1972 年 28 巻 10 号 p. 539-546
We presented previously a report on processing of aircraft noise around airports with an electronic computer. In this paper, we report about the results obtained by analyzing factors considered closely associated with aircraft noise using the method of factor analysis based on the quantification theory. The method of factor analysis permits assignment of the most suitable values to the categories of factors such as type of aircraft, take-off or landing which can not be represented by numerical values unless some special measures are taken. This process, therefore, makes it possible to accomplish various multidimensional analyses and to predict such values as noise peak from factors such as type of aircraft, take-off or landing and flight altitude. Factors analyzed are as follows:(1)Noise peak value[dB(A)]:Noise peak value in excess of 70dB(A) (2)Noise duration(sec):Duration of noise above 70dB(A) (3)Type of aircraft (4)Take-off and landing (5)Flight altitude(m) (6)Wind direction was also examined in addition to the above factors. The observation points are A and B shown in Figure 1. Regarding the wind direction, in addition to the above, C and D are used as observation points. Table 1 shows a part of the sample data. The noise peak value and noise duration are taken as external data Table 2 shows an example of results obtained by analyzing the various factors mentioned previously using the method of factor analysis. X is a value assigned to each factor category corresponding to type of aircraft, take-off or landing and altitude. The above-mentioned external data can be predicted from X, which can be obtained from the following equation:FX=A^*(1) In equation (1) the matrices F and A^* are obtained from the sample data shown in Table 1. In order to predict the external data from the results shown in Table 2, it suffices to add X, the value assigned to each factor category, to the mean value X^^^-. It should be noted here that X has been normalized in such a manner that the mean value of each factor becomes zero. For example, in case three categories;F4 Phantom, Take-off and Altitude of 601m or more are given(Sample No. 1 in Table 1), the noise peak value can be predicted from Table 2 as follows:6. 16+2. 39+(-0. 92)+83. 36=90. 99 dB(A) In this particular case, the actual observed value was 91 dB(A). The noise duration can be predicted in the same manner. The accuracy of analysis, namely, accuracy of prediction is represented in terms of a multiple correlation coefficient. Figure 4 shows the value calculated from the results of observations made at point A and indicates how the multiple correlation coefficient varies as 3 kinds of factors are added to external data one by one. The same tendency is also noted at point B, In Figure 5, the partial correlation coefficients of individual factors corresponding to the noise peak values at both point A and point B are shown. Weights of various factors at point A and point B related to the external data are compared with each other in Figure 6 and Figure 7. These weights correspond to the ranges of the factors such as those shown in Table 2. The weight and the partial correlation coefficient, as a rule, have the same tendency. Use of weight, however, is more convenient than the presentation in the partial correlation coefficients, for it permits direct comparison between physical values. Figure 9 shows how the external data are affected by the wind direction. It is known that the head wind and cross wind affect the external data positively, while the tail wind affects them negatively. Since the preliminary investigation has indicated that the effects of temperature and humidity on the noise peak value may not be negligible, this point deserves further investigation. The calculation of all the above statistics was made by using Hitac 8500.