JP2005265710A - Transmission line inspection system using unpiloted plane and method using it - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a transmission line inspection system using an unpiloted plane capable of automatically inspecting whether a cap defect and a crack are caused in the insulator used in a transmission line. <P>SOLUTION: The transmission line inspection system is equipped with a flight control system flying to the inspection place of the transmission line while autonomocisely flies, an unmanned helicopter equipped with a data collecting system for collecting various data containing a sound caused when a wood piece is allowed to impinge against the insulator of the inspection place, a control center equipped with a flight control/data collecting system for controlling the flight of the helicopter and collecting various data from the unmmaned helicopter to process the same and an insulator cap defect and the crack an insulator cap defect/crack inspection means 100 for subjecting the sound generated when the wood piece is allowed to impinge against the insulator collected by the data collecting system of the unmanned helicopter, to frequency analysis to detect the peak frequency of the sound to inspect whether there is the cap defect and crack is present in the insulator on the basis of the detected peak frequency. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a transmission line inspection system and method using an unmanned aerial vehicle, and more particularly, to inspect whether or not a cap used in an overhead transmission line is damaged or not using a unmanned aerial vehicle. The present invention relates to a transmission line inspection system and method using an unmanned aerial vehicle.

Conventionally, inspection of overhead power transmission lines (hereinafter referred to as “power transmission lines”) is performed by a patrolman riding a manned helicopter, flying along the power transmission lines, and checking the power transmission lines with binoculars for the presence or absence of abnormal locations. It was. However, inspection with binoculars is a burden on patrolmen (especially those who are not good at vehicles), and there is a risk of overlooking abnormal parts.
Therefore, a transmission line image was taken from a manned helicopter (high-vision shots, etc.), and a patrolman looked at the shot image to check for broken wires and arc marks on the transmission line, to measure the distance between trees approaching and cracking the insulator. There are also inspections.

However, inspecting a transmission line using a manned helicopter has a problem that it cannot be easily and quickly dealt with when the inspection is suddenly required, in addition to the high cost.
In addition, the inspection work of the power transmission line by taking an image also has a problem that the inspection of the final abnormal part is performed while the patrolman looks at the image, so that a quick and accurate inspection cannot be performed.

In addition, there exist some which are disclosed by the following two patent documents as a technique regarding the method of performing maintenance and monitoring, such as a power transmission line and the intake of a dam lake, using an unmanned helicopter.
JP 2003-127994 A JP 2003-127997 A

  The above-mentioned Patent Document 1 (Japanese Patent Laid-Open No. 2003-127994) allows a radio controlled helicopter to be ignored without being affected by topography by providing a radio signal helicopter and a ground station with a GPS signal receiving device and a satellite communication device. In addition, the coordinates of obstacles such as steel towers and power transmission lines are entered in advance with the flight route, and if the radio control helicopter gets too close to the obstacles, they will automatically avoid collisions by preventing them from colliding with obstacles. Disclose.

  The above-mentioned patent document 2 (Japanese Patent Laid-Open No. 2003-127997) makes it possible to control a radio controlled helicopter without being influenced by topography by providing a radio signal helicopter and a ground station with a GPS signal receiving device and a satellite communication device. At the same time, the coordinates of obstacles such as steel towers and power transmission lines are entered in advance, and if the radio controlled helicopter gets too close to the obstacles, an alarm will be generated or a collision accident to the obstacles will be avoided by autopilot. Disclose to prevent.

  An object of the present invention is to provide a power transmission line inspection system and method using an unmanned air vehicle capable of automatically inspecting whether or not a cap and a crack are generated in an insulator used for a power transmission line. It is in.

The power transmission line inspection apparatus using the unmanned air vehicle of the present invention has a flight control system (20) for flying to the inspection point of the transmission line (91) while flying autonomously, and when a piece of wood is applied to the insulator of the inspection point An unmanned air vehicle (10) having an information collecting system (30) for collecting various information including the sound of the unmanned air vehicle, and controlling the flight of the unmanned air vehicle (10) and the unmanned air vehicle (10) A control center (50) having a flight control / information collection system (60) for collecting and processing various kinds of information, and a piece of wood on the cocoon collected by the information collection system (30) of the unmanned air vehicle (10) Insulator / crack inspection means for detecting the peak frequency of the sound by frequency analysis of the sound when hit and checking whether the insulator has a cap and a crack based on the detected peak frequency (100) To.
Here, the information collecting system (30) of the unmanned aerial vehicle (10) fires the piece of wood toward the insulator, a piece of wood launcher (81), and the piece of wood fired from the piece of wood launcher (81). You may provide the highly directional microphone (82) which records the sound when a piece of wood hits the said insulator.
The frequency analysis means (101) for the frequency analysis of the sound when the insulator shade / crack inspection means (100) applies a piece of wood to the insulator recorded by the microphone (82), and the frequency analysis means ( 101) a peak frequency detecting means (102) for detecting a peak frequency based on the frequency characteristics of the sound obtained by (101), and the insulator according to the numerical value of the peak frequency obtained by the peak frequency detecting means (102). And determining means (103) for determining whether the coconut shell is a healthy insulator, a kasakashi insulator or a crack insulator.

If the peak frequency obtained by the peak frequency detection means (102) is greater than the peak frequency obtained for a healthy insulator, the determining means (103) determines that the insulator is an eggplant-shaped insulator. If the peak frequency obtained by the peak frequency detecting means (102) is smaller than the peak frequency obtained for a healthy insulator, the insulator may be determined to be a cracked insulator.
The information collecting system (30) of the unmanned air vehicle (10) further comprises distance measuring means (14, 15) for measuring the distance from the piece launching device (81) to the insulator, The frequency analysis means (101) of the inspection means (100) determines that the piece of wood is obtained from the distance measured by the distance measurement means (14, 15) and the initial velocity of the piece of wood fired from the piece firing device (81). The time hitting the insulator may be calculated, and the frequency analysis of the sound recorded by the microphone (82) may be performed during a predetermined period before and after the calculated time.

The insulator shade defect / crack checking means (100) may further comprise a determination result notifying means (104) for displaying the determination result by the determining means (103) on a display device and notifying a patrolman.
A host computer (53) included in the flight control / information collection system (60) of the control center (50) may include the insulator cap / crack inspection means (100).
The computer (21) included in the flight control system (20) of the unmanned aerial vehicle (10) may include the insulator cap / crack checking means (100).

According to the transmission line inspection method using the unmanned air vehicle of the present invention, the unmanned air vehicle (10) is allowed to fly autonomously under control of the control center (50) to fly to the inspection point of the power transmission line (91). (10) is used to collect various kinds of information including the sound when a piece of wood is applied to the insulator at the inspection location, and the sound when the piece of wood is applied to the insulator collected using the unmanned air vehicle (10). A frequency analysis is performed to detect a peak frequency of the sound, and based on the detected peak frequency, it is checked whether the insulator has a cap and a crack.
Here, if the detected peak frequency is larger than the peak frequency detected for a healthy insulator, it is determined that the insulator is a shaded insulator, and the detected peak frequency is detected for a healthy insulator. If the frequency is lower than the peak frequency, the insulator may be determined to be a cracked insulator.
Measure the distance from the unmanned aerial vehicle (10) to the insulator, calculate the time for the piece to hit the insulator from the measured distance and the initial velocity of the piece of wood, and collect before and after the calculated time The frequency analysis of the generated sound may be performed.

The power transmission line inspection system and method using the unmanned air vehicle of the present invention have the following effects.
(1) By inspecting the power transmission line using an unmanned air vehicle, the cost can be reduced, and even if the inspection is suddenly required, it can be dealt with simply and quickly.
(2) By performing frequency analysis of the sound when a piece of wood is applied to the insulator and detecting whether or not the insulator has a cap and a crack, a quick and accurate inspection can be performed.

  The purpose of automatically checking whether or not the insulators used in power transmission lines are clogged and cracked is to fly the unmanned air vehicle to the inspection location and attach a piece of wood from the unmanned air vehicle to the insulator of the power transmission line. This was realized by detecting whether or not a shade and a crack were generated in the insulator based on the peak frequency obtained by analyzing the frequency of the sound at this time.

Embodiments of a transmission line inspection system and method using an unmanned air vehicle of the present invention will be described below with reference to the drawings.
FIG. 1 is a diagram showing a schematic overall configuration of a power transmission line inspection system using an unmanned air vehicle according to an embodiment of the present invention.
As shown in FIG. 1, the power transmission line inspection system 1 according to the present embodiment controls and controls the radio control helicopter 10 (hereinafter referred to as “radio control helicopter 10”) as an unmanned air vehicle, the flight of the radio control helicopter 10, and the like. The control center 50 includes a host computer 53 that manages and inspects the transmission line using video information from the radio control helicopter 10.
Here, as shown in FIG. 2, the radio control helicopter 10 includes a communication antenna 11 that transmits and receives various types of information by wireless communication with the control center 50, and a GPS (Global Positioning System) artificial sensor for detecting the position of the radio control helicopter 10. A GPS antenna 12 that receives a signal from the satellite 100 (see FIG. 1), three types of surrounding surveillance cameras 13 that photograph the three directions forward and left and right to monitor the surrounding situation, and a desired inspection target The information collecting camera 14 for photographing the object, the distance sensor 15 for measuring the distance from the desired inspection object, and the piece of wood for firing a piece of wood or a ball of wood (hereinafter referred to as “wood piece”) toward the insulator to be inspected. A launching device 81, a highly directional microphone 82 for recording sound when a piece of wood fired from the wood launching device (81) hits the insulator, an information collecting camera 14, and a distance sensor 15 The storage case 16a for storing the wood chip launcher 81 and the microphone 82 is rotated about two axes in the horizontal direction and the vertical direction to operate the direction in which the information collecting camera 14, the distance sensor 15, the wood chip launcher 81 and the microphone 82 are directed. Direction operating device 16, observation sensor 17 fixed to the lower part of the storage case 16a and measuring the environment, and parachute device that relaxes the descent speed of the radio controlled helicopter 10 by starting in an emergency and expanding the parachute. Safety device 18, radio control helicopter 10 main body, communication antenna 11, GPS antenna 12, monitoring camera 13, information collecting camera 14, distance sensor 15, wood chip launching device 81, microphone 82, direction operation device 16, observation sensor 17 And a computer 21 for overall control of the parachute device 18 (see FIG. 3) Etc. and a control box 19 which is the housing.

As shown in FIG. 3, the radio control helicopter 10 also has, as a flight control system 20, a computer 21, a GPS unit 26 connected to the computer 21, a distance sensor 15, a control sensor 27, an infrared sensor 28, and a switch mechanism 24. (Hereinafter referred to as “SW / Mixer unit 24”), a modem 23 and a servo control unit 25 connected to the SW / Mixer unit 24, a data transmitter / receiver 22 connected to the modem 23, and a surrounding surveillance camera 13 And an image transmitter 29 connected to the surrounding monitoring camera 13 so that it can automatically fly to a desired position while autonomously flying.
The SW / Mixer unit 24 switches between automatic flight, semi-automatic flight or manual flight and flight control of the radio controlled helicopter 10 according to control information transmitted from the control center 50 via the data transceiver 22 and the modem 23. And switching the control level in hierarchical safety control. In addition, the servo control unit 25 controls each part 10 of the radio controlled helicopter 10 based on a control signal from the control center 50 or a control signal from the computer 21 via the data transceiver 22 and the modem 23 according to the switching of the SW / Mixer unit 24. Controls the drive of the servo motor that makes the 'function.

As shown in FIG. 4, the radio control helicopter 10 also serves as the information collection system 30 to record the information captured by the information collection camera 14, the microphone 82, and the information collection camera 14, and to record the sound recorded by the microphone 82. VTR (Video Tape Recorder) 31 for recording, observation sensor 17 for measuring the environment around the radio controlled helicopter 10 such as a concentration sensor of toxic gas, etc., and information collection in parallel with recording / recording to the VTR 31 A high compression / parallel processing unit 32 for encoding and compressing a captured image from the camera 14, a captured image compressed by the high compression / parallel processing unit 32, measurement data from the observation sensor 17, and a microphone 82. An image transmitter 29 for transmitting the collected sound to the control center 50 and a control received from the control center 50 via the data transceiver 22. And a servo control unit 36 for controlling the drive of a servo motor that operates the direction operating device 16 based on a control signal or the like.
Note that the information collecting camera 14 is not limited to a normal photographing camera, and may be a visible camera equipped with a special lens such as a high magnification, wide angle or fisheye lens when photographing a desired image. An infrared camera or an ultraviolet camera may be used to perform analysis or to observe corona discharge. Further, when transmitting the measurement data from the observation sensor 17, the image transmitter 29 can superimpose on the captured image from the high compression / parallel processing unit 32 or can transmit both of them simultaneously. It has become.

As shown in FIG. 5, the control center 50 includes a host computer 53, an operation panel 65 connected to the host computer 53, an information monitor 54 connected to the host computer 53, as a flight control / information collection system 60. A navigation system 63 (which constitutes a destination setting means, an obstacle setting means and a route determination means) connected to the host computer 53 and the information monitor 54, and the radio control helicopter 10 via the communication antenna 51 (see FIG. 1) Data transmitter / receiver 61 for transmitting / receiving various information between them, the modem 62 connected between the data transmitter / receiver 61 and the host computer 53, and the monitoring video information of the ambient monitoring camera 13 sent simultaneously from the radio controlled helicopter 10 And the video information of the information collecting camera 14 is received by the parabolic antenna 52 (see FIG. 1). Connected to the image receiver 64 that receives and decodes / decompresses, the safety monitoring monitor 55 that displays the monitoring video of the surrounding monitoring camera 13 input from the image receiver 64, and the image receiver 64 and the host computer 53. The collected video monitor 56 is provided. The image receiver 64 also receives sounds collected by the microphone 82 sent from the radio control helicopter 10.
Here, the collected video monitor 56 delivers the information collected video of the information collecting camera 14 and the measurement data of the observation sensor 17 to the host computer 53, and analyzes the noticed location etc. as a result of analyzing the video from the host computer 53. When the video is returned, it is displayed superimposed on the information collection video.
The modem 62 performs A / D conversion or D / A conversion so that various types of information processed by the host computer 53 can be exchanged with the data transceiver 61.

  As shown in FIG. 6, the host computer 53 includes a frequency analyzing unit 101, a peak frequency detecting unit 102, a determining unit 103, and a determination result notifying unit 104 as the cocoon shade missing / crack checking unit 100. It should be noted that the insulator cover / crack checking means 100 may be configured by software or hardware.

Next, the operation of the power transmission line inspection system 1 when inspecting whether or not the shade used in the power transmission line is damaged and cracked will be described with reference to FIGS. 7 and 8.
Based on a control program set in advance using the navigation system 63 or the like, a control signal instructing the fully automatic control of the radio control helicopter 10 is transmitted from the control center 50 to the radio control helicopter 10 to operate the flight control system 20 of the radio control helicopter 10. By doing so, the radio controlled helicopter 10 is automatically caused to fly along the power transmission line to the check point of the insulator. At this time, for example, an obstacle is detected by the infrared sensor 28, and the radio controlled helicopter 10 is automatically caused to fly while correcting the flight direction by the distance sensor 15 and the computer 21.
In the case of inspecting the wire breakage and arc trace of the power transmission line, the distance sensor 15 detects the distance from the power transmission line 91 stretched on the steel tower 90 specified by the infrared sensor 28, as shown in FIG. On the other hand, the flight control system 20 of the radio controlled helicopter 10 is operated so as to follow the power transmission line 91, and the direction of the wood chip launcher 81 and the microphone 82 is directed toward the insulator to be inspected when reaching the check point of the insulator. The operating device 16 is operated.

  As shown in an example of FIG. 8, there is a healthy eggplant and an eggplant with a cape (hereinafter referred to as “kasakazushi”) and an eggplant with a crack (hereinafter referred to as “crack insulator”). The peak frequency of the sound generated when you hit is different. That is, the sound generated when hitting a healthy insulator without a cap and a crack is a sound having a peak frequency of about 2.25 kHz (see FIG. 8A). On the other hand, the sound generated when hitting the Kasabiko is a sound having a peak frequency of about 2.45 kHz (see FIG. 8B). The sound generated when the crack insulator is struck is a sound having a peak frequency of about 2.05 kHz.

Therefore, in order to check the insulator, a piece of wood is fired toward the insulator from the wood piece launching device 81 stored in the storage case 16a of the radio controlled helicopter 10, and a sound when the piece of wood hits the insulator is recorded by the microphone 82. The sound recorded by the microphone 82 is sent to the host computer 53. The host computer 53 performs frequency analysis of the transmitted sound using the frequency analysis unit 101, and then detects the peak frequency using the peak frequency detection unit 102 based on the frequency characteristics of the sound obtained by the frequency analysis. To do. After that, the host computer 53 has a peak frequency larger than that of a healthy insulator in the case of Kasahashi insulator, and becomes smaller than that of a healthy insulator in the case of crack insulator (FIG. 8). After determining whether a sound insulator, a captive eggplant insulator or a crack insulator is used by the determination unit 103 according to the obtained peak frequency, the determination result is sent to the collected video monitor 56 using the determination result notification unit 104. Display.
As described above, the patrolman can check whether or not the shade used in the transmission line has a cap and a crack.

In addition, when recording the sound when the piece of wood hits the insulator with the microphone 82, it may affect the accuracy of the frequency analysis of the sound to be recorded with the sound of the rotor of the radio control helicopter 10 or the sound of the wind. Can be dealt with by taking the following measures.
(1) The distance to the insulator to be inspected is measured using the information collecting camera 14 or the infrared sensor 28 and the distance sensor 15, and the host computer 53 measures the measured distance and the piece of wood fired from the wood piece launcher 81. Calculate the time that the piece of wood hits the insulator from the initial velocity of the sound, analyze the frequency of the sound recorded in a predetermined period before and after the calculated time, and compare the obtained frequency characteristics, so that the piece of wood hits the insulator. Extract sounds that occur only when
(2) A piece of wood is applied to the insulator several times, and the above processes (1) and (2) are performed several times.

In the above description, the coconut cap missing / crack checking means 100 shown in FIG. 6 is provided in the host computer 53 of the control center 50, but the coconut cap missing / crack checking means 100 is provided in the computer 21 of the radio control helicopter 10, The inspection result of whether or not the insulator has a cap or a crack may be transmitted to the control center 50 via the image transmitter 29 and the data transmitter / receiver 22 and displayed on the collected video monitor 56.
Further, the radio control helicopter 10 was automatically flighted along the power transmission line 91 from the control center 50, but the radio control helicopter 10 was semi-automatically flighted or manually operated along the power transmission line 91 using the flight control / information collecting system 60 of the control center 50. You may fly.
Further, although the radio control helicopter 10 (unmanned helicopter) is used as an unmanned air vehicle, an unpopular sphere, an unmanned airship, an unmanned airplane, or the like may be used.

  As described above, the transmission line inspection system and method using the unmanned aerial vehicle according to the present invention uses the unmanned aerial vehicle to check whether or not a cap or a crack has occurred in the insulator used in the transmission line. It can be used when performing automatically.

1 is a diagram showing a schematic overall configuration of a power transmission line inspection system using an unmanned air vehicle according to an embodiment of the present invention. (Example 1) It is a figure which shows the structure of the radio controlled helicopter 10 shown in FIG. (Example 1) It is a figure which shows the structure of the flight control system 20 of the radio controlled helicopter 10 shown in FIG. (Example 1) It is a figure which shows the structure of the information collection system 30 of the radio controlled helicopter 10 shown in FIG. (Example 1) It is a figure which shows the structure of the flight control and information collection system 60 of the control center 50 shown in FIG. (Example 1) It is a figure which shows the structure of the coconut cap missing / crack inspection means 100 with which the host computer 53 shown in FIG. 5 is provided. (Example 1) It is a figure for demonstrating operation | movement of the power transmission line inspection system 1 shown in FIG. 1 at the time of inspecting whether the shade and the crack have arisen in the insulator. (Example 1) It is a figure for demonstrating operation | movement of the power transmission line inspection system 1 shown in FIG. 1 at the time of inspecting whether the shade and the crack have arisen in the insulator. (Example 1)

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Radio control helicopter 20 Flight control system 21 Computer 30 Information collection system 50 Control center 53 Host computer 60 Flight control / information collection system 81 Wood chip launcher 81 Microphone 100 Lion shade lack / crack inspection means 101 Frequency analysis means 102 Peak frequency detection means 103 Determination means 104 Determination result notification means

Claims (11)

A flight control system (20) for flying to the inspection point of the transmission line (91) while autonomously flying, and an information collection system for collecting various information including sound when a piece of wood is applied to the insulator of the inspection point ( 30) an unmanned air vehicle (10) comprising:
A control center (50) comprising a flight control / information collection system (60) for controlling the flight of the unmanned air vehicle (10) and collecting and processing the various information from the unmanned air vehicle (10);
The sound of the unmanned air vehicle (10) collected by the information collection system (30) is subjected to frequency analysis of the sound when a piece of wood is applied to the insulator and the peak frequency of the sound is detected. Insulator / crack inspection means (100) for inspecting whether or not there is a cap and a crack in the insulator,
A transmission line inspection system using an unmanned aerial vehicle. The information collection system (30) of the unmanned air vehicle (10)
A piece of wood launching device (81) for firing the piece of wood towards the insulator;
A highly directional microphone (82) for recording a sound when the piece of wood fired from the piece launcher (81) hits the insulator;
The transmission line inspection system using the unmanned air vehicle according to claim 1, comprising: The coconut cap missing / crack checking means (100)
Frequency analysis means (101) for performing frequency analysis of sound when a piece of wood is applied to the insulator recorded by the microphone (82);
Peak frequency detection means (102) for detecting a peak frequency based on the frequency characteristics of the sound obtained by the frequency analysis means (101);
A determination means (103) for determining whether the insulator is a healthy insulator, a kasakashi insulator or a crack insulator according to a numerical value of the peak frequency obtained by the peak frequency detection means (102);
The transmission line inspection system using the unmanned air vehicle according to claim 2, comprising: The determination means (103)
If the peak frequency obtained by the peak frequency detection means (102) is greater than the peak frequency obtained for a healthy insulator, it is determined that the insulator is a shaded insulator.
If the peak frequency obtained by the peak frequency detection means (102) is smaller than the peak frequency obtained for a healthy insulator, it is determined that the insulator is a cracked insulator.
The power transmission line inspection system using the unmanned air vehicle according to claim 3. The information collection system (30) of the unmanned air vehicle (10) further includes distance measuring means (14, 15) for measuring a distance from the piece launching device (81) to the insulator,
The frequency analysis means (101) of the cocoon caps / crack inspection means (100) uses the distance measured by the distance measurement means (14, 15) and the first of the pieces of wood fired from the wood piece launcher (81). Calculating the time that the piece of wood hits the insulator from the speed, and performing a frequency analysis of the sound recorded by the microphone (82) in a predetermined period before and after the calculated time,
The transmission line inspection system using the unmanned air vehicle according to claim 3 or 4,   The coconut cap missing / crack checking means (100) further comprises a determination result notifying means (104) for displaying a determination result by the determining means (103) on a display device and notifying a patrolman. A transmission line inspection system using the unmanned air vehicle according to any one of claims 3 to 5.   The host computer (53) included in the flight control / information collection system (60) of the control center (50) includes the insulator cap / crack inspection means (100). A transmission line inspection system using the unmanned air vehicle according to any one of the above.   The computer (21) included in the flight control system (20) of the unmanned aerial vehicle (10) includes the insulator caps / crack inspection means (100). A transmission line inspection system using the described unmanned air vehicle. Control the control center (50) to fly the unmanned air vehicle (10) autonomously and fly to the inspection point of the transmission line (91),
Collect various information including sound when a piece of wood is applied to the insulator of the inspection location using the unmanned air vehicle (10),
Frequency analysis of the sound when a piece of wood is applied to the insulator collected using the unmanned air vehicle (10) to detect the peak frequency of the sound,
Inspecting whether or not the insulator has a cap and a crack based on the detected peak frequency,
A power transmission line inspection method using an unmanned air vehicle. If the detected peak frequency is greater than the peak frequency detected for a healthy insulator, the insulator is determined to be a captive insulator;
If the detected peak frequency is less than the peak frequency detected for a healthy insulator, the insulator is determined to be a cracked insulator;
The transmission line inspection method using the unmanned air vehicle according to claim 9. Measure the distance from the unmanned air vehicle (10) to the insulator,
From the measured distance and the initial speed of the piece of wood, calculate the time for the piece of wood to hit the insulator,
Perform frequency analysis of sounds collected before and after the calculated time,
The transmission line inspection method using the unmanned aerial vehicle according to claim 9 or 10, wherein: