WO2016059462A1 - A method and apparatus for monitoring slender elements by means of dynamic measurements of structural asymmetry - Google Patents
A method and apparatus for monitoring slender elements by means of dynamic measurements of structural asymmetry Download PDFInfo
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- WO2016059462A1 WO2016059462A1 PCT/IB2015/001880 IB2015001880W WO2016059462A1 WO 2016059462 A1 WO2016059462 A1 WO 2016059462A1 IB 2015001880 W IB2015001880 W IB 2015001880W WO 2016059462 A1 WO2016059462 A1 WO 2016059462A1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
- G01M5/0025—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings of elongated objects, e.g. pipes, masts, towers or railways
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
- G01M5/0033—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings by determining damage, crack or wear
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
- G01M5/0066—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings by exciting or detecting vibration or acceleration
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
- G01M5/0091—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings by using electromagnetic excitation or detection
Definitions
- the invention relates to a method and a system for monitoring poles and in general slender elements (an antenna mast, a lamp post, a wind-turbine tower, a chimney stack, etc.) by means of at least two accelerometric sensors installed on the structure itself, aimed at detecting the structural integrity of the element monitored .
- a method for monitoring a slender structure that envisages a plurality of accelerometers capable of issuing a signal of acceleration and that operates with successive steps of acquisition and frequency transformation of the signals of the accelerometers in order to detect the variations in time of the frequency peaks thereof and then process these temporal variations so as to calculate both the mean values of the peak frequency, which represents the frequency of oscillation of the structure monitored, and a statistical value representing the variations in frequency with respect to the mean value.
- the method enables generation of an error signal.
- the main problem that limits the applicability of these techniques is that the values of the frequencies of the modes are not very sensitive to possible damage and are moreover susceptible to variations of temperature, formation of ice, deposition of snow, etc.
- sophisticated statistical techniques can mitigate these problems, but only partially.
- a first purpose of the present invention is hence to provide a monitoring device and a monitoring method that are free from the drawbacks of the systems of a known type. Summary of the invention
- a first advantage of the method according to the invention lies in the fact that it enables monitoring of the perturbations of the mode of vibration of the structure induced directly by phenomena of damage, and hence timely intervention to prevent any failure.
- FIG. 1 is a schematic illustration of a first example of application of an apparatus according to the invention
- Figure 2 is a schematic illustration of a second example of application of an apparatus according to the invention.
- Figure 3 is a schematic illustration of the amplitudes and the two directions of a doublet of modes of vibration of the structure
- Figure 4 is a schematic illustration of a further embodiment of an apparatus according to the invention.
- Figure 5 shows a diagram of an apparatus for implementation of the method according to the invention. Detailed description
- the method is implemented by means of an apparatus capable of acquiring the acceleration in two orthogonal directions by means of at least two accelerometric sensors 2 installed on the slender structure 1 parallel to the ground P and in directions x, y orthogonal to one another.
- the sensors 2 may for example be housed in a single device fixed to the structure. These sensors must be able to acquire the datum continuously for a sufficiently long time and store it for further processing.
- the above acquisition time must be considerably longer than the time of coherence of the structure .
- the time of coherence is approximately 300 s, but, in general the time of coherence of a structure can be measured as time of halving of the amplitude of the autocorrelation function of the accelerometric signal.
- the apparatus must then comprise measuring and processing means integrated with the sensor 2 or else connected to the sensor, such as a remote processor.
- Figure 2 represents schematically an alternative to the accelerometric sensors 2 constituted by installation of two inter ferometric radars oriented for irradiating the element/structure 1 from two, preferably mutually orthogonal, directions.
- a symmetrical structure (a pole, which may also be tapered, the base of which is a circle, an equilateral triangle, a square, or some other equilateral polygon) has, as is known, a certain number of modes of vibration characterized by a frequency of their own.
- a real structure will not, however, be altogether symmetrical, so that the structural asymmetry will produce splitting of the vibrational frequencies, which thus present in very close pairs or doublets.
- the invention exploits the fact that the possible opening of a crack at the base of the pole or slender structure or its inclination produces a much greater asymmetry, which can thus be measured, and a warning can be issued to signal that damage has occurred.
- the method according to the invention consequently comprises the following steps:
- the measurement of the variations of the difference between the two frequencies of the doublet is exploited, which is a direct measurement of possible structural damage or an anomalous inclination of the pole.
- a possible empirical formula for evaluating a threshold on the basis of which to issue an alarm is the following:
- fc is the central frequency of the vibration modes
- Afo is the splitting width measured during monitoring
- ⁇ is the splitting width predetermined or calculated in an observation or testing time TO.
- the constant a > 1 is a margin of tolerance that depends upon the structure under examination and can be estimated with a dynamic simulation of the structure.
- a variant of the technique just described consists in the detection of the variation of splitting of the higher-order modes, for example the second mode.
- the detection of the modes of vibration of the structure is more problematical because these modes are generally of smaller amplitude, but the variation of the frequency following upon damage or anomalous inclinations Af is greater and hence easier to measure.
- the method envisages the measurement of the ratio between the amplitudes of the two modes of the doublets as measurement representing the possible structural damage or an anomalous inclination of the pole.
- u and v represent the amplitudes and the two directions of the doublet and the ratio of the amplitudes of the two modes is a measurement of the asymmetry of the structure monitored.
- a possible empirical formula for issuing an alarm is the following :
- u is the mode of greater amplitude and v the mode of smaller amplitude.
- ⁇ depends upon the structure being monitored and can be estimated with an appropriate structural simulation.
- the method envisages as parameter that is an index of asymmetry the variation of the axes of symmetry .
- the angle ⁇ between the reference axis of the sensors (for example, the accelerometers) and the principal axis of symmetry can be estimated from the amplitudes measured in the two directions
- This angle is determined but for the sign.
- the sign can be obtained from the phase of the two signals (at the same frequency) , which in general may be either in phase or in phase opposition.
- this implementation of the method does not presuppose that the hypothesis of isotropicity of the vibrational stimulus is satisfied.
- a possible variant of the three methods described above makes use of a second biaxial sensor like the one installed on the structure, fixed to the ground in the proximity of the base of the pole.
- the two axes of this second sensor must be aligned to those of the first.
- the procedures described above apply in an altogether identical way to the accelerometric data correlated with the data acquired by the sensor fixed on the ground; namely,
- a x ,pole is the accelerometric datum acquired on the pole in the direction x, and is the accelerometric
- FIG. 5 is an apparatus for implementation of the method according to the invention, which envisages the sensors 2 or 4 connected to a computing unit 5 for sending the detection data, said unit being external or else integrated with the sensors and being in turn connected to a signalling device 6 that can be activated in response to calculation of a variation of the accelerometric data and/or of the displacements of the structure higher than pre-defined safety thresholds.
Abstract
A method for monitoring slender elements by means of dynamic measurements of structural asymmetry, comprising the following steps: continuous detection of accelerometric data (ax, ay) associated to pre-set points of the element (1); continuous measurement of the frequency (fx,y ) and/or of the amplitude (uxy; vxy) of the modes of vibration of the element (1) split into two as a result of a structural asymmetry of the element; calculation of variations of the difference in frequency monitored of the modes of vibration of each doublet of the element (1), and/or of the ratio in amplitude monitored of the modes of vibration of each doublet of the element (1), and/or of said angular variations (Θ); and issuing of an alarm ' message in response to a calculated value higher than a pre-set threshold value.
Description
METHOD AND APPARATUS FOR MONITORING SLENDER ELEMENTS BY
MEANS OF DYNAMIC MEASUREMENTS OF STRUCTURAL ASYMMETRY
******
Sector of the invention
The invention relates to a method and a system for monitoring poles and in general slender elements (an antenna mast, a lamp post, a wind-turbine tower, a chimney stack, etc.) by means of at least two accelerometric sensors installed on the structure itself, aimed at detecting the structural integrity of the element monitored .
Prior art
It is well known in the literature that the structural integrity of a slender element fixed at one end can be monitored by measuring its frequencies of oscillation. This can be done by installing one or more sensors (possibly pairs of sensors parallel to the ground, and orthogonal to one another) and exploiting as stimulus the loads induced by the wind, vehicle traffic in the vicinity, and earth tremors. These techniques are based upon the observation of the variation of the values of the frequencies of the modes with respect to an expected value, estimated with a theoretical model of the structure or with a statistical analysis .
From the patent application No. MI2009A001272, a method is known for monitoring a slender structure that envisages a plurality of accelerometers capable of issuing a signal of acceleration and that operates with successive steps of acquisition and frequency transformation of the signals of the accelerometers in order to detect the variations in time of the frequency peaks thereof and then process these temporal variations so as to calculate both the mean values of the peak frequency, which represents the frequency of oscillation of the structure monitored, and a statistical value representing the variations in frequency with respect
to the mean value.
In the case of deviation of the values beyond calculated ranges, the method enables generation of an error signal. However, the main problem that limits the applicability of these techniques is that the values of the frequencies of the modes are not very sensitive to possible damage and are moreover susceptible to variations of temperature, formation of ice, deposition of snow, etc. Furthermore, sophisticated statistical techniques can mitigate these problems, but only partially.
Purpose of the invention
A first purpose of the present invention is hence to provide a monitoring device and a monitoring method that are free from the drawbacks of the systems of a known type. Summary of the invention
The above and further purposes have been achieved with a device and a method for monitoring slender elements according to one or more of the annexed claims, which is able to exploit not only the value of the frequencies of the modes of vibration of the element monitored, but also the asymmetry of said modes induced by formation of a crack at the base of the structure or by the anomalous inclination of the slender structure itself.
A first advantage of the method according to the invention lies in the fact that it enables monitoring of the perturbations of the mode of vibration of the structure induced directly by phenomena of damage, and hence timely intervention to prevent any failure.
List of the drawings
The above and further advantages will be better understood by any person skilled in the branch from the ensuing description and from the annexed drawings, which are provided purely by way of non-limiting example and in which :
- Figure 1 is a schematic illustration of a first
example of application of an apparatus according to the invention;
Figure 2 is a schematic illustration of a second example of application of an apparatus according to the invention;
Figure 3 is a schematic illustration of the amplitudes and the two directions of a doublet of modes of vibration of the structure;
Figure 4 is a schematic illustration of a further embodiment of an apparatus according to the invention; and
Figure 5 shows a diagram of an apparatus for implementation of the method according to the invention. Detailed description
With reference to the attached drawings, there now follows a description of a method and an apparatus for monitoring slender elements by means of dynamic measurements of structural asymmetry.
In the embodiment described, the method is implemented by means of an apparatus capable of acquiring the acceleration in two orthogonal directions by means of at least two accelerometric sensors 2 installed on the slender structure 1 parallel to the ground P and in directions x, y orthogonal to one another.
In a preferred embodiment (illustrated in Figure 1), the sensors 2 may for example be housed in a single device fixed to the structure. These sensors must be able to acquire the datum continuously for a sufficiently long time and store it for further processing.
In particular, the above acquisition time must be considerably longer than the time of coherence of the structure .
By way of example, for a typical BTS (Base Transceiver Station) pole made of steel 40 m high, the time of coherence is approximately 300 s, but, in general the time of coherence of a structure can be measured as time of
halving of the amplitude of the autocorrelation function of the accelerometric signal. The apparatus must then comprise measuring and processing means integrated with the sensor 2 or else connected to the sensor, such as a remote processor.
Figure 2 represents schematically an alternative to the accelerometric sensors 2 constituted by installation of two inter ferometric radars oriented for irradiating the element/structure 1 from two, preferably mutually orthogonal, directions.
In the framework of the present invention, it is emphasized that, in general, a symmetrical structure (a pole, which may also be tapered, the base of which is a circle, an equilateral triangle, a square, or some other equilateral polygon) has, as is known, a certain number of modes of vibration characterized by a frequency of their own. A real structure will not, however, be altogether symmetrical, so that the structural asymmetry will produce splitting of the vibrational frequencies, which thus present in very close pairs or doublets.
These frequencies characterize mutually orthogonal vibrational modes.
The invention exploits the fact that the possible opening of a crack at the base of the pole or slender structure or its inclination produces a much greater asymmetry, which can thus be measured, and a warning can be issued to signal that damage has occurred.
The method according to the invention consequently comprises the following steps:
- continuous detection of accelerometric data ax, ay associated to pre-set points of the element 1 in at least two orthogonal directions x, y parallel to said plane, for a monitoring time Tm of a duration longer than the time of coherence of the structure;
- continuous measurement of the frequency fx, y and/or
of the amplitude uxy, vxy of the doublets of the modes of vibration of the structure 1 split into two as a result of the structural asymmetry, and/or continuous measurement of the angular variations Θ of the axes of symmetry of the element 1 with respect to the axes x, y;
continuous calculation, during the monitoring time, of the variations of the difference in frequency monitored Δfmxy, with respect to predetermined values AfOxy, of the modes of vibration of each doublet and/or of the ratio in amplitude monitored Um/Vm, and/or of the angular variations Θ; and
issuing of an alarm message in response to a calculated value of a variation (Afmxy - AfOxy) and/or of a ratio of amplitudes (Um/Vm) greater than a respective pre- set threshold value, and/or of an angular variation Θ greater than a pre-set threshold value.
In a first preferred embodiment of the method, the measurement of the variations of the difference between the two frequencies of the doublet is exploited, which is a direct measurement of possible structural damage or an anomalous inclination of the pole.
A possible empirical formula for evaluating a threshold on the basis of which to issue an alarm is the following:
where fc is the central frequency of the vibration modes, Afo is the splitting width measured during monitoring, ΔίΟ is the splitting width predetermined or calculated in an observation or testing time TO.
Since Afm may be too small to be measured, it is possible to assume this value as being equal to the measured spectral width of the frequency peak.
The constant a > 1 is a margin of tolerance that depends upon the structure under examination and can be estimated
with a dynamic simulation of the structure.
A variant of the technique just described consists in the detection of the variation of splitting of the higher-order modes, for example the second mode.
In this case, the detection of the modes of vibration of the structure is more problematical because these modes are generally of smaller amplitude, but the variation of the frequency following upon damage or anomalous inclinations Af is greater and hence easier to measure.
In a second embodiment, the method envisages the measurement of the ratio between the amplitudes of the two modes of the doublets as measurement representing the possible structural damage or an anomalous inclination of the pole.
With reference to Figure 3, if x and y are the directions of acquisition of the two accelerometers, u and v represent the amplitudes and the two directions of the doublet and the ratio of the amplitudes of the two modes is a measurement of the asymmetry of the structure monitored. A possible empirical formula for issuing an alarm is the following :
where u is the mode of greater amplitude and v the mode of smaller amplitude. The value β depends upon the structure being monitored and can be estimated with an appropriate structural simulation.
In a third embodiment, the method envisages as parameter that is an index of asymmetry the variation of the axes of symmetry .
With reference once again to Figure 3, the angle Θ between the reference axis of the sensors (for example, the accelerometers) and the principal axis of symmetry can be
estimated from the amplitudes measured in the two directions
This angle is determined but for the sign. The sign can be obtained from the phase of the two signals (at the same frequency) , which in general may be either in phase or in phase opposition.
A preferable alternative formula for measurement of the angle is the
It is emphasized that the measurement of the possible rotation of the principal axes of vibration (the angle Θ) is an important indicator of possible structural problems or anomalous inclinations of the structure. This technique is hence more sensitive both than the measurement of the variation of the widening of the difference in frequency of the modes of the doublet and than the measurement of the amplitude ratios.
Furthermore, this implementation of the method does not presuppose that the hypothesis of isotropicity of the vibrational stimulus is satisfied.
The methods described above have been implemented using sensors for acquiring accelerometr ic data applied to the slender structure monitored (Figure 1) or of inter ferometric radars arranged so as to irradiate the structure (Figure 2)
A possible variant of the three methods described above makes use of a second biaxial sensor like the one installed on the structure, fixed to the ground in the proximity of the base of the pole. The two axes of this second sensor
must be aligned to those of the first. The procedures described above apply in an altogether identical way to the accelerometric data correlated with the data acquired by the sensor fixed on the ground; namely,
where ax ,pole) is the accelerometric datum acquired on the pole in the direction x, and is the accelerometric
datum acquired on the pole in the direction y. The use of a second sensor enables normalization of the accelerometric datum with respect to the driving force due to the ground. This can improve the precision of the method described above, at the cost of a greater complexity of the system. Represented schematically in Figure 5 is an apparatus for implementation of the method according to the invention, which envisages the sensors 2 or 4 connected to a computing unit 5 for sending the detection data, said unit being external or else integrated with the sensors and being in turn connected to a signalling device 6 that can be activated in response to calculation of a variation of the accelerometric data and/or of the displacements of the structure higher than pre-defined safety thresholds.
The present invention has been described according to preferred embodiments thereof, but equivalent variants may be devised without thereby departing from the sphere of protection of the invention.
Claims
1. A method for monitoring slender elements by means of dynamic measurements of structural asymmetry, comprising the following steps:
continuous detection of accelerometric data (ax, ay) associated to pre-set points of the element (1) in at least two orthogonal directions (x, y) parallel to said plane, for a monitoring time (Tm) of a duration longer than the time of coherence of said element (1);
continuous calculation of the frequency (fx,y) and/or the amplitude (uxy; vxy) of the modes of vibration of the element (1) split into two as a result of a structural asymmetry of the element and constituting doublets of modes of vibration of the element (1), and/or of the angular variations (Θ) of the axes of symmetry of the element (1) with respect to the axes (x, y) ;
continuous calculation, during said monitoring time, of the variations of the difference in frequency monitored (Afmxy) , with respect to predetermined values (AfOxy) , of the modes of vibration of each doublet of the element (1), and/or of the ratio in amplitude monitored (Um/Vm) of the modes of vibration of each doublet of the element (1), and/or of said angular variations (Θ) ; and
issuing of an alarm message in response to a calculated value of a variation (Afmxy - AfOxy) and/or of a ratio of amplitudes (Um/Vm) greater than a respective preset threshold value, and/or of an angular variation (Θ) greater than a pre-set threshold value.
2. The method according to Claim 1, wherein said continuous calculation of the variations of the difference in frequency monitored (Afmxy) with respect to the mean value stored (AfOxy) is made by applying the formula
where fc is the central frequency of the mode of vibration and a is a threshold parameter of constant value.
3. The method according to Claim 1, wherein said predetermined value (AfOxy) is a mean value calculated preliminarily during a time of observation (To) of a duration longer than the time of coherence of said element (1) .
4. The method according to Claim 1, wherein said continuous calculation of the ratio in amplitude monitored (Um/Vm) of the modes of vibration of each doublet is made
where Urn is the mode of greater amplitude and Vm the mode of smaller amplitude, and the value of the parameter β is a value associated to the element (1) .
5. The method according to Claim 1, wherein said continuous calculation of said angular variations (Θ is made according to the formula
6. The method according to Claim 1, wherein said continuous calculation of said angular variations (Θ) is made according to the formula
7. The method according to any one of the preceding
llaims, wherein said accelerations (ax, ay) associated to pre-set points of the element (1) are accelerations correlated to accelerations detected by an accelerometr ic sensor fixed to the ground in the proximity of the base of the element (1) calculated according to the formula
where ax (pole) is an accelerometric datum of the element (1) in the direction x, is an accelerometric datum
detected by the sensor on the ground in the direction y, i s an accelerometric datum detected by the sensor on the ground in the direction x, and is an accelerometric datum of the element (1) in the direction y.
8. An apparatus for monitoring slender elements by means of dynamic measurements of structural asymmetry, comprising :
sensors (S1, S2) provided for continuous detection of accelerometric data (ax, ay) associated to pre-set points of a slender element (1) in at least two orthogonal directions (x, y) parallel to said plane, for a monitoring time (Tm) ;
measuring means (2, 3, 4) provided for continuous measurement of the frequency (fx,y) and/or of the amplitude (uxy; vxy) of the modes of vibration of the element (1) split into two as a result of a structural asymmetry of the element and constituting doublets of modes of vibration of the element (1), and/or of the angular variations (Θ) of the axes of symmetry of the element (1) with respect to the axes (x, y) ;
computing means (5) provided for continuous
calculation, during said monitoring time, of the variations of the difference in frequency monitored (Δfmxy) , with respect to predetermined values (ΔfOxy) , of the modes of vibration of each doublet of the element (1), and/or of the ratio in amplitude monitored (Um/Vm) of the modes of vibration of each doublet of the element (1), and/or of said angular variations (Θ) ; and
signalling means (6) provided for issuing an alarm message in response to a calculated value of a variation (Δfmxy - AfOxy) and/or of a ratio of amplitudes (Um/Vm) greater than a respective pre-set threshold value, and/or of an angular variation (Θ) greater than a pre-set threshold value.
9. The apparatus according to Claim 8, wherein said sensors comprise two accelerometric sensors (2) installed on the element (1) for measuring accelerometric data in the directions (x, y) , possibly housed in a single device fixed to the element ( 1 ) .
10. The apparatus according to Claim 8, wherein said sensors comprise two inter ferometric radars (3) that irradiate the element (1) preferably from two orthogonal directions .
11. An apparatus according to any one of Claims 8-10, wherein said sensors comprise two further accelerometric sensors (4) for measuring accelerometric data in the directions (x, y) , which are installed on the ground in the proximity of the base of the element (1) .
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| ITFI20140236 | 2014-10-17 | ||
| ITFI2014A000236 | 2014-10-17 |
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP3754321A4 (en) * | 2018-02-16 | 2021-04-14 | NEC Corporation | Facility state analyzing device, facility state analyzing method, and recording medium storing facility state analyzing program thereon |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4901575A (en) * | 1988-11-30 | 1990-02-20 | Gp Taurio, Inc. | Methods and apparatus for monitoring structural members subject to transient loads |
| EP1517141A1 (en) * | 2003-09-19 | 2005-03-23 | SAG Energieversorgungslösungen GmbH | Method for testing stability of partially burried metal poles |
| WO2011007249A1 (en) * | 2009-07-17 | 2011-01-20 | Vodafone Group Plc | Method and system for monitoring a thin structure |
-
2015
- 2015-10-15 WO PCT/IB2015/001880 patent/WO2016059462A1/en active Application Filing
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4901575A (en) * | 1988-11-30 | 1990-02-20 | Gp Taurio, Inc. | Methods and apparatus for monitoring structural members subject to transient loads |
| EP1517141A1 (en) * | 2003-09-19 | 2005-03-23 | SAG Energieversorgungslösungen GmbH | Method for testing stability of partially burried metal poles |
| WO2011007249A1 (en) * | 2009-07-17 | 2011-01-20 | Vodafone Group Plc | Method and system for monitoring a thin structure |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP3754321A4 (en) * | 2018-02-16 | 2021-04-14 | NEC Corporation | Facility state analyzing device, facility state analyzing method, and recording medium storing facility state analyzing program thereon |
| US11946603B2 (en) | 2018-02-16 | 2024-04-02 | Nec Corporation | Facility state analyzing device, facility state analyzing method, and recording medium storing facility state analyzing program thereon |
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