CC BY
27Electronic Journal «Technical Acoustics» http://webcenter.ru/~eeaa/ejta/
2005, 22
Hitoshi Ogawa1 , Mitsuo Ohta2, Hirofumi Iwashige3
1 Faculty of Management & Information Systems, Prefectural University of Hiroshima 1-1-71 Ujina-Higashi, Minami-ku, Hiroshima City, 734-8558 Japan 2Professor Emeritus of Hiroshima University 1-7-10-1106Matoba, Minami-ku, Hiroshima City, 732-0824 Japan 3 Graduate School of Education, Hiroshima University 1-1-1, Kagamiyama, Higashi-Hiroshima City 739-8524 Japan
Some objective and subjective evaluation methods for room sound, illuminance, temperature and electromagnetic environment
Received 04.05.2005, published 01.08.2005
It is very important to explore the compound effect of heterogeneous environmental factors for improving the quality of living environment with popularization of electronic and/or information equipments. First, for an objective evaluation, three kinds of environmental factors: sound, illuminance and
electromagnetic field of video (or visual) display terminal (VDT) are focused, especially from a stochastic viewpoint. From this experiment, some mutual correlation between sound and illuminance in peripheral environment of VDT was found. And also, another mutual correlation between electromagnetic field and
illuminance environment of VDT was obtained. Secondly, for a subjective
evaluation, three kinds of environmental factors: sound, temperature and
illuminance are especially focused. If an optimum relationship among these environmental factors can be found, it seems that some improvements of our living environment can be discussed from psychological and/or stochastic viewpoint. From these studies, subjective and objective evaluation methods for room environmental factors will be considered.
1. INTRODUCTION
Nowadays, in our modern living environment like home, office and/or car rooms, along with rapid popularization of electronic and/or information technology, it is well-known that an effect of electromagnetic wave has to be taken into consideration as one of physical environmental factors in addition to the effect of sound, illuminance, temperature, moisture, ventilation, etc. So, more than two kinds of heterogeneous environmental factors affect each other. The combined effects of environmental factors lead to complex interactions. It is very important to explore the compound effect of heterogeneous environmental factors for improving the quality of residential environment in our daily life. First, for an objective evaluation, we focus on three kinds of environmental factors: sound, illuminance and electromagnetic field of VDT, especially from a stochastic viewpoint. From this experiment, some higher order mutual correlation between sound and illuminance in peripheral
Corresponding author, e-mail: [email protected]
environment of VDT and also another mutual correlation between electromagnetic field and illuminance environment of VDT were found, though it is at an early stage of study. Next, for a subjective evaluation, we focus especially on three kinds of environmental factors: sound, temperature and illuminance. Our human subjects were exposed to above three factors simultaneously in an experimental climate chamber. If an optimum relationship among these environmental factors is found as little as possible even in a linear correlation form, some improvement of our living environment seems to be able to be discussed from psychological and/or stochastic viewpoint. From these studies, objective and subjective evaluation methods for room environmental factors will be considered to make our living life comfortable.
2. OBJECTIVE EVALUATION INEXPLICITLY CONCERNED WITH HUMAN CHARACTER
2.1. Extended regression analysis based on the objective viewpoint
Along with the previously published papers [1-4], in order to evaluate quantitatively and hierarchically the complicated relationship between two wave environmental factors (e.g. sound and light) leaked from many electronic information equipments, first, let us introduce some generalized regression analysis method [5] employing not only the linear correlation but also the nonlinear correlation information among many stochastic environmental variables. Especially, in the case with a prediction variable x and a criterion variable y , it must be noticed that every information on mutual correlation of lower and higher orders between them is included in the conditional probability distribution P(y|x):
the random variables. Thus, the information on the various types of linear and nonlinear stochastic correlations between x and y is reflected hierarchically in each expansion
coefficient Amn [6].
After employing an orthogonal series expansion expression of y appearing in Eq. (3) and
(1)
(2)
where P0(y) denotes the fundamental probability distributions of y . ^(x) and ^2)(y) are the orthonormal polynomials with two weighting functions P0 (x) , the fundamental probability of x, and P0 (y), respectively. (•) denotes an averaging operation with respect to
the orthonormal condition of ^2)(y) , the regression function as a typical regression relationship between x and y can be explicitly given in Eq. (4), as follows:
y=E C1 MP(y),
j=0
w 1
EIC1nA^^^)(x)
(y|x)=^----------------=
()i
(3)
E Am0^!»)(x)
(4)
m=0
where the expansion coefficients C10 and C11 are calculated in advance through the
realization of the orthonormal polynomial ^(y). Thus, after estimating the expansion
coefficient Amn defined by Eq. (2) on the basis of the observed data on x and y , the
regression function between x and y can be evaluated.
Furthermore, a specific probability distribution Ps (y) of y based on an arbitrary type
random fluctuation of regressively related stochastic variable x can be predicted by an averaging operation based on Eq. (1), as follows:
w
Ps (y)=(P(y|x ))x = p0 (y )E Bn^( )(y),
n=0
(5)
r w \
E AmnP(m)(x)
m=0
E Am0^^)(x)i
(6)
m=0
Concretely, the well-known normal distribution can be practically introduced as two fundamental probability functions P0 (x) and P0 (y). By utilizing Hermite polynomials H t (•),
the regression function (y|x) in Eq. (4) and the regression parameter Amn in Eq. (2) can be
realized respectively, as follows:
E a..
CHx) = My +CT,
m=0
4m!
H
E a.
yfm\
A = ( — mn \ / T
iVm!
Hm
x zMx
V ® x J
4n!
H
Hn
(7)
(8)
Furthermore, specific probability distribution Ps (y) in Eq. (5) and the parameter Bn in Eq. (6) can be finally realized respectively, as follows:
x
1
1
m=0
1
X, y
(9)
B.
n
(
(10)
2.2. Mutual prediction of specific probability distribution based on regression information among fluctuating environmental factors
The proposed method is applied to the measured data leaked by a VDT while playing video games in the living room environment. In this paper, only an essential point is described here. The sound pressure level [dBA], the illuminance [lx] and the r.m.s value of the electric field [V/m] are simultaneously measured. Figure 1 shows a schematic drawing of the experiment.
The experiment has been carried out inside of a simple anechoic room. The slowly fluctuating 500 data of non-stationary type for each stochastic variable are sampled with a sampling interval of 10 second. Based on the former 400 data points, the regression parameter: Amn is calculated by use of Eq. (8). In this paper, only four figures of our
experimental results are shown from Figure 2 to Figure 5.
Figures 2 and 3 show the comparisons between experimentally sampled conditional mean values (,y|x) and theoretically estimated regression curves by use of Eq. (7). The regression
curves in Figure 2 estimate sound based on the statistics of light and in Figure 3, estimate light based on the statistics of electric field respectively. The order of approximation (i.e. 18th. in the caption of Figure 2) means a number of the truncated term m =18 in the infinite expansion expression of Eq. (7). The truncated term is determined by convergence property of the regression curves given by successively increasing their orders. Basically, the higher order
20mm —►
Electromagnetic Field Survey Meter _
Personal
Computer
Figure 1. A schematic drawing of the experiment
we adopt, the more precisely theoretical curve estimates the experimentally sampled conditional mean values. But in the actual situation, dips and peaks often appear in a part of the theoretical curve when we adopt notwithstanding higher order truncated term because the observed data is not confidence enough to calculate the higher order statistics owing to the finite number of data (see Figure 2).
<1
m
d[
рч
Illuminance [lx]
Figure 2. A comparison between experimentally sampled conditional mean values (A) and
theoretically estimated regression curves (-----------: 1st. approx., — : 18th. approx.) of sound
based on the statistics of light
Electric field strength [V/m]
Figure 3. A comparison between experimentally sampled conditional mean values (A) and
theoretically estimated regression curves (---------: 1st. approx.,-------: 7th. approx.) of light based
on the statistics of electric field
Figures 4 and 5 show the comparisons between experimentally sampled specific probability distribution Ps (y) and theoretically estimated distribution curves by use of
Eqs. (9) and (10). The distribution curves in Figure 4 estimate sound based on the statistics of light and in Figure 5 estimate light based on the statistics of electric field respectively. The order of approximation (ex. 18-10th. in the caption of Figure 4) means a number of the truncated term m =18 in Eq. (10) and a number of the truncated term n =10 in Eq. (9). The truncated terms are determined by convergence property of the distribution curves given by successively increasing their orders.
Sound pressure level [dBA]
Figure 4. A comparison between experimentally sampled specific probability distribution (o)
and theoretically estimated distribution curves (------------: 1st. approx., ------: 18-10th. approx.)
of sound based on the statistics of light
Illuminance [lx]
Figure 5. A comparison between experimentally sampled specific probability distribution (o)
and theoretically estimated distribution curves (----: 1st. approx.,-----: 7-18th. approx.) of
light based on the statistics of electric field
From these figures, it was found that all theoretical curves show a fairly good agreement with experimentally sampled points, in spite of an early stage of study. Hereafter, there remains an important problem to be solved on how higher order expansion parameter Amn is connected concretely with human character.
3. SUBJECTIVE EVALUATION CONCERNED WITH HUMAN CHARACTER
3.1. Experimental Setting
These experiments are carried out in our climate chamber. The room is illuminated by twelve sets of white incandescent ceiling lamps. A white noise is fed into the chamber by loudspeakers. The temperature of the chamber is controlled by heat pump type air conditioners. Environmental factors for experiment are chosen under the actual conditions of daily life. Four categories of thermal exposure, four categories of noise level, five categories of illuminance exposure are used. Two kinds of Magnitude Estimation (ME) Methods are employed to obtain the evaluation value for many complex living conditions. All subjects were healthy young men and women.
3.2. Evaluation Method Giving No Prior Information
Some psychological environment evaluation can be done from this experiment. The subjective evaluation with which a human being is concerned can be found by these procedures. In this experiment, Magnitude Estimation Method without standard value is employed.
Figure 6 shows the experimental noise evaluation values for noise level change, under four kinds of room temperature and the illuminance in the room is 50 lx (note that the vertical axis uses the logarithmic scale, so the value 2.8 means 1028 for example). From this experiment, there is some clear mutual correlation between the noise evaluation values and the noise stimulus, even in a linear correlation form.
Noise level [dBA]
Figure 6. The noise evaluation values for noise level change, under four kinds of room
temperature and illuminance 50 lx
Figure 7 shows the experimental noise evaluation values for room temperature change, under four kinds of noise level and the illuminance in the room is 100 lx (note that the vertical axis uses the logarithmic scale). From this figure, a high room temperature gives higher experimental noise evaluation values more than that of lower room temperature.
Temperature [°C]
Figure 7. The experimental noise evaluation values for room temperature change, under four
kinds of noise level and illuminance 100 lx
Figures 8 and 9 show the normalized values of noise evaluation and/or illuminance evaluation. In this case, all evaluation values are normalized as follows: X = (x - ')/<jx
where X is set up as a normal distribution with /u = 0 and a2 = 1.
Figure 8 shows the normalized value of noise evaluation for room temperature change, under four kinds of noise level and the illuminance in the room is 200 lx. Figure 9 shows the normalized value of illuminance evaluation for room temperature change, under five kinds of illuminance level and the noise in the room is 60 dBA. From these experiments, we can find the normalized values of evaluation value of noise or illuminance. After this procedure, we can also recognize the difference of evaluation value caused by room temperature.
-2,0 -I--------1-------1------1-------1-------1-------
10 15 20 25 30 35 40
Temperature [oC]
Figure 8. The normalized values of noise evaluation for room temperature change, under
noise level and illuminance 200 lx
-2,0
10 15 20 25 30 35 40
Temperature [oC]
Figure 9. The normalized values of illuminance evaluation for room temperature change,
under illuminance and noise level 60 dBA
3.3. Evaluation Method Giving A Prior Information
The subjective evaluation with which a human being is concerned can be also found by these procedures. In this experiment, Magnitude Estimation Method with the standard value is employed. Figure 10 shows a little the relationship (even in a linear correlation form) between the Noise Stimulus ratio and the Evaluation ratio in the case of room illuminance 200 lx and temperature 20°C.
10.0
_o
CG >
w
0.1
0.01 0.1 1 10 100 1000 Noise stimulus ratio
Figure 10. The relationship between the Noise stimulus ratio and the Evaluation ratio, under
illuminance 200 lx and room temperature 20°C
In this experiment, the evaluation values are classified in 5 steps (central evaluation values are 50, 100, 200, 400 and 800), and the mean value of every step is obtained. Here, we set up noise 60 dBA to be equal to evaluation value 100 as standard. So, 1.0 value of horizontal axis is equal to 60 dBA, and 1.0 value of vertical axis is equal to evaluation value 100. From this experiment, exponent ( value of power law by S. S. Stevens is obtained as 0.29. This is similar value of these proposed by Stevens for noise [7, 8].
Figure 11 shows the relationship between the illuminance level and the normalized value of noise evaluation in room temperature 20°C. The relative fluctuations of evaluation value are included in normalized value of noise evaluation.
2,0 -1,5 -s 1,0 -
13
v0,5
N 0,0 -
1 '0,5 -I -1,0 -
'1,5 '2,0 -
10 100 1000 10000 Illuminance [lx]
Figure 11. The normalized values of noise evaluation for illuminance change, under noise
level and room temperature 20 °C
20oC
—♦
—80dBA
kr - m —A ~
^ 60
X 50
Figures 12 and 13 show the conditional mean values, and the regression curves to noise level or to illuminance level. In figure 12, it is shown the conditional mean values of noise level to which human subjects suppose 100 evaluation value, for illuminance change. In figure 13, it is also shown the conditional mean values of illuminance level which is considered to be equal to 100 evaluation value, for sound pressure level change. In these figures, the regression curves explain the tendency of conditional mean value by higher order approximation (m = 3 for noise level and m = 5 for illuminance) of theoretical regression curves.
65
<1
m
'■d
> 60 <D
55
Conditional mean values
■ 1st. Approx. line
■ 2nd. Approx. line 3rd. Approx. line
250 500 750
Illuminance [lx]
1000
0
Figure 12. The conditional mean value of noise level, and the regression curve for illuminance
change
Noise level [dBA]
Figure 13. The conditional mean value of illuminance, and the regression curve for noise level
change
4. CONCLUSION
The purpose of this study is to find some trial based on objective and subjective evaluation methods for living environmental factors in a room. If more than two kinds of heterogeneous environmental factors affect each other, the combined effects of environmental factors lead to complex interactions.
Firstly, for an objective evaluation, physical environmental factors are measured from stochastic viewpoint. In order to evaluate quantitatively the relationship between two kinds of environmental factors (e.g. sound and illuminance) emit from electronic information equipment, we introduced a generalized regression analysis method. The regression function as a typical regression relationship between two random variables can be given. The specific probability distribution is predicted in order to confirm the effectiveness of our proposed method based on the proposed regression analysis.
Secondly, from a psychological viewpoint, one of the subjective evaluation is obtained by Magnitude Estimation (ME) Method with and/or without standard value. There is some mutual correlation (even in a linear correlation form) between the noise evaluation values and the noise stimulus, and high room temperature gives higher noise evaluation values. The normalization procedure of evaluation value makes similar experimental results as noise evaluation values themselves. By this ME Method, we obtained the reasonable exponent value for Stevens' Power law for noise and/or illuminance. We also obtained the conditional mean values of noise level or illuminance, being equal to 100 evaluation value from subjective viewpoint. It was found that all theoretical curves show a fairly good agreement with experimental sampled points even through these principle experiments.
From these studies, objective and subjective evaluation methods are proposed for environmental factors. However, because of an early stage of study, further studies should be concerned.
ACKNOWLEDGEMENTS
We would like to express our cordial thanks to Prof. Kazutatsu Hatakeyama, Prof. Akira Ikuta, Prof. Yoshifumi Fujita, Prof. Yasuo Mitani, Mr. Satoshi Mukai and Mr. Daisuke Morie for their helpful assistance and discussion.
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