Selection and objective comparison of actuator models Ernő Kovács 1, Viktor Füvesi 2 1,2 University of Miskolc 1 Department of Electrical and Electronic Engineering 2 Research Institute of Applied Earth Sciences, Department of Research Instrumentation and Informatics 1 HU-3515 Miskolc-Egyetemváros 2 HU-3515 Miskolc-Egyetemváros, POB. 2 1 elkke@uni-miskolc.hu; 2 fuvesi@afki.hu International Scientific Conference 21-22 march 2013
Outlines Brief introduction of starter motor Measurement arrangement Hardware, software ANN modeling of starter motor Structure of ANN Training process Model selection Lookup table model Structure Model selection Comparison of models 2/24
Measurement arrangement 1 - starter motor 2 clutch 3 powder brake 1 2 4 controller of the brake Shaft torque Velocity 3 4 Current Battery voltage Control the break Measure different parameters 500 Hz sample frequency 3/24
Measurements Constant load with different value Different characteristic of load 4/24 Parameters unit lower range upper range Armature current (I) A 0 300 Voltage of the battery (U) V 9.5 13 Velocity of the motor (ω) rpm 0 5000 Shaft torque (T shaft ) % 0 100
Transformation Transformation Developed observers Current Battery voltage Estimation of velocity Black Box model Current Battery voltage Estimation of torque of shaft 5/24
Developed models NN based model Lookup table based model 6/24
Datasets Measurement data were formatted Filtered with low-pass filter Scaled and normalised to 0,1-0,9 interval Different datasets were developed for training and validating Type Size of epoch Training dataset 55500 Validation dataset 7300 7/24
Virtual inputs (m) Virtual inputs (m) Applied NN structure and dynamics Feedforward neural network was used One hidden layer Perceptron neuron structure Elliott transfer function In hidden and output layer Bias neurons u(t) Z -1 u(t-d) MISO Multi Input Single Output System FIR external dynamics was applied Input layer Hidden Layer Output Layer ~ y ( t 1) v(t) Z -1 v(t-d) Z -1 u(t-md) Z -1 v(t-md) ~ y( t 1) f ut, ut d,..., ut md, v( t), v( t d),..., v( t md) m 1,...,4 d 10,..., 220 (1) 8/24
Number of virt. inputs (m+1) 2,, 5 Training process Setting up the number of inputs (Changing from 1 to 5 by 1 during the simulation series) Setting the training and validating datasets (Changing the size of delay between virt. inputs) Setting up the number of hidden neurons (Size: Double of the iactual nputs ) Training the configured neural network Initialization: Nguyen-Widrow method Training algoritm: Rprop BP algorithm Activation function: Elliott function Maximal iteration number: 4000 epochs Performance critirea: MSE, AIC, BIC, FPE for validating sets N 10, 20, 30,, 220 Y End of building ANN Delay between virt. inputs (d) 9/24
Number of virt. inputs (m+1) 2,, 5 Training process Results 88 velocity observer model 88 torque observer model 10, 20, 30,, 220 Delay between virt. inputs (d) 10/24
MSE AIC Compare models MSE 1 n n y ~ y i1 2 (2) Delay between virt. inputs (d) Delay between virt. inputs (d) AIC MSE w b nlog 2 (3) 11/24
BIC FPE Compare models BIC nlog MSE w blogn (4) Delay between virt. inputs (d) Delay between virt. inputs (d) FPE nlog n w b n w b MSE nlog (5) 12/24
Best NN models Model Number of virtual inputs Number of delays between regressors Velicity observer MSE for validation dataset PCC for validation dataset Torque observer MSE for validation dataset PCC for validation dataset NN1 5 50 26598.72 0.992 0.071 0.961 NN2 5 60 32055.84 0.990 0.055 0.967 NN3 4 80 15769.38 0.995 0.059 0.965 NN4 5 110 37488.74 0.988 0.032 0.981 Pearson s correlation coefficient: PCC n i1 n i1 y y~ y ~ y n 2 y y ~ y ~ y i i i i1 i 2 (6) 13/24
Developed models NN based model Lookup table based model 14/24
Lookup table based models Measurement data were formatted Filtered with low-pass filter Different datasets were used to developed the reference database (lookup table) and different for validation ~ z( t) ( d1z4 d2z3 d3z2 d4z1)/( d1 d2 d3 d 4 ) (6) d i 2 ( x x) ( y y) i i 2 (7) 15/24
Number of used reference points 2,, 5 Current Find the best model Voltage Using brute force algorithm Changed the size of lookup table Changed the number of used reference points to calculate the actual estimation value 50, 150, 200,, 1750 Number of reference points on one side of the database 16/24
Normalised Totalised MSE for validation datasets Influence of grid density Close to regressive exponential function can be found between the Totalizes MSE and the number of divisions The number of used reference points has not so significant influence to the result Number of divisions in one side of the lookup table 17/24
Computation time [s] Influence of grid density Computation time is close to exponential in the function of grid density 400 Comp. time vs grid density of database 350 300 250 200 150 100 50 0 50 100 150 200 250 300 350 400 450 500 550 Number of divisions in one side of the lookup table CPU: Core2Duo E8400 3GHz Memory: 4GB OS: Fedora 16 C compiler: GCC 18/24
Best lookup based models Model Number of divisions Number of used reference points Velicity observer MSE for validation dataset PCC for validation dataset Torque observer MSE for validation dataset PCC for validation dataset LU1 1750 2 224439,95 0,929 0,298 0,815 LU2 1550 3 256034,58 0,919 0,341 0,790 LU3 1550 4 268877,10 0,915 0,367 0,776 LU4 1250 5 283690,91 0,911 0,40 0,760 19/24
Comparison of models NN1 NN2 Velocity S. Torque Velocity S. Torque MSE 26598,72 0,071 32055,84 0,055 PCC 0,992 0,961 0,990 0,967 LU1 LU2 Velocity S. Torque Velocity S. Torque MSE 224439,95 0,298 256034,58 0,341 PCC 0,929 0,815 0,919 0,790 NN3 NN4 Velocity S. Torque Velocity S. Torque MSE 15769,38 0,059 37488,74 0,032 PCC 0,995 0,965 0,988 0,981 LU3 LU4 Velocity S. Torque Velocity S. Torque MSE 268877,10 0,367 283690,91 0,40 PCC 0,915 0,776 0,911 0,760 20/24
Usage of the models Model-based fault detection tasks Detect different additive faults in analysed system Model-based fault diagnostic tasks More than detection Establish some parameter the fault Separation of the different faults 21/24
Summary Using measurements 4 black box models were developed Programs were developed in C++ Data pre-processing, filtering Simulations NN trainning Data post-processing Compare different models using MSE, PCC 22/24
Acknowledgement The described work was carried out as part of the TÁMOP 4.2.1.B-10/2/KONV-0001-2010 project in the framework of the Hungarian Development Plan. The realization of this project is supported by the European Union, co-financed by the European Social Found. 23/24
Thank you for your kind attention! 24/24