CN117073634A - Goods shelf inclination monitoring and early warning system - Google Patents

Goods shelf inclination monitoring and early warning system Download PDF

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Publication number
CN117073634A
CN117073634A CN202311045700.8A CN202311045700A CN117073634A CN 117073634 A CN117073634 A CN 117073634A CN 202311045700 A CN202311045700 A CN 202311045700A CN 117073634 A CN117073634 A CN 117073634A
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signal
shelf
change
light
value
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CN117073634B (en
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王志明
仲朝建
宣国义
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Suzhou Orgrima Storage Equipment Co ltd
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Suzhou Orgrima Storage Equipment Co ltd
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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
    • G01C9/02Details
    • G01C9/06Electric or photoelectric indication or reading means
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C9/00Measuring inclination, e.g. by clinometers, by levels
    • G01C9/02Details
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10Complex mathematical operations
    • G06F17/11Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/13Differential equations
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C9/00Measuring inclination, e.g. by clinometers, by levels
    • G01C9/02Details
    • G01C9/06Electric or photoelectric indication or reading means
    • G01C2009/066Electric or photoelectric indication or reading means optical

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Abstract

The application relates to an inclination monitoring technology, in particular to a shelf inclination monitoring early warning system, which comprises a group of light sources arranged on a shelf top, wherein a plane mirror is fixedly arranged on a shelf bottom right below each light source, the plane mirrors are obliquely arranged, one side of a mirror surface of each plane mirror is fixedly provided with a light sensor, the light sensors are used for converting light signals into electric signals, the light sensors are electrically connected with an upper computer, the upper computer is used for acquiring signals of the two light sensors, and the inclination degree of a shelf is determined according to the characteristics of the signals of the two light sensors. The application solves the problems in the prior art.

Description

Goods shelf inclination monitoring and early warning system
Technical Field
The application relates to an inclination monitoring technology, in particular to a shelf inclination monitoring and early warning system.
Background
In the related art, detection of the inclination of the shelf is generally achieved by a dedicated sensor, such as a force sensor, a distance sensor, or a sensor employing image monitoring, or monitoring using image monitoring and image analysis. However, this type of technology has a number of drawbacks. For example, the first problem is that in the case of monitoring using a sensor, the sensor is generally not stable for a long period of time with high accuracy, and in the case of monitoring using image monitoring and image analysis, image recognition often cannot achieve the resolution required for the image, so that the effect is poor. In the related prior art, the inclination of the goods shelf is detected by using a light interference principle, and the detection precision is high, the stability is high, but certain problems exist. The problem of this kind of detection is mainly that, in the second class of problems, when the accuracy of detection is too high, misjudgment and false alarm often occur. Mainly because a certain self-vibration amplitude exists when a common shelf is placed, particularly when the shelf is placed at a high position, due to the action of air and the slight shaking of a related building or foundation and the like, the self-vibration amplitude is small, and the slight shelf inclination can be caused, but the caused shelf inclination does not influence the gravity center position of the shelf, and the shelf is not changed greatly, namely the shelf is not inclined. And generally only when external forces act or the structure of the shelf itself is greatly changed, the tilting of the shelf may cause the shift of the center of gravity and thus the tilting.
Therefore, in the inclination detection of the shelf, since the shelf itself generally has a certain amplitude of natural shake, when the accuracy of the inclination detection device based on optical interference is adjusted too high, the natural shake of the shelf may be misjudged as dangerous inclination of the shelf, and thus a false alarm may occur.
Disclosure of Invention
The application aims to provide a shelf inclination monitoring and early warning system so as to solve the problems in the background technology.
In order to solve the technical problems, the application provides the following technical scheme:
the utility model provides a goods shelves slope monitoring early warning system, is including setting up a set of light source on the frame top, all fixed a plane mirror that sets up on the frame bottom under each light source, the plane mirror slope sets up, and the mirror surface one side of each plane mirror is all fixed to set up a light sensor, light sensor be used for converting light signal into the signal of telecommunication, light sensor and host computer electricity be connected, the host computer is used for obtaining the signal of two light sensors, confirms goods shelves inclination according to the signal characteristics who obtains two light sensors.
Further, a concave lens is fixedly arranged between the plane mirror and the light sensor, and the concave lens is fixedly arranged on the second mirror seat.
Further, the light sensor comprises a circular sensing collection area.
Further, the plane mirrors are arranged on the first mirror base, at least two groups of plane mirrors are arranged, and two groups of light sources and two groups of light sensors are correspondingly arranged.
Further, determining the degree of shelf tilt based on the signal characteristics of the two light sensors includes: the upper computer is used for acquiring signal value change time points of the two light sensors, sequencing the signal change values of the two light sensors according to the change time point intervals, calculating the change frequency of the signals, and determining the inclination degree of the goods shelf according to the change frequency of the signals.
Further, determining the degree of shelf tilt based on the signal characteristics of the two light sensors includes: the upper computer is used for acquiring signal value change time points of the two light sensors, sequencing the signal change values of the two light sensors according to the change time point intervals, calculating the change direction of the signals, and determining the inclination degree of the goods shelf according to the change direction of the signals.
Further, determining the inclination degree of the shelf according to the change direction of the signal specifically includes calculating the corresponding direction value of the change direction of the signal, obtaining the change time points of the signal values of the two light sensors, and sequencing the signal change values of the two light sensors according to the change time point interval, wherein the signal change value of one light sensor is used as a positive direction number, the signal change value of the other light sensor is used as a negative direction number, setting 0 when none of the light sensors has signal change, continuously inclining the signal change value to one of the positive direction and the negative direction in a certain period, indicating that the signal has a definite direction, and the maximum value of the continuous inclination is the direction value of the signal value.
Further, determining the tilt of the shelf based on the signal characteristics of the two light sensors includes determining the tilt of the shelf based on the functional characteristics of the signals: specifically, signal value change time points of two light sensors are obtained, the signal change values of the two light sensors are ordered according to the change time point intervals, the signal change value of one light sensor is used as a positive direction number, the signal change value of the other light sensor is used as a negative direction number, 0 is set when no signal change exists in any one light sensor, all the obtained signal change values are processed into function values related to time variables in a certain period, time sequence analysis, first derivative time ordering and second derivative time ordering are carried out on the obtained function values related to the time variables in the certain period, then a differential equation of the function values related to the time variables is established, then the differential equation is solved to obtain a corresponding general equation of the function values related to the time variables, and the inclination degree of the shelf at a future time point is estimated according to the general equation of the function values related to the time variables.
Further, a differential equation of the function value with respect to the time variable is established as follows:
f (2) +bf (1) +af=exp(r*t)(Q n1 (t)sinαt)+Q n2 (t)cosαt);
f is a hypothetical general equation, f (1) Is the first order derivative of f (2) A, b are corresponding constant coefficients, t is a time variable, r is an exponential coefficient, Q n1 (t),Q n2 (t) is a pending polynomial, n1, n2 are the corresponding powers; time frequency parameter with alpha being t; calculation of general equation front a, b, r, n1, n2, α and Q n1 (t),Q n2 (t) can be determined;
the general equation for solving the differential equation to obtain the corresponding function value with respect to the time variable is: f=t c *exp(r*t)(p 1 m (t)cosαt)+(p 2 m (t)sinαt);
Wherein c is determined by the method that when r+iα orC=0 when r-iα is not the root of the characteristic equation of the differential equation, and c=1 when r+iα or r-iα is the root of the characteristic equation of the differential equation; wherein i is-1 (1/2) Is an imaginary number value; wherein r is an index coefficient in the formula, m=max (n 1, n 2), p 1 m (t),p 2 m (t) polynomials each of which is t, m is the power of the corresponding polynomial, p 1 m (t),p 2 m The 1,2 in (t) is not the power but a distinguishing logo.
Furthermore, the upper computer adopts a PC.
Compared with the prior art, the application has the beneficial effects that:
the application does not calculate the inclination degree specifically aiming at the measured value of the sensor, but essentially judges the inclination degree by the characteristic of the numerical value difference of the two sensors in different directions. In practice, even if the sensor is used for a long time, the accuracy of the sensor is not stable, and the judgment result is not affected, because the application does not judge by using the measured value of the sensor, does not judge by using the absolute value, but judges by using the difference between two sensors and the characteristics thereof, such as the time domain characteristics, namely a relative value or the derivative value of the relative value, that is, in practice, even if the judgment of the sensor is not very accurate, the difference between the sensors still has the characteristics of reference significance and accurate characterization in practice, and can accurately characterize the inclination degree of a shelf, so that the accurate judgment can be made; unlike available technology, the present application has two kinds of sensor to detect change in the inclination of the shelf, and the change may be determined to be natural in certain limit or in normal range, and the alarm may not be given. Otherwise, the data analysis judges that the shelf scenario belongs to a dangerous scenario, belongs to a gravity center offset scenario, and alarms.
In summary, the present application can solve both the first type of problems and the second type of problems raised in the background art.
Drawings
FIG. 1 is a schematic diagram of the overall structure of the present application;
fig. 2 is a schematic view of the structure of the photosensor according to the present application.
In the figures, the pallet 100; a light source 200; a plane mirror 300; a first lens holder 400; a concave lens 500; a second lens holder 600; a photosensor 700; an upper computer 800; a roof 101; a frame base 102; the acquisition region 701 is sensed.
Detailed Description
The technical solutions of the embodiments of the present application will be clearly and completely described below in conjunction with the embodiments of the present application, and it is apparent that the described embodiments are only some embodiments of the present application, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
In a specific implementation, the application discloses a shelf inclination monitoring and early warning system, as shown in fig. 1, which is applied to a shelf 100, wherein the shelf 100 at least comprises an upper shelf top 101 and a lower shelf bottom 102, the shelf inclination monitoring and early warning system comprises a group of light sources 200 arranged on the shelf top 101, a plane mirror 300 is fixedly arranged on the shelf bottom 102 right below each light source 200, the plane mirror 300 is obliquely arranged, an optical sensor 700 is fixedly arranged on one side of a mirror surface of each plane mirror 300, the optical sensor 700 is used for converting optical signals into electric signals, a concave lens 500 is fixedly arranged between the plane mirror 300 and the optical sensor 700, the concave lens 500 is fixedly arranged on a second mirror base 600, the plane mirror 300 is arranged on a first mirror base 400, generally at least two groups of plane mirrors 300 are arranged, one group of plane mirrors 300 is used for detecting the inclination of the horizontal plane in the x-axis direction (such as the one shown in the drawing), the other group of plane mirrors 300 is used for detecting the inclination of the horizontal plane in the y-axis direction (i.e. the direction perpendicular to the drawing), as shown in fig. 2, the optical sensor 700 comprises a circular ring-shaped sensing collection area 701, because the scattered light of the concave lens 500 acts on the edge of the optical sensor 700, the circular ring-shaped sensing collection area 701 is arranged, and the distance adjustment enables more light to be collected in the sensing collection area 701 when the shelf 100 is completely horizontal and static, the optical sensor 700 is electrically connected with the upper computer 800, in particular through serial communication, and the upper computer 800 is used for acquiring signals of the two optical sensors 700 to determine the inclination degree of the shelf according to the signal characteristics of acquiring the two optical sensors 700.
In practice, the present application does not specifically calculate the degree of tilt for the measured values of the sensor in application. In essence, the application judges the inclination degree by the characteristic of the numerical difference of two sensors in different directions. In practice, even if the sensor is used for a long time, the accuracy of the sensor is not stable, and the judgment result is not affected, because the application does not judge by using the measured value of the sensor, does not judge by using the absolute value, but judges by using the difference between two sensors and the characteristics thereof, such as the time domain characteristics, namely a relative value or the derivative value of the relative value, that is, in practice, even if the judgment of the sensor is not very accurate, the difference between the sensors still has the characteristics of reference significance and accurate characterization in practice, and can accurately characterize the inclination degree of the shelf, thereby making a correct judgment.
The application basically detects the inclination of the shelf by adopting the light transmission and light detection principle, and is different from the prior art in that when the inclination of the shelf naturally shakes, the application adopts two groups of sensors to detect two inclinations which are changed, when the difference value of the change amplitude of the two changes is maintained within a certain limit, the change can be judged to belong to natural change, or the change frequency can be judged to belong to natural change in a normal range, and no alarm is given. Otherwise, the data analysis can judge that the shelf scenario belongs to the dangerous scenario, belongs to the scenario with the gravity center offset, and can give an alarm, the alarm can be jointly reminded to give an alarm by using sound and light, the specific upper computer 800 is electrically connected with a control circuit of a loudspeaker and an alarm lamp, and can be jointly reminded by using sound and light when the alarm is needed, and the positions of the loudspeaker and the alarm lamp can be on the shelf 100 or other positions convenient to remind.
The application can solve the first type of problems and the second type of problems which are improved in the background technology at the same time.
The first problem is that in the case of monitoring using a sensor, the sensor is generally not stable for a long period of time with high accuracy, and in the case of monitoring using image monitoring and image analysis, image recognition often cannot achieve the resolution required for the image, so that the effect is poor. The second problem is that when the detection accuracy is too high, misjudgment and false alarm often occur. Mainly because a certain self-vibration amplitude is usually present when a typical shelf is placed, particularly when the shelf is placed at a high level, due to the action of air and the slight shaking of the related building or foundation and the like.
Specifically, determining the degree of shelf tilt based on the signal characteristics of the two light sensors 700 includes:
the upper computer is configured to obtain signal value change time points of the two light sensors 700, sort the signal change values of the two light sensors 700 according to the change time point intervals, calculate a change frequency of the signal, and determine a shelf inclination degree according to the change frequency of the signal, for example, determine whether the frequency meets a condition. This allows to solve both the first and the second type of problems raised in the background art.
Specifically, the upper computer is configured to obtain signal value change time points of the two light sensors 700, sort the signal change values of the two light sensors 700 according to the change time point intervals, calculate a change direction of the signal, and determine a shelf inclination degree according to the change direction of the signal;
determining the inclination of the shelf according to the change direction of the signal specifically includes calculating the corresponding direction value of the change direction of the signal, obtaining the change time points of the signal values of the two light sensors 700, sorting the signal change values of the two light sensors 700 according to the change time point interval,
the signal change value of one optical sensor 700 is used as a positive direction number, the signal change value of the other optical sensor 700 is used as a negative direction number, and the signal change value of the other optical sensor 700 is set to 0 when no signal change exists in any optical sensor 700, for example, two optical sensors of A and B are shared, if the signal change values collected by the first and second optical sensors are respectively 1 and 2 in the case of collecting the first and second optical sensors, the signal change values collected by the first and second optical sensors are respectively 2 and 1 in the case of collecting the second optical sensors, the signal change values collected by the first and second optical sensors are respectively 3 and 1 in the case of collecting the second optical sensors, and after interval sorting, a signal change value group is obtained: 1. -2, -1,3, -1, wherein the first sensor signal variation number is a positive direction number and the second sensor signal variation number is a negative direction number, and wherein the signal variation number continuously tilts in one of the positive direction or the negative direction within a certain period, indicating that the signal has a definite direction, and the maximum value of the continuous tilt is the direction value of the signal value. And specifically judging the inclination degree of the goods shelf according to whether the direction value meets the threshold value. This also enables to solve both the first and second type of problems raised in the background art.
Therefore, the inclination degree of the whole goods shelf can be predicted by analyzing the change frequency and the change direction of the signals.
In a more specific implementation, to make a prospective prediction on a shelf, the present application determines the degree of shelf inclination based on the characteristics of the signals from which the two light sensors 700 are derived, including determining the degree of shelf inclination based on the functional characteristics of the signals: specifically, the time points of signal value changes of the two light sensors 700 are obtained, the signal change values of the two light sensors 700 are ordered according to the intervals of the time points of the changes, the signal change value of one light sensor 700 is used as a positive direction number, the signal change value of the other light sensor 700 is used as a negative direction number, the value is set to 0 when no signal change occurs in any one light sensor 700, all the obtained signal change values are processed into function values about time variables in a certain period (in the case, no definite function relation is provided, the function values about the time variables are only assumed), time series analysis, first derivative time ordering and second derivative time ordering are performed on the obtained function values about the time variables in the certain period, then a differential equation about the time variables is established, then the corresponding function value about the time variables is obtained by solving the differential equation, and the shelf inclination degree of the shelf at the future time points can be predicted in advance according to the function value about the general equation of the time variables.
Establishing a differential equation of the function value with respect to the time variable, and then solving the differential equation to obtain a general equation of the corresponding function value with respect to the time variable, wherein the general equation is established by the following specific steps (because the function value of the signal variation value with respect to the time variable has the characteristic of a trigonometric function, the trigonometric function is also taken as a framework in the basic composition of the differential equation):
f (2) +bf (1) +af=exp(r*t)(Q n1 (t)sinαt)+Q n2 (t)cosαt);
f is a hypothetical general equation, f (1) Is the first order derivative of f (2) A, b are corresponding constant coefficients, t is a time variable, r is an exponential coefficient, Q n1 (t),Q n2 (t) is a pending polynomial, n1, n2 are the corresponding powers; time frequency parameter with alpha being t;
calculation of general equation front a, b, r, n1, n2, α and Q n1 (t),Q n2 (t) can be determined;
such as: in practice one embodiment has the general formula: f (f) (2) +f=t*cos2t;
A=1, b=0, r=0 (exp (r×t) =1), Q n1 (t)=0,Q n2 (t)=t,n1=0,n2=1,α=2。
Then, the differential equation is solved to obtain a general equation of the corresponding function value with respect to the time variable as f=t c *exp(r*t)(p 1 m (t)cosαt)+(p 2 m (t)sinαt);
Wherein c is determined by c=0 when r+iα or r-iα is not the root of the characteristic equation of the differential equation, and c=0 when r+iα or r-iα is the root of the characteristic equation of the differential equation1, a step of; wherein i is-1 (1/2) Is an imaginary number value; wherein r is an index coefficient in the formula, m=max (n 1, n 2), p 1 m (t),p 2 m (t) polynomials each of which is t, m is the power of the corresponding polynomial, p 1 m (t),p 2 m 1,2 in (t) is not a power but a distinguishing logo;
for example, when in practice one embodiment has the general formula f (2) +f=t×cos2t is f= (at+b) sin2t+ (dt+e) cos2t according to the general equation of the method described above; a, B, D, E are all undetermined coefficients, and the above formula f= (at+b) sin2t+ (dt+e) cos 2t=t×cos2t is obtained after solving, i.e. f= (-1/3) t×cos2t+ (4/9) sin2t is obtained.
The predictive function value can be output by inputting the time variable t of the future time point through a general equation, the future signal change value can be predicted, and early warning can be performed in advance when the predicted future signal change value exceeds a threshold value.
It will be appreciated that the functions of the present application can be implemented by means of program code, corresponding program code stored on a machine-readable medium, which can be a tangible medium, which can contain, or store the program for use by or in connection with the instruction execution system, apparatus, or device. The machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium.
The machine-readable medium may include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples of a machine-readable storage medium would include an electrical connection based on one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. To provide for interaction with a user, the host computer described herein may be implemented on a computer, which can employ a PC machine, the computer having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to a user; and a keyboard and pointing device (e.g., a mouse or trackball) by which a user can provide input to the computer. Other kinds of devices may also be used to provide for interaction with a user; for example, feedback provided to the user may be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user may be received in any form, including acoustic input, speech input, or tactile input.

Claims (10)

1. The utility model provides a goods shelves slope monitoring early warning system, its characterized in that, including setting up a set of light source on the frame top, all fixed setting up a plane mirror on the frame bottom under each light source, the plane mirror slope sets up, and the mirror surface one side of each plane mirror is all fixed to set up a light sensor, light sensor be used for converting light signal into the signal of telecommunication, light sensor and host computer electricity be connected, the host computer is used for obtaining the signal of two light sensors, confirms goods shelves inclination according to the signal characteristics who obtains two light sensors.
2. The shelf inclination monitoring and early warning system according to claim 1, wherein a concave lens is fixedly arranged between the plane mirror and the light sensor, and the concave lens is fixedly arranged on the second mirror base.
3. The shelf tilt monitoring and warning system of claim 2, wherein the light sensor comprises a circular sensor collection area.
4. The shelf inclination monitoring and early warning system according to claim 1, wherein the plane mirrors are arranged on the first mirror base, at least two groups of plane mirrors are arranged, and two groups of light sources and two groups of light sensors are correspondingly arranged.
5. The shelf tilt monitoring and warning system of claim 1, wherein determining the degree of shelf tilt based on the signal characteristics of the two light sensors comprises: the upper computer is used for acquiring signal value change time points of the two light sensors, sequencing the signal change values of the two light sensors according to the change time point intervals, calculating the change frequency of the signals, and determining the inclination degree of the goods shelf according to the change frequency of the signals.
6. The shelf tilt monitoring and warning system of claim 1, wherein determining the degree of shelf tilt based on the signal characteristics of the two light sensors comprises: the upper computer is used for acquiring signal value change time points of the two light sensors, sequencing the signal change values of the two light sensors according to the change time point intervals, calculating the change direction of the signals, and determining the inclination degree of the goods shelf according to the change direction of the signals.
7. The system of claim 6, wherein determining the degree of tilt of the shelf according to the direction of change of the signal comprises calculating a corresponding direction value of the direction of change of the signal, obtaining time points of signal values of the two light sensors, and sorting the signal values of the two light sensors according to the time point of change, wherein the signal value of one light sensor is a positive direction number, the signal value of the other light sensor is a negative direction number, setting to 0 when none of the light sensors is changed, and continuously tilting the signal value in one of the positive direction and the negative direction within a certain period, wherein the maximum value of the continuous tilt is the direction value of the signal value.
8. The shelf tilt monitoring and warning system of claim 1, wherein determining the degree of tilt of the shelf based on the characteristics of the signals from the two light sensors comprises determining the degree of tilt of the shelf based on the characteristics of the function of the signals: specifically, signal value change time points of two light sensors are obtained, the signal change values of the two light sensors are ordered according to the change time point intervals, the signal change value of one light sensor is used as a positive direction number, the signal change value of the other light sensor is used as a negative direction number, 0 is set when no signal change exists in any one light sensor, all the obtained signal change values are processed into function values related to time variables in a certain period, time sequence analysis, first derivative time ordering and second derivative time ordering are carried out on the obtained function values related to the time variables in the certain period, then a differential equation of the function values related to the time variables is established, then the differential equation is solved to obtain a corresponding general equation of the function values related to the time variables, and the inclination degree of the shelf at a future time point is estimated according to the general equation of the function values related to the time variables.
9. The shelf tilt monitoring and warning system of claim 8, wherein establishing a differential equation of the function value with respect to the time variable is as follows:
f (2) +bf (1) +af=exp(r*t)(Q n1 (t)sinαt)+Q n2 (t)cosαt);
f is a hypothetical general equation, f (1) Is the first order derivative of f (2) A, b are corresponding constant coefficients, t is a time variable, r is an exponential coefficient, Q n1 (t),Q n2 (t) is a pending polynomial, n1, n2 are the corresponding powers; time frequency parameter with alpha being t; calculation of general equation front a, b, r, n1, n2, α and Q n1 (t),Q n2 (t) can be determined;
the general equation for solving the differential equation to obtain the corresponding function value with respect to the time variable is: f=t c *exp(r*t)(p 1 m (t)cosαt)+(p 2 m (t)sinαt);
The determination method of c is that c=0 when r+iα or r-iα is not the root of the characteristic equation of the differential equation, and c=1 when r+iα or r-iα is the root of the characteristic equation of the differential equation; wherein i is-1 (1/2) Is an imaginary number value; where r is the index coefficient in the formula, m=max (n1,n2),p 1 m (t),p 2 m (t) polynomials each of which is t, m is the power of the corresponding polynomial, p 1 m (t),p 2 m The 1,2 in (t) is not the power but a distinguishing logo.
10. The shelf inclination monitoring and early warning system according to claim 1, wherein the upper computer is a PC.
CN202311045700.8A 2023-08-18 2023-08-18 Goods shelf inclination monitoring and early warning system Active CN117073634B (en)

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