Kohonen Maps for Chip Form Classification in Turning

1

• Kohonen Maps for Chip Form Classification in
  Turning
• D. DAddona, R. Teti
• Dept. of Materials and Production Engineering
• University of Naples Federico II, Italy

2
 
Introduction

• Today, the development of very reliable machining
  processes is requires to achieve higher material
  removal rates with high degrees of automation in
  truly untended manufacturing systems
• One of the aspects notably affecting the
  efficiency of machining processes is the
  monitoring and control of the chip form
• Efficient chip form monitoring and control is
  needed to allow for the formation of chip shapes
  that can be easily and reliably evacuated from
  the working zone
• Decision making on chip form through the analysis
  of sensor signal features was performed using an
  unsupervised neural network methodology based on
  Kohonen or self-organising maps (SOM)
• The selection of the parameters and variants of
  the map, during the training phase, are studied
  to improve the quality of the SOM.

3
 
Materials and Experimental Procedures

• The cutting process was longitudinal turning of
  C45 (AISI 1045) steel with coated carbide tool
  inserts (TNMG 332 or grade 4025) and variable
  cutting conditions, yielding different chip forms
  (snarled, short and short spiral) classified
  according to ISO 3685 standard

• Characteristics of cutting force signals
• Longitudinal turning of C45 steel with coated
  carbide inserts and different chip forms
  (snarled, short and short spiral)
• Cutting parameters Cutting speed 150, 250
  m/min Feed 0.08, 0.13, 0.20, 0.30 mm/rev
  Depth of cut 1.0, 1.5, 2.0, 3.0 mm
• Cutting force signal samples digitized at 2500 Hz
  for about 3 s (data sequence 7500 points)

4
 
Scheme of the Cutting Force Monitoring System
5
Signal analysis of CFS specimens

• Force signal specimen analysis
• spectral estimation achieved through a parametric
  method
• feature extraction from force signal frequency
  spectrum
• From the signal specimen, p 4 features, a1
  a4, characteristic of the spectrum model, were
  obtained through linear predictive analysis (LPA)
• Features a1 a4 were utilized to train and test
  unsupervised the SOM NN for chip form
  classification

6
SOM NN Structure

• The SOM architecture comprises the input layer
  and a two-dimensional map, called competitive
  layer

7
SOM NN Structure

• A SOM map is formed by a grid of neurons, also
  called nodes or units, which the stimuli are
  presented to

• A stimulus is a vector of dimension d describing
  the case to be classified
• It is identified by the cutting force 4-component
  feature vectors a1, , a4

• Each stimulus, or input vector, is associated
  with its corresponding encoded chip form (label)
  short, short spiral and snarled.

8
 
SOM NN Data Processing

• During the training phase, for each input vector,
  the winner neuron is determined by a competition
  and the initially random weights of the
  connections to this neuron and to its neighboring
  neurons are adapted until the network reaches a
  more or less stable state

• After training, the map should be topologically
  ordered the input vectors are judged
  topologically close on the basis of some distance
  measure (e.g. Euclidean distance) and are
  allocated in adjacent map neurons or even in the
  same single map neuron

• The SOM maps can be visualized using the Unified
  Distance Matrix, or U-matrix the distances of
  each map unit from each of its immediate
  neighbours are calculated and visualised using a
  colour image for the matrix

9
SOM NN Optimal Architecture

• The determination of the optimal architecture of
  an unsupervised neural network is an important
  and a difficult task
• The classical neural network topology
  optimization methods select weight(s) or unit(s)
  from the architecture in order to give a high
  performance of a learning algorithm
• The performance of the SOM is influenced by learn
  methods and SOM NN parameters
• The resultant quality of the topological
  formation of the SOM is also highly dependent
  onto the learning rate and the neighborhood
  function
• The values of the training parameters were
  changed to find the optimal SOM structure with
  the best quality in terms of quantization and
  topographic error

10
SOM NN Quality Measure

• Typically, the quality of the map is measured in
  terms of the training data. The returned quality
  measures are the average quantization error, qe,
  and the topographic error, te.
• The average quantization error, qe, is the
  average distance between each data vector and its
  Best-Matching Unit (BMU) it measures the map
  resolution.
• The topographic error, te, is the proportion of
  all data vectors for which first and second BMUs
  are not adjacent units. The te measures topology
  preservation.

11
SOM NN Quality Optimization

• There are two initialization (random and linear)
  and two training (sequential and batch)
  algorithms implemented in the basic SOM Matlab
  Toolbox. The simplest way to initialize and train
  a SOM is to use the function som_make sM
  som_make(sD).
• The som_make function both initializes and trains
  the map
• The training is done is two phases
• rough training with large (initial) neighborhood
  radius and large (initial) learning rate
• fine tuning with small radius and learning rate

12
SOM NN Quality Optimization

• The som_make function selects map size and
  training parameters automatically although it has
  a number of arguments to give preferences of for
  example map size.
• To have tighter control over the training
  parameters, it can use the relevant
  initialization and training parameters directly
  in the function som_make(D, argID, value,
  ...).
• The valid argument IDs and corresponding values
  that can be selected are
• - 'init, initialization parameter 'randinit' or
  'lininit'
• - 'algorithm', training algorithm 'seq' or
  'batch'
• - 'training', training length 'short',
  'default', 'long'
• - 'neigh' neighborhood function, 'gaussian',
  'cutgauss', 'ep' or 'bubble'
• - 'shape', map grid shape 'sheet', 'cyl' or
  'toroid'
• - 'lattice', map grid lattice 'hexa' or 'rect'
• - 'mapsize' small, normal or big map.

13
Training parameter values and corresponding
quantization and topographic errors
14
Combination of training parameter values and
corresponding quantization and topographic errors
Best combination
15
SOM NN Data Processing

• The 4-component input vectors a1, , a4 for the
  Fp component of the cutting force were utilized
  for training and testing of SOM with optimal
  configuration.
• The sequence of 28 4-component input vectors made
  up a set of 28 stimuli to be applied to the SOM
  according to the leave-k-out method with k 1.
• The input data is in an ASCII file containing the
  names of the variables. Each of the following
  lines gives one data sample beginning with
  numerical variables and followed by labels (chip
  form).

4-component input vectors and corresponding
labels (Sho Short Sna Snarled Sh.Sp Short
Spiral)
16
 
20000 step trained SOM. Cutting force component
Fp Labels Sho Short Sna Snarled Sh.Sp
Short Spiral. Chip form test sh.sp_test
17
 
20000 step trained SOM. Cutting force component
Fp Labels Sho Short Sna Snarled Sh.Sp
Short Spiral. Chip form test sho_test
18
 
20000 step trained SOM. Cutting force component
Fp Labels Sho Short Sna Snarled Sh.Sp
Short Spiral. Chip form test sna_test
19
 
Conclusions

• Sensor monitoring of chip form was performed
  through cutting force sensor signal detection and
  analysis. Classification of chip form was
  obtained on the basis of a SOM NN processing of
  cutting force sensor data.
• The obtained results showed that the unsupervised
  NN approach allows for excellent data group
  separability and chip form identification (100
  success rate).
• On this basis, an on-line real time chip form
  classification, making use of cutting force
  sensor signal features, could be developed and
  implemented for industrial applications.

20

• Kohonen Maps for Chip Form Classification in
  Turning
• D. DAddona, R. Teti
• Dept. of Materials and Production Engineering
• University of Naples Federico II, Italy