阅读说明：本技术 一种电磁波信号幅值衰减与传播距离关系曲线的拟合方法 (Fitting method for relation curve of amplitude attenuation and propagation distance of electromagnetic wave signal ) 是由 徐友刚 陈敬德 沈晓峰 马韬韬 陆敏安 黄晨宏 吴继健 方祺 顾华 肖远兵 曹基 于 2021-08-12 设计创作，主要内容包括：本发明公开了一种电磁波信号幅值衰减与传播距离关系曲线的拟合方法,包括步骤1信号异常值剔除步骤,将采集到的信号数据的分布视为高斯分布,概率密度分布符合N～(μ,σ～(2)),对数据中分布在平均值2倍方差以外的异常值进行剔除；步骤2采用卡尔曼滤波算法进行滤波；步骤3采用半参数回归模型拟合。本发明通过时间采集序列的滤波方法,提升了特高频接收信号强度的真实性,在此基础上采用非参数回归模型,提高了拟合精度。(The invention discloses a fitting method of an electromagnetic wave signal amplitude attenuation and propagation distance relation curve, which comprises a step 1 of eliminating abnormal signal values, wherein the distribution of collected signal data is regarded as Gaussian distribution, and the probability density distribution conforms to N to (mu, sigma) 2 ) Removing abnormal values distributed in the data and distributed outside the variance 2 times of the average value; step 2, filtering by adopting a Kalman filtering algorithm; and 3, fitting by adopting a semi-parameter regression model. According to the invention, the authenticity of the ultrahigh frequency receiving signal intensity is improved by a filtering method of a time acquisition sequence, and the fitting precision is improved by adopting a non-parametric regression model on the basis.)

1. A fitting method for an electromagnetic wave signal amplitude attenuation and propagation distance relation curve is characterized by comprising the following steps:

step 1, signal abnormal value elimination step, wherein the distribution of the collected signal data is regarded as Gaussian distribution, and the probability density distribution conforms to N to (mu, sigma)²) Removing abnormal values distributed in the data and distributed outside the variance 2 times of the average value;

step 2, a filtering step, namely filtering by adopting a Kalman filtering algorithm, wherein the filtering step comprises two stages of prediction and updating;

the prediction stage introduces the state equation and observation equation of the system, such as formula

x(k)＝Ax(k-1)+Bu(k)+w(k) (1)

z(k)＝Hx(k)+v(k) (2)

Wherein, formula (1) is a differential equation of the state of the system itself, formula (2) is an observation output equation of the system at the current moment, in formula (1), x (k) is the state of the system at the moment k, u (k) is the system control input quantity, w (k) is the system excitation noise, a is the state transition matrix, B is the gain coefficient of the input quantity, in formula (2), z (k) represents the observation value of the system at the moment k, H is the observation constant, v (k) is the observation error of the system;

predicting the state of the system at the moment k according to the state of the system at the moment k-1, wherein the optimal predicted output of the system at the moment k is as follows:

x(k|k-1)＝Ax(k-1|k-1)+Bu(k) (3)

in the formula (3), x (k | k-1) is based on the state of the system at the previous moment, the estimation on the state of the system at the current moment is carried out, x (k-1| k-1) is the optimal state prediction output of the system at the previous moment, and u (k) represents the control input quantity, and the covariance of the state of the system at the previous moment needs to be updated because the predicted value changes due to iterative update;

P(k|k-1)＝AP(k-1|k-1)A'+Q (4)

in the formula (4), P (k | k-1) is a covariance corresponding to the estimated output x (k | k-1) of the system at the time k;

after the prediction stage is finished, reading the real measured value of the system state at the current moment, and comparing the predicted value of the system state at the previous moment with the measured value at the current moment to obtain the optimal prediction result at the current moment as shown in the formula (5)

x(k|k)＝x(k|k-1)+Kg(k)(Z(k)-Hx(k|k-1)) (5)

Wherein z (k) represents the observed quantity of the system at the current time, kg (x) represents the kalman gain, and the expression thereof is shown in formula (6)

After the optimal output result is obtained, the system covariance at the current moment needs to be updated again so as to estimate the system state at the next moment, and the update equation is shown as formula (7)

P(k|k)＝(1-Kg(k)H)P(k|k-1) (7)

Step 3, fitting a semi-parametric regression model, wherein in the non-parametric regression model, the measured sample data is assumed to be (RSSI)_i,d_i) (i-1, 2, …, n), where RSSI is the received electromagnetic signal power and is a dependent variable; d is the distance of signal propagation, is an independent variable, assuming RSSI_i(i-1, 2, …, n) independently and identically distributed, and establishing a non-parametric regression modelThe following were used:

RSSI_i＝m(d_i)+ε_i i＝1,2,…,n (8)

where m (d) is an unknown regression function and ε is a random error satisfying a Gaussian distribution.

The optimal regression function that satisfies the model should minimize the sum of the squared errors of the regression function outputs, i.e.:

generally, m (d) is considered to be d after the known transmission distance, and the condition of the RSSI of the receiving end is expected, namely:

m(d)＝E(RSSI|d) (10)

estimating the regression function by adopting a weight function method, wherein the estimation method comprises the following steps:

for given sample data d_i(i ═ 1,2, …, n), the weight of each sample data item is different when estimating the function m (d). Let { W_i(d)＝W_i(d|d₁,…,d_n) i ═ 1,2, …, n } denotes the sample point (d) when estimating the regression function_i,RSSI_i) The corresponding regression function is then estimated as:

the estimation method obtains the following estimation of the regression function:

wherein K (-) is a kernel function for determining RSSI of each sample point in the process of estimating the regression function m (d)_iThe occupied proportion is large, h is the window width, the size of the local neighborhood is controlled, and the accuracy of non-parameter estimation is determined.

Technical Field

The invention relates to a fitting method of an electromagnetic wave signal amplitude attenuation and propagation distance relation curve in the field of substation partial discharge monitoring.

Background

The total station space positioning technology of the transformer substation is to complete the monitoring of partial discharge of the power equipment in the whole transformer substation by only one set of discharge monitoring equipment. The Time of Arrival (TOA) or Time Difference of Arrival (TDOA) methods, which are currently used, have very high-speed synchronization requirements (GHz sampling frequency and ns-level synchronization accuracy) for a sampling system, and are expensive in hardware cost and difficult to apply in the field. Recently, a spatial partial discharge positioning method based on Received Signal Strength Indicator (RSSI) of the very high frequency signal is proposed. At present, most of RSSI positioning which is researched more is based on a fingerprint map positioning technology, a characteristic information base about geographical position information and received signal strength needs to be established, field deployment is difficult, and later maintenance cost in field implementation is high. In addition, a partial discharge positioning technology based on the relationship between the signal amplitude attenuation characteristic and the propagation distance is also widely studied, and the main reason for limiting the positioning method is that the relationship between the propagation distance and the signal attenuation cannot be accurately measured. The free space propagation model is a linear propagation model of signals between a signal source and a receiving end in an ideal environment, the influence of two different propagation media, namely earth and air, on signal transmission is considered in the double-line ground reflection model, and the two models have large use limitation and cannot be applied in the field. The Shadowing model is based on the results of statistical analysis of a large number of experiments, the error amount of Gaussian random distribution is added, and the Shadowing model has larger calculation error in application.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provides a fitting method of an electromagnetic wave signal amplitude attenuation and propagation distance relation curve.

One technical scheme for achieving the above purpose is as follows: a fitting method of an electromagnetic wave signal amplitude attenuation and propagation distance relation curve comprises the following steps:

step 1, signal abnormal value elimination step, wherein the distribution of the collected signal data is regarded as Gaussian distribution, and the probability density distribution conforms to N to (mu, sigma)²) Removing abnormal values (meaning that the credibility probability is less than 5%) distributed in the data beyond 2 times of variance of the mean value;

step 2, a filtering step, namely filtering by adopting a Kalman filtering algorithm, wherein the filtering step comprises two stages of prediction and updating;

the prediction stage introduces the state equation and observation equation of the system, such as formula

x(k)＝Ax(k-1)+Bu(k)+w(k) (1)

z(k)＝Hx(k)+v(k) (2)

Wherein, formula (1) is a differential equation of the state of the system itself, formula (2) is an observation output equation of the system at the current moment, in formula (1), x (k) is the state of the system at the moment k, u (k) is the system control input quantity, w (k) is the system excitation noise, a is the state transition matrix, B is the gain coefficient of the input quantity, in formula (2), z (k) represents the observation value of the system at the moment k, H is the observation constant, v (k) is the observation error of the system;

predicting the state of the system at the moment k according to the state of the system at the moment k-1, wherein the optimal predicted output of the system at the moment k is as follows:

x(k|k-1)＝Ax(k-1|k-1)+Bu(k) (3)

in the formula (3), x (k | k-1) is based on the state of the system at the previous moment, the estimation on the state of the system at the current moment is carried out, x (k-1| k-1) is the optimal state prediction output of the system at the previous moment, and u (k) represents the control input quantity, and the covariance of the state of the system at the previous moment needs to be updated because the predicted value changes due to iterative update;

P(k|k-1)＝AP(k-1|k-1)A'+Q (4)

in the formula (4), P (k | k-1) is a covariance corresponding to the estimated output x (k | k-1) of the system at the time k;

after the prediction stage is finished, reading the real measured value of the system state at the current moment, and comparing the predicted value of the system state at the previous moment with the measured value at the current moment to obtain the optimal prediction result at the current moment as shown in the formula (5)

x(k|k)＝x(k|k-1)+Kg(k)(Z(k)-Hx(k|k-1)) (5)

Wherein z (k) represents the observed quantity of the system at the current time, kg (x) represents the kalman gain, and the expression thereof is shown in formula (6)

After the optimal output result is obtained, the system covariance at the current moment needs to be updated again so as to estimate the system state at the next moment, and the update equation is shown as formula (7)

P(k|k)＝(1-Kg(k)H)P(k|k-1) (7)

Step 3, fitting a semi-parametric regression model, wherein in the non-parametric regression model, the measured sample data is assumed to be (RSSI)_i,d_i) (i-1, 2, …, n), where RSSI is the received electromagnetic signal power and is a dependent variable; d is the distance of signal propagation, is an independent variable, assuming RSSI_i(i ═ 1,2, …, n) were independently identically distributed, and a non-parametric regression model was built as follows:

RSSI_i＝m(d_i)+ε_i i＝1,2,…,n (8)

where m (d) is an unknown regression function and ε is a random error satisfying a Gaussian distribution.

The optimal regression function that satisfies the model should minimize the sum of the squared errors of the regression function outputs, i.e.:

generally, m (d) is considered to be d after the known transmission distance, and the condition of the RSSI of the receiving end is expected, namely:

m(d)＝E(RSSI|d) (10)

estimating the regression function by adopting a weight function method, wherein the estimation method comprises the following steps:

for given sample data d_i(i ═ 1,2, …, n), the weight of each sample data item is different when estimating the function m (d). Let { W_i(d)＝W_i(d|d₁,…,d_n) i ═ 1,2, …, n } denotes the sample point (d) when estimating the regression function_i,RSSI_i) The corresponding regression function is then estimated as:

the estimation method obtains the following estimation of the regression function:

wherein K (-) is a kernel function for determining RSSI of each sample point in the process of estimating the regression function m (d)_iThe occupied proportion is large, h is the window width, the size of the local neighborhood is controlled, and the accuracy of non-parameter estimation is determined.

The fitting method of the electromagnetic wave signal amplitude attenuation and propagation distance relation curve has the following advantages:

1) and a relatively efficient processing algorithm is used in the data acquisition stage and the curve fitting stage, so that the authenticity of the acquired data is improved, a more accurate relation curve is established, and the discharge distance can be calculated more accurately according to the acquired signals.

2) The time sequence of partial discharge data is processed by adopting a Kalman filtering algorithm, and the state value of the current system is corrected by adopting an observation value, so that the uncertainty of the whole signal sequence is reduced, and the state value of the current moment is not influenced by the past moment.

3) The non-parametric regression model is adopted to fit the attenuation curve of the signal amplitude, the model is more flexible than a Shadowing model based on parameter fitting, the problem that the parameter model only considers the limitation of the overall optimal solution is solved, the detection characteristic of the sensor can be better reflected, and the fitting effect is better.

Drawings

FIG. 1 is a waveform diagram of a signal sequence before removing abnormal values in the embodiment;

FIG. 2 is a waveform diagram of a signal sequence after outlier rejection in the embodiment;

FIG. 3 is a graph showing signal attenuation characteristics in an example;

FIG. 4 is a graph of attenuation characteristics after Kalman filtering is applied in the embodiment;

FIG. 5 is a graph of a fit of a relationship curve using the Shadowing model;

FIG. 6 is a graph of a relationship curve fit using the nonparametric regression model of the invention.

Detailed Description

In order to better understand the technical solution of the present invention, the following detailed description is made by specific examples:

a fitting method of an electromagnetic wave signal amplitude attenuation and propagation distance relation curve comprises the following steps:

step 1, signal abnormal value elimination step, wherein the distribution of the collected signal data is regarded as Gaussian distribution, and the probability density distribution conforms to N to (mu, sigma)²) Removing abnormal values distributed in the data and distributed outside the variance 2 times of the average value;

step 2, a filtering step, namely filtering by adopting a Kalman filtering algorithm, wherein the filtering step comprises two stages of prediction and updating;

the prediction stage introduces the state equation and observation equation of the system, such as formula

x(k)＝Ax(k-1)+Bu(k)+w(k) (1)

z(k)＝Hx(k)+v(k) (2)

Wherein, formula (1) is a differential equation of the state of the system itself, formula (2) is an observation output equation of the system at the current moment, in formula (1), x (k) is the state of the system at the moment k, u (k) is the system control input quantity, w (k) is the system excitation noise, a is the state transition matrix, B is the gain coefficient of the input quantity, in formula (2), z (k) represents the observation value of the system at the moment k, H is the observation constant, v (k) is the observation error of the system;

predicting the state of the system at the moment k according to the state of the system at the moment k-1, wherein the optimal predicted output of the system at the moment k is as follows:

x(k|k-1)＝Ax(k-1|k-1)+Bu(k) (3)

in the formula (3), x (k | k-1) is based on the state of the system at the previous moment, the estimation on the state of the system at the current moment is carried out, x (k-1| k-1) is the optimal state prediction output of the system at the previous moment, and u (k) represents the control input quantity, and the covariance of the state of the system at the previous moment needs to be updated because the predicted value changes due to iterative update;

P(k|k-1)＝AP(k-1|k-1)A'+Q (4)

in the formula (4), P (k | k-1) is a covariance corresponding to the estimated output x (k | k-1) of the system at the time k;

after the prediction stage is finished, reading the real measured value of the system state at the current moment, and comparing the predicted value of the system state at the previous moment with the measured value at the current moment to obtain the optimal prediction result at the current moment as shown in the formula (5)

x(k|k)＝x(k|k-1)+Kg(k)(Z(k)-Hx(k|k-1)) (5)

Wherein z (k) represents the observed quantity of the system at the current time, kg (x) represents the kalman gain, and the expression thereof is shown in formula (6)

After the optimal output result is obtained, the system covariance at the current moment needs to be updated again so as to estimate the system state at the next moment, and the update equation is shown as formula (7)

P(k|k)＝(1-Kg(k)H)P(k|k-1) (7)

Step 3, fitting a semi-parametric regression model, wherein in the non-parametric regression model, the measured sample data is assumed to be (RSSI)_i,d_i) (i-1, 2, …, n), where RSSI is the received electromagnetic signal power and is a dependent variable; d is the distance of signal propagation, is an independent variable, assuming RSSI_i(i ═ 1,2, …, n) were independently identically distributed, and a non-parametric regression model was built as follows:

RSSI_i＝m(d_i)+ε_i i＝1,2,…,n (8)

where m (d) is an unknown regression function and ε is a random error satisfying a Gaussian distribution.

The optimal regression function that satisfies the model should minimize the sum of the squared errors of the regression function outputs, i.e.:

generally, m (d) is considered to be d after the known transmission distance, and the condition of the RSSI of the receiving end is expected, namely:

m(d)＝E(RSSI|d) (10)

estimating the regression function by adopting a weight function method, wherein the estimation method comprises the following steps:

for given sample data d_i(i ═ 1,2, …, n), the weight of each sample data item is different when estimating the function m (d). Let { W_i(d)＝W_i(d|d₁,…,d_n) i ═ 1,2, …, n } denotes the sample point (d) when estimating the regression function_i,RSSI_i) The corresponding regression function is then estimated as:

the estimation method obtains the following estimation of the regression function:

wherein K (-) is a kernel function for determining RSSI of each sample point in the process of estimating the regression function m (d)_iThe occupied proportion is large, h is the window width, the size of the local neighborhood is controlled, and the accuracy of non-parameter estimation is determined.

The method is verified by the following specific examples.

In order to verify the effectiveness of the processing method, experimental data collected outdoors are processed and verified. The experiment is firstly carried out in an open outdoor environment, the discharge lasts for 3 minutes at a single discharge point, and the time sequence signal of the amplitude is recorded. Setting a discharge point every 0.5m, collecting 0-8m experimental data, and fitting the experimental result.

Firstly, abnormal values of the acquired signals are removed.

Please refer to the comparison of the waveforms of the signal sequence before the removal of the abnormal value in fig. 1 and after the removal of the abnormal value in fig. 2.

Then, the time series signal sequence is subjected to smooth filtering by using a Kalman filtering algorithm. The signal attenuation characteristic diagram in fig. 3 and the attenuation characteristic diagram after kalman filtering in fig. 4 show the attenuation characteristic of the RSSI signal sequence along with the increase of the propagation distance, and the effect is more obvious after the kalman filtering algorithm is used.

Fig. 5 shows the fitting of a relationship curve using the Shadowing model, and fig. 6 shows the fitting of a relationship curve using the non-parametric regression model of the present invention. It can be seen that the present invention has a better fitting effect by using the sum of squared differences (RMS) between the fitted value and the true value as a criterion of the fitting effect.

It should be understood by those skilled in the art that the above embodiments are only for illustrating the present invention and are not to be used as a limitation of the present invention, and that changes and modifications to the above described embodiments are within the scope of the claims of the present invention as long as they are within the spirit and scope of the present invention.