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Research Papers: Thermal Systems

A Parameter-Estimation Method Using the Ensemble Kalman Filter for Flow and Thermal Simulation in an Engine Compartment

[+] Author and Article Information
Kazuya Kusano

Hitachi, Ltd.,
Research & Development Group,
832-2, Horiguchi,
Hitachinaka 312-0034, Ibaraki, Japan

Hironobu Yamakawa

Hitachi, Ltd.,
Research & Development Group,
832-2, Horiguchi,
Hitachinaka 312-0034, Ibaraki, Japan

Kenich Hano

Hitachi Construction Machinery Co., Ltd.,
650, Kandatsu,
Tsuchiura 300-0013, Ibaraki, Japan

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 23, 2018; final manuscript received July 30, 2018; published online September 5, 2018. Assoc. Editor: Sara Rainieri.

J. Heat Transfer 140(12), 122801 (Sep 05, 2018) (8 pages) Paper No: HT-18-1249; doi: 10.1115/1.4041188 History: Received April 23, 2018; Revised July 30, 2018

The feasibility of the parameter estimation on the basis of the ensemble Kalman filter (EnKF) for a practical simulation involving model errors was investigated. The three-dimensional flow and thermal simulations for the engine compartment of a test excavator were simulated, and several unknown temperatures used for boundary conditions were estimated with the method. The estimation method was validated in two steps. First, the estimation method was tested with the influence of the model errors removed by virtually creating true values with a simulation. These results showed that the proposed parameter-estimation method can successfully estimate surface temperatures. They also suggested that the appropriate ensemble size can be evaluated from the number of unknown parameters. Second, the estimation method was tested under a practical condition including model errors by using actual measurement data. Model errors were statistically estimated using prior obtained error data concerning other design configurations, and they were added to the observation error in the EnKF. These results showed that taking model errors into account in the EnKF provides more-accurate parameter-estimation results. Moreover, the uncertainty of an estimated parameter can be evaluated with the standard deviation of its distribution.

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References

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Figures

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Fig. 2

Engine compartment, (a) exterior configuration and (b) interior configuration

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Fig. 3

Computational domain

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Fig. 4

Temperature measurement

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Fig. 5

Flowchart of parameter estimation for flow and thermal simulation using EnKF

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Fig. 6

Locations of estimated boundary conditions and temperature-measurement points, (a) front side and (b) rear side

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Fig. 7

Streamlines colored with fluid temperature contour and temperature contour on solid surfaces

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Fig. 8

Comparison of measured and simulated temperatures at points a-u

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Fig. 9

Convergence of estimation process

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Fig. 10

Influence of ensemble size on prediction error

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Fig. 11

Predicted temperatures at points a-u with estimated parameters in case 3

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Fig. 12

Estimated results of temperatures on surfaces

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Fig. 13

Predicted temperatures at points a-u with estimated parameters in case 5

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Fig. 14

Histories of parameter distributions in case 5, (a) S1, (b) S2, (c) S3, (d) S4, (e) S5, (f) S6, and (g) S7

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Fig. 15

Estimated and measured temperatures on surfaces

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Fig. 16

Components of column vectors in sensitivity matrix S

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Fig. 17

Euclidean norms of column vectors in sensitive matrix S

Tables

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