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Research on Discretization Algorithm of Continuous Attribute Based on PCNN in a Bridge Erecting Machine Safety Monitoring System Na Chen1,2, Shaopu Yang2, Cunzhi Pan2, and Erfu Guo2 1

School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China 2 Shijiazhuang Tiedao University, Shijiazhuang, China [email protected]

Abstract. PCNN (Pulse Coupled Neural Network) model is suitable for implementing clustering algorithm because of its unique neighbor coupled feature. This paper presented a new discretization algorithm of continuous attribute based on simplified PCNN model. Measured signals of the bridge erecting machine safety monitoring system are computed on this algorithm. Then decision rules are gained by using Rough Sets model to analyze the discretized result, among which the ratio of deterministic rules is 100 percent. Obviously it improves the certainty of decision and analysis better. Keywords: PCNN (Pulse Coupled Neural Network), discretization, a bridge erecting machine, safety monitoring, Rough Sets.

1 Introduction The function of discretization of continuous attribute is to extend learning algorithms in discretized space to continuous feature space[2]. Through discretizion of feature space or dimension reduction, more simplified classifier can be obtained, which reduces data storage space, enhances learning speed and precision. It is a valid pretreatment method for many knowledge discovery systems such as Rough Sets theory[1]. Normal discretization algorithms are equal-width, equal- frequency, k mean value, etc. We apply some kinds of discretization algorithms to measured continuous signals of the bridge erecting machine safety monitoring system and combine feature extracted to divide the objects in the universe. As a result there are errors in the classification, which makes the presence of nondeterministic rules after decision and inference. Therefore, in this paper we present a new discretization algorithm[3] of continuous attribute based on PCNN in order to decrease or remove the false division and the nondeterministic rules and to enhance the certainty in decision making. Simulation experiment is made by using measured signals of the bridge erecting machine safety monitoring system, and comparative analysis is also done among some different kinds of algorithms. D. Zeng (Ed.): ICAIC 2011, Part II, CCIS 225, pp. 708–714, 2011. © Springer-Verlag Berlin Heidelberg 2011

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2 Description of Discretization Problem The process of discretization of continuous attribute can be described as following. By selecting proper division points the whole value domain of continuous attribute can be divided into several intervals, and each interval is given an integer to denote this interval’s attribute value. At the same time, computing method for corresponding discretized interval of any point in the value domain is provided. A decision information S=(U,A {d},V,f) consists of :U is a nonempty, finite set called universe; A is a nonempty, finite set of attributes; A is a finite set of condition attributes and{d} is a finite set of a decision attribute; V= Va , in which Va is called the domain of a; f ∪ is an information function f: U × A→V.

∪

∈ A, a∈ A

if va = [la , ra ) ⊂ R is its value domain, in which R is a set of real numbers. A partition of va is defined as For each a

pa = {[c0a , c1a ],[c1a , c2a ],⋅ ⋅ ⋅, [ckaa ckaa ]} where la = c0a < c1a < c2a < ⋅ ⋅ ⋅ < ckaa < ckaa +1 = ra ;

va = [c0a , c1a ) ∪ [c1a , c2a ) ∪ ⋅ ⋅ ⋅ ∪ [ckaa , ckaa +1 ) .

The set of cuts of a is defined as C = {Ca | a ∈ A} . And a partition P of A is uniquely denoted as sets of sets C, shown as P

P = ∪ pa .Obviously, a∈A

P converts S into a

discrete system S , and S = (U , A ∪ {d }, V , f ) is the so-called discretization of S, where A P = {a p : a ∈ A} and a P ( x) = i ⇔ a( x) ∈ [cia , cia+1 ] . P

P

3 Clustering Algorithm Based on PCNN PCNN is called as the 3rd generation artificial neural network[7], which is presented by Eckhorn according to synchronizing pulses of animals’ cerebral vision cortex. PCNN has embodied its advantage and applied to fields such as image processing, object recognition, communication synchronization, pattern recognition and decision optimization. In this paper we use PCNN simplified model, in which the input of the model is one-dimensional attribute value and the classification result is described by the pulsed time. A. PCNN simplified model Fi [n] = S i

(1)

Li [ n] = ∑ wik Yk [n − 1]

(2)

U i [ n] = Fi [ n](1 + β Li [ n])

(3)

⎧1, U i [n] > θ i [n] Yi [ n] = ⎨ ⎩0, U i [n] ≤ θ i [ n]

(4)

θ i [n] = αθ i [n − 1]

(5)

k

In the above equations, Si is external input excitation; Fi is input item; Li, Ui, Y and θi are respectively link input, interior activity item, pulse output and dynamic

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threshold; w denotes neighborhood neuron; β is link intensity; α is attenuation coefficient of threshold; n is iterative times. B. Algorithm description In the algorithm, threshold θ is initialized by the maximal attribute value, and each neuron is on the extinction state. With threshold decaying, the neuron of bigger attribute value is fired firstly when the result of (4) is 1. In next iteration, when n increases, (2) can generate link input L from fired neighbor neurons. And the generation of link input increases the interior activity U in (3). Then the neuron with increased interior activity maybe fired in (4). That is to say, neurons fired firstly increase their interior activity through their neighborhood link input. At the same time dynamic thresholds decrease with iteration going. Finally all the neurons are fired. Only but the time when each neuron is fired is different. And the order of firing time is the classificatory information we need.

4 Processing Measured Data on PCNN Model In the bridge erecting machine wireless sensor safety monitoring system, the whole work process can be divided into 9 steps, and they are static preparation, front end lifting, first beam moving, rear end lifting, rear end lifting, second beam moving, beam placement, installing beam, lower leading beam moving and lengthways moving. According to theoretical and practical testing, the signals collected from the sensor point of inside of frange plate at the bending of rear landing leg are the most sensitive and valid[5]. Therefore, in this paper we verify discretization algorithm based on signals at this monitoring point. A. Creating decision table With collecting signals from the sensor position of inside of frange plate at the bending of rear landing leg and recording the whole work process of the bridge erecting machine, we extract features from measured signals in different work steps. Table 1. sampling 1 2 3 4 5 6 7 8 9 10 11

3.8230 4.7386 3.8326 4.2204 1.9428 1.9738 1.8814 2.0670 4.7489 5.8826 4.7502

IF

CG 0.1312 0.1405 0.1320 0.1643 0.0405 0.0468 0.0384 0.0486 0.0870 0.0933 0.0838

Dx 0.7402 0.6686 0.7362 0.6210 12.6971 0.6385 11.6192 2.2126 16.7771 17.1638 9.8428

α4 0.8225 2.7702 0.8050 0.6654 2.8579e+003 1.0178e+003 3.0265e+003 858.6449 1.0695e+003 651.7212 485.4563

D 1 1 1 1 2 2 2 2 3 3 3

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Table 1. (continued) samplings 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

3.5733 2.6048 2.5867 3.7712 5.2563 1.4880 2.8751 1.6313 2.0872 2.3612 4.3385 1.9295 4.4534 1.6866 6.2410 2.4235 4.6895 3.4916 5.1548 2.7515 3.9822 2.5219 5.8330 2.5074 5.5663

IF 0.0531 0.0457 0.0425 0.0241 0.1600 0.0553 0.0501 0.0340 0.0510 0.0211 0.0493 0.0173 0.0639 0.0216 0.1731 0.0245 0.0885 0.0620 0.0777 0.0298 0.0693 0.0174 0.0927 0.0172 0.0874

CG

Dx

18.8545 2.7753 0.3228 7.4257 1.2037 0.5338 0.5926 6.5953 0.8104 1.9801 6.3736 0.4526 0.7362 0.6209 0.3786 1.1222 2.6811 1.3613 0.6040 1.0718 0.3746 4.2128 0.6628 4.0619 0.9764

α4

D

670.8314 545.2688 413.8693 3.4975e+003 174.5679 496.1297 436.9572 1.0539e+004 893.7270 6.5352e+003 437.8209 4.8963e+003 536.5724 4.3107e+003 5.3436 2.5721e+003 43.3860 2.1714e+003 45.0176 1.6041e+003 48.7299 1.5357e+004 13.6522 1.5419e+004 28.3394

3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9

The feature IF denotes the complexity of FFT spectrum; CG is the central frequency of spectrum; Dx reflects square deviation of time series and displays unstable degree of time domain; α4 denotes peak value of time series. We set feature set of {IF,CG, Dx, α4} as condition attribute and set work step as decision attribute D. And information decision table[4] can be created and shown as table 1. B. Discretization based on PCNN clustering algorithm We treat many samplings of different work steps as nerve cells, make condition attribute set as neuron input and set up PCNN model. Applying pulsing time as classification standard, discretization results of each attribute can be gained, shown as table 2.

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IF

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

3 2 3 2 4 5 5 4 2 1 2 3 4 3 2 1 5 4 5 4 3 2 3 2 3 1 3 2 2 1 3 3 3 1 2 1

CG 1 1 1 1 4 4 4 3 2 2 3 4 4 4 5 1 3 4 5 4 5 4 5 3 5 1 4 2 3 3 4 3 5 2 5 2

D

α4

Dx 4 4 4 4 1 3 1 2 1 1 1 1 2 4 2 3 4 4 2 4 3 2 4 4 4 5 4 3 3 4 4 4 2 3 2 3

5 4 5 5 1 2 1 2 2 2 2 2 2 2 1 2 2 2 1 2 1 2 1 2 1 4 1 3 1 3 1 3 1 3 1 3

1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9

C. Setting Parameters There are two parameters in our PCNN simplified model. They are respectively dynamic attenuation coefficient of threshold α and link intensity β. The dynamic attenuation coefficient of threshold α decides attenuation speed of threshold, and it also effects pulsing times of neurons. We can conclude from (3) that activity of neuron is not only decided by its input stimulation but also by the states of neurons in neighborhood. Therefore dynamic attenuation coefficient of threshold α has limit influence on pulsing time. In our model a same dynamic attenuation coefficient of threshold 0.45 is set according to different condition attribute. That is to say, the key

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of PCNN model considers neighborhood information and reflects increasing interior activity of neighboring neurons, which can make the time of neuron pulsed earlier and make neurons with similar value or close position being pulsed more possibly. And so link intension β is a very important parameter that affects pulsing time of all the neurons through link relationship among neighborhood neurons. Considering the four condition features from left to right in table 1, we set value 0.8, 0.7, 0.4, 0.1 to link intense parameter for each feature in turn. D. Comparative analysis for several different algorithms Decision table is gained after discretization based on PCNN clustering. Combining rough sets model we obtain decision rules by processing the discretized decision table[6]. According to attribute value of different feature the current work condition can be derived, which can direct controlling and monitoring better. 25 rules are gotten from our model, which are all deterministic and improve the certainty of decision. In this paper equal-frequency and FCM discretization algorithms are also applied to the same information decision system, in which rules are gained too. The number and certainty ratio of these rules are listed in table 3. Table 3. Discretization algorithm

Number of rules

Equal-frequency Based on FCM Based on PCNN

33 26 25

Number of deterministic rules 32 22 25

Number of indeterministic rules 96.9% 84.6% 100%

In the three algorithms above, each attribute is classified into 5 classes. Under the situation of similar knowledge granularity, the ratio of deterministic rules is 100 percent computed by discretization algorithm based on PCNN. It accounts for the validity of this algorithm in analyzing measured signals in the bridge erecting machine safety monitoring system.

5 Conclusion PCNN is a kind of new neural network model, and its core is coupling mechanism in neighborhood. The order of pulsing time denotes the result of neuron clustering. In this paper we present a new discretization algorithm of continuous attribute based on PCNN clustering. Aiming at measured signals in the bridge erecting machine safety monitoring system, we have gained discretizied result. Combining rough sets model with discretized result, decision rules are obtained, in which the ratio of deterministic rules is 100 percent. Compared with other algorithms, the algorithm based on PCNN has improved the certainty of decision analysis. And it has a good guidance for controlling and monitoring in actual application system.

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Although two parameters in our PCNN model are discussed, self-adaptive empirical parameters have not been realized in this paper, which should be improved later.

References 1. Pawlak, Z.: Rough set. International Journal of Computer and Information Science 11, 341–356 (1982) 2. Lenarcik, A., Piasta, Z.: Discretization of condition attributes space. In: Intelligent Decision Support, pp. 373–389. Kluwer, Dordrecht (1992) 3. Dougherty, J., Kohavi, R., Sahami, M.: Supervised and unsupervised discretiazation of continuous features. In: Proc. the 12th International Conferece, pp. 194–202 (1995) 4. Slowinski, R.: Intellligent Decision Support. In: Handbook of Applications and Advances of Rough Sets Theory. Kluwer Academic Publishing, Dordrecht (1992) 5. Chen, N., Yang, S., Pan, C., Tang, Y.: Research on Validity of Sampling Points in a Bridge Erecting Machine Safety Monitoring System using Variable Precision Rough Sets. In: 2010 3rd International Conference on Computer and Electrical Engineering (2010) 6. Ziarko, W., Slowinski, R.: Rough set approach to multiattribute decision analysis, Invited Review. European Journal of Operational Research 72, 443–459 (1994) 7. Johnson, J.L., Padgett, M.L.: PCNN Models and Applications. IEEE Trans. on Neural Networks 10(3), 480–498 (1999)