularized reduced rank growth curve models

Obtaining initial parameter estimates for chaotic dynamical systems using linear associative memories

The analyses performed in this study relate to the method of quasigeoid modelling which uses the geophysical gravity data inversion technique (GGI method). The purpose of the analyses was to estimate the optimal values of quantitative parameters of selected input data used in the calculations. In particular, the following parameters were investigated: extents of a digital elevation model and the Moho depth model, the extent of the area covered by gravity data and density of gravity data. In order to perform the analyses, a series of local quasigeoid models was determined with different values of the above-mentioned parameters. The optimal values of the parameters were subsequently estimated based on the analyses of changes of quasigeoid models.

Inconel 718 (IN 718) powder is used for a laser powder bed fusion (LPBF) printer, but the mechanical properties of the as-built object are not suited to cold deep drawing applications. This study uses the Taguchi method to design experimental groups to determine the effect of various factors on the mechanical properties of as-built objects produced using an LPBF printer. The optimal printing parameters are defined using the result for the factor response to produce an as-built object with the greatest ultimate tensile strength (UTS), and this is used to produce a specimen for post-processing, including heat treatment (HT) and surface finishing. The HT parameter value that gives the maximum UTS is the optimal HT parameter. The optimal printing and HT parameter values are used to manufacture a die and a punch to verify the suitability of the manufactured tool for deep drawing applications. The experimental results show that the greatest UTS is 1091.33 MPa. The optimal printing parameters include a laser power of 190 W, a scanning speed of 600 mm/s, a hatch space of 0.105 mm and a layer thickness of 40 μm, which give a UTS of 1122.88 MPa. The UTS for the post-processed specimen increases to 1511.9 MPa. The optimal parameter values for HT are heating to 720 °C and maintaining this temperature for 8 h, decreasing the temperature to 620 °C and maintaining this temperature for 8 h, and cooling to room temperature in the furnace. Surface finishing increases the hardness to HRC 55. Tools, including a punch and a die, are manufactured using these optimized parameter values. The deep drawing experiment demonstrates that the manufactured tools that are produced using these values form a round cup of Aluminum alloy 6061. The parameter values that are defined can be used to manufacture IN 718 tools with a UTS of more than 1500 MPa and a hardness of more than 50 HRC, so these tools are suited to cold deep drawing specifications.

In this research, the EISHP (Estimation of Individual Soil Hydraulic Parameters) model was developed for estimation of the individual soil hydraulic parameters of van Genuchten‘s equation (α, n, Ks, θs, and θr). This model was used to predict soil water content and pressure head at different soil depths by implicitly solving the Richards equation, applying the finite difference method. In this model, the objective function (OF) was computed by summation of squared differences between measured and estimated soil water content and pressure head up to ten days after wetting of soil columns. In the EISHP model, each parameter was optimized separately by achieving the minimum value of OF using the Newton-Raphson method and keeping the remaining parameters constant. The optimized parameter value was then used in optimizing the other parameters. Iteration was continued until the difference between the two computational steps of OF was negligibly small and a unique value had been estimated for each parameter. The main contribution of this research is presentation of a methodology for the optimization of individual parameters, which guarantees the uniqueness of parameter values. In contrast, simultaneous optimization of the entire parameter set would not necessarily lead to unique values.

The maximum efficiency of dynamic vibration dampers (DD) is achieved at optimal values of their parameters. Inertial DD are tuned according to their own frequency and damping, and the optimal values of the absorber parameters depend on the spectral composition of the suppressed oscillations. For nonlinear DD, the optimal values of parameters (for example, gap or precompression) also depend on the intensity of external influences on the object. For multi-element DDs, the number of damper inertial elements should also be optimized. The conditions for optimal tuning of the inertial DD are the conditions of antiresonance. In this work, the tuning of an impact DD with viscous friction has been studied. To determine the optimal value of the gap between the mass of the absorber and its body, a nonlinear problem was solved by the method of point transformations. The influence of deviations from the optimal setting of the shock DD on the amplitude of oscillations is determined. It has been established that small deviations from the optimum cause significant increments in the oscillation range (by 2...5 times), which leads to the need to tune the shock DD with high accuracy. The sensitivity of the vibration damper to the optimization error of its parameters is estimated in the work. In addition, the tuning features of multi-element DDs built into the boring bar for eight types of absorbers were studied with varying their design features. When studying the frequency characteristics, the ratio of the maximum values A0 max/AD max was taken as a measure of efficiency, where A0 max is the oscillation amplitude in the system without a damper. The influence of the diametral clearance and the axial compression force on the efficiency of various types of DDs has been established.

A vacuumed artificial mouth has been assembled and tested to measure reed velocity for a Bb clarinet along the width of the reed. Reed velocity measurements may be useful for better estimation of parameters in physical models, such as the relevant surface area of the vibrating reed. Use of a vacuum system instead of a pressurized mouth chamber allows straightforward observation and manipulation of the mouthpiece apparatus. Point measurements of reed velocity were obtained via a laser-Doppler vibrometer directed at the reed surface when artificially blown. Simultaneous high-speed exposures were recorded to visualize reed motion. Preliminary results indicate that the velocity amplitude of any torsional motion in the reed is negligible compared to an asymmetric reed velocity, likely caused by natural limitations of the clarinet ligature. Velocity measurements also indicate that the reed may sometimes rebound against the mouthpiece in its oscillatory period. High-speed exposures support this conclusion by vis...

4.07 - Slip Inversion

Our objective was to identify the best fit mathematical models for in vitro gas production kinetics using rumen fluid and forage plants commonly used in ruminant feed to obtain better estimates of parameters that describe the rumen fermentation. Four mathematical models were tested, two unicompartmental (M1 = first order, M2 = Gompertz) and two bicompartmental (M3 = M1 + M2; M4 = M2 + M2). Two temperate grasses were evaluated, as well as four tropical grasses and three temperate [...]

The statistical behavior of some common parameter estimation methods is investigated by simulation. The methods based on the maximum likelihood principle give the best estimates of parameters in a given model. An analysis of the possibilities for detecting systematic errors by means of the maximum likelihood method showed that this method gives at best the same information as other well known tests.

For pt.I see ibid., vol.5, no.2, p.366-73 (1990). A comprehensive analysis of the transient performance of a permanent magnet (PM) synchronous motor operating from a variable source is described. Internal damping is modeled, and optimum values of design parameters which improve transient performance are obtained. The effects of varying the supply voltage and frequency on the optimum values of these parameters are demonstrated. Simulated nonlinear response to a load change and starting performance are discussed. The results illustrate that significant improvement in transient performance can be achieved over a wide range of voltage and frequencies when some parameters are properly chosen. >

This paper suggests some new estimators of the ridge parameter for binary choice models that may be applied in the presence of a multicollinearity problem. These new ridge parameters are functions of other estimators of the ridge parameter that have shown to work well in the previous research. Using a simulation study we investigate the mean square error (MSE) properties of these new ridge parameters and compare them with the best performing estimators from the previous research. The results indicate that we may improve the MSE properties of the ridge regression estimator by applying the proposed estimators in this paper, especially when there is a high multicollinearity between the explanatory variables and when many explanatory variables are included in the regression model. The benefit of this paper is then shown by a health related data where the effect of some risk factors on the probability of receiving diabetes is investigated.

An algorithm is presented for ESPRIT (estimation of signal parameters via rotational invariance techniques) direction of arrival estimation when the expected value of the covariance of the measurement noise is different from a constant multiple of an identity matrix. The algorithm is based on a modification of the generalized singular value decomposition (GSVD) of two data matrices and requires only unitary transformations. The modification results in a significant simplification of the GSVD-based ESPRIT algorithm and produces more accurate solutions than prewhitening.

Frequency versus time domain parameter estimation: Application to a slot milling operation

This study focuses on parameter estimation in the presence of multicollinearity for the count response that follows the Waring distribution. The Waring regression model deals with over-dispersion. So, this study proposed the Waring ridge regression (WRR) model as a solution for multicollinearity with over-dispersion. We conducted a theoretical comparison between the ridge estimator and the maximum likelihood estimators using matrix and scalar mean squared error as a performance evaluation criterion. Several ridge parameters are considered for the WRR estimator. The performance of these parameters is numerically evaluated using a Monte Carlo simulation study and a real application. The results of the simulation and application demonstrate the superiority of the WRR model with different ridge parameters over the maximum likelihood estimator.

Three different estimators of the variance parameters in the growth curve model with generalized uniform correlation structure are compared on the basis of mean square error. Since the situation in general depends on specific choice of the structure matrix, we investigate two important special cases.