1. INTRODUCTION
To respond to the changes of market demands, manufacturing systems
must be able to adapt to the production of a variety of products
automatically, without manual changes to hard tooling. That is, the
attributes of intelligence and flexibility must be built into
manufacturing systems/subsystems. Manufacturing subsystems that
perform the task of visual inspection or part/object identification
must likewise exhibit the flexibility and adaptability required of
intelligent and flexible manufacturing systems. Newman and Jain (1995) distinguish between inspection and
recognition/identification. According to them, inspection is the
process of determining if a product (e.g., part, object, or item) deviates
from a given set of specifications to satisfy certain quality criteria
(e.g., surface finish, geometric dimensions). Recognition involves the
positive identification of an object (e.g., correct orientation of a
part). It has been recognized that machine-based vision systems can
identify materials and components, and locate and orient parts prior to
assembly. These systems can perform inspection and measurement tasks
during manufacturing processes and prior to shipment (Rosandich, 1997; Pham & Alcock,
2003). However, the automation of visual inspection has not kept
pace with the automation of the manufacturing process (Newman & Jain, 1995). Rosandich (1997) suggested several factors that have limited the
feasibility of such systems as follows:
- Installation of such systems often requires specialists'
knowledge (e.g., illumination, cameras, computer interfacing, programming,
and image processing).
- Installation often requires undesirable or inconvenient process
changes (e.g., product line has to be stopped or separated or special
equipment installed for illumination).
- Current systems lack flexibility, as each had to be custom designed
for a specific task.
Similar limitations can be argued for machine-based vision systems
used for recognition of objects.
Recognition of object or part features can be achieved using either
machine vision (e.g., camera) or other sensors (e.g., fiber optics).
Machine vision requires the integration of many aspects such as lighting,
cameras, handling equipment, human–computer interfaces, and working
practices, in addition to designing image-processing algorithms. Parts are
fed from one station to another via conveyor, or fed in correct
orientation for the downstream process using vibratory bowl feeders.
Hence, real-time recognition of the part's features performed under
motion would be a desirable capability in any part feeders. Although
machine vision systems can recognize parts under motion, they would incur
high computational overheads of image processing (e.g., motion analysis,
correspondence of adjacent frames, etc.), which may be detrimental to
achieving real-time performance.
This paper attempts to address these limitations inherent in machine
vision systems by investigating how flexibility and on-line learning of
features can be incorporated in an optical sensor-based system using
neural networks to perform the task of feature recognition of parts in
motion. To demonstrate the real-time recognition of parts under motion,
the vibratory bowl feeder, a common parts feeding device in mass
production is used. To facilitate automated flexible orientation of parts
in batch production, the feeder has to accommodate a wide range of parts,
has a short changeover time between parts, and delivers them in the
appropriate orientation. To achieve flexibility, cleverly designed
mechanical devices are attached to the traditional bowl feeder, which may
reject a part in an undesired orientation back into the bowl, and machine
vision or sensing devices is added as a means of determining part
orientation. The nature of motion of the parts ensures that the sensing,
and hence recognition, is subjected to noise.
Some researchers (Suzuki & Kohno, 1981;
Cronshaw, 1980; Warnecke et
al., 1991; Causey & Quinn, 1997) have
employed machine vision (using CCD cameras), whereas others (Smals, 1985; Maul & Ou-Yang,
1987; Maul & Jaksic, 1994; Chua et al., 1997) have used sensor devices to capture
the images of the feeding parts to recognize the parts orientation. In
general, a recognition system is first taught to recognize the possible
input orientations of a part in the learning/training mode in which
patterns are stored in the computer system as reference signatures (i.e.,
templates). In the operation mode, the image acquired is compared to the
reference signatures for identification of orientation (i.e., template
matching). Using “template-matching” algorithms, the
recognition system compares data acquired by the sensors with the
prestored templates that represent the desired orientations of the parts.
If a match occurs, the parts orientation can be determined. However, the
disadvantage of the template-matching approach is that it is sometimes
difficult to select a good template for each pattern class and define a
proper matching criterion. Furthermore, this approach lacks flexibility in
adapting to new parts requirements. When new parts are added due to
changes in production demands, the process of retraining the system is
required, leading to an increased down time.
Various types of neural networks have been used for applications that
require feature recognition. Lankalapalli et al. (1997) have applied the self-organizing neural network
ART2, which is based on adaptive resonance theory (ART; Carpenter &
Grossberg, 1987a, 1987b) to the problem of feature recognition
from a boundary representation (B-rep) solid model of nine different
features. The results obtained indicate that the network has a
significance potential for application to the problem of feature
recognition. Sim et al. (2003) investigated the
pattern recognition capability of three neural network models (namely,
backpropagation, ART2, and ARTMAP) to identify the orientations of the
parts moving in a programmable vibratory bowl feeder. Backpropagation
(Rumelhart & McClelland, 1986) represents a
class of neural networks that learn under supervised training but does not
promote plasticity in its memory. ART2 is selected because it exhibits
plasticity in its memory under unsupervised learning. ARTMAP (Carpenter et
al., 1991a, 1991b) exhibits plasticity but lacks the
ability to learn unsupervised. Of these models, ARTMAP is shown by Sim et
al. (2003) to exhibit high recognition
capability and flexibility in accommodating new parts without retraining.
Hence, the flexibility that is sought in a parts feeder is achieved
through the adaptability of ARTMAP in its pattern recognition performance
of different parts features without the need of retraining.
The paper consists of the following sections. Section 2 describes the
key characteristics of a family of neural networks referred to as ART and
the parameters that characterize ARTMAP to achieve real-time recognition
of parts' features. Section 3 describes the programmable vibratory
bowl, the parts used in the experiments, and Section 4 describes the data
acquisition and data preprocessing processes prior to parts recognition.
Section 5 describes the details of two experiments conducted in terms of
the organization of the training and testing data and the experimental
procedures. The first experiment was conducted to optimize the ARTMAP
parameters that have influence on the pattern recognition capability of
the system. The second experiment was conducted to study the influence of
sampling rates on performance of the fiber optic sensors in acquiring
features of different moving parts. Section 6 presents the results of the
two experiments, and Section 7 discusses the evaluation of the results in
terms of ARTMAP parameters and the sampling rates on the pattern
recognition capability of the vibratory bowl feeder system. Hence, the
results obtained may provide some useful insights in solving a class of
manufacturing problems that is characterized by pattern recognition of
parts/objects in motion in real time and yet subjected to noise.
2. THE ARTMAP MODEL
ART, which was developed by Carpenter and Grossberg (1987a, 1987b), refers to a family of self-organizing
neural architectures that cluster the pattern space and produce archetypal
weight vector templates (Gurney, 1997). ART1
(Carpenter & Grossberg, 1987a),
being the first member of the family, clusters only binary input patterns.
ART2 (Carpenter & Grossberg, 1987b)
overcomes the limitation of ART1 in that it can process analogue input
patterns in addition to binary patterns. One of the main claims made for
ART is that it overcomes the plasticity–stability dilemma in a
natural way, so that the net is continually immersed in a training
environment where there are no separate learning and testing phases (Gurney, 1997). In overcoming the
plasticity–stability dilemma, ART2 is therefore able to retain
existing patterns learned while learning new patterns.
The use of ART2 does not guarantee success in recognizing the
orientations of the feeding parts. Several problems still exist. First, if
the input patterns that belong to different categories are very similar,
the only way to distinguish them is to set a high value for the vigilance
parameter (ρ). However, a high ρ value causes the categories
produced by ART2 to have less generalization ability, and hence, leads to
poor recognition result. Second, when training ART2, a user cannot affect
the learning process because of the self-organizing property. Therefore, a
user cannot instruct ART2 how to learn the input patterns. This can result
in misclassification of the input patterns.
Carpenter et al. (1991a) developed
a supervised neural network architecture called ARTMAP. ARTMAP can
autonomously learn to classify many arbitrarily ordered vectors into
recognition categories based on predictive success. Hence, ARTMAP is also
referred to as predictive ART network, and it is capable of fast, yet
stable, on-line recognition learning and hypothesis testing, given a
stream of input patterns (vectors). Although different ART modules can be
incorporated into ARTMAP networks, here the choice of these modules is to
facilitate on-line training of features of more than one part.
2.1. ARTMAP parameters
The ARTMAP model consists of three parts: ARTa,
ARTb, and the map field. A control structure actively
regulates learning and information flow. ARTa is used
to receive training patterns, and ARTb is used to
receive the target value of each training pattern. During training, a
training pattern a will form a cluster in
ARTa, although its target value b (a category
of a) will also form a cluster in ARTb. The
map field will be responsible for associating these two clusters (e.g.,
a belongs to the b category). During testing, an input
pattern, which is received by the ARTa model, is
assigned to the cluster made by training pattern a; the map field
will associate this cluster to the cluster formed by b in
ARTb as trained before. As a result, this input
pattern is recognized by the ARTMAP model to be the b
category.
In this study, ART 2-A (Carpenter et al.,
1991b) was selected as the ARTa model,
and the ART1 model was selected as the ARTb model.
ART2-A adopts the fast learning version of ART2 to facilitate on-line
training. In addition, the ART2 model differs from the ART1 network
primarily in the implementation of the F1 layer (i.e.,
the input layer). Rather than a single structure of units, the
F1 layer contains a number of sublayers that serve to
remove noise, to enhance contrast, and to normalize an analogue input
pattern. ART2, hence, is suitable for the application here because on-line
learning subjected to noise is an important requirement of the pattern
recognition task of the flexible and programmable vibratory bowl feeder.
According to the training process of the ARTMAP model, different target
values must be assigned to different clusters of ARTb
to represent each category (i.e., the orientation of the part). Therefore,
the clusters formed in ARTb must be very specific. As
a result, the vigilance parameter ρb must be very
high. The value of ρb is set to 0.999, which
implies that the only parameter that governs the training and testing of
the ARTb model of ARTMAP (represented by ART1) is
fixed. Only the parameters of the ART 2-A model, (represented by the
ARTa model of ARTMAP), can be changed when the
performance of ARTMAP is studied.
2.2. ART 2-A parameters
In defining an ART 2-A model, the three parameters that can be changed
during training, and testing phases are α, θ, and ρ. As a
fast learning mode is desirable for rapid recognition of parts, the
learning rate (β) is set to 1.
2.2.1. Parameter α
Parameter α corresponds to the initial value of the components in
ART 2-A F1 (input layer) to F2
(competitive layer) weight vector. The constraint for α is
,
where M is the dimension of the input vector of the ART 2-A
model (i.e., the number of input nodes of the ART 2-A model). Setting
α close to
biases the ART 2-A model toward the selection of an uncommitted node over
committed nodes that only partially match the training pattern. That is,
when α is high, the ART 2-A model biases to form more clusters to
represent the same training patterns compared to the number of clusters
used to train the model when α is low.
2.2.2. Parameter θ
Parameter θ corresponds to the threshold value of the nonlinear
noise suppression and contrast enhancement function that is applied in the
preprocessing layer F0 of the ART 2-A model. The
constraint for θ is
,
where M is also the dimension of the input vector of the ART 2-A
model. The value of θ is critical to the contrast enhancement and
noise suppression of the preprocessing layer. Subthreshold signals of the
normalized input pattern are set to zero, whereas suprathreshold signals
are amplified by the subsequent normalization step at the top
F0 layer.
2.2.3. Parameter ρ
Parameter ρ corresponds to the vigilance parameter value of the
ART 2-A model. The constraint for ρ is 0 ≤ ρ ≤ 1. During
training, the value of ρ determines if a training pattern belongs to a
category that has already been trained or it represents a new category.
During testing, the value of ρ determines whether an input pattern
belongs to one of the trained categories of the ART 2-A model, or it is an
unrecognized pattern.
In the experiments described below, the value of these three
parameters will be varied within the allowable range to see how they
affect the success rate of the ARTMAP model.
3. THE FLEXIBLE VIBRATORY BOWL FEEDER
SYSTEM
Here, the description of the programmable vibratory bowl feeder and
the details of parts used in the experiments provide background knowledge
for the experiments described in Section 5. Figure
1 shows the schematic diagram of the flexible and programmable
vibratory bowl feeding system. It has three subsystems as follows:
- a vibratory bowl feeder,
- a sensing cum recognition subsystem using ARTMAP neural network,
and
- a programmable logic controller (PLC).
A schematic diagram of the feeding system.
Parts poured into the vibratory bowl feeder move along the track of
the feeder. After passing through the wiper blade station (LS1) and
programmable width station (LS2), only parts of certain width and height
are allowed through to the first singularization station (PS1; see Fig. 2), which ensures that only one part at a time
proceeds to the scanning station 1 (PS2). At PS2, each part passes under
three analogue sensors (i.e., S1, S2, S3; see Fig.
2). The analogue signals of the part's surface are sent to the
data acquisition card. These will be converted into digital signals, which
are then processed by the pattern recognition subsystem that is
implemented here using the ARTMAP neural network. Upon recognizing the
part's orientation, a signal will be sent by the computer to the PLC.
If the part is in the wrong orientation, the PLC will send a signal to the
flipping station (PS3) to flip the part. The part then progresses to the
second singularization station (PS4) and the second scanning station (PS5)
to validate if the part is in the correct orientation by passing under
three fiber optic sensors (i.e., S4, S5, and S6). The rotation station
(PS6) will correct an incorrectly orientated part before it moves to PS7
for the next process action.
The singularizing station and scanning station 1. [A color
version of this figure can be viewed online at www.journals.cambridge.org]
4. DATA ACQUISITION AND PREPROCESSING
This section gives an insight into the difficulties faced in data
acquisition, as well as the steps taken to acquire parts' signatures
that may be subjected to noise and likely variations in the loading of the
bowl feeder as parts leave the feeder.
4.1. Feeding parts
Although two similar parts (parts 1 and 2) have been used for the
experiments reported in Sim et al. (2003), here
only part 2 has been used. Part 2 has the dimensions given in Figure 3. It has 24 possible orientations when
traveling on the track of the vibratory bowl feeder. After passing through
the flexible orientating devices (LS1 and LS2), only four of these
orientations are permissible. These orientations are to be recognized by
the neural network system (i.e., the ARTMAP model). Figure 4 illustrates these four orientations and the
corresponding representation codes. Among these orientations, B1 is the
desired orientation of part 2.
Feeding part 2 used in the experiments.
Four feed orientations that ARTMAP should identify.
4.2. Calibration of the analogue sensors
The scanned signature of a part serves as input to the neural network
model whose primary function is to recognize the orientation of the part.
Hence, the quality of the scanned signature is very important to the
pattern recognition capability of the neural network model. If the scanned
signature cannot depict the part's surface correctly, the orientation
determined by neural networks will be incorrect. Therefore, the purpose of
calibration is to adjust the sensors to the correct settings so that they
produce the same readings for a given height of a part. The calibration
can be achieved through a program that gives on-line readings of the
analogue channels.
Part 2, with a flat surface of a height of 5 mm, is first placed under
the sensors. The range of A/D conversion of the data acquisition card
is set from −5 to +5 V. The sensors are calibrated by either turning
the sensitivity notches or adjusting the positions of the sensor tips
until the reading of all three sensors just reached 5 V. This process of
calibration is repeated for all the features of the part (i.e., the
part's flat surface, the groove, and the through hole).
4.3. Settings of the data acquisition card
The pacer rate (p) of the data acquisition card is given
by
where C1 and C2 are the user
programmable parameters of the card. Their values range from 2 to
65,535.
Different pacer rates can result in different data quantity in a given
time. If the rate is too high, a large signature data file will be input
to the neural network. This tends to increase the computation time of the
neural network, which may impede the on-line pattern recognition process.
If the rate is too low, the signature acquired may lose some important
features of the part.
Because the sampling rate can have a significant influence on the
pattern recognition of the neural network, its influence on input data to
the ARTMAP was investigated. When the sampling rates change, the size of
the input data also changes, resulting in a different number of input
nodes for the ARTMAP model. This will affect the range of α and θ
according to the constraint formula given in Sections 2.2.1 and 2.2.2. In
the experiments described below, different sampling rates were used to
acquire the parts' surface signatures. Table
1 shows the sampling rates, the corresponding number of sampling
per sensor, together with the range of values for parameters α and
θ under different sampling rates.
The range of parameters α and θ under different sampling
rates
4.4. Data acquisition
A part's surface is scanned for its surface signature by the
scanning station (i.e., PS2), which consists of three fiber optic sensors
(i.e., S1, S2, and S3). Figure 5 illustrates the
scanning of the parts using part 1 as an example. Scanning begins when
each sensor senses the leading edge of the parts and the data acquisition
card begins the A/D conversion. When the part passes through the
scanning station, the analogue sensors receive the reflected light from
the part, and convert the light signal to an electrical signal depending
on the intensity of the light reflected. The section with a greater
thickness will reflect a stronger light signal back to the sensor because
it is closer to the sensor. Therefore, the sensor transforms a higher
voltage for this section of the part to the data acquisition card. Through
this method, scanned signatures are to depict the profile of a part's
surface. As each sensor acquires 25 data, the data acquisition card
performs 75 times A/D conversion. Hence, the input vector to a neural
network model is fixed at 75.
4.4.1. Scanned signature
Figure 6 shows the scanned signatures of
different orientations of part 2. From the figure, it can be seen that the
scanned signatures depict the features of a part (i.e., the groove and the
through hole). However, the signatures are not stable even for the same
height of a feeding part. This is due to the vibration of the bowl feeder
that imparts a forward and upward flight to a part moving along the
bowl's track.
Scanned signatures of part 2 in different orientations.
4.4.2. Problems of data acquisition
Due to the vibratory agitation of the bowl feeder, Boothroyd et al.
(1982) show that a part can be subjected to
different states of motion during each vibration cycle (i.e., slide
forward, slide backward, and bounce). Although not every state occurs in
each cycle, the different motion states will definitely affect the scanned
signature. For example, the bounced state tends to give rise to unstable
signatures. Hence, due to the presence of the unstable signatures acquired
during the scanning process there is a need for ARTMAP to perform parts
recognition under such noisy conditions. Although there are many types of
scanned signatures that can possibly be acquired by the sensors, here
three different types of scanned signatures are identified for the purpose
of highlighting the need to preprocess the data before they are used as
inputs into the neural network model (see Figs. 7, 8, and 9).
Figure 7 shows the scanned signature of a
feeding part (part 1) that passed through the scanning station at an ideal
speed. The ideal speed is defined as a speed that gives good correlation
between the sampling rate and the parts' speed. If the sample rate is
400 Hz, then this occurs when the whole part will just pass through the
scanning station at the end of 25 times A/D conversion.
A scanned signature of part 1 where the speed is ideal.
Figure 8 shows the scanned signature of part
1 in the same orientation (as that shown in Fig.
7) at a speed that was too slow. It can be seen that the
part's signature is incomplete (i.e., the hole in the left end of the
part's surface cannot be captured). Therefore, slow speed often
causes the loss of the part's feature.
A scanned signature of part 1 where the speed is too
slow.
Figure 9 shows the scanned signature of part
1 in the same orientation at a speed that was too fast. Comparing Figure 9 with Figure 7, it
can be seen that the size of the hole is reduced. In Figure 7, the two zeros representing the hole feature,
but only one zero in Figure 9. Hence, the
scanned signature does not depict the part's actual surface. In
general, a fast speed reduces the part's scanned signature.
A scanned signature of part 1 where the speed is too
fast.
In general, parts traveling at a fast speed or slow speed will present
difficulties in recognizing the part's orientation by the neural
network. Hence, there is a need to ensure that the scanned signatures
should be as similar as possible to that achieved in the ideal speed.
4.5. Data preprocessing: Normalization of the scanned
signature
To overcome the problems described above, data preprocessing of the
scanned signatures called normalization was performed. A more general
solution has been provided by Maul and Jaksic (1994) for parts that are contiguous and overlapping
traveling under different parts velocities using two sensor algorithms and
a variable called “precision” that is dependent on the
part's length in the control program. Here, normalization is used to
expand the short scanned signature proportionally to the correct number of
data readings. For example, in Figure 9, the
first 15 data in the scanned signature are considered as representing the
feature whereas zero readings from the 16th data onward can be considered
as errors as they do not represent the real feature. The portion of the
scanned signature that has erroneous readings will be deleted, and the
useful portion expanded proportionally to the last data (i.e., 25th
value). Figure 10 illustrates the normalized
parts signature of the scanned signature shown in Figure 9. However, the normalized signature may not
always have the fidelity of the original scanned signature.
A scanned signature of part 1 after normalization.
Unfortunately, normalization can only be applied for the parts
traveling at high speed. It is ineffective for the case where the scanned
signature is incomplete (shown in Fig. 8). One
of the ways to solve this problem is to increase the number of the A/D
conversion, so that normalization can be applied to parts with the lowest
speeds. This speed can be achieved by increasing the feeding speed of
vibratory bowl feeder from zero to a value when one of the parts begins to
move.
5. DESCRIPTION OF THE EXPERIMENTS
CONDUCTED
From discussion in Sections 2 and 4, it can be seen that the pattern
recognition capability of the flexible vibratory bowl feeder system is
dependent on two major factors:
- the parameters that influence the formation of clusters in the
structure of ARTMAP and
- the rate of the data acquisition process (i.e., the sampling rate)
and the influence of the mean speed of the parts in the bowl feeder.
Hence, the purpose of the two experiments described here was to
investigate the influence of these factors on the pattern recognition
capability of performance of the system. The two experiments conducted are
referred to as experiment A and experiment B.
5.1. Organization of training and testing set
To investigate the influence of the different parameter settings on
the success rates of the ARTMAP model, the scanned signatures of part 2
were used to train and test the ARTMAP model. The ARTMAP model is trained
to recognize four desirable orientations of part 2 (i.e., 2A, 2B, 2C, and
2D, shown in Fig. 4).
5.1.1. Training and testing sets organization
To investigate the effects of the parameters, all other conditions
should remain unchanged during the experiments. Therefore, the same
training and testing set were required to train and test the ARTMAP model
under different parameter settings. The size of the training set was 20;
the data files that comprised the training set are 2A1–2A5,
2B1–2B5, 2C1–2C5, and 2D1–2D5. The testing set consists
of the training set and all other scanned signature data files for each
orientation.
5.2. Experiment A
The influence of the parameter α on the pattern recognition of
ARTMAP has been investigated by others (Carpenter et
al., 1991a). As mentioned in Section 2, a high α value
biases the ARTMAP model to form more clusters in its
ARTa model to represent the same training patterns.
The purpose of experiment A, therefore, is to investigate the value(s) of
α in the ARTMAP model(s) that will achieve an optimal pattern
recognition capability.
5.2.1. Procedure of experiment A
1. One hundred signatures per orientation of part 2 were
recorded at PS2 of the vibratory bowl feeder and each signature was saved
as a data file in the computer. The sampling rate used was 600
Hz.
2. The values of the parameters (α, θ, and ρ)
that characterize ART 2-A (the ARTa model of ARTMAP)
were selected as given in Table 2. Each ARTMAP
model was trained with the training set as described in Section
5.1.
3. The recognition performance of the trained model was
evaluated using the testing set. The success rate (SR) was calculated as
follows:
4. From the results, the effect of parameters on the
recognition performance was analyzed.
Chosen values for parameters used to form different ARTMAP models
(α, θ, and ρ) in experiment A
5.3. Experiment B
The purpose of experiment B is to study the effect of parameter θ
and the sampling rate on the performance of the ARTMAP model, hence, to
find the optimal values of these two parameters.
5.3.1. Procedure of experiment B
- One hundred signatures per orientation of part 2 were recorded from
the scanning station, PS2 of the vibratory bowl feeder for each of the
sampling rates (i.e., 800 and 1000 Hz), and each signature was saved as a
data file in the computer. In this experiment, the data files recorded in
experiment A at 600 Hz were also included.
- For each sampling rate, the same set of data files was used for
training and testing the ARTMAP models. The size of the training set was
20; the data files that comprised the training sets are 2A1–2A5,
2B1–2B5, 2C1–2C5, and 2D1–2D5.
- A range of values for the parameters θ, ρ, and α was
selected as given in Table 3 for ART 2-A (the
ARTa model of ARTMAP) to form different ARTMAP models.
The values of α chosen were near the optimal value found in experiment
A. Hence, in experiment B, the value of α for each sampling rate
selected is close to
(i.e., α = 0.07, 0.08, and 0.09). Each ARTMAP model was trained with
the training set organized in step 2. The trained models were tested with
the testing set, which has the same sampling rate as the training set. The
success rates of recognition were calculated. From the results, the effect
of parameters θ, ρ, and sampling rate were analyzed.
Chosen values for parameters used to form different ARTMAP models
(α, θ, and ρ) in experiment B
6. EXPERIMENTAL RESULTS
6.1. Results of experiment A
A total number of 48 ARTMAP models was configured using different
combinations of the chosen values of the parameters α, θ, and
ρ; these parameters can have a significant influence on the
performance of ARTMAP. The success rates of parts recognition for these 48
ARTMAP models are illustrated in Figure 11.
The success rate of ARTMAP models composed of different α values.
[A color version of this figure can be viewed online at www.journals.cambridge.org]
From Figure 11, it can be seen that for all
values of θ and ρ, the success rates of ARTMAP models that have
lower α values (α = 0.05, α = 0.01) were not always greater
than the models that have a higher α value (α = 0.09). When the
value of ρ was increased beyond 0.96, the success rates appeared to be
the independent of α for a given value of θ. For each combination
of ρ and θ, where θ > 0.01 and ρ > 0.93, it can be
observed that the success rates of the ARTMAP models were the same for all
the values of α.
The reason why the value of α can affect the success rate of
ARTMAP is due to its influence on the training result of the
ARTa model when subjected to the same training set. As
discussed in Section 3, ARTa models with high values
of α form more clusters to represent the same training patterns
compared to trained models with low values of α. To understand the
influence of α, the training of ARTa in three
ARTMAP models with different parameter setting were studied. For these
models, the values of θ and ρ were set at 0.09 and 0.9,
respectively, but the values of α were varied. Table 4 shows the training results of
ARTa in the three ARTMAP models.
ARTa training results for ARTMAP model using part
2
From Table 4, it can be seen that the
ARTa model formed seven clusters when α = 0.09,
compared to six clusters when α = 0.05. The F2
layer of the ARTa model is a competitive layer in
which only the uninhibited node with the largest net input has a nonzero
activation: that is, the node with the largest input will be chosen to
learn the training pattern. During training, when the training pattern 2A4
(see Table 4) was processed in the
F2 layer, the ARTa model will
choose an uncommitted node rather than a previous committed node (cluster
0) to learn the training pattern when α = 0.09. However, when αs
were set to 0.05 or to 0.01, the ARTa model chose the
previous committed node (cluster 0) to learn the training pattern 2A4,
thus forming less clusters after training.
Different training results led to different testing results. Figure 11a shows the different success rates of the
three ARTMAP models. From the testing results, it can be seen that a high
α value produces a high success rate. That is, for the same values of
ρ and θ, the formation of more clusters in the
ARTa model is indicative that the network is subjected
to better training for a given training set. From Table
3, because the training resulted in the same number of clusters
being formed when α = 0.05 and 0.01, the success rates for the two
ARTMAP models were also the same. It can also be seen that α tends to
loose its influence on training when the value of vigilance parameter
ρ was increased. This is because when the value of ρ increases,
the criteria that the ARTa model commits a node to
learn new training pattern becomes stricter. When training an ARTMAP model
with a low α value, the selection of the committed node to learn a new
training pattern will be rejected by the reset process of the
ARTa model because of the increased ρ value. The
results shown in Figure 11 indicate that setting
α close to its upper constraint value
can result in a better success rate of the ARTMAP model in this feeding
system for values of ρ < 0.93.
6.2. Results of experiment B
From Table 3, it can be seen that there were
three training and testing sets organized for three different sampling
rates (i.e., 600, 800, and 1000 Hz, corresponding to α = 0.09, 0.08,
and 0.07, respectively). Hence, for each sampling rate, values were chosen
for parameters θ and ρ to form 40 different ARTMAP models. To
compare the recognition performance of these 40 models, each of these
ARTMAP models was trained and tested by the same training and testing set,
respectively.
Figures 12 and 13
show the success rates of these 40 ARTMAP models for sampling rates of 600
and 1000 Hz, respectively. It can be seen that the trend of success rates
of the ARTMAP models for each sampling rate has something in common.
First, the success rate decreases when the value of ρ increases close
to 1.0, its upper constraint value. Second, the highest success rate
always occurs when θ = 0.01. Third, the success rates of ARTMAP
models with higher θ values are always lower than that of ARTMAP
models with lower θ values for the given ρ value.
The success rate of ARTMAP models composed of different θ and
ρ values (sampling rate = 600 Hz, α = 0.09). [A color version
of this figure can be viewed online at www.journals.cambridge.org]
The success rates of ARTMAP models for different values of θ and
ρ (sampling rate = 1000 Hz, α = 0.07). [A color version of
this figure can be viewed online at www.journals.cambridge.org]
It can be seen that increasing the sampling rate did not increase the
success rate significantly, because ARTMAP models can achieve high success
rate for each sampling rate. However, increasing the sampling rate does
increase the stability of the scanned signatures of the feeding part. This
can be seen from the success rates when ρ = 0.99; the higher sampling
rate always produce a higher success rate than the lower sampling rate.
Hence, stable scanned signatures may indicate that the success rate of the
ARTMAP model is less affected by the parameter settings.
Figures 12 and 13
show that the success rates decrease when ρ tends to the value of 1.0.
This can be explained by the fact that the generalization ability of each
cluster formed in the ARTa model decreases when ρ
increases. Therefore, less testing patterns can be correctly recognized
for a higher ρ value if the testing patterns that belong to the same
cluster are not very stable. Because of the vibration of the feeding
system and the manufacturing tolerance of the feeding parts, it is
expected that differences do exist among the scanned signatures even for
the same orientation. Hence, if clusters that represent the part's
orientations do not exhibit sufficient generalization ability, the success
rate will be affected.
However, not every increase of the ρ value leads to a decrease in
the success rate. From Figure 12, it can be
observed that the success rates of the ARTMAP models remain fairly
constant for certain range of ρ (0.9–0.94). This is due to the
similarity of the input patterns that belong to the same cluster. If the
input patterns are sufficiently similar it can be seen that over a certain
range of values of ρ, the success rates do not vary significantly.
However, when ρ is increased close to its maximum limit of 1, the
generalization ability of the network tends to decrease. When this
happens, any difference between training and testing patterns will cause
error for the ARTMAP model. Therefore, the success rate decreases
dramatically. From Figure 12 it can be seen that
the success rates of the ARTMAP models tested for different ρ values
have some fluctuation when θ = 0.09 and 0.06. The same inference can
be derived for Figure 13 when θ = 0.07 and
0.05. As discussed in Section 2, the ARTa model tends
to form more clusters when ρ is increased.
To explain the influence of ρ on the number of clusters formed,
the training results of ARTa for the success rates
shown in Figure 12 when θ = 0.09 were
tabulated in Table 5 for different values of
ρ. From Table 5, it can be seen that the
ARTa model formed seven clusters when ρ = 0.91
compared to eight clusters when ρ = 0.92. Due to the increase in the
number of clusters formed, the success rate of the ARTMAP model when ρ
= 0.95 is lower than that of the model when ρ = 0.93. Hence, it can be
seen that as ρ tends to be 1, the success rates for the ARTMAP models
shown in Figure 12 tend to decrease.
ARTa training results for training part 2 using ARTMAP
model
7. DISCUSSION
Experiments A and B investigated the effect of the parameters of the
ARTMAP model on the pattern recognition capability as measured by the
success rates. The experimental results show that to achieve a better
success rate of pattern recognition by the ARTMAP model, the α value
should be set close to
,
and the θ value should be set very small such as 0.01 for each
sampling rate. Hence, for given values of α and θ, the results
indicate that an optimal value of the vigilance parameter ρ can be
selected. For example, in Figure 12, when θ
= 0.01 and α = 0.09, the highest success rate of the ARTMAP model was
99% was achieved when ρ values vary from 0.90 to 0.95. To select an
optimal value for ρ, there is a need to consider the two types of
errors in the ARTMAP models, namely the misclassified error and the
unrecognized error. The misclassified error occurs when a certain
orientation of the feeding part is recognized by the ARTMAP model to be
that of another orientation. For example, a part moving in orientation 2A
may be recognized by the ARTMAP model to be moving in orientation 2C. The
misclassified error can cause the feeding parts to remain in the undesired
orientation when they exit the feeding system, making the feeding system
unreliable. The unrecognized error occurs when the part's orientation
cannot be recognized by the ARTMAP model. The unrecognized error will
cause the rejection station to reject the feeding part, resulting in
recirculation later. Therefore, it will not contribute to the error of the
feeding system.
For these reasons, the error of the ARTMAP model should consist only
of the unrecognized error. In this case, the error of the ARTMAP models,
which were tested in experiment B, was investigated. Figures 14 and 15 illustrate the
number of misclassified errors (Fig. 14) and
unrecognized errors (Fig. 15) for a sampling
rate of 600 Hz.
The misclassified error distribution of ARTMAP models using different
values of θ and ρ (sampling rate = 600 Hz, α = 0.09). [A
color version of this figure can be viewed online at www.journals.cambridge.org]
The unrecognized error distribution. [A color version of this
figure can be viewed online at www.journals.cambridge.org]
From these figures it can be seen that the misclassified error
decreases when the value of the ρ value increases, whereas the
unrecognized error increases when the ρ value increases. This is
because when ρ is increased, the clusters formed in the
ARTa model become more specific, hence causing the
misclassified error to decrease and the unrecognized error to increase.
When the ρ value is increased to a certain value, the misclassified
error decreased to zero, and only the unrecognized error is left. However,
when the ρ value was too high (i.e., close to 1), the unrecognized
error becomes very large because the generalization ability of the
clusters formed in the ARTa model becomes almost
nonexistent. Therefore, the optimal ρ value for maximum recognition is
achieved when the misclassified error approaches zero. From Figures 11, 12, 13, 14, and 15, it is reasonable to infer that this optimal value
for ρ is 0.96 or 0.97. For example, when the sampling rate is 600 Hz,
α is 0.09 and θ is 0.01; as shown in Figure
12, the maximum success rates were achieved when ρ = 0.96 and
0.97, and the misclassified error as indicated in Figure 14 is 0. Although the success rate is not the
highest, it can ensure the reliability of the feeding system. Therefore,
the optimal ρ value for the ARTMAP model of the feeding system should
be set to 0.96 or 0.97.
8. CONCLUSION
By using a flexible and programmable vibratory bowl feeder as the
testbed for the identification and orientation of parts, this paper has
demonstrated that ARTMAP is an appropriate neural network for the on-line
pattern recognition of moving parts with varying mean speeds whose
patterns are time sensitive and subjected to noise. ARTMAP that learns
under supervision incorporates ART2-A as the ARTa
model, which receives training patterns, and ART1 as the
ARTb, which receives the target value of each training
pattern. It has been shown that the pattern recognition capability of
ARTMAP is related to the parameter settings of ART2-A through α,
θ, and ρ.
The scanned signatures of the moving parts were acquired through
optical sensors using varying sampling speeds that have a direct influence
on the size of the input vector to the neural network model (i.e.,
ARTMAP). The size of the input vector is governed by the parameter α.
From the results of the experiments, it has been shown that the values for
parameter α should be set as close to
as possible. Because the scanned signatures are subjected to noise, the
noise suppression and contrast enhancement feature of ART2-A governed by
θ should be set a low value (e.g., 0.01) for a given sampling rate.
Under these settings of α and θ, the optimal value for the
vigilance parameter is from 0.96 to 0.97 to achieve high success rates for
pattern recognition.
It is reasonable to suggest that similar applications that involve the
task of pattern recognition of moving parts can benefit from the use of
ARTMAP as a neural network model for pattern recognition provided
appropriate values are chosen for parameters that govern the size of the
input vector α, the noise suppression and normalization of input
vector θ, and the vigilance parameter ρ that discriminates
between different classes of patterns. If fast learning of patterns is a
requirement, then ART2-A should be used in receiving input patterns for
the ARTMAP model and the learning rate set to 1.
