The knowledge of microstructure is essential to compute mechanical properties of hot rolled steel. Depending on process data and the chemical composition of the steel, a physical model is used to calculate microstruct...
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The knowledge of microstructure is essential to compute mechanical properties of hot rolled steel. Depending on process data and the chemical composition of the steel, a physical model is used to calculate microstructure parameters such as grain size, recrystallization and the γ-α-transformation. In addition to the physical model an artificial neural network is employed to calculate mechanical properties. New results from hot rolling mills are presented. The on-line application of the monitor system allows a quick release of strips after rolling and the saving of costs for quality control measurements. Process parameters could be adjusted to achieve desired mechanical properties of the product. Process data can either be obtained on-line from the process itself or can be simulated off-line, e.g. by Siemens’ HYBRid EXpert System HYBREX. Its central component is a high-performance flowsheet simulator, which enables complex plants to be modeled, simulated and evaluated. The architecture and capability of HYBREX will be presented as well as the newly achieved possibilities by integrating the microstructure model to the simulation tool.
A Newton algorithm is discussed. This algorithm allows for studying nonlinear material behavior, such as plasticity and viscoplasticity. The material behavior is described by so-called internal variables. The model ap...
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A Newton algorithm is discussed. This algorithm allows for studying nonlinear material behavior, such as plasticity and viscoplasticity. The material behavior is described by so-called internal variables. The model applied in this paper was developed by Lemaitre and Chaboche. The Newton algorithm is implemented as a user-subroutine in the commercial finite-element method package ABAQUS. The results of a numerical analysis of the rotation of an aircraft turbine disk are presented. Cyclic loading conditions are studied, and the results are compared with numerical results in the literature.
The Allen-Cahn equation is a simple model of a nonlinear reaction-diffusion process. It is often used to model interface motion in time, e.g. phase separation in alloys. It has applications in many areas including mat...
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The Allen-Cahn equation is a simple model of a nonlinear reaction-diffusion process. It is often used to model interface motion in time, e.g. phase separation in alloys. It has applications in many areas including material sciences, biology, geology, as well as image processing. We will consider a simple scalar Allen-Cahn equation subject to distributed control. Here, the nonlinear reaction term is obtained from using the standard double-well potential, leading to a cubic nonlinearity. We will describe a nonlinear feedback control strategy based on the concept of Model Predictive Control (MPC). We also show how to obtain the open-loop trajectory and control using numerical techniques for PDE-constrained optimization. The feedback control scheme is then applied to the spatially semi-discretized nonlinear optimal control problem. For the prediction and control step within the MPC scheme, we apply a linear-quadratic regulator/Gaussian design problem. The arising computational challenge consisting in solving the associated large-scale algebraic Riccati equations has already been shown in the literature to be feasible using reasonably fine discretizations.
Lyapunov equations are key mathematical objects in systems theory, analysis and design of control systems, and in many applications, including balanced realization algorithms, procedures for reduced order models, Newt...
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Lyapunov equations are key mathematical objects in systems theory, analysis and design of control systems, and in many applications, including balanced realization algorithms, procedures for reduced order models, Newton methods for algebraic Riccati equations, or stabilization algorithms. A new iterative accuracy-enhancing solver for both standard and generalized continuous- and discrete-time Lyapunov equations is proposed and investigated in this paper. The underlying algorithm and some technical details are summarized. At each iteration, the computed solution of a reduced Lyapunov equation serves as a correction term to refine the current solution of the initial equation. The best available algorithms for solving Lyapunov equations with dense matrices, employing the real Schur(-triangular) form of the coefficient matrices, are used. The reduction to Schur(-triangular) form has to be done only once, before starting the iterative process. The algorithm converges in very few iterations. The results obtained by solving series of numerically difficult examples derived from the SLICOT benchmark collections for Lyapunov equations are compared to the solutions returned by the MATLAB and SLICOT solvers. The new solver can be more accurate than these state-of-the-art solvers and requires little additional computational effort.
Purpose: We have designed and implemented a new stereotactic machine QA test. The method is used to characterize gantry sag, couch wobble, cone placement, MLC offset and room lasers position relative to radiation isoc...
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Purpose: We have designed and implemented a new stereotactic machine QA test. The method is used to characterize gantry sag, couch wobble, cone placement, MLC offset and room lasers position relative to radiation isocenter. An image containing a series of test patterns is generated in a direct and integrated fashion. Method and Materials: Two MLC star patterns, a cone pattern and the laser lines are recorded on the same imaging medium, enabling 0.1 mm accuracy measurements. Phosphor plates are used as the imaging medium due to their unique property that the red light of wall laser erases the radiation information stored on phosphor plates. The room lasers position relative to the radiation isocenter can be measured. The developed QA method consists of four images that measure the gantry sag between 0 0 and 180 0 gantry angles, the position and stability of couch rotational axis, the sag between 90 0 and 270 0 gantry angles, the accuracy of cone placement on the collimator and the position of laser lines relative radiation isocenter. Results: The inherent precision of the numerical algorithms developed is +/− 0.05mm. The inherent accuracy of the method as a whole is +/− 0.1mm. The total irradiation/illumination time is about 10 min per image. Automating the generation of collimator star patterns can reduce this time. The data analysis (including the phosphor plate scanning) is less than 5min. Conclusion: The presented method reproducibly characterizes the radiation isocenter geometry with the high accuracy required for stereotactic surgery. It can replace the standard ball test and it can provide a highly accurate QA procedure for the non-stereotactic machines.
Model problems of aircraft tracking are considered for the case when an aircraft moves in the horizontal plane under conditions of uncertainty in measurements of its geometric coordinates. Estimation of the phase stat...
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Model problems of aircraft tracking are considered for the case when an aircraft moves in the horizontal plane under conditions of uncertainty in measurements of its geometric coordinates. Estimation of the phase state is implemented by means of the informational sets. The results of numerical constructing the informational sets in the three- and four-dimensional phase spaces are discussed.
In this paper we discuss algorithms for the computation of the ℒ ∞ -norm of transfer functions related to descriptor systems, both in the continuous- and discrete-time context. We show how one can achieve this goal b...
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In this paper we discuss algorithms for the computation of the ℒ ∞ -norm of transfer functions related to descriptor systems, both in the continuous- and discrete-time context. We show how one can achieve this goal by computing the eigenvalues of certain structured matrix pencils. These pencils can be transformed to skew-Hamiltonian/Hamiltonian matrix pencils which are constructed by only using the original data. Furthermore, we apply a structure-preserving algorithm to compute the desired eigenvalues. In this way we increase robustness and efficiency of the method. Finally, we present numerical results in order to illustrate the advantages of our approach.
A method is proposed for estimating both the weights and the state of a multiple model system with one common state vector. In this system, the weights are related to the activation of each individual model. For the r...
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A method is proposed for estimating both the weights and the state of a multiple model system with one common state vector. In this system, the weights are related to the activation of each individual model. For the resulting nonlinear estimation problem a method is developed that efficiently decomposes the total problem into two separate parts, one for estimating the model weights and one for estimating the state. The method has been validated on a component, actuator and sensor fault detection and identification problem for a linearized model of an aircraft.
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