On Using Quasi-Newton Algorithms of the Broyden Class for Model-to-Test Correlation

Klement, Jan

doi:10.5028/jatm.v6i4.373

Cited by 12 publications

(8 citation statements)

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“…In this section, the concepts developed in previous sections are applied to solve the Klement's 4-node model [14], by determining the correction {fc*} needed to minimize the error, using (4.4). Klement's 4-node model is sketched in Fig.…”

Section: Klement's 4-node Model (K4 Model)mentioning

confidence: 99%

Correlation of spacecraft thermal mathematical models to reference data

et al. 2018

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Model-to-test correlation is a frequent problem in spacecraft-thermal control design. The idea is to determine the values of the parameters of the thermal mathematical model (TMM) that allows reaching a good fit between the TMM results and test data, in order to reduce the uncertainty of the mathematical model. Quite often, this task is performed manually, mainly because a good engineering knowledge and experience is needed to reach a successful compromise, but the use of a mathematical tool could facilitate this work. The correlation process can be considered as the minimization of the error of the model results with regard to the reference data. In this paper, a simple method is presented suitable to solve the TMM-to-test correlation problem, using Jacobian matrix formulation and Moore-Penrose pseudoinverse, generalized to include several load cases. Aside, in simple cases, this method also allows for analytical solutions to be obtained, which helps to analyze some problems that appear when the Jacobian matrix is singular. To show the implementation of the method, two problems have been considered, one more academic, and the other one the TMM of an electronic box of PHI instrument of ESA Solar Orbiter mission, to be flown in 2019. The use of singular value decomposition of the Jacobian matrix to analyze and reduce these models is also shown. The error in parameter space is used to assess the quality of the correlation results in both models.

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Section: Klement's 4-node Model (K4 Model)mentioning

confidence: 99%

Correlation of spacecraft thermal mathematical models to reference data

et al. 2018

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“…For automatic correlation methods, see for instance the software TAUMEL, based on an optimization algorithm and developed by Frey, Trinoga et al for Airbus Defense and Space [74,75,79]. Other techniques are presented by Torralbo et al [80], Jouffroy and Durand [81], Beck et al [82], Van Zijl et al [83], Anglada and Garmendia [76] and Klement [84,85]. In case an automatic technique is used for improving the model correlation, it is important to keep the physical meaning of the model parameters.…”

Section: Discussionmentioning

confidence: 99%

Quasi-Autonomous Spacecraft Thermal Model Reduction

Rico¹

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“…De esta manera se pueden analizar diferentes situaciones manteniendo un número manejable de parámetros. El modelo que se va a utilizar está basado en el descrito en [36]. Como se muestra en [15], el modelo propuesto es interesante para este tipo de estudios, pero los casos de carga propuestos no son los más idóneos.…”

Section: Capítulo 4 Modelo 4 Nodosunclassified

“…Although this 4-node TMM may appear to be a non-realistic model, in fact it could represent a real reduced thermal mathematical model of some unit, as is the case of the PHI E-Unit presented in [65]. In addition, this model was used by [36] and showed itself to be good starting point for comparison.…”

Section: Chaptermentioning

confidence: 99%

“…Como se ha presentado en el apartado 2, partiendo de una función objetivo que minimizar (2.2) es posible obtener a una expresión general para calcular la variación que hay que introducir en los parámetros del modelo para queéste proporcione una estimación los más ajustada posible a las temperaturas de referencia.En este apartado se presenta la implementación práctica realizada de este método.Como se ha indicado en el apartado 1.3, uno de los objetivos principales de la tesis es la integración del método descrito en el trabajo del ingeniero de control térmico.Para ello se han desarrollado las herramientas necesarias de tal manera que el ajuste del modelo se pueda realizar con facilidad utilizando directamente los archivos que genera el software ESATAN-TMS[7].Además, primero se explicarán una serie de requisitos que se han de cumplir para que el ajuste del modelo sea exitoso. Siguiendo la linea descrita en[36] se va a definir un conjunto de requisitos que se han de cumplir para poder aplicar el método.3.1.1. Características del modelo matemáticoUna limitación del método propuesto es que cada temperatura obtenida a través del modelo debe ser una función monótona y diferenciable respecto a los parámetros.Estas condiciones en general se cumplen en el espacio de soluciones de un TMM, salvo en ciertas regiones que merecen un estudio aparte.En las misiones espaciales las condiciones de contorno son muy extremas y a menudo se recurre a dispositivos tales como heaters 1 , heat pipes.…”

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Correlation of spacecraft termal mathematical models to reference data

Gimeno¹

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Model-to-test correlation is a frequent problem in spacecraft-thermal control design. The goal of correlation is to determine the values of the parameters of the thermal mathematical model (TMM) that allows reaching a good fit between the TMM results and test data. This way the uncertainty of the mathematical model is reduced. Quite often, this task is performed manually, mainly because a good engineering knowledge and experience is needed to reach a successful compromise, but the use of a mathematical tool could undoubtedly facilitate this work. The correlation process can therefore be considered as the selection of the model parameters that minimize the error of the model results with regard to the reference data. In this doctoral dissertation, a simple method (GIPI) is presented. The method is suitable to solve the TMM-to-test correlation problem, using Jacobian matrix formulation and Moore-Penrose pseudo-inverse, generalized to include several load cases. Aside, in simple cases, this method also allows for analytical solutions to be obtained, which helps to analyze some problems that appear when the Jacobian matrix is singular. To show the implementation of the method, two problems have been considered, one more academic, consisting of a simple 4-node model, and the other one a complex model, the TMM of the optical unit of PHI, one of the remote sensing instruments of the ESA mission Solar Orbiter. The method has given satisfactory reslts in both cases. The convergence of the method has been studied and compared with several methods and the time required by this method (GIPI) subtantially outperforms the other methods.

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On Using Quasi-Newton Algorithms of the Broyden Class for Model-to-Test Correlation

Cited by 12 publications

References 5 publications

Correlation of spacecraft thermal mathematical models to reference data

Correlation of spacecraft thermal mathematical models to reference data

Quasi-Autonomous Spacecraft Thermal Model Reduction

Correlation of spacecraft termal mathematical models to reference data

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