Development of an analytical mirror model addressing the problem of thermoelastic deformation

Myers, Craig J.; Allen, Richard C.

doi:10.1364/ao.24.001933

Cited by 11 publications

(8 citation statements)

References 9 publications

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“…The three-dimensional thermoelastic problem has in general no analytical solution. Nevertheless, some authors have studied the deformations of mirrors heated by lasers [2][3][4][5][6][7][8] ; but they almost always consider the static regime with sometimes fuzzy boundary conditions. Therefore we find it useful to publish our attempt to treat the boundary conditions and the time dependence precisely.…”

Section: Introductionmentioning

confidence: 99%

Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams

Hello

Vinet

1990

J. Phys. France

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Section: Introductionmentioning

confidence: 99%

Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams

Hello

Vinet

1990

J. Phys. France

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“…In (20) we assumed that the data matrix Z (l) 0,p−1 has a full row rank. This is, we assume that the persistency of excitation condition is satisfied [18].…”

Section: B Estimation Of the Varx Modelmentioning

confidence: 99%

“…This parameter is a user choice. To summarize, to find the estimate of the past window, we need to compute p max least-squares solutions (20), and using such solutions to find w for which the quantity in ( 21) has the smallest value.…”

Section: B Estimation Of the Varx Modelmentioning

confidence: 99%

“…That is, the temperature dynamics is inherently infinite-dimensional. Furthermore, in many engineering applications, it is coupled with other physical processes such as elastic deformations and a fluid flow [16], [19], [20]. Consequently, the structure selection and model order estimation of the temperature dynamics are challenging system identification problems.…”

Section: Introductionmentioning

confidence: 99%

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Subspace Identification of Temperature Dynamics

Haber

2019

Preprint

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Data-driven modeling and control of temperature dynamics in mechatronics systems and industrial processes are challenging control engineering problems. This is mainly because the temperature dynamics is inherently infinite-dimensional, nonlinear, spatially distributed, and coupled with other physical processes. Furthermore, the dominant time constants are usually long, implying that in practice due to various economic and time constraints, we can only collect a relatively small number of data samples that can be used for data-driven modeling. Finally, since sensing and actuation of temperature dynamics are often spatially discrete, special attention needs to be given to sensor (actuator) placement and identifiability problems. Motivated by these challenges, in this manuscript, we consider the problem of data-driven modeling and validation of temperature dynamics. We have developed an experimental setup consisting of a long aluminum bar whose temperature dynamics is influenced by spatially distributed heat actuators and whose temperature is sensed by spatially distributed thermocouples. We address the noise reduction problem and perform step response and nonlinearity analyses. We combine predictor based subspace identification methods with time series analysis methods to identify a multiple-input multiple-output system model. We provide detailed treatments of model structure selection, validation, and residual analysis problems under different modeling and prediction scenarios. Our extensive experimental results show that the temperature dynamics of the experimental setup can be relatively accurately estimated by low-order models.

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“…For pursuing accurate modeling of the water-cooled mirror, the problem should be divided into two major tasks [5]. The first task is to obtain accurate temperature field expression, which completely characterizes thermal diffusion and convective heat transfer behavior for arbitrary spatial and temporal loading of boundary, convective term, and initial conditions.…”

Section: Introductionmentioning

confidence: 99%

Heat Transfer and Thermal Deformation Characteristics of Liquid-Cooled Laser Mirror

Zhu

et al. 2014

Advances in Mechanical Engineering

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A coupled finite volume-element method is developed to simulate the transient thermal deformation of water-cooled mirror by considering fluid flow and convective heat transfer. The simulation process consists of two steps: the 3D finite volume models of fluid flow and heat transfer equation are solved to obtain the time-dependent temperature field by using CFD; then, the obtained temperature field used as final temperature field is unidirectionally coupled to the finite element model for solving the thermoplastic equation. It is concluded that fluid flow not only affects the magnitude of temperature rise and thermal deformation, but also affects the distribution of temperature and thermal deformation. The temperature gradient in the thickness direction (z direction) is found to be much larger than that in transverse direction. It is found that the temperature and the consequent deformation of water-cooled mirror increase significantly in the first seconds and gradually become steady state in the subsequent time. Experiments are conducted to estimate the precision of numerical models, and the experimental results agree well with the simulated results.

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Development of an analytical mirror model addressing the problem of thermoelastic deformation

Cited by 11 publications

References 9 publications

Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams

Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams

Subspace Identification of Temperature Dynamics

Heat Transfer and Thermal Deformation Characteristics of Liquid-Cooled Laser Mirror

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