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1

Gauss-Markov model with random parameters to adjust results of surveys of geodetic control networks

Banaś Marek, Czaja Józef, Dąbrowski Janusz

Reports on Geodesy and Geoinformatics

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2021

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Vol. 111

1--6

EN

Alignment of an engineering object project in the field is always conducted at the points of the geodetic control network, the coordinates of which are determined on the basis of the results of its elements survey and with connection to the national spatial reference system. The points of the national spatial reference system determined on the basis of previous surveys have specified coordinates with adequate accuracy, which is included in their covariance matrix. The coordinates of the geodetic control network points are determined more accurately than the points of the national spatial reference system and this means that the results of surveys of the geodetic control network have to be adequately incorporated into the coordinates of the reference points. In order to perform this incorporation, it may be assumed that the coordinates of the reference points are random, that is, they have acovariance matrix, which should be used in the process of adjusting the results of the geodetic control network observation. This research paper presents the principles for the estimation of the Gauss-Markov model parameters applied in case of those geodetic control networks in which the coordinates of the reference points have random character. On the basis of the observation equations δ+AX=L for the geodetic control network and using the weighting matrix Pand the matrix of conditional covariances [wzór] for the observation vector L, the parameter vector X is estimated in the form of the derived formula [wzór]. The verification of these estimation principles has been illustrated by the example of a fragment of a levelling geodetic control network consisting of three geodetic control points and two reference points of the national spatial reference system. The novel feature of the proposed solution is the application of covariance matrices of the reference point coordinates to adjust the results of the survey of geodetic control networks and to determine limit standard deviations for the estimated coordinates ofgeodetic control network points.

2

Strains and self-stresses estimation in the expansive concrete members reinforced with GFRP bars

Tur V., Semianiuk V.

Inżynieria Bezpieczeństwa Obiektów Antropogenicznych

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2016

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Nr 4

3--9

EN

Advantages of the self-stressed concrete members with FRP reinforcement are described. Analytical model for the restrained expansion strains (self-stresses) estimation in the self-stressed concrete members reinforced with FRP bars is proposed. Established modified strains development model (MSDM) is based on deformation compatibility approach in combination with taking into account imposed internal force in reinforcement as an additional restriction for the expansion strains development. Comparison of experimentally established and predicted data that was obtained in accordance with the proposed model for the case of GFRP bars uniaxially symmetrically reinforced high expansion energy capacity concrete members is presented. Verification of the proposed MSDM has shown a good agreement between calculated and experimental values that indicates its validity for the design of the self-stressed concrete members with GFRP reinforcement.

3

Model-based techniques for virtual sensing of longitudinal flight parameters

Hardier G., Seren C., Ezerzere P.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 1

23--38

EN

Introduction of fly-by-wire and increasing levels of automation significantly improve the safety of civil aircraft, and result in advanced capabilities for detecting, protecting and optimizing A/C guidance and control. However, this higher complexity requires the availability of some key flight parameters to be extended. Hence, the monitoring and consolidation of those signals is a significant issue, usually achieved via many functionally redundant sensors to extend the way those parameters are measured. This solution penalizes the overall system performance in terms of weight, maintenance, and so on. Other alternatives rely on signal processing or model-based techniques that make a global use of all or part of the sensor data available, supplemented by a model-based simulation of the flight mechanics. That processing achieves real-time estimates of the critical parameters and yields dissimilar signals. Filtered and consolidated information is delivered in unfaulty conditions by estimating an extended state vector, including wind components, and can replace failed signals in degraded conditions. Accordingly, this paper describes two model-based approaches allowing the longitudinal flight parameters of a civil A/C to be estimated on-line. Results are displayed to evaluate the performances in different simulated and real flight conditions, including realistic external disturbances and modeling errors.

4

Application of statistical formulas to hydrodynamic torque converter modelling

Kesy A., Kadziela A.

Archives of Civil and Mechanical Engineering

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2009

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Vol. 9, no 4

33-48

EN

In this paper a numerical estimation of hydrodynamic torque converter model is discussed. During the estimation it was assumed that the flow through in working area contains multiple flow streams. A contribution of each individual flow stream in transferring torque was assumed based on a pre-selected torque function. Model estimation relied upon proper equation and function parameter selection that provided minimization of the modelling error. Statistical factors were selected for accuracy evaluation of the modelled torque function. In this case torque functions were converted to diverging series, where values of fundamental statistical factors were calculated. Based on tests and numerical calculations for a pre-selected hydrodynamic torque converter it was concluded that there is a relation between modelling accuracy and values of some of the statistical factors. Application of statistical factors drastically simplified numerical calculations during modelling estimation.

PL

Artykuł dotyczy estymacji numerycznego modelu przekładni hydrokinetycznej, w którym założono, że przepływ w przestrzeni roboczej składa się z wielu strug. W tym modelu udział poszczególnych strug w przenoszeniu momentu obrotowego określono na podstawie arbitralnie dobranej funkcji rozkładu momentu. Estymacja modelu polegała na doborze postaci równania i parametrów tej funkcji, tak żeby uzyskać najmniejszy błąd modelowania. Do oceny funkcji rozkładu momentu pod kątem dokładności modelu zaproponowano użycie wskaźników statystycznych. W tym celu dobierane funkcje rozkładu momentu zamieniono na szeregi rozdzielcze, dla których następnie obliczano wartości podstawowych wskaźników statystycznych. Na podstawie badań doświadczalnych i obliczeń numerycznych wybranej przekładni hydrokinetycznej wykazano, że istnieje związek między dokładnością modelu, a wartościami pewnych wskaźników statystycznych. Użycie wskaźników statystycznych znacznie upraszcza obliczenia numeryczne podczas estymacji.