Real-Time Force and Moment Estimation for Mechanical Gas Face Seal Systems Using Reduced-Order Kalman Filters

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Haojiong Zhang ◽  
Robert G. Landers ◽  
Brad A. Miller
Keyword(s):  
Real Time ◽  
Axial Force ◽  
Kalman Filters ◽  
Face Seal ◽  
Reduced Order ◽  
Moment Estimation ◽  
Wide Range ◽  
Motion Measurements ◽  
Gas Face Seal ◽  
Proper Orthogonal

A method using reduced-order Kalman filters is developed to estimate the thin gas film axial force and moments in real time for mechanical gas face seal systems in a flexibly mounted stator configuration. First-order Gauss–Markov stochastic models, combined with the stator motion equations, form the basis for the reduced-order Kalman filter estimators. Two schemes are presented to estimate axial force and moments based on stator motion measurements. In one scheme, the force and moments are directly estimated and, in another scheme, a set of proper orthogonal decomposition weighting functions is estimated, from which the gas film force and moments are computed. Both estimators are shown to approximate the gas film axial force and moments successfully for different forcing functions over a wide range of compressibility numbers.

Nonlinear Modeling of Mechanical Gas Face Seal Systems Using Proper Orthogonal Decomposition

2006 ◽  
Vol 128 (4) ◽  
pp. 817-827 ◽  
Author(s):  
Haojiong Zhang ◽  
Brad A. Miller ◽  
Robert G. Landers
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Initial Conditions ◽  
Nonlinear Modeling ◽  
Orthogonal Decomposition ◽  
Galerkin Projection ◽  
Face Seal ◽  
Reduced Order ◽  
Wide Range ◽  
Gas Face Seal ◽  
Proper Orthogonal

An approach based on proper orthogonal decomposition and Galerkin projection is presented for developing low-order nonlinear models of the gas film pressure within mechanical gas face seals. A technique is developed for determining an optimal set of global basis functions for the pressure field using data measured experimentally or obtained numerically from simulations of the seal motion. The reduced-order gas film models are shown to be computationally efficient compared to full-order models developed using the conventional semidiscretization methods. An example of a coned mechanical gas face seal in a flexibly mounted stator configuration is presented. Axial and tilt modes of stator motion are modeled, and simulation studies are conducted using different initial conditions and force inputs. The reduced-order models are shown to be applicable to seals operating within a wide range of compressibility numbers, and results are provided that demonstrate the global reduced-order model is capable of predicting the nonlinear gas film forces even with large deviations from the equilibrium clearance.

Nonlinear Modeling of Mechanical Gas Face Seal Systems Using Proper Orthogonal Decomposition

2005 ◽  
Author(s):  
Haojiong Zhang ◽  
Brad A. Miller ◽  
Robert G. Landers
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Initial Conditions ◽  
Nonlinear Modeling ◽  
Orthogonal Decomposition ◽  
Simulation Studies ◽  
Face Seal ◽  
Model Order ◽  
Reduced Order ◽  
Gas Face Seal ◽  
Proper Orthogonal

A nonlinear reduced-order modeling approach based on Proper Orthogonal Decomposition (POD) is utilized to develop an efficient low order model, based on ordinary differential equations, for mechanical gas face seal systems. An example of a coned mechanical gas face seal in a flexibly mounted stator configuration is presented. The axial mode is modeled, and simulation studies are conducted using different initial conditions and forcing inputs. The results agree well with a fully meshed finite difference model, while the resulting model order is significantly decreased.

scholarly journals SHM and Efficient Strategies for Reduced-Order Modeling

2021 ◽  
Vol 2 (1) ◽  
pp. 98
Author(s):  
Giorgio Gobat ◽  
Saeed Eftekhar Azam ◽  
Stefano Mariani
Keyword(s):  
Real Time ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Order Model ◽  
Model Order ◽  
Reduced Order ◽  
Degradation Processes ◽  
Model Update ◽  
Real Time Computing ◽  
Proper Orthogonal

Within model-based approaches to structural health monitoring (SHM), numerical simulations must be tailored to continuously adapt to the degradation processes and to the possibly changing environment. This model update stage of the analysis brings two competing requirements: the accuracy of the model, with a more detailed description of the phenomena required where damage is supposed to take place; the efficiency of the model, to reduce the overall computational burden and allow for real-time (or close to real-time) computing. Without resorting to AI-based strategies, approaches solely based on proper orthogonal decomposition (POD) and domain decomposition (DD) techniques proved rather efficient in handling the aforementioned trade-off between the diverging requirements of accuracy and efficiency. In this work, we discuss a further improvement over our recently proposed methodology that consists of: a DD of the entire structure into sub-regions, which can be designed to decouple regions more prone to get damaged from regions that are instead less affected by the degradation processes; a POD-based selective model order reduction for all the domains, with adjustable and heterogeneous accuracy requirements. The approach is assessed through an illustrative example related to beam dynamics, with results provided in terms of both accuracy and computational efficiency, or speedup with respect to the full-order model.

Modeling the Turbulent Wake Behind a Wall-Mounted Square Cylinder

2020 ◽  
Author(s):  
Christian Amor ◽  
José M Pérez ◽  
Philipp Schlatter ◽  
Ricardo Vinuesa ◽  
Soledad Le Clainche
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Turbulent Wake ◽  
Orthogonal Decomposition ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Square Cylinder ◽  
Complex Flow ◽  
Reduced Order ◽  
Mode Decomposition ◽  
Proper Orthogonal

Abstract This article introduces some soft computing methods generally used for data analysis and flow pattern detection in fluid dynamics. These techniques decompose the original flow field as an expansion of modes, which can be either orthogonal in time (variants of dynamic mode decomposition), or in space (variants of proper orthogonal decomposition) or in time and space (spectral proper orthogonal decomposition), or they can simply be selected using some sophisticated statistical techniques (empirical mode decomposition). The performance of these methods is tested in the turbulent wake of a wall-mounted square cylinder. This highly complex flow is suitable to show the ability of the aforementioned methods to reduce the degrees of freedom of the original data by only retaining the large scales in the flow. The main result is a reduced-order model of the original flow case, based on a low number of modes. A deep discussion is carried out about how to choose the most computationally efficient method to obtain suitable reduced-order models of the flow. The techniques introduced in this article are data-driven methods that could be applied to model any type of non-linear dynamical system, including numerical and experimental databases.

Separate-bias estimation with reduced-order Kalman filters

1998 ◽  
Vol 43 (7) ◽  
pp. 983-987 ◽  
Author(s):  
D. Haessig ◽  
B. Friedland
Keyword(s):  
Kalman Filters ◽  
Bias Estimation ◽  
Reduced Order

A New Flexible Rapid Thermal Processing System

1995 ◽  
Vol 389 ◽  
Author(s):  
K. C. Saraswat ◽  
Y. Chen ◽  
L. Degertekin ◽  
B. T. Khuri-Yakub
Keyword(s):  
Control System ◽  
Real Time ◽  
Processing System ◽  
Process Conditions ◽  
Temperature Uniformity ◽  
Real Time Control ◽  
Wafer Temperature ◽  
Time Control ◽  
Wide Range ◽  
Optical Flux

ABSTRACTA highly flexible Rapid Thermal Multiprocessing (RTM) reactor is described. This flexibility is the result of several new innovations: a lamp system, an acoustic thermometer and a real-time control system. The new lamp has been optimally designed through the use of a “virtual reactor” methodology to obtain the best possible wafer temperature uniformity. It consists of multiple concentric rings composed of light bulbs with horizontal filaments. Each ring is independently and dynamically controlled providing better control over the spatial and temporal optical flux profile resulting in excellent temperature uniformity over a wide range of process conditions. An acoustic thermometer non-invasively allows complete wafer temperature tomography under all process conditions - a critically important measurement never obtained before. For real-time equipment and process control a model based multivariable control system has been developed. Extensive integration of computers and related technology for specification, communication, execution, monitoring, control, and diagnosis demonstrates the programmability of the RTM.

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