Fourier Series Correction Method for Micro-Noise Output of Nutt Sensors

Abstract

The present invention discloses a Nat sensing output micro-noise Fourier series correction method. By sensing the changes in the geomagnetic field of the surrounding environment through Nat sensors, the displacement changes of the instrument itself in the x, y, and z directions can be calculated. Connecting multiple Nat sensors in series can measure the deformation of the roadbed. The displacement change of the slope surface is collected through Nat sensors within a preset time period. For Nat sensors, the non-periodic discrete data collected is fitted by the Fourier series. When the fitting coefficient R2 > 0.9, the discrete data is decomposed into the form of the sum of trigonometric functions, and the non-periodic discrete data is fitted with a periodic function. According to the fitting result, the data drift of the Nat sensors is corrected, and the corrected value is the displacement change value collected by the instrument itself in the x, y, and z directions.

Description

Technical Field

[0001] The present invention relates to the field of sensor data correction, and in particular to a Fourier series correction method for the micro-noise output of a Nutt sensor. Background Art

[0002] With the rapid development of the national economy and the level of science and technology, human engineering activities have become increasingly frequent and large-scale. In recent years, China has vigorously developed infrastructure construction, and a series of construction problems such as dam foundations, highways, high-speed railways, long-span bridges, and high-difficulty tunnels have been solved by Chinese engineers one by one. The problem of slope stability appears almost in all engineering constructions. The slope instability has characteristics such as suddenness and great destructiveness. How to implement real-time continuous monitoring of a large range of slopes and take appropriate early warning measures when the deformation exceeds the threshold, notify the on-site safety person in charge to promptly do emergency work such as evacuation, and minimize property losses and casualties has undoubtedly become the top priority of the slope stability problem. At the same time, many scholars are also contributing their part to slope deformation monitoring, looking forward to solving this difficult problem at an early date.

[0003] As is well known, excessive local deformation of slopes is a precursor to geological disasters such as landslides. Using engineering technologies such as sensors can not only greatly improve the monitoring efficiency, save labor, but also enable staff to understand the deformation of slopes under various working conditions in real time, which is an inevitable development trend for the intelligentization and automation of slope monitoring.

[0004] Whether using traditional total stations to monitor slope deformation or using sensors to monitor slope deformation, there will be errors caused by the instrument itself and environmental factors. At the same time, due to the all-weather monitoring of slopes, the stored and processed data will be more and more, resulting in gradually larger errors in the recording and prediction of slope deformation, and the accuracy and precision of sensor measurements cannot be guaranteed.

[0005] A Nutt sensor is a sensor for monitoring slope displacement based on the geomagnetic field. The sensor internally has a chip that can sense changes in the geomagnetic field. By measuring the changes in the geomagnetic field in the x, y, and z directions, the displacement change amounts Δx, Δy, and Δz of the Nutt sensor in the x, y, and z directions can be calculated. Furthermore, the displacements of multiple Nutt sensors can be superimposed and the displacement points can be connected to reflect the slope displacement, so as to do a good job in the safety early warning of the slope. This sensor has characteristics such as 24-hour real-time monitoring and high operability, and is widely used in actual engineering construction.

[0006] Based on the advantages of the Nutt sensor such as real-time performance and high operability, it is widely used in engineering constructions such as slope and tunnel deformation monitoring.

[0007] However, all electronic components will have drift, which generally refers to zero drift and temperature drift. There are many reasons for the zero drift of sensors.

[0008] For intelligent sensors: ① Time drift - that is, for the system, as time increases, it is equivalent to aging the system. In this way, the structural characteristics of the system will change, resulting in drift; ② Temperature drift - the zero point instability caused by temperature. Under the form of the highly developed modern science and technology, the requirements for measurement accuracy are getting higher and higher. Therefore, it is particularly important to reduce or eliminate the sensor error caused by temperature.

[0009] The present invention uses Fourier series to fit non-periodic discrete data. When the fitting coefficient R 2 > 0.9, the discrete data can be decomposed into the form of the sum of trigonometric functions, and the non-periodic discrete data is fitted with a periodic function, which is beneficial to correcting the data drift of the sensor. By analyzing the periodic function after fitting, the spectral characteristics of the discrete data can be obtained, and further analyze the reasons for the drift phenomenon of the sensor, in order to fundamentally eliminate the influence of drift on the sensor in future monitoring. Summary of the Invention

[0010] The present invention aims to solve at least one of the technical problems existing in the prior art. For this reason, the present invention discloses a Nat sensing output micro-noise Fourier series correction method. By using Nat sensors to sense the change of the earth's magnetic field in the surrounding environment, the displacement changes of the instrument itself in the x, y, and z directions can be calculated. Connecting multiple Nat sensors in series can measure the deformation of the roadbed. The displacement change amount of the slope surface is collected by Nat sensors within a preset time period. For Nat sensors, Fourier series is used to fit the collected non-periodic discrete data. When the fitting coefficient R 2 > 0.9, the discrete data is decomposed into the form of the sum of trigonometric functions, and the non-periodic discrete data is fitted with a periodic function, and the data drift of the Nat sensor is corrected according to the fitting result.

[0011] Furthermore, the data obtained by the sensor affected by drift is defined as the measured value. The weighted average is calculated according to the frequency of the statistical original data, and the weighted average is defined as the theoretical value. Then, the difference between the measured value and the theoretical value is obtained as the drift value, and the Fourier series fitting is performed on the drift value. Define the fitting coefficient R 2 as a parameter to evaluate the fitting degree. The meaning of R 2 is the proportion of the variance of the variables that the prediction model can explain. The variance measures the dispersion degree or fluctuation range of the variable values. The smaller the variance, the smaller the fluctuation of the variable. Finally, the difference between the measured value and the drift value after fitting is used to correct the data drift of the Nat sensor.

[0012] Furthermore, define the fitting coefficient R 2 The expression is as follows:

[0013]

[0014] where y i is the drift value, y is the fitted value, and is the average value.

[0015] Furthermore, the value range of R 2 is as follows:

[0016] R 2 = 1, in the ideal case, indicating that the model accurately predicts all true values;

[0017] 0 < R 2 < 1, in the common case, indicating that the fitting level of the model is better than that of the mean model;

[0018] R 2 = 0, indicating that the fitting level of the model is close to that of the mean model, and the model has no value;

[0019] R 2 < 0, indicating that the fitting level of the model is inferior to that of the mean model;

[0020] R 2 The range is (-∞, 1].

[0021] Furthermore, when the number of collected data reaches the preset number of data, the Fourier expansion order n 2 corresponding to the maximum of the fitting coefficient R max is obtained, and the linear relationship between the number of data and the optimal Fourier expansion order n max is obtained. Therefore, when the number of data increases, the optimal n can be obtained according to the linear relationship between the number of data and the optimal Fourier expansion order, reducing the calculation amount.

[0022] Furthermore, let f(x) be a periodic function with a period of 2π and can be expanded in the following form:

[0023]

[0024] where:

[0025]

[0026] Among them, is called the Fourier coefficient of f(x). When f(x) satisfies the Dirichlet sufficient condition, the Fourier series converges; the Dirichlet sufficient condition is as follows:

[0027] Let f(x) be a periodic function with a period of 2π. If it satisfies the condition:

[0028] First, f(x) is continuous on [-π, π] or has only a finite number of first-kind discontinuity points;

[0029] Second, the function f(x) has only a finite number of extreme points on [-π, π],

[0030] then the Fourier series of f(x) converges, and there is

[0031] a. When x is a continuous point of f(x), the series converges to f(x);

[0032] b. When x is a discontinuous point of f(x), the series converges to

[0033] Furthermore, a nautical sensor is a device that senses the change of the geomagnetic field in the surrounding environment and then calculates the displacement changes of a single instrument itself in the x, y, and z directions. Connecting multiple nautical sensors in series can measure the deformation of the roadbed:

[0034] Δx = L × sinγ × cosθ (Equation 5)

[0035] Δy = L × sinγ × sinθ (Equation 6)

[0036] Δz = L × cosγ (Equation 7)

[0037] where γ is the angle between the axis of the nautical sensor and the magnetic north axis; θ is the angle between the projection of the axis of the nautical sensor in the horizontal direction and the x-axis.

[0038]

[0039] where x n , y n , z n —— the three-dimensional coordinates of the nth node;

[0040] x0, y0, z0 are the three-dimensional coordinates of the initial node.

[0041] Furthermore, when fitting discrete data, three situations may occur: underfitting of the model, normal fitting of the model, and overfitting of the model. Among them, both underfitting and overfitting of the model are not good situations. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The present invention can be further understood from the following description in conjunction with the drawings. The components in the drawings are not necessarily drawn to scale, but the emphasis is placed on showing the principles of the embodiments. In the drawings, the same reference numerals designate corresponding parts in different views.

[0043] Figure 1It is a schematic diagram of the displacement of the Nat sensor at the same burial depth but different days in an embodiment of the present invention.

[0044] Figure 2 It is a diagram showing the change of the temperature of the Nat sensor over time in an embodiment of the present invention.

[0045] Figure 3 It is a pie chart of the displacement of the i-th section of the sensor in an embodiment of the present invention.

[0046] Figure 4 It is the fitting coefficient R 2 in an embodiment of the present invention, and the relationship diagram with the Fourier series expansion order n.

[0047] Figure 5 It is a diagram of the drift value and fitting curve of the i-th section of the sensor when n = nmax in an embodiment of the present invention.

[0048] Figure 6 It is a relationship diagram between nmax and the number of data in an embodiment of the present invention.

[0049] Figure 7 It is a comparison diagram of the corrected measured value, measured value and weighted average value in an embodiment of the present invention.

[0050] Figure 8 It is the fitting coefficient R 2 and the relationship diagram with the Fourier series expansion order n in two cases. Among them, (a) is the diagram of the under-fitting case, and (b) is the diagram of the over-fitting case. Specific embodiments

[0051] The technical solution of the present invention will be further specifically described below through specific embodiments in conjunction with the accompanying drawings:

[0052] The present invention uses the Fourier series to fit non-periodic discrete data. When the fitting coefficient R 2 > 0.9, the discrete data can be decomposed into the form of the sum of trigonometric functions, and the non-periodic discrete data is fitted with a periodic function, which is beneficial to correcting the data drift of the sensor. By analyzing the periodic function after fitting, the spectral characteristics of the discrete data can be obtained, and further analyze the reasons for the drift phenomenon of the sensor, so as to fundamentally eliminate the influence of the drift on the sensor in future monitoring.

[0053] The present invention studies the relationship between the fitting coefficient R 2 and the Fourier expansion order n when the number of data is certain. The fitting coefficient shows a law of first increasing and then decreasing and symmetric distribution with the increase of the Fourier expansion order, and at the same time, the phenomena of "under-fitting" and "over-fitting" also appear.

[0054] The present invention studies the relationship between the number of Fourier expansion terms \(n\) and the number of data points, and obtains the Fourier expansion term \(n\) corresponding to the maximum fitting coefficient \(R\) when the number of data points is fixed. 2 Furthermore, the linear relationship between the number of data points and the optimal Fourier expansion term \(n\) is obtained. Therefore, when the number of data points increases, the optimal \(n\) can be obtained according to the linear relationship between the two, reducing the computational complexity. max Furthermore, the linear relationship between the number of data points and the optimal Fourier expansion term \(n\) is obtained. max Therefore, when the number of data points increases, the optimal \(n\) can be obtained according to the linear relationship between the two, reducing the computational complexity.

[0055] The French mathematician Fourier discovered that any periodic function can be represented by an infinite series composed of sine and cosine functions (the reason for choosing sine and cosine functions as basis functions is that they are orthogonal). Later generations call the Fourier series a special trigonometric series. According to Euler's formula, trigonometric functions can be transformed into exponential forms, so the Fourier series is also called an exponential series.

[0056] Let \(f(x)\) be a periodic function with a period of \(2\pi\) and can be expanded in the following form:

[0057]

[0058] where:

[0059]

[0060] are called the Fourier coefficients of \(f(x)\). When \(f(x)\) satisfies the Dirichlet sufficient condition, the Fourier series converges. The Dirichlet sufficient condition is as follows:

[0061] Let \(f(x)\) be a periodic function with a period of \(2\pi\). If it satisfies the conditions:

[0062] First, \(f(x)\) is continuous on \([-\pi,\pi]\) or has only a finite number of first-kind discontinuity points;

[0063] Second, the function \(f(x)\) has only a finite number of extreme points on \([-\pi,\pi]\),

[0064] then the Fourier series of \(f(x)\) converges, and

[0065] a. When \(x\) is a continuous point of \(f(x)\), the series converges to \(f(x)\);

[0066] b. When \(x\) is a discontinuity point of \(f(x)\), the series converges to

[0067] The Nat sensor is a device that senses the changes in the geomagnetic field of the surrounding environment and then calculates the displacement changes of the instrument itself in the \(x\), \(y\), and \(z\) directions. Connecting multiple Nat sensors in series can measure the deformation of the roadbed.

[0068] \(\Delta x = L\times\sin\gamma\times\cos\theta\) (Equation 5)

[0069] Δy = L × sinγ × sinθ (Equation 6)

[0070] Δz = L × cosγ (Equation 7)

[0071] Where γ is the angle (°) between the axis of the nautical sensor and the magnetic north axis;

[0072] θ is the angle (°) between the projection of the axis of the nautical sensor in the horizontal direction and the x-axis.

[0073]

[0074] Where x n , y n , z n ——The three-dimensional coordinates of the nth node;

[0075] x0, y0, z0 are the three-dimensional coordinates of the initial node.

[0076] Through the collection and collation of the data of the nautical sensor, it is found that there is a drift phenomenon in the data. All electronic components will have drift, and drift generally refers to zero drift and temperature drift. There are many reasons for the zero drift of the sensor.

[0077] For intelligent sensors: ① Time drift - that is, for the system, as time increases, it is equivalent to aging the system. In this way, the structural characteristics of the system will change, resulting in drift; ② Temperature drift - the zero point instability caused by temperature. Under the form of the highly developed modern science and technology, the requirement for the measurement accuracy is getting higher and higher. Therefore, it is particularly important to reduce or eliminate the sensor error caused by temperature. The nautical sensor has the function of monitoring temperature, and the change of temperature over time is shown as Figure 2 shown below:

[0078] From Figure 2 it can be seen that the temperature range of each day of the sensor is less than 0.1 °C. Therefore, it is considered that the influence of temperature on the sensor data drift is small. Further analysis of the displacement data shows that there is a certain periodicity in the data. Therefore, the Fourier series is introduced to analyze the displacement data. The following takes the data of the ith section of the sensor as an example for the specific correction method.

[0079] (1) The data obtained by the sensor is the data affected by drift, which is called the measured value. The frequency of the original data is statistically calculated and the weighted average is calculated to obtain the weighted average, which is called the theoretical value. From Figure 3 it can be seen that the proportion of 6-minute data is between 13% and 15%, and the difference is not large. The proportion of 0.433 mm is 10.3%. To a certain extent, this provides support for verifying the hypothesis that there is periodicity in the sensor data.

[0080] (2) The drift value is obtained by taking the difference between the measured value and the theoretical value, and the Fourier series fitting is performed on the drift value. Define the fitting coefficient R 2 as a parameter to evaluate the fitting degree. R 2 represents the proportion of the variance of the variables that can be explained by the prediction model. Variance measures the degree of dispersion or the range of fluctuations of the variable values. The smaller the variance, the smaller the fluctuations of the variable. R 2 has the following possibilities:

[0081] R 2 = 1, ideal situation, indicating that the model predicts all true values accurately;

[0082] 0 < R 2 < 1, common situation, indicating that the fitting level of the model is better than that of the mean model;

[0083] R 2 = 0, indicating that the fitting level of the model is close to that of the mean model and the model has no value;

[0084] R 2 < 0, indicating that the fitting level of the model is not as good as that of the mean model.

[0085] R 2 ranges from (-∞, 1].

[0086]

[0087] where y i is the drift value, y is the fitted value, is the average value.

[0088] The relationship between the fitting coefficient and the number of Fourier series expansions when the number of data is fixed is studied. From Figure 4 it can be seen that the fitting coefficient shows a symmetric distribution law, that is, when the number of data is fixed, there is an n max such that the fitting coefficient reaches the maximum value, and the fitting degree is the highest at this time. At this time, the drift value fitting curve when n = n max can be obtained Figure 5 as shown.

[0089] For long-term monitoring of data, the relationship between the number of data and n max is also studied as Figure 6 shown. From Figure 6 it can be seen that n max has a strong linear relationship with the number of data, providing a reference for selecting an appropriate n when the number of data increases in the future.

[0090] (3) The difference between the measured value and the fitted drift value is taken to obtain the corrected measured value as Figure 7 shown.

[0091] For Figure 4 the fitting coefficient R 2 in, the change with the Fourier series expansion order n is further explained to obtain Figure 8 (a) and Figure 8 (b) Two cases of the relationship between the fitting coefficient R 2 and the Fourier series expansion order n.

[0092] Among them, when fitting discrete data, three situations may occur: model underfitting, model normal fitting, and model overfitting. Among them, both model underfitting and model overfitting are not good situations.

[0093] Underfitting means that it is not possible to learn useful data patterns well from the training data, so that good prediction effects cannot be obtained for both the training data and the data to be predicted. Normal fitting of the model means that the trained model can learn a model with strong generalization ability and small prediction error from the training data set, and at the same time, the model can also make good predictions for the data to be tested and obtain satisfactory prediction effects. Overfitting refers to the phenomenon that a specific data set is too precisely matched, resulting in the obtained model being unable to fit other data well or predict future observation results. If the model is overfitted, the bias of the model will be very small, but the variance will be very large.

[0094] It should also be noted that the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, commodity or device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, commodity or device. Without further limitation, an element defined by the statement "comprising one..." does not exclude the existence of another identical element in the process, method, commodity or device comprising the said element.

[0095] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0096] Although the present invention has been described above with reference to various embodiments, it should be understood that many changes and modifications can be made without departing from the scope of the present invention. Therefore, it is intended that the above detailed description be considered illustrative rather than restrictive, and it should be understood that the following claims (including all equivalents) are intended to define the spirit and scope of the present invention. These embodiments should be understood to be only for illustrating the present invention and not for limiting the protection scope of the present invention. After reading the content recorded in the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A method for correcting the Fourier series of the output micro-noise of a Nutt sensor, characterized in that, The ambient geomagnetic field changes are sensed by a nT sensor, and then the displacement changes of a single instrument itself in the x, y, and z directions are calculated. The slope displacement changes are collected by the nT sensor, that is, the deformations of the roadbed within a preset time period are measured by connecting multiple nT sensors in series. For the nT sensor, the non-periodic discrete data collected is fitted by the Fourier series, and when the fitting coefficient R 2 > 0.9, the discrete data is decomposed into the form of the sum of trigonometric functions, the non-periodic discrete data is fitted with a periodic function, and the data drift of the nT sensor is corrected according to the fitting result. The data obtained by the sensor is the data affected by the drift. The data measured by the sensor is defined as the measured value. The weighted average is calculated according to the frequency of the statistical original data, and the weighted average is defined as the theoretical value. Then, the difference between the measured value and the theoretical value is obtained as the drift value, and the Fourier series fitting is performed on the drift value; the fitting coefficient R 2 is defined as a parameter for evaluating the fitting degree, and the meaning of R 2 is the proportion of the variance of the variables that the prediction model can explain. The variance measures the dispersion degree or the fluctuation range of the variable values. The smaller the variance, the smaller the fluctuation of the variable. Finally, the difference between the measured value and the fitted drift value is used to correct the data drift of the nT sensor. Among them, the expression of the fitting coefficient R 2 is: where y i is the drift value, and y is the fitted value, is the average value.

2. The Fourier series correction method for the output micro-noise of a Nutt sensor according to claim 1, characterized in that, R 2 The value range of R 2 = 1, in the ideal situation, indicating that the model accurately predicts all true values; 0 < R 2 < 1, a common situation, indicating that the fitting level of this model is better than that of the mean model; R 2 = 0 indicates that the fitting level of the model is close to the mean model, and the model has no value; R 2 <0 indicates that the fitting level of this model is inferior to that of the mean model; R 2 ranges from (-∞, 1].

3. A method for correcting the Fourier series of the micro-noise output of a Nutt sensor according to claim 1, characterized in that, When the number of collected data reaches a preset number of data, the fitting coefficient R 2 The Fourier expansion order n corresponding to the maximum max , a linear relationship between the number of data and the optimal Fourier expansion order n max is obtained. Therefore, when the number of data increases, the optimal n is obtained according to the linear relationship between the number of data and the optimal Fourier expansion order, reducing the amount of calculation.

4. A Fourier series correction method for the output micro-noise of a Nutt sensor as described in claim 1, characterized in that, Let \(f(x)\) be a periodic function with a period of \(2\pi\) and can be expanded in the following form: where: Among them, are called the Fourier coefficients of \(f(x)\). When \(f(x)\) satisfies the Dirichlet sufficient condition, the Fourier series converges; the Dirichlet sufficient condition is as follows: Let \(f(x)\) be a periodic function with a period of \(2\pi\). If it satisfies the conditions: First, \(f(x)\) is continuous on \([-\pi,\pi]\) or has only a finite number of first-kind discontinuity points; Second, the function \(f(x)\) has only a finite number of extreme points on \([-\pi,\pi]\), then the Fourier series of \(f(x)\) converges, and there is a. When \(x\) is a continuous point of \(f(x)\), the series converges to \(f(x)\); b. When x is a discontinuous point of f(x), the series converges to 5. A method for Fourier series correction of the output micro-noise of a Knuth sensor according to claim 1, characterized in that, The Nat sensor is a sensor that calculates the displacement changes of a single instrument itself in the \(x\), \(y\), and \(z\) directions by sensing the changes in the geomagnetic field of the surrounding environment. Connecting multiple Nat sensors in series can measure the deformation of the roadbed: \(\Delta x = L\times\sin\gamma\times\cos\theta\) (Equation 5) \(\Delta y = L\times\sin\gamma\times\sin\theta\) (Equation 6) \(\Delta z = L\times\cos\gamma\) (Equation 7) where \(\gamma\) is the angle between the axis of the Nat sensor and the magnetic north axis; \(\theta\) is the angle between the projection of the axis of the Nat sensor in the horizontal direction and the \(x\)-axis; where x n 、y n 、z n —— the three-dimensional coordinates of the nth node; \(x_0\), \(y_0\), \(z_0\) are the three-dimensional coordinates of the initial node.

6. A method for correcting the Fourier series of the output micro-noise of a Nutt sensor according to claim 1, characterized in that, When fitting discrete data, three situations may occur: underfitting of the model, normal fitting of the model, and overfitting of the model. Among them, both underfitting and overfitting of the model are bad situations.

Images