Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 3 (December 2017) 205–208___________________________________________________________________________________________________________Parameter Estimation of a Skill Evaluation ModelKazuo Kawada

Department of Technology and Information Education, Hiroshima University,
1-1-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8524, JapanTeruyuki Tamai

Matsuyama City Kamogawa Junior High School,
2-7-19 Kamogawa, Matsuyama, Ehime 791-8004,JapanToru Yamamoto

Division of Electrical, System and Mathematical Engineering, Hiroshima University,
1-4-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8527,JapanE-mail: kawada@hiroshima-u.ac.jp, E-mail: tama.wr@gmail.com, yama@hiroshima-u.ac.jp
www.hiroshima-u.ac.jp

Abstract
In this study, the aim is to construct a "teacher-student model" for optimal skill acquisition. To support the optimal
skill acquisition, modeling and estimation of an individual learning process are very important. The first-ordersystem with time delay is introduced as an individual learning process model based the control engineering
approach. These system parameters included in the skill evaluation model are estimated by using a real-coded
genetic algorithm. In order to evaluate the effectiveness of the proposed scheme, it is employed for the parts
classification task.
Keywords: Skill evaluation model, Teacher-student model, Learning process, First-order system, Real-coded
genetic algorithm, Parameter estimation.

delay" system in the control engineering1. The meaningof each parameters of the time constant T, time delay L
and system gain K in the model of skill evaluation
model was considered. However, it has not been studied
how to estimate parameters of skill evaluation modelfrom initial learning data. In this paper, the estimate
method of the skill evaluation model is proposed byusing real-coded genetic algorithm2 (GA) frommeasured trial data. In addition, the results of estimating
the parameters of the skill evaluation model from theinitial learning performance data are also discussed.

1. Introduction
In order to effectively promote skill acquisition in thelearning and the work, it is necessary to grasp thelearning situation of individual learners and workers andto appropriate support based on the learning situation.
From the initial learning performance, if the futurelearning process can be predicted based on individual
learning characteristics, the optimum learning support
according to individuals can be performed. In responseto that problem, the modeling was proposed in whichskill evaluation was regarded as "first order + time

Copyright © 2017, the Authors. Published by Atlantis Press.
This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
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Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 3 (December 2017) 205–208___________________________________________________________________________________________________________2. Parameter Estimation of Skill Evaluation Model

where T denotes the time constant, K denotes the systemgain, and L denotes the time delay. The method tocalculate these parameters (T, K and L) from measured
trial data.
The procedure for obtaining T, K and L from themeasured trial data is as follows.
[1] Measure each response time TR [1... n ] from 1
time to n times.
[2] a , b and c included in the following Eq.(2) arecalculated by the real-coded GA. The estimatedresponse time required for the n-th task is asfollows:

2.1. Fitness value considering characteristics of skill
evaluation modelIn order to estimate parameters of the skill evaluation
model, it is necessary to eliminate variations in task
execution time. Such variations can be divided into twofactors: task factors and learner's factors. Variations due
to task factors are changed due to the order of tasks to
be started from among many tasks. On the other hand,the variation due to the learner's factors changes due toaccidental delay in execution time or trial and error.
Therefore, the estimation of the skill evaluation model
excluding learner's factor variations is considered using"part classification task" with small variations due to thetask factors.

(2)TˆR [n] = aˆ + bˆe − cˆt [ n ]where t [n] represents the real learning time from
1 time to n times, and is expressed by thefollowing equation.
nt [n] = ∑ (TR [i ] − aˆ )2.2. TKL model
As a requirement of the skill evaluation model, thefollowing is necessary.
1) It is exponential.
2) The parameters can be determined individually.
Generally, the controlled object given in the higher
order system is described as the "first-order + timedelay" system, and the control system is designed byrough system characteristics. In this paper, it is difficult
to make the skill evaluation model strict. However, if
the reference is set at the learning start, it can be
represented by the model shown in Fig. 1.

[3] Calculate T, K and L by the following equation,using a , b and c obtained using the real-coded
GA.

1,cˆ
L = TR [1] − aˆ

T=K = bˆe− cˆ L

(4)
(5)
(6)

3. Parameter Estimation using Genetic Algorithm
The parameters a , b and c of skill evaluation modelare arranged as cells included in a string, whose
structure is shown in Fig. 2. These parameters includedin the string are given by real values. The real-coded
GA is employed, which is explained as follows.
(i) Initialization
The generation number G is set, and the initialindividuals are produced with random real-codes
within the initial domain which is set in advance.
Here, the number of population is set as N .
(ii) Selection
The fitness value f (l ) is calculated which isgiven byFig. 1 Skill levels and learning time.

t endf (l ) = 1 /{1 + ∑ (TˆR [k ] − TR [k ]) 2 .

“First order + time delay” system (TKL model) is
described in the following equation.

K − LsG(s) =e
1 + Ts

(3)

i =1

k =1

(7)

where TˆR and TR respectively denote thelearning time and the estimated learning time by
the parameters of skill evaluation model a , band c . Each individual Pl is arranged in order,

(1)

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Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 3 (December 2017) 205–208___________________________________________________________________________________________________________based on the fitness value. Then, α percent
individuals with superior fitness values areselected, and saved in the next generation.
(iii) Crossover
The (100 − α ) percent remaining are generated
by the crossover. Two individuals, Pa and Pb
are chosen from among the superior α percent,and new individuals Pc and Pd are generated
by employing the following procedure:

Pd (i ) = Psup (i ) +Pa (i ) − Pb (i )4
Pa (i ) − Pb (i )4,a b cPFig. 2 Structure of the GA string.

(8)

Initial Individual Population

(9)

abc

P2abc

P3abcP4abc...

where Psup in Eq.(8) and Eq.(9) refers to theindividual with the superior fitness value, i.e.,
Pa or Pb . Note that this procedure is employed
for every cell included in Pa and Pb .
(iv) Mutation
Of all individuals which are randomly selected
and given by the crossover, β percent arechosen and replaced with randomly determinedvalues within the initial domain.
(v) Update
The procedure from (i) through (iv) is repeatedfor generations.
This procedure is summarized in Fig. 3.

P1

PN

...

Pc (i ) = Psup (i ) −T = 588 , K = 176 and L = 178 were obtained byusing these values a , b and c . Fig.5 is shown fromthese T, K and L.
Next, Fig.6 shows the relationship between the initial
learning point and the estimated parameters. From thisfigure, it is clear that T, K and L are almost possible toestimate at the initial learning 4 points.

abc

Fitness function

Selection
abc

P6

abc

6.6

4. Experimental Results for Part Classification
TaskPN

abc

P1

abc

5.7 generation

The parameters T, K and L of the skill evaluation modelof the parts classification are calculated and considered.
The fourteen kinds of parts shown in Fig. 4 were placedin the mixed state, and tasks for classifying the same
parts were prepared. The number of each part is shownin Table 1. The subject was a university student, and hehad no experience of executing parts classification task.
Subject took 3 minutes break and between each task,
and carries out the total of 11 tasks and measured thetime required for each task. The execution results areshown in Table 2. It was reduced from the required time
179[s] in the first task to 54[s] in the 11th task. The skill
level is the time obtained by subtracting the minimum
required time a from the response time in each task inTable 2, and the learning time to each task is the skill
level added.
a , b and c were searched by using the real-coded GA,
a = 0.13 , b = 238 and c = 0.0017 were obtained. T, Kand L were obtained from Eq.(4)-Eq.(6), and...

f(ｌ)

P9P3

8.7

Next

3.7

b...

...
aHighc0.3

Low

Crossover
Parenats

ChildrenPa

PcPbPdMutation
β% cells are replaced with random values.
ChildPabc

Fig. 3 Calculation flow of the evolutionary computation.

207

T

Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 3 (December 2017) 205–208___________________________________________________________________________________________________________(b)(c)(g) (h)(d) (e) (f)

(i)

(j)

(k) (l)

K

(a)

(m)

L

Fig. 4 Parts to be classified.
Table 1 Number of parts.

Fastener Components
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)

Number2020202010101020
10520
2020

Initial learning points
Fig. 6 Relationship between initial learning points andestimated parameters.

5. Conclusion
In order to realize an optimum learning support system
by individual skill evaluation in the learning process,the validity of the skill evaluation model based on thecontrol engineering approach was discussed. Next, byapplying to the classification work of parts, parametersof the skill evaluation model are estimated from theresults of the initial learning, and the effectiveness wasshown. In the future, it will be applied to thecomputational learning etc. and plan to develop thelearning support system.
This work was supported by JSPS KAKENHI Grant
Numbers JP16K12760, JP16H02921.

Table 2 Number of task and response time.
Number of Task
1234567891011t [s]
179
310
441
534612697754813
867917971

TR [s]
179
1311319378855759545054

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140

Degree of Skill

12010080604020T =588, K =176, L=178

0-20100

200

300

400

500

600

700

800

900

1000

Learning time t [s]Fig. 5 Estimated skill evaluation model.

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