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Genetic polynomial regression as input selection algorithm for non-linear identification

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Abstract

The performance of non-linear identification techniques is often determined by the appropriateness of the selected input variables and the corresponding time lags. High correlation coefficients between candidate input variables in addition to a non-linear relation with the output signal induce the need for an appropriate input selection methodology. This paper proposes a genetic polynomial regression technique to select the significant input variables for the identification of non-linear dynamic systems with multiple inputs. Statistical tools are presented to visualize and to process the results from different selection runs. The evolutionary approach can be used for a wide range of identification techniques and only requires a minimal input and a priori knowledge from the user. The evolutionary selection algorithm has been applied on a real-world example to illustrate its performance. The engine load in a combine harvester is highly variable in time and should be kept below an allowable limit during automatic ground speed control mode. The genetic regression process has been used to select those measurement variables that have a significant impact on the engine load and that will act as measurement variables of a non-linear model-based engine load controller.

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Abbreviations

Symbol:

Description

A:

Matrix of p+1 polynomial model parameters

a i :

ith polynomial model parameter

C p :

Mallow’s Cp

d :

Polynomial degree

LI(x i ):

Lifetime Index (%)

n :

number of candidate input variables

N min :

Final number of regressor variables

N runs :

Number of selection runs

n tot :

Initial number of candidate regressor variables

N :

Number of data samples

R2 p :

Adjusted coefficient of determination

RMSE p :

Residual Mean Squared Error

R uu (τ):

Auto-correlation function

R yu (τ):

Cross-correlation function

sd j :

Combination of maximum d input variables

X :

Initial set of n tot candidate input variables

x I :

Candidate input variable i

X sel (n):

Selected set of n input variables

y :

Output signal

γ yu :

Normalized cross-correlation coefficient

ρ uu (τ):

Auto-correlation coefficient

σ 2 yy , σ 2 uu :

Variance of output signal y and input signal u

τ:

Time lag (s)

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Author notes

  1. K. Maertens

    Present address: CNH Belgium, Innovation Competence Center, Leon Claeysstraat 3A, B8210, Zedelgem, Belgium

Authors and Affiliations

  1. Laboratory for Agro-Machinery and Processing, Katholieke Universiteit Leuven, Kasteelpark Arenberg 30, B-3001, Leuven, Belgium

    K. Maertens

  2. Department of Biosystems, Katholiekie Universiteit Leuven, Kasteelpark Arenberg 30, B3001, LEUVEN (Heverlee), Belgium

    J. De Baerdemaeker

  3. Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628 CD, Delft, The Netherlands

    R. Babuška

Authors
  1. K. Maertens
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  2. J. De Baerdemaeker
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  3. R. Babuška
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Corresponding author

Correspondence to K. Maertens.

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Maertens, K., Baerdemaeker, J.D. & Babuška, R. Genetic polynomial regression as input selection algorithm for non-linear identification. Soft Comput 10, 785–795 (2006). https://doi.org/10.1007/s00500-005-0008-8

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  • DOI: https://doi.org/10.1007/s00500-005-0008-8

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