LU505792B1 - A REAL-TIME MONITORING AND EARLY WARNING SYSTEM FOR KARST COLLAPSE BASED ON MEMS SENSORS - Google Patents

Abstract

The present invention discloses a real-time monitoring and early warning system for karst collapse based on MEMS sensors, which includes a series of multi-cascade connection lines, a data line, a data statistics module, a coordinate display module, an algorithm calculation module, and a monitoring and alarm module. The data statistics module includes a MEMS sensor, a pressure sensor, among others. The coordinate display module matches the coordinate information of the monitored area with the coordinate information hidden in each sensor, determines whether the MEMS sensor is faulty, and displays the position in the form of an image. The algorithm calculation module takes the real-time tilt and acceleration information received from the data statistics module and calculates it using a time domain integration algorithm. The monitoring and alarm module determines whether the real-time data of the sensor and the calculated data exceed the critical value, and at the same time sends out geological disaster warning information. The real-time karst collapse monitoring and warning system and method using the above-described structure of the present invention is capable of monitoring the development of karst cavities in real time and providing early warning of karst soils that are about to collapse.

Description

A real-time monitoring and early warning system for karst collapse based on MEMS sensors

Technical part

The present invention relates to the field of karst subsidence measurement technology and in particular to a karst subsidence bottom hole monitoring and early warning system for

Measurement of the change in depth displacement within the soil body.

Technology in the background

At present, domestic and foreign research on karst subsidence disaster mainly focuses on the following aspects: (1) Exploring the conditions for the development of

Karst subsidence; (2) Investigation of the process, mechanism and critical

Conditions for the development of karst subsidence; (3) Establishment of a basic

Database on karst subsidence; (4) Prediction of the risk of karst subsidence and

risk assessment; and (5) prediction and early warning of karst subsidence.

The development of karst subsidence is due to the unevenness of the

Karst development and the cyclical influence of karst water and has made the

Characteristics of concealment in space, the cumulative development process and the sudden

occurrence of subsidence, which poses many problems for monitoring work, and it is generally difficult to predict and monitor subsidence by conventional means on the ground.

The formation and development of karst subsidence is a complex process controlled and influenced by a variety of factors, which makes it difficult to prevent and control subsidence. The formation and development of land subsidence is the result of a combination of human activities and natural influences. In recent years, the frequent occurrence of karst subsidence accidents has caused great concern in society, and karst subsidence occurs in populated areas, seriously endangering the safety of life and property, urban construction and even economic development.

For karst subsidence that has already occurred and is likely to continue or recur, as well as for those that are likely to occur, it is necessary to develop suitable

To use methods for long-term real-time monitoring, early warning and other work.

The monitoring methods for karst subsidence can be divided into direct monitoring method and indirect monitoring method. The direct monitoring method is the method of judging land subsidence by directly monitoring the deformation of the underground soil body, and the indirect monitoring method mainly monitors the dynamic change of water and gas pressure in the karst pipeline system, and this

Patent aims precisely at achieving the monitoring and early warning of karst subsidence through the direct monitoring method. Since the monitoring of building foundations in

karst areas and in areas threatened by karst subsidence, a

Monitoring of the foundations is required. Currently, the investigation of the

Formation modes of bottom holes showed that karst bottom holes can be transformed into submerged bottom holes, sand leak bottom holes and mudflow bottom holes through the three pathways of submerged erosion, sand particle leakage and soft soil loss, respectively.

Content of the invention

The present invention, to solve the deficiencies of the existing technology, provides a

Real-time monitoring and early warning system for karst collapse based on MEMS$US05792

Sensors that mainly uses the location angle of the MEMS sensors and the change of

Earth pressure to assess the development and formation of different types of karst

Soil voids, so as to achieve the effect of monitoring and early warning.

A real-time monitoring and early warning system for karst collapse based on

MEMS sensors, including:

A number of multi-cascade interconnection lines and data lines buried in the monitored area in a distributed state, and real-time transmission of

Position changes and data information from the MEMS sensors to a computer in the

Monitoring and warning center.

A number of MEMS sensors and pressure sensors, with the two devices connected by a

colloidally connected to each other for real-time monitoring of the displacement and

Pressure changes within the soil body of a karst collapse bottom hole as it forms.

Each MEMS sensor and pressure sensor is assigned a unique ID number, and each ID number address corresponds to the depth of the location where the MEMS sensor and the

Pressure sensor is buried.

A series of communication ports, a page with several

Cascade connections and data line connections and a side connected to a computer for real-time input of sensor information.

Monitoring and warning center computer for receiving real-time

Data information sent by the MEMS sensors to calculate the

ground displacement and pressure change of each monitoring device received, for

Establish a real-time information database and combine the ground collapse deformation data obtained in the physical collapse model test to

Perform real-time monitoring and alerting after calculating the critical

Deformation value of the monitoring device;

The frame slot, which is buried in a distributed state in the monitored area, is inside a frame structure with a receiving space for storing several

cascade connection wires and data wires and has polished smooth wire holes at the left and right ends thereof for guiding wires. The frame channel is provided with the MEMS

sensors, and the length of the connection is determined by the size of the soil hole determined by the soil survey conducted at the monitoring site.

Preferably, the multi-stage connection cable and the data cable are connected to the MEMS

Sensor or pressure sensor.

Preferably, at the interface of the multi-stage connecting line and the

A waterproof plating layer is applied to the data cable.

Preferably, the MEMS sensor model WT901C-485

Preferably the pressure sensor model AT81

Preferably, the communication port is a USB extender that can be connected to several

MEMS sensors and pressure sensors can be connected externally to the same computer.

Ideally, the monitoring and warning center computer includes:

A data statistics module that records the received acceleration, time, angle, pressure and other information transmitted by each sensor, a

information database, generates a data trend report and sends the data to a

coordinate display and data processing module. At the same time, the

Acceleration and pressure values of each MEMS sensor are assessed and if the warning value/505792 is exceeded, it is transmitted to the monitoring and alarm module.

The coordinate display module sets the coordinate information of the monitored

area with the coordinate information of each buried sensor.

The data statistics module determines whether the MEMS sensor is defective and displays the coordinates in the form of an image. Based on the data transmitted by the data statistics module,

Using inclination information, the condition of the sensor is determined and the collapse of the soil body is assessed.

The algorithm calculation module that processes the data received from the data statistics module

Real-time inclination and acceleration information and passes it through the

Time domain integration algorithm is calculated as shown in Figure 2 to derive the pressure value of the monitored area and the displacement of the sensor due to the collapse. The

Displacement is calculated as follows: (I) Preprocessing of acceleration: The acceleration elimination error takes into account the motion characteristics of the soil body within the karst collapse, and the acceleration signal is divided into three phases, i.e. stable, accelerated and smooth, and the average value of the sampling points in the three phases is calculated: a= nn a, (1)

In the above equation (1), N stands for the number of detection points, a for the detected

Acceleration signals and a, for the three-stage sampling average.

Subtracting the acceleration of each stage from the average value of that stage gives the initial distance of the DC component of a, =a, —a(k =1,2,3-—N) 2)

In the above equation (2), a is the acceleration at which the DC component was initially removed. (IT) Base deflection removal: If it is found that the base of the MEMS

sensor is deflected during the collapse movement, the regional

Gravity acceleration component must be subtracted to obtain the acceleration without

To obtain the base deflection: a,-g sin 6 a,-g sine de = es = Views ©

In the above equation (3): a, is the acceleration recording to eliminate the

base deflection in horizontal direction; the collapse inclination is ©; g is the

Gravitational acceleration. (IID) Elimination of the trend term in the time domain: The trend term in the time domain is

Polynomial fitting by least squares removed. For polynomials: x, =b, +bx+b,x* ++ b x" (m=1,2,3-—7) (4)

In equation (4) above, m is the coefficient of the most significant term of the polynomial, b; (m=1,2,3,......, m) is the polynomial coefficient and x,, is the fitted trend term.

The coefficients b of x are determined by the method of coefficients to be determined so that the sum of the squares of the errors of the polynomial and the

acceleration signal a, is minimized, i.e.:

mink = EE, Om — a)? (5505/92

In the above equation (5): E is the minimum value of the equation

If satisfied with extreme values, b, for polynomial coefficients, the partial

Derivatives 2 = 0 to obtain a system of (m+1) element linear equations,

J to solve the system of equations to satisfy the conditions of (m+1) coefficients b,(j=1,2,3 ......m) are obtained. (IV) Time domain integration algorithm for calculating speed and

Displacement signals: Simpson’s law is used to integrate the

Acceleration and velocity time scale used: v(t) = ve —1y+ WD + 40) + a+) —_ Ha (6)

In the above equation (6): a(t) is the acceleration signal after preprocessing and processing of the base deflection; v(t) is the velocity signal, where t=0,1,2, ......N-1,

At is the sampling time. s@= sh + HERDED a (7)

In the above equation (7): s(t) is the path signal.

Calculate the energy of the velocity and displacement signals:

N-1 N-1

SZ OT Sm 2 SO ®

In the above equation (8), v, and S, are the velocity and speed respectively.

Displacement energy.

The integral energy is calculated after removing the trend term using the method of least

Squares calculated:

N-1 N-

Vy = V2 (1)? S, = >, s(t)? (9)

In equation (9) above, v, and S, are the integral energy after removing the trend term, respectively.

Describe the energy loss for the velocity and distance signals after removing the trend term: (1) S(f) ( ) V.v, SS, ( )

In the above equation (10), v(f) and S(#) are the available speed and velocity values, respectively.

Way signals.

The monitoring and alarm module compares the received

Real-time data information from the sensor and the displacement data from the algorithm

Calculation module with the data threshold set by the system, determines whether the

Real-time data from the sensor exceeds the threshold, makes a prediction of the geological disaster that will occur and simultaneously sends a geological

Disaster warning message.

By adopting the above-mentioned technical solution, the present invention, in comparison with the prior art, carries out real-time monitoring of the ground deformation in the area threatened by karst subsidence by burying MEMS sensors and pressure sensors on a plurality of monitoring bands in the monitored area and collecting 5 acceleration and pressure information of the ground in the monitoring section. Based on the monitoring information, the computer of the

Monitoring and Early Warning Centre, an information database was set up, a

Data trend report prepared and monitoring and early warning of karst subsidence by

Comparison with the critical data of ground subsidence recorded in the physical

Subsidence model test were realized.

Description of the attached drawings

Figure 1 shows a schematic diagram of the connection of the device of the present

invention

Figure 2 shows a schematic diagram of the time domain integration algorithm in the

Displacement calculation method

Figure 3 shows a schematic diagram of the basic sensor deflection at the

Deflection calculation method

Figure 4 shows a schematic diagram of the sensor in a submerged bottom hole in a physical model test

Figure 5 shows a schematic diagram of the sensor in an hourglass-shaped hole in the ground in a physical model experiment.

Figure 6 shows a schematic diagram of the sensor in a mudflow borehole in a physical model test.

Detailed description

The present invention is a real-time monitoring and

Karst collapse early warning system based on MEMS sensors as shown in Figure 1, which includes a series of multi-cascade interconnection lines and data lines buried in a distributed state in the monitored area, and

Real-time information such as attitude angle, acceleration, time, etc. of the MEMS devices to a

Communication port and then to a computer of the monitoring and

Early Warning Center.

The monitoring and warning center computer for receiving real-time

Data information sent by the monitoring device to calculate the

ground displacement and pressure change of each monitoring device received, for

Establish a real-time information database and combine the ground collapse deformation data obtained in the physical collapse model test to

Perform real-time monitoring and alerting after calculating the critical

Terrain deformation value of the monitoring device;

The monitoring and warning center computer includes:

A data statistics module that calculates the received acceleration, time, angle and

Records pressure information transmitted from each MEMS sensor and pressure sensor, builds a database with the information, creates a data trend report and transmits the data to a coordinate display and data processing module. At the same time, the acceleration and pressure values of the individual sensors are evaluated and

Exceedance of the warning values is transmitted to the monitoring and alarm module.

The coordinate display module sets the coordinate information of the monitored/>05792

area with the coordinate information of each buried sensor.

The data statistics module determines whether the MEMS sensors are defective and displays the data in the form of an image. Based on the data transmitted by the data statistics module,

Tilt information is used to determine the state of the sensor and then the collapse of the

soil body is assessed.

The algorithm calculation module that processes the data received from the data statistics module

Real-time inclination and acceleration information and passes it through the

Time domain integration algorithm calculated as shown in Fig. 2 to derive the pressure value of the monitored area and the displacement of the sensor due to the collapse. The

Displacement is calculated as follows: (I) Acceleration preprocessing: The acceleration elimination error takes into account the motion characteristics of the soil body within the karst collapse, and the acceleration signal is divided into three phases, i.e., stable, accelerated and smooth, and the average value of the sampling points in the three phases is calculated: a= nn a, (1)

In the above equation (1), N stands for the number of detection points, a for the detected

Acceleration signals and a, for the three-stage sampling average.

Subtracting the acceleration of each stage from the average value of that stage gives the initial distance of the DC component of a, =a, —a(k =1,2,3-—N) 2)

In the above equation (2), a is the acceleration at which the DC component was initially removed. (IT) Base deflection removal: If it is found that the base of the MEMS

sensor is deflected during the collapse movement, the regional

Gravity acceleration component must be subtracted to obtain the acceleration without

To obtain the base deflection: a,-g sin 6 a,-g sine de = es = Views ©

In the above equation (3): a, is the acceleration recording to eliminate the

base deflection in horizontal direction; the collapse inclination is 6; g is the

Gravitational acceleration. (IID) Elimination of the trend term in the time domain: The trend term in the time domain is

Polynomial fitting by least squares removed. For polynomials: x, =b, +bx+b,x* ++ b x" (m=1,2,3-—) (4)

In equation (4) above, m is the coefficient of the most significant term of the polynomial, b; (m=1,2,3,......; m) is the polynomial coefficient and x,, is the fitted trend term.

The coefficients b of x are determined by the method of coefficients to be determined so that the sum of the squares of the errors of the polynomial and the

acceleration signal a, is minimized, i.e.: minE = Der (x, — ap)? (5)

In the above equation (5): E is the minimum value of the equation

; _ LU505792

If satisfied with extreme values, b, for polynomial coefficients, the partial

Derivatives 2 = 0 to obtain a system of (m+1) element linear equations,

J to solve the system of equations to satisfy the conditions of (m+1) coefficients b,(=1,2,3......m) are obtained. (IV) Time domain integration algorithm for calculating speed and

Displacement signals: Simpson’s law is used to integrate the

Acceleration and velocity time scale used: vo =v LEDER AD as (6)

In the above equation (6): a(t) is the acceleration signal after preprocessing and processing of the base deflection; v(t) is the velocity signal, where t=0,1,2, ......N-1,

At is the sampling time. s@= sh + HERDED a m

In the above equation (7): s(t) is the path signal.

Calculate the energy of the velocity and displacement signals:

SZ SE ®)

In the above equation (8), v, and S, are the velocity and speed respectively.

Displacement energy.

The integral energy is calculated after removing the trend term using the method of least

Squares calculated:

ET 8 = 0% ©)

In equation (9) above, v, and S, are the integral energy after removing the trend term, respectively.

Determine the energy loss for the speed and distance signals after removing the trend term: v(t) S(f)

Wf) = — S(t) = — 10 ( ) V.v, SS, ( )

In the above equation (10), v(f) and S(#) are the available speed and velocity values, respectively.

Way signals.

The monitoring and alarm module compares the real-time data information from the received sensors and the displacement data from the algorithm calculation module with the data threshold set by the system, determines whether the real-time data from the

Sensors exceed the threshold, makes a prediction of the geological disaster that will occur and at the same time sends out the geological disaster warning information.

In the present invention, the sensor comprises a MEMS sensor and a

Pressure sensor, where the MEMS sensor model is WT901C-485 and the pressure sensor model is AT81.

The early warning system of the present invention uses a database management system to extract and analyze data from each monitoring area and store it in two

databases in a unified manner to manage various types of monitoring data reasonably and efficiently. It manages, stores, analyzes and outputs these data in a unified

and combines it with the critical data of the collapse on the opposite

Page, which were determined in the physical collapse model test to determine the

To accurately determine the monitoring section near the critical data to judge whether there is any deformation damage of the soil body to provide early warning of soil collapse.

In the following, in connection with the MEMS sensor monitoring and warning system, the monitoring method of the warning device is explained in particular.

A. A variety of surveillance belts are selected in the monitored area, and

MEMS sensors are buried under the monitoring soil line, and the MEMS sensors achieve monitoring of the acceleration and direction of the soil body in the

monitoring line, and the multiple cascade connection wires transmit the

Real-time data from the MEMS sensors to a monitoring and warning center computer, and the MEMS sensors will transmit the data to the monitoring and warning center computer at the frequency calculated by 0.2 seconds,

B. The MEMS sensors have on both the left and right side

Frame slots in which the multi-cascade connecting wires are housed, so that the MEMS sensors are in a downward position during a karst collapse and the initial formation of a sinkhole within the soil body. Since the

frame slot is buried in the ground, the cascade wires are connected to the outer end of the

frame slot is subjected to the tensile force in the ground, and the MEMS sensor will not move downward. When the ground hole expands to a certain range, the

Multi-cascade connecting wire is not subjected to the tensile force in the ground, and the MEMS sensor falls down. The height of the ground hole formed by the karst collapse can be determined by the

Time domain shift algorithm, and the width of the bottom hole formed by the karst collapse can be determined by the length of the multi-cascade connecting wire at the outer

End of the pre-embedded frame slot must be known.

C. Comparison of real-time sensor displacement and acceleration data with the critical ground collapse data obtained from the preset physical

collapse model test, determining whether the real-time data of the MEMS gyroscope exceeds the critical value, predicting the impending geological disaster, and simultaneously sending out the warning information about the geological disaster.

The following describes a monitoring method of the warning device in conjunction with a pressure sensor monitoring and warning system.

A. Multiple monitoring bands are selected in the monitoring area, and the

Pressure sensor is mounted above the MEMS sensor, and the pressure sensor realizes the

Monitoring the pressure in the monitoring segment. The data line transmits the

Real-time data from the pressure sensor to the monitoring and warning computer.

B. Based on the real-time monitoring data transmitted via the data line, the

Computers at the monitoring and warning center maintain an information database and generate trend reports on the data.

C. If the deep soil of the monitoring section has been affected by erosion, loss of

Sand particles and loss of soft soil form a bottom hole, the pressure value/>05792 of the pressure sensor at its upper part changes, and the real-time pressure value is compared with the critical

Compared with ground collapse data obtained from the preset physical model test to determine if a ground sinkhole is forming here, and if it does form, it can be closely observed.

Physical model test of a karst collapse:

Due to the advantages of MEMS sensors, such as low weight, low

Power consumption, high reliability, high sensitivity, easy remote monitoring and unique distributed sensing characteristics. The application of MEMS sensors can continuously measure the physical parameters inside and outside the monitoring section, while simultaneously monitoring the state of the spatial distribution of the measured physical

parameters and the information about the change over time.

Through the physical model test, the whole process of karst development is reproduced under different indoor conditions, and from then on, the relationship between sensor pressure, displacement and soil deformation and settlement is established to determine the

To achieve the early warning effect.

From the analysis of the physical model test, the following laws can be derived: (1) As the bottom hole develops, the pressure value of the pressure sensor inside it will gradually decrease, and when the pressure sensor data is 0, the formation of the bottom hole can be judged. (2) With the further development of the bottom hole, the MEMS sensor inside is not constrained by the stress of the surrounding soil and shows a downward

movement, and the final vertical displacement is essentially the same as the square integral displacement of the acceleration in the time domain. (3) From the perspective of the width of the bottom hole formation, by adjusting the distance between the two frame slots, the width of the bottom hole formation can be judged and a

(4) When the Z-axis acceleration of the MEMS sensor exceeds 0.9g, it can be considered that the development of the bottom hole is completed and the warning value set by the bottom hole collapse is reached.

The above examples are only intended to illustrate the technical

program of the present invention without limiting it, and any modification of the program described above based on the technical substance of the present

Invention or an equivalent replacement and a modification of some technical features fall within the scope of the program of the present invention.

Claims (6)

Claims LU505792 1. A real-time karst collapse monitoring and early warning system based on MEMS sensors, characterized in that it comprises a number of multi-cascade connection lines and data lines, a number of MEMS sensors and pressure sensors, a frame groove containing the multi-cascade connection lines, a communication port, and a monitoring and early warning center computer. The monitoring and warning center computer includes a data statistics module, a coordinate display module, an algorithm calculation module, and a monitoring and alarming module. The data statistics module is connected to the communication port. 2. A real-time karst collapse monitoring and early warning system based on MEMS sensors according to claim 1, characterized in that the MEMS sensors, pressure sensors, each of the MEMS sensors and pressure sensors is provided with a unique ID number, and each ID number address corresponds to the depth of the position at which the MEMS sensors and pressure sensors are buried. 3. A real-time karst collapse monitoring and early warning system based on MEMS sensors according to claim 1, characterized in that the frame slot, which is a frame structure with an accommodation space for a multi-cascade connection line and a data line inside, is provided with polished smooth line holes at its left and right ends for fixing a transmission line. The distance between the frame slot and the MEMS sensors is determined by the size of the ground hole determined by the ground survey conducted at the monitoring site. 4. A real-time karst collapse monitoring and early warning system based on MEMS sensors, characterized by MEMS sensors, the method comprising the steps of: 1) selecting a plurality of monitoring belts in the monitored area, burying MEMS sensors under the monitoring soil line, the MEMS sensors realize the monitoring of the acceleration and direction of the soil body in the monitoring line, and the multi-cascade connection line transmits the real-time data from the MEMS sensors to the computer of the monitoring and warning center, and the MEMS sensors will transmit the data to the computer of the monitoring and warning center at the frequency calculated at the rate of 0.2 seconds; (2) There are frame slots on the left and right sides of the MEMS sensors to store the cascade connecting lines, so that when a karst collapse occurs and a soil hole is initially formed in the soil body, the MEMS sensors are in a downward movement. Because the buried frame slot is buried in the soil body, the cascade wires supported at the outer end of the frame slot will be subjected to the tensile force in the soil and the MEMS sensors will not move downward, while when the soil hole expands to a certain range, the cascade wires will not be subjected to the tensile force in the soil and the MEMS sensors will fall downward. The height of the soil hole formed by the karst collapse can be determined by the time domain shift algorithm, and the width of the soil hole formed by the karst collapse can be determined by the length of the pre-buried multi-cascade connecting wire at the outer end of the frame slot. (3) Comparison of real-time soil load data with the critical data of the ground collapse data obtained from the specified physical collapse model test) 505792 Determining whether the real-time data of the MEMS gyroscope exceeds the critical value, predicting the onset of the geological disaster, and simultaneously sending the warning information of the geological disaster. 5. A real-time monitoring and early warning system for karst collapse based on MEMS sensors, characterized by a pressure sensor, the method comprising the steps of: (1) selecting a plurality of monitoring bands in the monitoring section, the pressure sensor is installed above the MEMS sensor, and the pressure sensor realizes monitoring of pressure in the monitoring section. A data line transmits real-time data from the pressure sensor to a monitoring and warning computer. (2) According to the real-time monitoring data transmitted through the data line, the said computer of the monitoring and warning center establishes an information database and generates data trend reports. (3) When the deep soil in the monitoring section forms holes due to erosion, loss of sand particles and loss of soft soil, the pressure value of the pressure sensor at its upper part changes. The real-time pressure value is compared with the critical ground collapse data obtained from the preset physical model test to determine whether a sinkhole has formed here, and if it has formed, it can be closely monitored. 6. A real-time karst collapse monitoring and early warning system based on MEMS sensors according to claim 4, characterized in that the MEMS sensor which internally collects acceleration signals can obtain the displacement of the sensor in the three-axis direction by integrating the acceleration signals in the time domain. The displacement is calculated as follows: (I) Acceleration preprocessing: The acceleration elimination error takes into account the motion characteristics of the soil body within the karst collapse, and the acceleration signal is divided into three phases, i.e., stable, accelerated and smooth, and the average value of the sampling points in the three phases is calculated: LY a ow In the above equation (1), N represents the number of detection points, a, represents the detected acceleration signals, and a, represents the three-stage sampling average. Subtracting the acceleration of each stage from the average value of that stage gives the initial removal of the DC component of a! = a, —a(k =1,2,3--+-N) 2) In the above equation (2), a; is the acceleration at which the DC component was initially removed. (II) Removal of the base deflection: If the base of the MEMS sensor is found to be deflected during the collapse motion, the regional gravity acceleration component must be subtracted to obtain the acceleration without base deflection: a,-gsin6 a,-gsin6 a =e = Viento © In the above equation (3): a, is the acceleration record for removing the Base deflection in the horizontal direction; the collapse tendency is 0; g is dt&}05792 gravitational acceleration. (IID) Elimination of the trend term in the time domain: The trend term in the time domain is removed in the polynomial fitting by the least squares method. For polynomials: x, = D, HD X HD x) +: 4+b„ x" (m=1,2,3--7) (4) In the above equation (4), m is the coefficient of the most significant term of the polynomial, b; (m=1,2,3,......, m) is the polynomial coefficient and x,, is the fitted trend term. The coefficients b of x, are determined by the method of coefficients to be determined so that the sum of the squares of the errors of the polynomial and the acceleration signal a, is minimized, i.e.: minE = Yi, (nm — A)" 6) In the above equation (5): E is the minimum value of the equation If satisfied with extreme values, b, for polynomial coefficients, the partial derivatives = = 0, to obtain a system of (m+1) element linear equations, J can be obtained to solve the system of equations to satisfy the conditions of the (m+1) coefficients to be determined b ,(G=1,2,3......m). (IV) Time domain integration algorithm for calculating velocity and displacement signals: Simpson's law is used to integrate the acceleration and velocity time scale: vo =v LEDER AD as (6) In the above equation (6): a(t) is the acceleration signal after preprocessing and base deflection processing; v(t) is the velocity signal, where t=0,1,2, ..... N-1, At is the sampling time. s()=s@-1)+ PTS x At (7) In the above equation (7): s(t) is the displacement signal. Calculate the energy of the velocity and displacement signals: Vv, = JE, v09 S, => sy (8) In the above equation (8), v, and S, are the velocity and displacement signals, respectively. Displacement energy. The integral energy is calculated after removing the trend term using the least squares method: N-1 N-1 VE OS = se) ©) In the above equation (9), v, and S, are the integral energy after removing the trend term, respectively. Determine the energy loss for the speed and distance signals after removing the trend term: S(t) LU505792 v(t) = — S(t) = — 10 ( ) V.v, SS, ( ) In the above equation (10), v(f) and S(#) are the available speed and speed coefficients, respectively. Way signals.