CC BY
3TECHNICAL SCIENCES
SOUND SOURCE LOCATING USING ACOUSTIC SENSORS
Semenchenko V.,
Student of the 4th year of the NTUU "Kyiv Polytechnic Institute. Igor Sikorsky", Faculty ofInformatics and
Computer Technology, Department of Computer Engineering
Simonenko V.
Professor of the NTUU "Kyiv Polytechnic Institute. Igor Sikorsky ", Faculty of Informatics and Computer
Technology, Department of Computer Engineering
Abstract
This article concernes the task of sound source locating using acoustic sensors. The proposed system is decentralized, can be effectively scaled depending on size of the area and precision of acoustic sensors themselves. Proposed two methods of calculating distance to the sound source which can be used depending on which one can give better possible results
Keywords: acoustic sensors, sound location.
When an acoustic wave arrives at the sensor, it transmits the signal and the time it arrives at the server, where the data from all sensors are collected, processed and can be used for further action.
Two approaches will be used to find the distance to the sound source.
The first one requires at least three acoustic sensors and provides better accuracy, provided that the distance to the sound source is not much greater than the distance between the sensors.
Fig. 1 demonstrates the basic principle of the first method. To simplify, consider it first in a two-dimensional space.
The sensors 2, 3, 4 are located on the same line, with the sensor 3 in the middle between the sensors 2 and 4 and the distance to each of them is L.
The signal source has coordinates (xx; yx) and the acoustic sensors - (x2;y2), (x3;y3) and (x4;y4). They are located at a distance R2,R3,R4 from the signal source 1, and the time when the sensors receive a signal will be t2,t3,t4. Let's take a reference point when the signal arrives at the sensor 3, then the time the signal arrives at the sensors will be (t2 - t3), 0, (t4 - t3) respectively.
Figure 1. Schematic representation of the geometric principle of determining the distance to the source of sound.
1 - sound source; 2, 3, 4 - acoustic sensors.
Assume that the sensor 3 is at a distance d from the sound source. Then, assuming that the sound speed is equal to V, the sensors 2 and 4 are at a distance (d + d2) and (d + d4) respectively, where
(4*d2+4*d4)*d = l2 - 2*d2-2*d% (7)
Then divide the left and right sides by (4 * d2 + 4 * d4) and get.
d2=V*(t2- t3) d4=V*(t4- t3)
We use the median formula
V2*b2 + 2*c2-a2
and substitute the necessary values
^ _ V2*(d + d2)2 + 2*(d+d4)2-l2
(1) (2)
(3)
(4)
^ _ l2-2*d%-2*d4 4*d.2+4*d4
(8)
Multiplying the left and right sides by 2 and bringing them to the square, we obtain
4*d2 = 2* (d + d2)2 + 2 * (d + d4)2 - I2 (5)
Expand braces and simplify the same terms.
4*d2*d + 2*d2+4*d4*d + 2*d2~l2 = 0 (6)
We group the terms and transfer known constants to one side.
Thus, the distance d was obtained from the signal source to the acoustic sensor 3.
The second method uses the properties of the sound, in which the ratio of the pressure at two points is inversely proportional to the square of the distance from the source of the signal and delay between sound arrival. In this case it is similar to how human ears work[1][2].
- = 4 (9)
P2 Rl w
It requires only two acoustic sensors and can be effectively used on large distances. It is worth noting that combining the results obtained by the first and second methods at medium distances can yield more accurate results than using only one of them. The disadvantage of this method is the dependence on the accuracy of determining the sound pressure of the acoustic sensors.
The principle of this method is depicted in Fig. 2.
Figure 2. Schematic representation of the principle of determining the distance to the source of sound using 2
sensors. 1, 2 - acoustic sensors
2
2
Let sensors (d + d1), where
1 and 2 be at a distance d and
di = ti *V
(10)
and t1- the difference between the time when sensors 1 and 2 received signals.
Assuming that at the moment of receiving the signal on the sensor 1 and 2, the sound wave pressures are P1 and P2 respectively we obtain the following equation
After making the transformation, we obtain a formula for determining the distance to the the sound signal source.
d=^~ (12)
(d + d1)2
Pi P2
To find the position of the sound source, we will draw circles with centers at points (x2;y2), (x3;y3),(x4;y4) and radii (d + d2),d,(d + d4) respectively.
Intersection of these circles of these circles will be (11) the point (x1;y1). This can be seen in Fig. 3.
Figure 3. Intersection of the circuits formed by the sensors and their distance to the source of the signal.
1 - sound source; 2, 3, 4 - acoustic sensors
Thus, we obtain a system of equations
(x - X2)2 + (y- y2)2 = (d + d2)2
(x - X3)2 + {y- y3)2 = d2 (x - X4)2 + (y- y4)2 = (d + d4)2
solving which we obtain d - the distance from the sensor 3 to the source of sound.
Similarly for three-dimensional space:
(13)
(x — X2)2 + (y- y2)2 + (z — Z2)2 = (d + d2)
(x — x3)2 + (y — y3)2 + (z — z3)2
d2
(x — X4)2 + (y — y^j2 + (z — Z4)2 = (d + d4)2
(x — x5)2 + (y — y5)2 + (z — z5)2 = (d + d5)2
-1
where fe^X fe^X fe^X (x5;y5) - coordinates of sensors and(d + d2), d, (d + d4), (d + d5) -their distance to the signal source, respectively.
To ensure better mobility and improve the accuracy of locating the sound source, for each acoustic sensor, its distance to the source of sound will be calculated. To do this, you need to find such sets of 4 sensors that they will not be in the same plane by counting the determinant of matrix (15).
The weight for each set of sensors will be calculated as
— Х0 Уз — Уо з — Zo
Xl — Х0 yl — Уо l — Z0 (15)
*2 — Х0 У2 — Уо 2 — Z0
X = ■
z = ■
YH=lWi*xi
YZ=lwi*yj
Tj=lWj*Zi
(16)
where xi, yi, zi - coordinates of the source of the acoustic signal received by the i-th set of sensors, wi -the weight of the i-th set of sensors.
w = П=оТ
(17)
Where (Xo;yo), (x1;y1), fe^X fe^ - coordinates of sensors.
For each set of sensors for which the determinant is not equal to 0, the distance to the source of sound will be calculated by one of the proposed methods and the coordinates of the sound source are determined. Based on the calculated data for each set of sensors, the location of the source of sound will be calculated.
Since each sensor can have different sensitivity and resistance, it is worthwhile to give preference to the results obtained from the data provided by more precise acoustic sensors. To do this we use an arithmetic mean weighted.
where Rd - the ratio of the input impedance to the output impedance of the amplifier of the acoustic sensor, and S - the sensitivity of the acoustic sensor.
Typically, electrical impedance is divided into low (50 - 2500 ohm), medium (2500 - 17500 ohm) and high (17500+ ohm). The greater the ratio of the input electrical resistance to the output resistance of the amplifier of the acoustic sensor, the better the signal will be obtained. Sensitivity will determine the minimum noise that the microphone can capture and can be measured in decibels or in the electric voltage of the external electric circuit[3]. In this case, it was decided to use voltage.
This averaging method is extremely important for the second method since its basis is the calculation based on the change in pressure with increasing distance.
However, for a method using three microphones and a difference in delay time of arrival, the accuracy of the microphone does not have such impact on the result. Thus, it is better for him to use the just arithmetic mean.
References
1. Middlebrooks JC, Makous JC, Green DM. Directional sensitivity of sound-pressure level in the human ear canal, 1989.
2. Parvaneh Parhizkari. Binaural Hearing-Human Ability of Sound Source Localization, Sweden, 2008.
3. J.-P.Dalmont. Acoustic impedance measurement, part I: a review: "Journal of Sound and Vibration", 2001.
нестационарный процесс пластической деформации при изгибе
ЗАГОТОВОК
У
Бровман Т.В.
Тверской государственный технический университет, д.т.н., доцент
NONSTATIONARY PROCESS PLASTIC DEFORMATION IN BENDING OF WORKPIECES
Brovman T.
Tver state University technical University, PhD, associate Professor
Аннотация
При изгибе пластическая деформация может происходить не по всему объему деформируемой заготовки, а только в части этого объема. Размер зоны деформации изменяется в течение всего процесса изгиба, т.е. имеет место нестационарный процесс пластической деформации Abstract
When bending, plastic deformation can occur not throughout the volume of the deformable workpiece, but only in part of this volume. The size of the deformation zone varies throughout the bending process, i.e. there is a non-stationary process of plastic deformation
Ключевые слова: изгиб, нестационарная, зона, пластическая деформация Keywords: bending, non-stationary, zone, plastic deformation
