GB2556967A - A sensor device with a tilt meter, wireless communication facility and magnetic fixing - Google Patents

A sensor device with a tilt meter, wireless communication facility and magnetic fixing Download PDF

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Publication number
GB2556967A
GB2556967A GB1713214.3A GB201713214A GB2556967A GB 2556967 A GB2556967 A GB 2556967A GB 201713214 A GB201713214 A GB 201713214A GB 2556967 A GB2556967 A GB 2556967A
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United Kingdom
Prior art keywords
tunnel
section
magnets
sensor device
tilt
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Granted
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GB1713214.3A
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GB201713214D0 (en
GB2556967B (en
Inventor
Maddison Simon
Wright Peter
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SENCEIVE Ltd
Halcrow Group Ltd
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SENCEIVE Ltd
Halcrow Group Ltd
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Priority to GB1713214.3A priority Critical patent/GB2556967B/en
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C9/00Measuring inclination, e.g. by clinometers, by levels
    • G01C9/18Measuring inclination, e.g. by clinometers, by levels by using liquids
    • G01C9/24Measuring inclination, e.g. by clinometers, by levels by using liquids in closed containers partially filled with liquid so as to leave a gas bubble
    • G01C9/26Details
    • G01C9/28Mountings
    • EFIXED CONSTRUCTIONS
    • E21EARTH OR ROCK DRILLING; MINING
    • E21BEARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B47/00Survey of boreholes or wells
    • E21B47/02Determining slope or direction
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16MFRAMES, CASINGS OR BEDS OF ENGINES, MACHINES OR APPARATUS, NOT SPECIFIC TO ENGINES, MACHINES OR APPARATUS PROVIDED FOR ELSEWHERE; STANDS; SUPPORTS
    • F16M13/00Other supports for positioning apparatus or articles; Means for steadying hand-held apparatus or articles
    • F16M13/02Other supports for positioning apparatus or articles; Means for steadying hand-held apparatus or articles for supporting on, or attaching to, an object, e.g. tree, gate, window-frame, cycle
    • F16M13/022Other supports for positioning apparatus or articles; Means for steadying hand-held apparatus or articles for supporting on, or attaching to, an object, e.g. tree, gate, window-frame, cycle repositionable
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C7/00Tracing profiles
    • G01C7/06Tracing profiles of cavities, e.g. tunnels
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01FMAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
    • H01F7/00Magnets
    • H01F7/02Permanent magnets [PM]
    • H01F7/0231Magnetic circuits with PM for power or force generation
    • H01F7/0252PM holding devices

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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • General Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Electromagnetism (AREA)
  • Mechanical Engineering (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Geology (AREA)
  • Mining & Mineral Resources (AREA)
  • Multimedia (AREA)
  • Arrangements For Transmission Of Measured Signals (AREA)
  • Environmental & Geological Engineering (AREA)
  • Geochemistry & Mineralogy (AREA)
  • General Life Sciences & Earth Sciences (AREA)
  • Fluid Mechanics (AREA)
  • Geophysics (AREA)

Abstract

A method for calculating deformation within a tunnel. The tunnel has a cross-section comprising multiple sections (1...N) on each side of a vertical line down the centre of the tunnel; the first section (1) being attached to the base of the tunnel at an assumed fixed point and the endpoint of the upper section (N) representing the highest point of the tunnel cross-section. The method comprises fitting each section 1 to N with a tilt meter and measuring the tilt for that section; the measured tilt for that section is used in conjunction with the known length and initial angle of the section to calculate the horizontal and vertical components of the sectional movement. The horizontal movement of the sections 1 to N are summed to obtain the horizontal movement of the tunnel, and the vertical movement of the sections 1 to N are summed to obtain the vertical movement of the tunnel.

Description

(56) Documents Cited:
CN 102878975 A JP 2006162539 A
JP 2006038681 A (58) Field of Search:
INT CL E21B, G01B, G01C
Other: EPODOC, WPI & Patent Fulltext (71) Applicant(s):
Senceive Ltd (Incorporated in the United Kingdom)
Hurlingham Studios, Ranelagh Gardens, LONDON, SW6 3PA, United Kingdom
Halcrow Group Limited (Incorporated in the United Kingdom)
Elms House, 43 Brook Green, LONDON, W6 7EF, United Kingdom (72) Inventor(s):
Simon Maddison Peter Wright (74) Agent and/or Address for Service:
D Young & Co LLP
120 Holborn, LONDON, EC1N 2DY, United Kingdom (54) Title of the Invention: A sensor device with a tilt meter, wireless communication facility and magnetic fixing Abstract Title: Tunnel distortion detection method using sections 1 to N each side of the vertical axis of the tunnel and tilt sensors on each section to record movement (57) A method for calculating deformation within a tunnel. The tunnel has a cross-section comprising multiple sections (1 ...N) on each side of a vertical line down the centre of the tunnel; the first section (1) being attached to the base of the tunnel at an assumed fixed point and the endpoint of the upper section (N) representing the highest point of the tunnel cross-section. The method comprises fitting each section 1 to N with a tilt meter and measuring the tilt for that section; the measured tilt for that section is used in conjunction with the known length and initial angle of the section to calculate the horizontal and vertical components of the sectional movement. The horizontal movement of the sections 1 to N are summed to obtain the horizontal movement of the tunnel, and the vertical movement of the sections 1 to N are summed to obtain the vertical movement of the tunnel.
Sensor Electronics 110
201A
/* FIG. 3
100
100
201B
202C
201C
60mm
FIG. 7
201A
FIG. 9
Sensor Housing 105
210
FIG. 11 c (n=3) \ D (n=3)
FIG. 12
A SENSOR DEVICE WITH A TILT METER, WIRELESS COMMUNICATION FACILITY AND MAGNETIC FIXING
Field of the Invention
The present invention relates to a sensor device containing a tilt meter and a wireless communication facility, the sensor device also having a magnetic fixing for attaching the housing to a surface of a structure to be monitored by the tilt meter.
Background of the Invention
The construction industry uses a variety of instrumentation to perform monitoring of structures such as tunnels, bridges, buildings and so on. Such instrumentation typically comprises sensor devices that are rigidly attached, for example by screws, to a structure to be monitored. In many situations, the monitoring is performed at locations that do not have a pre-existing or at least a readily accessible wired infrastructure for providing power and for supporting data communications to/from the sensors. In these circumstances, it is attractive forthe sensors to use wireless communications and to be battery-powered devices. Senceive Ltd (see wwwAencejvejx)m) provides wireless sensor devices that create and utilise a wireless mesh network for data communications, thereby allowing the nodes to work cooperatively to monitor (for example) environments, structures, plant and buildings. The wireless mesh network offers great flexibility to the operator in terms of where the sensors are to be located (or relocated). However, existing approaches to the deployment of sensor devices make it difficult to exploit the full potential of such flexibility.
Summary of the Invention
One aspect of the invention provides a method for calculating the distortion within a tunnel. The tunnel has a cross-section comprising multiple sections (1 ...N) on each side of a vertical line down the centre of the tunnel, each section having a known length and initial angle. The section (1) is attached to the floor or base of the tunnel at an assumed fixed point. The endpoint of section (N) represents the highest point of the tunnel cross-section. The method comprises fitting each section 1 to N with a tilt meter and measuring the tilt for that section using the tilt meter (for example, this may be done using a sensor device as described herein). For each section 1 to N, the measured tilt for that section is used in conjunction with the known length and initial angle of the section to calculate the horizontal and vertical components of the movement of the section. The horizontal movement of the sections 1 to N are summed to obtain the horizontal movement of the tunnel, and the vertical movement of the sections 1 to N are summed to obtain the vertical movement of the tunnel. (Two values of the vertical movement of tunnel are obtained initially, one from the left side of the tunnel, the other from the right side of the tunnel - these can be readily combined into a single best estimate for the vertical tunnel movement).
One embodiment of the invention provides a sensor device comprising: a housing containing a tilt meter and a wireless communication facility configured to transmit data from the tilt meter; and a fixing for attaching the housing to a surface of a structure to be monitored by the tilt meter. The fixing has a triangular configuration of first, second and third magnets for magnetically supporting the sensor device on the surface. The magnets are located substantially on the periphery of the fixing. When the housing is attached onto the surface by the magnets for use of the tilt meter, the first and second magnets are spaced apart from one another in a substantially horizontal direction, and the third magnet is located vertically above or below and horizontally between said first and second magnets.
The use of the magnets for fixing the sensor device to a surface allows the sensor device to be rapidly and conveniently installed onto the surface, and also rapidly and conveniently removed from the surface (for potential redeployment elsewhere). The use of such a magnetic fixing is complemented by the wireless communication facility, so that the sensor device does not require a fixed communications infrastructure for data communications. For example, the wireless communication facility may allow the sensor device to function as a node within a wireless mesh network (in which other sensor devices generally act as nodes within the network). Accordingly, multiple sensor devices might be supported by an existing (or newly installed) wireless access point. The sensor device may also be battery powered, so that the sensor device does not require a fixed infrastructure for power supply. Thus the battery and wireless data communications obviate the need for a hard-wired or intrusively-fixed electrical installation, while the magnetic fixing in complementary fashion avoids the need for a hard-wired or intrusively-fixed mechanical installation. Accordingly, the sensor devices can be readily and conveniently reconfigured on a dynamic basis to satisfy ongoing needs.
The triangular configuration of magnets supports positioning the sensor device so that it is level (i.e. approximately horizontal), which facilitates correct operations of the tilt meter. This positioning support is helpful, since the magnets will tend to draw the sensor device towards the surface, and a different configuration may tend to pull the sensor device slightly away from the correct orientation. Stability of the magnetic fixing may be improved by having the smallest internal angle of the triangular configuration being at least 45 degrees (this can also be seen as minimising the footprint of the sensor device on the wall for a given level of stability). Horizontal positioning of the sensor device is further facilitated by having the third magnet located halfway between the first and second magnets, so that the triangular configuration comprises an isosceles triangle which is symmetrical about a vertical axis.
In some embodiments, the third magnet is located vertically above the first and second magnets. The fixing may comprise a bracket having a base portion which is attached to the underside of the sensor housing and an upright portion supporting the triangular configuration of magnets. Accordingly, the upright portion of such a bracket supports the fixing onto the wall, while the base portion supports the housing onto the bracket. In some embodiments, the magnets are held onto the fixing by screws passing through the magnets, and the housing may be held onto the fixing by screws. A slightly different approach is to have the fixing formed as part ofthe housing, e.g. so that the fixing and housing are integrated together into a single unit.
In some embodiments, each magnet comprises a neodymium rare earth magnet, although the skilled person will be aware of other suitable materials. Each magnet may produce a direct force in the range 5-25 kgf for attaching the housing to a surface - more usually a direct force in the range 10-20 kgf. (The force of attraction is generally measured with respect to removing the magnet directly from a plate of steel at least 1mm thick). Having a magnet force in the range mentioned above provides for secure attachment ofthe magnet to the inside ofthe tunnel, while also allowing workmen to remove the sensor device from the tunnel wall when desired without undue difficulty.
A sensor device as described herein may be used to measure distortion or movement of a structure to which the sensor device is attached. Typically multiple sensor devices (a network of such devices) are attached to the structure to provide a more accurate determination of any movement or distortion across a larger region ofthe structure. Examples of such structures are tunnels (for the underground/subway, for ordinary rail or road traffic, etc), buildings, bridges, rail networks, steel sheet pile walls, and so on. In some cases the structure may be formed or lined at least in part using a suitable (magnetic) metal which can then be used to magnetically fix the sensor device(s) to the structure. Alternatively, a structure may be provided with a set of metal plates specifically for attaching sensor devices to the structure at desired locations.
Another aspect ofthe invention provides a sensor device comprising: a housing containing a tilt meter and a wireless communication facility configured to transmit data from the tilt meter; and a fixing for attaching the housing to a surface of a structure to be monitored by the tilt meter. The fixing has a triangular configuration of first, second and third magnets for magnetically supporting the sensor device on the surface. The magnets are located substantially on the periphery ofthe fixing so that the fixing is not significantly larger than the sensor as a whole, with the longest side of the triangular configuration being no more than twice the length ofthe shortest side ofthe triangular configuration.
Brief Description ofthe Drawings
Various embodiments ofthe invention will now be described in detail by way of example only with reference to the following drawings:
Figure 1 is an image showing a number of sensor devices deployed in an underground (metro) tunnel;
Figure 2 is a schematic diagram ofthe main functional components ofthe sensor device of Figure 1;
Figure 3 is a side view (elevation) of a sensor device of Figure 1;
Figure 4 is a view from underneath the sensor device of Figure 3;
Figure 5 is a back view (i.e. as seen in effect through the surface to which the sensor device is to be attached) ofthe sensor device of Figure;
Figure 6 is an image showing the sensor device of Figures 3-5 as deployed;
Figure 7 is another image showing the sensor device of Figures 3-5 as deployed (from a somewhat different angle compared with Figure 6);
Figure 8 is a simplified version of the back view of Figure 5 for explaining how the sensor device is attached to and removed from a surface;
Figure 9 is a back view of a sensor device;
Figures 10 and 11 are schematic views of the sensor device attached to a surface; and
Figure 12 is a schematic diagram corresponding to a deployment situation such as shown in Figure 1, whereby readings from sensor devices such as shown in Figures 3-5 are used to measure any distortion of the tunnel in which the sensor devices are located.
Detailed Description
Figure 1 shows an underground (metro/subway) tunnel which is part of the London Underground (RTM) network during an engineering project. The tunnel lining comprises a set of metal structures (segments), with each metal structure (segment) having: (i) a base portion 30 which is generally rectangular (ignoring the curvature of the tunnel) and which extends around the circumference of the tunnel, i.e. the base portions 30 are generally perpendicular to a radial direction of the tunnel; (ii) a first pair of opposing walls or flanges 40 protruding from respective edges of the base portion into the tunnel, where these flanges 40 run in a circumferential (azimuthal) direction, i.e. the flanges 40 are generally perpendicular to an axial direction of the tunnel; and (iii) a second pair of opposing walls or flanges 50 protruding from respective edges of the base portion into the tunnel, where these flanges run in an axial direction, i.e. the flanges 50 are generally perpendicular to a circumferential direction of the tunnel. It will be appreciated that the base portions 30 in effect separate the tunnel from the external environment, while the two pairs of walls 40 and 50 are used for joining the structures together and for enhancing mechanical strength.
One of the problems in maintaining the structural integrity of tunnels such as shown in Figure 1 is that material immediately outside the tunnel, such as soil, can be eroded, for example by water. This leaves a gap on the outside of the base portion 30 which can impact the distribution of stress, etc.. One known counter-measure to this problem is to supply concrete grouting at pressure to the outside of the tunnel (through suitable openings in the tunnel lining), thereby providing more reliable and consistent external bracing for the tunnel.
On the other hand, it is also important that the grouting procedure itself does not cause any distortion of the tunnel. Therefore, during the grouting procedure, the tunnel lining can be provided with multiple sensor devices 100 in order to detect any such distortion. As shown in Figure 1, these sensor devices 100 are attached to the inwardly-directed, circumferential flanges 40. Since the sensor devices may potentially remain in position while trains pass through the tunnel (whether for passenger services or for engineering tasks), it is important that the sensor devices do not protrude past the rim of the flanges 40 - i.e. they do not extend further towards the centre of the tunnel than the flanges themselves. This ensures that the sensor devices will not be struck by any passing train.
It is also important that the sensor devices 100 are reliably attached to tunnel lining, so that they do not fall from the wall - especially in the event of air turbulence caused by a passing train.
Figure 2 is a schematic diagram of the sensor electronics 110 within the sensor devices 100 shown in Figure 1 in accordance with one embodiment of the invention. The dashed lines shown in Figure 2 indicate power supply lines, while the solid lines shown in Figure 2 represent data communications links. The sensor electronics include a tilt sensor 127 to measure movement (especially tilt about two axes). The tilt sensor may comprise, for example, an accelerometer or an electrolevel sensor, and may be fabricated, for example, as a MEMS (micro-electro-mechanical system) sensor. The output from the tilt sensor 127 is passed via an analog-to-digital convertor 125 to a processor unit 123, which controls the overall operation of the sensor device. The sensor electronics also include a radio module 121 to allow the output from the tilt meter to be passed from the sensor device itself 100 to a suitable destination using a suitable wireless communications protocol, and likewise command instructions to be received into the sensor device 100. The sensor device is usually provided with an external antenna (not shown in Figure 2) to support these wireless communications. The sensor electronics 110 further include a battery 129 to provide power to the various electrical components of the sensor device 100. The battery may be large enough to allow for an operational lifetime measured in one or more years before recharging or replacement is required.
In one embodiment, the sensor devices 100 communicate at a frequency of 2.4 GHz within the ISM (industry, scientific and medical) band in compliance with IEEE 802.15.4. The data rate is 250 kbits per second, with a typical duty cycle of 1%. The point-to-point range between one sensor device 100 and another sensor device (or the wireless access point) is generally tens of meters (and may be over 100 meters outdoors). It will be appreciated that other sensor devices 100 may have different communication parameters according to the requirements and considerations of any particular implementation.
In one embodiment, the sensor devices 100 form a homogeneous set of nodes within a mesh network. Thus any individual sensor device, in particular the radio module 121, may transmit its own results to another node (sensor device) in the network, and/or forward results from one or more other nodes over the mesh network. The sensor results can then be collected from (and via) the mesh network by a wireless access point for analysis and review. Likewise, the wireless access point can be used to transmit commands and so on to the nodes over the mesh network. The wireless access point can interface to any appropriate network. For example, in some implementations, the wireless access point may link to a local computer - and from there to a wide area network, such as the Internet. In another implementation, the wireless access point may serve as a gateway to a GPRS (general packet radio service) link. The skilled person will be aware of other potential forms of connectivity for the wireless access point.
The use of a mesh network for connecting the sensor devices 100 provides a robust communications architecture, in that even if one path might fail, for example, because a given sensor device fails (at least in part), or because of the presence of an obstacle, devices that were using this path may be able to maintain communications via an alternative path over the mesh network. Furthermore, the mesh network supports dynamic reconfiguration, for example, if the sensor devices are moved with respect to one another or if one or more sensor devices are added to or removed from an existing network. This dynamic reconfiguration may result in the network forming new links between nodes (sensor devices) that are now able to communicate with one another; conversely, the reconfiguration may result in the network breaking (ending) old links between sensor nodes that are no longer able to communicate with one another - for example, because they are now separated by some obstacle, or because one of the sensor nodes has been removed from the network. Note that such dynamic reconfiguration in terms of the wireless communications occurs automatically (it does not have to be controlled or specifically commanded by an operator). Further information about wireless mesh sensor networks can be found, inter alia, in “The SECOAS Project - Development of a Self-Organising, Wireless Sensor Network for Environmental Monitoring” by Britton and Sacks, available at: http;//wyAyjancs,ac,Ark/Maff/01grshaj2/sgcpas/gANFA?2004-Brjttgn,pdf, and “Wireless Sensor Network Survey” by Yick et al, in Computer networks, Volume 52, Issue 12, 22 August 2008, pages 2292-2330.
The provision of the battery 129 in sensor devices 100 and the use of the wireless mesh network facility for communications remove any need for an existing wired infrastructure to provide power or data communications to the sensor devices 100. At most, an operator has to provide at least one wireless access point within range of the overall mesh network (and even if such a wireless access point does not already exist, it is generally much simpler to introduce this single access point than it is to introduce a complete wired infrastructure for multiple different sensor devices). Accordingly, a wireless mesh sensor network provides great freedom and flexibility for how the sensor devices 100 are deployed. Moreover, the ability to perform dynamic reconfiguration supports frequent repositioning of the sensor devices if required by the relevant project. For example, in the situation illustrated in Figure 1, support for dynamic reconfiguration of the wireless mesh sensor network allows the sensor devices 100 to be moved regularly to new positions in the tunnel as the engineering work (concrete grouting) progresses along the tunnel.
Although the wireless mesh sensor network avoids the need for the sensor devices 100 to have fixed electrical connections for power and data communications, the sensor devices must still have a secure mechanical attachment to the tunnel lining in order to allow the sensor devices to properly measure any movement of the tunnel lining. Indeed, the stability of this mechanical attachment is of great importance, since if the attachment is not secure, then the position of the sensor device might be altered (for example) by air turbulence resulting from a passing train, which would then make the output of the tilt meter 127 unreliable for the purpose of measuring any tunnel distortion. In addition, the security of the attachment of the sensor devices 100 to the tunnel lining is also important to prevent a sensor device becoming dislodged from the tunnel lining and falling onto or into the path of a passing train.
The approach described herein using a magnetic fixing to attach a sensor device 100 to a desired surface. This magnetic fixing is illustrated in Figures 3, 4 and 5, which provide a side view, underside view, and a back view of a sensor device 100 in accordance with one embodiment of the invention (where a back view would, in effect, be looking perpendicularly through a wall or surface to which the sensor device is attached in use). Please note that although these diagrams include measurements, these are for provided only as examples of dimensions by way of illustration to give an indication of approximate scale. It will be appreciated that other embodiments may have different dimensions, according to the particular needs of any given sensor device 100 and fixing surface.
The sensor device comprises a housing 105 and a bracket 210. The housing 105 is generally rectangular (cuboid) in shape and made of plastic (e.g. polycarbonate) or some other suitable (e.g. metallic) material. The housing 105 contains the sensor electronics 110, such as shown in Figure 2. As noted above, the housing 105 is provided with an external antenna (not shown in the Figures 3-5) to support wireless communications by the radio module 121.
The bracket 210 is used for attaching the sensor housing 105 and the sensor electronics 110 contained therein to a (substantially vertical) wall (the wall or other surface is not shown in Figures 35). The bracket 210 comprises a base portion 212, which sits under and supports the sensor housing 105. This base portion is generally horizontal when the sensor is attached to a vertical surface, thereby supporting the sensor electronics, especially tilt sensor 127, in a correct, horizontal configuration. The sensor housing 105 is fastened to the base portion 212 of the bracket 210 via screw holes 218B and 218A. It will be appreciated that the exact number, positioning and configuration of screws used to attach the sensor housing 105 to the bracket 210 may vary from one embodiment to another. In addition, other embodiments may use a different approach for attaching the sensor housing 105 to the bracket 210, for example a form of latch or other mechanical fastening. Furthermore, in other embodiments the sensor housing 105 and bracket 210 may be integrated into a single unit or structure.
The horizontal (base) portion 212 of the bracket 210 is generally flat and rectangular in shape, but could be any shape to provide appropriate support for the sensor housing 105. For example, the base portion might comprise two or more tines or prongs extending underneath the sensor housing. The base portion 212 of Figure 3 is joined to a vertical (fixing or upright) portion 216 by curved portion 214. In one embodiment, bracket 210 is formed from a flat sheet of metal which is bent into the configuration shown in Figures 3-5, namely base portion 212, curved portion 214, and upright portion 216. The central part of the curved portion 214 of Figures 3-5 is shaped into a raised ridge 215. It will be appreciated that this raised ridge 215 adds stiffness to help prevent the base portion 212 flexing with respect to the upright portion 216. (In other embodiments, the bracket 210 may be sufficiently rigid without the need for ridge 215, for example, because the bracket is made of thicker material).
The upright portion 216 supports three magnets, 201A, 201B and 201C, which are positioned on the side of the upright portion away from the sensor housing 105 in order to make contact with the support surface such as tunnel wall 40. In the embodiment illustrated in Figures 3-5, the magnets 201 are circular in shape (in effect, shallow cylinders), and each magnet has a central hole (202A, 202B and 202C respectively) which is used for fixing the magnets to the upright portion 216 of the bracket 210. It will be appreciated that in other embodiments, the magnets may have a different shape and/or a different mechanism of fastening to the bracket 210.
In one embodiment, the magnets are neodymium rare earth magnets, which provide a good combination of pull against volume/size. In particular, the magnets 201 illustrated in Figures 3-5 are pot magnets with a diameter of 25mm and a thickness of 8mm thick. Each magnet provides a nominal direct force of approximately 17 kgf (about 170N), assuming they are fixed to a steel surface having a thickness of at least 1mm, although the actual force provided may be somewhat less - e.g. around 10 kgf. (The force against shear removal, moving sideways rather than directly away from the surface, is usually somewhat less than this amount). As noted above, the magnets 201 illustrated in Figures 3-5 are drilled countersunk magnets to allow a screw fixing through central hole 202. One alternative mechanism for fixing the magnets 201 to the bracket 210 is to use a studded magnet of the same or similar dimensions - this can have a higher pull of approximately 20 kgf (about 200N) per magnet. It will be appreciated that the size, shape and/or material of the magnets 201 can be changed depending on the properties of the sensor 100 to be used (and the surface to which the sensor is to be attached).
The mechanical fixing provided by magnets 201 allows the sensor device 100 to be rapidly and accurately positioned on a desired surface. Similar, the use of magnets 201 allows the sensor device 100 to be quickly removed from the surface without leaving any marks, fixtures, etc. Accordingly, the magnetic fixing complements the battery power and wireless mesh network in supporting rapid deployment and (quick) dynamic reconfiguration. This can be especially important in an environment such as the underground deployment shown in Figure 1, in which there are only very limited 4-hour night working shifts for maintenance and engineering operations, after which the tunnel must be made available again for passenger traffic.
Moreover, the magnetic fixing has been subject to rigorous testing and found to provide very secure attachment to a tunnel wall 40. For example, dummy nodes (i.e. having no sensor electronics 110 in the sensor housing 105, but just an equivalent mass) were put in running tunnels for a period of time, but surrounded by a protective mesh or net to ensure that they could not fall onto the track. Performance during this testing was extremely good, and there was no indication of any movement of the devices, except in one case where there appeared to be significant dirt and dust underneath a magnet. Accordingly, prior to attaching the magnets 201 to the surface 40, it is important that the surface 40 is reasonably free of dirt, especially brake dust and rust. If such dirt is found to be present, the surface can be cleaned, for example by using a wire brush, and this then allows a secure attachment to be formed.
Figures 6 and 7 are images showing examples of a sensor device 100 such as illustrated in Figures 3-5 being deployed within a railway tunnel, such as shown in Figure 1. In particular, the sensor device is fixed to wall 40 so that it is held close to the tunnel lining, namely wall 30, and is therefore out of the way of any passing train. The sensor housing 105 (and hence sensor device 100) is provided with an antenna 115, as mentioned above, to support wireless communications. Although this antenna 115 is shown in Figures 6 and 7 as extending straight from the sensor housing 105 away from the wall 40, the antenna 115 is provided with a joint 116 to allow it to be bent or folded in a different direction, depending on the available space. This then enables the sensor device 100 to be fitted into a wider range of locations.
The sensor housing 105 is supported by a bracket 210 comprising base portion 212 which is joined to the upright portion 216 by curved portion 214. A ridge 215 is formed in the curved portion 214 to enhance stiffness. The bracket is fixed to the wall 40 by magnets 201 A, 201B, 201C. The magnets are fixed to the upright portion 216 by screws, see for example screw 203A which passes through hole 202A (see Figure 5). The bracket 210, in particular base portion 212, is in turn fixed to sensor housing 105 by screws to provide rigid support for the sensor, see for example screw 219B which passes through hole 218B (see Figure 4).
The use of (exactly) three magnets to attach the sensor device 100 to a desired surface, such as flange 40 (see Figure 1), has various advantages. Having three magnets has been found to provide an appropriate amount of fixing force - i.e. sufficient to reliably and robustly support the sensor device 100 on a desired surface, while at the same time not being so excessive as to make it difficult for a human operator to remove the sensor device from the surface if/when the sensor device needs to be repositioned. A further advantage is that the use of three magnets generally ensures that all three of the magnets are in direct and stable contact with the support surface, even if the support surface is not entirely flat. In contrast, if just one or two magnets were to be used, there would be an increased possibility that the sensor device could be wobbled somewhat in its attached position (e.g. about an axis formed by a line joining the two magnets), which would then impact the readings from the tilt sensor 127. Likewise, if four or more magnets were to be used, there is a possibility that at least one of the magnets might not make direct contact with the attachment surface due to variations in the level of the surface (analogous to a wobbly table). Again, this leads to an increased likelihood that the sensor device could be wobbled somewhat in its attached position and hence might produce spurious readings from the tilt sensor 127.
A further benefit of using (exactly) three magnets 201 for fastening the sensor device 100 to a surface is that when the sensor device has to be removed from the surface, an operator only needs to overcome the force of a single magnet at a time. This is illustrated in the schematic diagram of Figure 8 (which omits some of the details of Figure 5 for clarity). Thus the sensor device 100 can be removed by first pulling the top of the upright portion 216 of bracket 210, and in particular, magnet 201 A, away from the attachment surface. This movement in effect rotates the bracket 210 about line X1-X1 (shown as a dashed line in Figure 8), which passes through the two remaining magnets 201B, 201C. Accordingly, this rotation primarily has to overcome the attraction of magnet 201A to the fixing surface, but not the attraction of magnets 201B, 201C. The bracket 210 can then be rotated about line X2-X2, which passes vertically through magnet 201B, to remove magnet 201C from the surface (alternatively rotating about a line passing vertically through magnet 201C to remove magnet 201B from the surface is an equivalent approach). The bracket 210 can then be lifted away from the fixing or attachment surface to break the hold of the final magnet (201B or 201C).
The triangular configuration of magnets shown in Figures 5 and 8 has two magnets 201B,
201C spaced apart from one another at the same horizontal level (according to the orientation when the sensor device 100 is in use), and a third magnet 201A located vertically above and between the two horizontal magnets. One advantage of this approach is that when removing the sensor device 100 from a surface, the rotational movements described above occur about a horizontal axis (X1-X1) and then a vertical axis (X2-X2) as shown in Figure 8. It will be appreciated that it is relatively easy for an operator to judge such horizontal and vertical axes. (In contrast, it is somewhat harder for an operator to judge a rotation about an inclined axis, such as from magnet 201A to magnet 201B, which would be needed if it were desired, for example, to remove magnet 201C first from the surface).
In some embodiments, a further consideration for the configuration of the magnets is that the sensor device 100 must be attached to a desired surface so that the tilt sensor is approximately level,
i.e. so that base portion 212 of the bracket 210 is substantially horizontal. Note that as the magnets approach the wall 40 (or other fixing surface), they start to attract the sensor device 100, and in particular upright plate 216, strongly towards the wall 40 (such an attraction does not exist, for example, if only a screw fixing is being used to attach a sensor device to a surface). It is important that this strong attraction does not bias or prevent the sensor device from being positioned with the correct (horizontal) orientation for base portion 212.
The horizontal spacing of magnets 201B and 201C facilitates the attachment of the sensor device 100 to wall 40 at the correct orientation. One approach for such fixing is to tilt the base plate forwards by rotating about line X1-X1 in Figure 8, so that the magnet 201A makes initial contact with the wall 40. The magnet can then be tilted back so that the upright portion 216 is vertical again by rotating about an axis parallel to line X1-X1 but through magnet 201A (rather than through magnets 201B and 201C). This brings magnets 201B and 201C into contact with surface 40, thereby fixing the sensor device to the surface using all three magnets 201. Note that this approach only involves rotation about horizontal axes, which is relatively easy for an operator to assess, and since magnets 201B and 201C approach the wall in unison, there is no tendency to twist or bias the orientation of the bracket away from having the base portion 212 substantially horizontal.
An alternative approach is to fix the sensor device 100 to wall 40 in substantially the reverse of the procedure described above for removing the sensor device from the wall - namely, one of the two horizontally spaced magnets (say 201B) is first attached; the bracket is then rotated about vertical line X2-X2 to attach the other horizontal magnet (201C); and finally the bracket is rotated about horizontal line X1-X1 to attach the remaining, vertically separated magnet 201 A.
The most sensitive part of the fixing procedure occurs when attaching the second magnet to the surface, since the second magnet must attach to the wall at the correct position to ensure the appropriate final orientation (with the base portion 212 substantially horizontal). Having the triangular configuration of magnets shown in Figures 5 and 8 supports such a result. For example, if magnet 201A is attached to the wall first, the second (and third) magnets can be fixed to the wall at the same time as one another through rotation about a horizontal axis through magnet 201A (parallel to the surface of the wall 40). Alternatively, if magnet 201B or 201C is attached to the wall first, the rotation used to attach the second magnet is performed about a vertical axis, perpendicular to the horizontal spacing of magnets 201B and 201C (such as axis X2-X2 shown in Figure 8). It is generally easier for a human operator to judge and maintain this rotation about a horizontal or vertical axis, compared with rotation about an inclined axis. Accordingly, the triangular configuration of magnets shown in Figures 5 and 8, and in particular having two magnets level with one another (in terms of vertical positioning) but with a horizontal spacing, helps a human operator to attach the sensor device with the appropriate final orientation (with the base portion 212 substantially horizontal), despite the fact that the magnets 202 will be strongly attracted towards the wall during the fixing operation.
As shown in Figure 5, the magnets 201 are generally located around the periphery of the upright portion 216 of bracket 210. This positioning maximises the footprint of the fastening onto the desired surface compared to the size of the upright portion 216, which improves the stability of the fastening. Conversely, it effectively minimises the size of the upright portion 216 for a given footprint of magnetic fastening onto the desired surface. This is helpful, since the sensor device must often be positioned in a relatively confined space, such as on the flange 40 shown in Figure 1. Accordingly, the upright portion 216 of the bracket 210 will have a generally triangular shape to match the triangular configuration of the magnets 201.
This triangular shape may in effect be pointing up (as shown in Figure 5) or down (if the vertically spaced magnet is below the two horizontally spaced magnets). Both orientations offer the benefits described above in terms of fixing the sensor to the wall, or removing the sensor device from the wall. The best configuration (triangle pointing up or down) for any given implementation may depend on the particular geometry of the location in which a sensor device 100 is to be located. For example, in the tunnel environment shown in Figure 6, having the triangular configuration pointing upwards helps to fix the sensor device 100 at the desired location in the upper shoulder of the tunnel, since the incline of the triangular configuration of upright portion 216 approximately matches the incline of wall 40. In addition, the upright configuration of Figure 6 allows the sensor housing 105 to be supported from underneath without causing the footprint of the upright portion 216 to extend significantly outside the footprint of the sensor housing itself (when viewed from the end of the antenna 115). Conversely, having the triangle point down can help to fix the sensor device 100 at other locations, such as the lower shoulder in the tunnel.
The triangular configuration shown in Figure 5 is isosceles, with magnet 201A midway between magnets 201B and 201C. This symmetrical arrangement reflects the generally symmetrical configuration of the sensor itself. In addition, the internal angles of the triangular configuration are all reasonably large, for example, greater than 30 degrees. This assists with stability, since having a very small internal angle would result in a more linear configuration, approximating the presence of only two magnets and weakening the fixing.
Figure 9 illustrates another embodiment of the bracket 210, showing a rear or back view analogous to that of Figure 5. In the embodiment of Figure 9, the triangular configuration of three magnets 201 is retained, but the vertical separation is reduced compared with that of Figure 5. In particular, the vertical height of the upright portion 216 which is shown as 90 mm for the embodiment of Figure 5 is only 60 mm for the embodiment of Figure 9 (other aspects of the embodiment of Figure 9 generally match those of Figures 3-5). It will be appreciated of course that Figures 5 and 9 are presented only as examples, and many other sizings and configurations are possible.
Figures Wand 11 are schematic views of alternative configurations for the fixing the sensor device 100 to a surface 300 in accordance with further embodiments of the invention. In the embodiment of Figure 10, the sensor device fits snugly into curve 214 of bracket 210 (in comparison with the embodiment of Figures 3-5). This can lead to a more compact configuration in the dimension perpendicular to the wall 300 (which may be important for some implementations).
In the embodiment of Figure 11, the bracket 210 comprises just a single flat plate 216 which is vertical when the sensor device is attached to wall 300. This bracket 210 is attached to the back of the sensor housing (i.e. the wall of the housing closest to wall 300), rather than to the underside of the sensor housing 105 as for the embodiments of Figures 3-5. In this embodiment, the bracket 210 extends below (rather than above) the sensor housing 105: the triangular configuration of magnets 202 would therefore probably (although not necessarily) be arranged to point downwards in order to make the sensor device more compact overall. This shape of plate 216 would tend to fit better into a lower shoulder of a tunnel (for example). It will be appreciated that the embodiments of Figures 10 and 11 are provided by way of example only, and the skilled person will be aware of further potential configurations depending on the particular implementation. For example, the bracket 210 may be formed as an integral part of the sensor housing 105 - e.g. the bracket 210 in the embodiment of Figure 11 may represent an extension of the back wall of sensor housing 105, so that the magnets 201 are, in effect, attached directly to the sensor housing without the need for an additional (separate) bracket 210.
Figure 12 illustrates the method used to compute ring height deformation and ring width deformation for the tunnel grouting project shown in Figure 1 using a ring of sensor devices such as shown in Figures 3-5. As depicted in Figure 12, the tunnel is modelled as a regular octagon having a side of approximate length L=1500mm, with sensor devices located at locations A, B, C, D, E and F, and the bottom of the tunnel is assume to be fixed, as shown in Figure 12. Each location A ...F corresponds to a side (or section) of the tunnel. On each side of the tunnel we can define a sequence of sides (n=1, n=2, n=3) leading from the base of the tunnel, assumed to comprise fixed points F1 and F2 (one on each side of the tunnel) up to the highest point of the tunnel (V1), where side C and side D meet. The vertical deformation of the tunnel can then be determined based on the movement of point V1. The horizontal deformation of the tunnel is measured from the horizontal movement at points H1 and H2, which represent the vertices (where two sides join) that are horizontally furthest from the centre of the tunnel. If H1 and H2 both move in towards the centre of the tunnel, there is horizontal compression, and if they both move out, there is horizontal expansion. If H1 and H2 move together in the same direction (left or right), there is no net compression or expansion.
The movements of H1 and H2 are determined from the tilt measurements obtained by the sensor devices 100. Thus A rotating clockwise and F rotating anticlockwise will result in horizontal compression, while F rotating clockwise and A rotating anticlockwise will result in horizontal expansion. In particular, the horizontal movement at H1 is the result of the horizontal component of A rotating. Assuming an angle of movement (tilt) by A of a (degrees), H1 will move orthogonally to A by a distance of a=L.sin(a). The horizontal component of this movement is then given by HA=cos(22.50).a=cos(22.5°).1500.sin(a), where 22.5° is the angle between the vertical and the wall having a sensor device at location A (based on the geometry of a regular octagon). Similarly, the horizontal component of the movement of location F is given by HF=cos(22.5°).1500.sin(p), where β is the angle of movement (measured tilt) of F. The horizontal deformation is then given by HA- HF
The vertical deformation is measured by the vertical movement at point V1 - if it moves down, there is compression, if it moves up, there is expansion. This vertical movement is the aggregate of the individual vertical components arising from sides A, B & C, and also from sides D, E and F.
These two combinations of sides should produce the same vertical movement for point V1, although there may be a slight difference due to any distortion in the segments. One approach is to take the average vertical movement obtained from the two sides of the tunnel (A, B, C and D, E, F).
The vertical movement at H1 is the result of the vertical component of A rotating and is given by VA=sin(22.5°).1500.sin(a) (using analogous reasoning to that given above for the horizontal movement of H1). The movement for side B is 1500.sin(p), where β is the measured tilt or rotation for side B. The vertical component of this movement is VB = sin(22.5°).1500.sin^) since side B is also 22.5° from the vertical (and of length 1500). Finally, the movement for side C is 1500.sin(y), where γ is the measured tilt or rotation for side C. The vertical component of this movement is Vc=sin(67.5°).1500.sin(Y) since side C is 67.5° from the vertical (and of length 1500). The overall vertical distortion is therefore given by -VA+VB+VC= VD+VE-VF (the negative signs for VA and VF arise from the definition for the positive direction of rotation, which would tend to reduce the vertical height of these sides).
Although the above calculations have been performed for a regular octagon shaped tunnel having a particular length and angle, the same approach can generally be applied to any polygon shape. In particular, assuming the length and initial angle of the sides are known, then the tilt measurement angle can be converted (resolved) into a horizontal movement and vertical movement for that side by suitably adapting the calculations described above. The contributions (orthogonal components) for each side can then be summed to provide the total horizontal movement and the total vertical movement. In addition, the example of Figure 12 assumes only one sensor per side (section or segment). However, in some circumstances it may be appropriate to place multiple sensors along a single side or section in order to detect movement within this side or section (rather than just at a corner joining two sections).
Although the sensor devices described herein have primarily been deployed in an underground tunnel, they could be deployed instead in a wide variety of other structures, including: overground (non-metro) train tunnel; car tunnel; bridge; office building; railway embankment, a sheet pile wall, and so on. In some cases, such an environment may naturally have suitable locations with magnetic materials for magnetically fixing the sensor devices, e.g. as per the tunnel of Figure 1 to desired locations for monitoring. In addition, for structures that do not have existing metallic (magnetic) locations for attaching the sensor devices, metallic plates (such as steel) could be fitted to the structure to provide such locations. Note that the fitting of these metallic plates has a number of advantages compared with fitting the sensor devices directly to a non-metallic (say concrete) wall by some non-magnetic mechanical fixing (e.g. screws). For example, the metallic plates can be fitted once in a single pass or phase, and do not need to be removed from the wall each time the sensor devices are reconfigured. Further, the metallic plates should provide a good mechanism contact between the sensor device and the structure itself, thereby enabling more reliable measurements from the tilt meters. (Of course, the particular calculations described with reference to Figure 12 are generally applicable only to a tunnel - the skilled person will be able to develop suitable calculations for analysing movement in other types of structure).
Various embodiments of the invention are recited by way of example in the following numbered clauses:
1. A sensor device comprising:
a housing containing a tilt meter and a wireless communication facility configured to transmit data from the tilt meter; and a fixing for attaching the housing to a surface of a structure to be monitored by the tilt meter, said fixing having a triangular configuration of first, second and third magnets for magnetically supporting the sensor device on the surface, wherein the magnets are located substantially on the periphery of the fixing;
wherein when the housing is attached onto the surface by the magnets for use of the tilt meter, the first and second magnets are spaced apart from one another in a substantially horizontal direction, and the third magnet is located vertically above or below and horizontally between said first and second magnets.
2. The sensor device of clause 1, wherein the third magnet is located vertically above the first and second magnets.
3. The sensor device of clause 2, wherein the fixing includes a base portion which is attached to the underside of the sensor housing.
4. The sensor device of clause 3, wherein the fixing comprises a bracket having said base portion and an upright portion supporting said triangular configuration of magnets.
5. The sensor device of any preceding clause, wherein the smallest internal angle of said triangular configuration is at least 45 degrees.
6. The sensor device of any preceding clause, wherein the third magnet is located halfway between the first and second magnets, so that said triangular configuration comprises an isosceles triangle.
7. The sensor device of any preceding clause, wherein the housing is held onto the fixing by screws.
8. The sensor device of any of clauses 1 to 6, wherein the fixing forms part of the housing.
9. The sensor device of any preceding clause, wherein the magnets are held onto the fixing by screws passing through the magnets.
10. The sensor device of any preceding clause, wherein each magnet comprises a neodymium rare earth magnet.
11. The sensor device of any preceding clause, wherein each magnet produces a force in the range 5-25 kgf for attaching the housing to a surface.
12. The sensor device of clause 11, wherein each magnet produces a force in the range 10-20 kgf for attaching the housing to a surface.
13. The sensor device of any preceding clause, further comprising a battery for powering the wireless communication facility.
14. The sensor device of any preceding clause, wherein the wireless communication facility allows the sensor device to function as a node within a wireless mesh network.
15. A wireless mesh sensor network comprising multiple sensor devices as in clause 14 configured as nodes within a wireless mesh network.
16. The use of a wireless mesh sensor network as defined in clause 15 to measure distortion or movement of said structure.
17. The use of a sensor device as described in any of clauses 1 to 14 to measure distortion or movement of said structure.
18. The use of a sensor device as described in clause 16 or 17, wherein said structure comprises a tunnel.
19. The use of a sensor device as described in clause 18, wherein said tunnel is lined with metal.
20. The use of a sensor device as described in any of clauses 16 to 18, further comprising fitting the structure with metal plates for attaching the sensor device in different locations.
In conclusion, various embodiments ofthe invention have been described. The skilled person will appreciate that these embodiments are provided only by way of example, and different features from different embodiments can be combined as appropriate. Furthermore, the details of a sensor device will depend upon the particular environment in which it is installed, and the intended usage. Accordingly, the scope ofthe presently claimed invention is to be defined by the appended claims and their equivalents.

Claims (7)

Claims
1. A method for calculating the distortion within a tunnel, said tunnel having a cross-section comprising multiple sections (1 ...N) on each side of a vertical line down the centre of the tunnel, each section having a known length and initial angle, and wherein section (1) is attached to the floor or base of the tunnel at an assumed fixed point, and wherein the endpoint of section (N) represents the highest point of the tunnel cross-section, said method comprising:
fitting each section 1 to N with a tilt meter and measuring the tilt for that section using the tilt meter;
for each section 1 to N, using the measured tilt for that section in conjunction with the known length and initial angle of the section to calculate the horizontal and vertical components of the movement of the section;
summing the horizontal movement of the sections 1 to N to obtain the horizontal movement of the tunnel; and summing the vertical movement of the sections 1 to N to obtain the vertical movement of the tunnel.
2. The method of claim 1, wherein 2<N<20.
3. The method of claim 1 or 2, wherein the vertical movement is summed for sections 1 to N on each of the two sides of the tunnel, and the method further comprises determining the average vertical movement obtained from the two sides of the tunnel.
4. The method of any preceding claim, wherein the tunnel has a polygonal shape.
5. The method of claim 4, wherein the tunnel has a regular octagon shape.
6. The method of any preceding claim, wherein multiple sensors are located along a single side or section of the tunnel in order to detect movement within this side or section.
7. The method of any preceding claim, wherein the tilt meter fitted to each section is provided in a sensor device comprising:
a housing containing the tilt meter and a wireless communication facility configured to 35 transmit data from the tilt meter; and a fixing for attaching the housing to a surface of a structure to be monitored by the tilt meter, said fixing having a triangular configuration of first, second and third magnets for magnetically supporting the sensor device on the surface, wherein the magnets are located on the periphery of the fixing;
wherein when the housing is attached onto the surface by the magnets for use of the tilt meter, the first and second magnets are spaced apart from one another in a substantially horizontal direction, and the third magnet is located vertically above or below and horizontally between said first and second magnets.
29 03 18
Intellectual
Property
Office
Application No: GB1713214.3 Examiner: Mr Christopher Kent
7. The method of any preceding claim, wherein the tunnel is adapted for an underground railway.
8. The method of any preceding claim, wherein the tilt meter fitted to each section is provided in a sensor device comprising:
a housing containing the tilt meter and a wireless communication facility configured to transmit data from the tilt meter; and a fixing for attaching the housing to a surface of a structure to be monitored by the tilt meter, said fixing having a triangular configuration of first, second and third magnets for magnetically supporting the sensor device on the surface, wherein the magnets are located substantially on the periphery of the fixing;
wherein when the housing is attached onto the surface by the magnets for use of the tilt meter, the first and second magnets are spaced apart from one another in a substantially horizontal
5 direction, and the third magnet is located vertically above or below and horizontally between said first and second magnets.
Amendments to the Claims have been filed as follows:29 03 18
Claims
1. A method for calculating the distortion within a tunnel, said tunnel having a cross-section comprising multiple sections (1 ...N) on each side of a vertical line down the centre of the tunnel, each
5 section having a known length and initial angle, and wherein section (1) is attached to the floor or base of the tunnel at an assumed fixed point, and wherein the endpoint of section (N) represents the highest point of the tunnel cross-section, said method comprising:
fitting each section 1 to N with a tilt meter and measuring the tilt for that section using the tilt
10 meter;
for each section 1 to N, using the measured tilt for that section in conjunction with the known length and initial angle of the section to calculate the horizontal and vertical components of the movement of the section;
summing the horizontal movement of the sections 1 to N to obtain the horizontal movement of 15 the tunnel; and summing the vertical movement of the sections 1 to N to obtain the vertical movement of the tunnel.
2. The method of claim 1, wherein the vertical movement is summed for sections 1 to N on each 20 of the two sides of the tunnel, and the method further comprises determining the average vertical movement obtained from the two sides of the tunnel.
3. The method of any preceding claim, wherein the tunnel has a polygonal shape.
25 4. The method of claim 3, wherein the tunnel has a regular octagon shape.
5. The method of any preceding claim, wherein multiple sensors are located along a single side or section of the tunnel in order to detect movement within this side or section.
30 6. The method of any preceding claim, wherein the tunnel is part of an underground railway.
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