• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.913-921
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• 2010

The derivative influence measure is adapted to the Cholesky decomposition of a covariance matrix. Formulas for the derivative influence of observations on the Cholesky root and the inverse Cholesky root of a sample covariance matrix are derived. It is easy to implement this influence diagnostic method for practical use. A numerical example is given for illustration.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.465-474
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• 1998

Results on the analytic behavior to the limiting spectral distribution of matrices of sample convariance type. studied in Marcenko and Pastur [2] are derived. using the Stieltjes transform it is shown that the limiting distrbution has a continuous derivative away from zero the derivative being analytic whenever it is positive and the behavior of it resembles the behavior of a square root function near the boundary of its support.

• Wind and Structures
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• v.9 no.2
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• pp.159-178
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• 2006

For the slender and flexible cable supported bridges, identification of all the flutter derivatives for the vertical, lateral and torsional motions is essential for its stability investigation. In all, eighteen flutter derivatives may have to be considered, the identification of which using a three degree-of-freedom elastic suspension system has been a challenging task. In this paper, a system identification technique, known as covariance-driven stochastic subspace identification (COV-SSI) technique, has been utilized to extract the flutter derivatives for a typical bridge deck. This method identifies the stochastic state-space model from the covariances of the output-only (stochastic) data. All the eighteen flutter derivatives have been simultaneously extracted from the output response data obtained from wind tunnel test on a 3-DOF elastically suspended bridge deck section-model. Simplicity in model suspension and measurements of only output responses are additional motivating factors for adopting COV-SSI technique. The identified discrete values of flutter derivatives have been approximated by rational functions.

• Wind and Structures
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• v.7 no.3
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• pp.173-186
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• 2004

Flutter derivatives provide the basis of predicting the critical wind speed in flutter and buffeting analysis of long-span cable-supported bridges. In this paper, one popular stochastic system identification technique, covariance-driven Stochastic Subspace Identification(SSI in short), is firstly presented for estimation of the flutter derivatives of bridge decks from their random responses in turbulent flow. Secondly, wind tunnel tests of a streamlined thin plate model and a ${\Pi}$ type blunt bridge section model are conducted in turbulent flow and the flutter derivatives are determined by SSI. The flutter derivatives of the thin plate model identified by SSI are very comparable to those identified by the unifying least-square method and Theodorson's theoretical values. As to the ${\Pi}$ type section model, the effect of turbulence on aerodynamic damping seems to be somewhat notable, therefore perhaps the wind tunnel tests for flutter derivative estimation of those models with similar blunt sections should be conducted in turbulent flow.

• Wind and Structures
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• v.14 no.5
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• pp.413-434
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• 2011

Without output covariance estimation, one reference-based Stochastic Subspace Technique (SST) for extracting modal parameters and flutter derivatives of bridge deck is developed and programmed. Compared with the covariance-driven SST and the oscillation signals incurred by oncoming or signature turbulence that adopted by previous investigators, the newly-presented identification scheme is less time-consuming in computation and a more desired accuracy should be contributed to high-quality free oscillated signals excited by specific initial displacement. The reliability and identification precision of this technique are confirmed by a numerical example. For the 3-DOF sectional models of Sutong Bridge deck (streamlined) and Suramadu Bridge deck (bluff) in wind tunnel tests, with different wind velocities, the lateral bending, vertical bending, torsional frequencies and damping ratios as well as 18 flutter derivatives are extracted by using SST. The flutter derivatives of two kinds of typical decks are compared with the pseudo-steady theoretical values, and the performance of $H_1{^*}$, $H_3{^*}$, $A_1{^*}$, $A_3{^*}$ is very stable and well-matched with each other, respectively. The lateral direct flutter derivatives $P_5{^*}$, $P_6{^*}$ are comparatively more accurate than other relevant lateral components. Experimental procedure seems to be more critical than identification technique for refining the estimation precision.

• Transactions of the Korean Society of Automotive Engineers
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• v.5 no.2
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• pp.120-126
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• 1997

In this study, an effective estimation method of wheel acceleration is presented. The wheel acceleration is mainly used in the ABS(anti-lick brake system) and the TCS(traction control system). The wheel acceleration is a derivative term of the wheel speed which is generally measured by the wheel speed sensors. The results of a simple differentiation of the signal and an observation of the signal by Kalman filter show that Kalman filter has better performance than the simple differentiation. The differentiated sine signal which is contaminated with random noise shows a rugged signal compared with the signal which is filtered by the Kalman filter. The covariance of the differentiated signal is higher than that of the Kalman-filtered signal, too. The presented Kalman filter technique shows an effective way of solution to get the estimated wheel acceleration value which is sufficient to be applied to ABS or TCS control algorithms.

• Microbiology and Biotechnology Letters
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• v.21 no.4
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• pp.354-365
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• 1993

A novel control method with automatic tuning of PID controller parameters has been developed for efficient regulation of dissolved oxygen concentration in fed-batch fermentations of Escherichia coli. Agitation speed and oxygen partial pressure in the inlet gas stream were chosen to be the manipulated variables. A heuristic reasoning allowed improved tuning decisions from the supervision of control performance indices and it coule obviate the needs for process assumptions or disturbance patterns. The control input consisted of feedback and feedforword parts. The feedback part was determined by PID control and the feedforward part is determined from the feed rate. The proportional gain was updated on-line by a set of heuristics rules based on the supervision of three performance indices. These indices were output error covariance, the average value of output error, and input covariance, which were calculated on-line using a moving window. The integral and derivative time constants were determined from the period of output response. The specific growth rate was maintained at a low level to avoid acetic acid accumulation and thus to achieve a high cell density. The specific growthe rate was estimated from the carbon dioxide evolution rate. In fed-batch fermentation, the simutaneous control of dissolved oxygen concentration (at 0.2; fraction of saturated value) and specific growth rate (at 0.25$hr^{-1}$) was satisfactory for the entire culture period in spite of the changes in the feed rate and the switching of control input.

• Wind and Structures
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• v.11 no.3
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• pp.209-220
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• 2008

Flutter derivatives provide the basis of predicting the critical wind speed in flutter and buffeting analysis of long-span cable-supported bridges. Many studies have been performed on the methods and applications of identification of flutter derivatives of bridge decks under wind action. In fact, strong wind, especially typhoon, is always accompanied by heavy rain. Then, what is the effect of rain on flutter derivatives and flutter critical wind speed of bridges? Unfortunately, there have been no studies on this subject. This paper makes an initial study on this problem. Covariance-driven Stochastic Subspace Identification (SSI in short) which is capable of estimating the flutter derivatives of bridge decks from their steady random responses is presented first. An experimental set-up is specially designed and manufactured to produce the conditions of rain and wind. Wind tunnel tests of a quasi-streamlined thin plate model are conducted under conditions of only wind action and simultaneous wind-rain action, respectively. The flutter derivatives are then extracted by the SSI method, and comparisons are made between the flutter derivatives under the two different conditions. The comparison results tentatively indicate that rain has non-trivial effects on flutter derivatives, especially on and $H_2$ and $A_2$thus the flutter critical wind speeds of bridges.

• Asian-Australasian Journal of Animal Sciences
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• v.5 no.3
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• pp.567-570
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• 1992

Variance components were estimated for calf daily gain from birth to 45 days of age in small (S), medium (M) and large (L) lines of beef cattle. Analyses involved records collected on 682 (S), 510 (M) and 228 (L) calves in Iowa, USA from 1978 to 1986. Cytoplasmic lines were determined based on the foundation female in the maternal lineage of each animal. Data were analyzed separately by size line using a derivative-free restricted maximum likelihood procedure under an animal model including additive direct (a), additive maternal (m), cytoplasmic lineage effects and covariance (a, m). The heritabilities for direct and maternal, and the cytoplasmic effects, were 0.13, 0.35 and 0.00 for S, 0.14, 0.32 and 0.00 for M, and 0.05, 0.33 and 0.03 for L. Genetic correlations (a, m) for S, M and L were -0.33, -0.57 and -1.00, respectively. The maternal genetic effect was the most important for calf growth between birth and 45 dyas of age and cytoplasmic variances were not important in any line.

• Journal of Astronomy and Space Sciences
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• v.20 no.1
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• pp.21-28
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• 2003

In case that we independently obtain orbital informations about the low earth satellites of foreign countries using radar systems, we develop the orbit determination algorithm for this purpose using a SGP4 model with an analytical orbit model and the extended Kalman filter with a real-time processing method. When the state vector is Keplerian orbital elements, singularity problems happen to compute partial derivative with respect to inclination and eccentricity orbit elements. To cope with this problem, we set state vector osculating to mean equinox and true equator cartesian elements with coordinate transformation. The state transition matrix and the covariance matrix are numerically computed using a SGP4 model. Observational measurements are the type of azimuth, elevation and range, filter process to each measurement in a lump. After analyzing performance of the developed orbit determination algorithm using TOPEX/POSEIDON POE(precision 0.bit Ephemeris), its position error has about 1 km. To be similar to performance of NORAD system that has up to 3km position accuracy during 7 days need to radar system performance that have accuracy within 0.1 degree for azimuth and elevation and 50m for range.