CN113701618B - Eddy current sensor data processing method and system based on Kalman filtering - Google Patents
Eddy current sensor data processing method and system based on Kalman filtering Download PDFInfo
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Abstract
The invention discloses a Kalman filtering-based eddy current sensor data processing method and a Kalman filtering-based eddy current sensor data processing system, wherein the method comprises the following steps: step S1, digital detection is carried out on a voltage signal output by an eddy current sensor, and a high-frequency carrier signal in the voltage signal is eliminated, so that an actually required measurement voltage signal is obtained; step S2, carrying out phase detection on the voltage signal to determine the positive value and the negative value of the voltage signal; and step S3, carrying out fixed-point operation by using a Kalman filter according to the measured voltage signal and the positive and negative values, and carrying out filtering treatment on random noise. The method can meet the requirements of engineering projects on speed and bottom signal processing, simultaneously can reduce occupied resources, flexibly improves the functions of the system, and can realize the resolution of 100 nm.
Description
Technical Field
The invention relates to the technical field of eddy current sensor detection, in particular to an eddy current sensor data processing method and system based on Kalman filtering.
Background
The digital eddy current sensor takes an FPGA digital output signal as a square wave excitation source to realize the digitization of a carrier wave source; based on FPGA on-chip programming, digital detection, phase detection, digital filtering and other modules of the sensor signal are designed, and the digital processing of the sensor signal is completed, so that the advantage of reducing the power consumption of a simplified circuit is used for gradually replacing the traditional amplitude modulation type eddy current displacement sensor.
In the related art, a design of a digital eddy current displacement sensor based on an amplitude modulation type eddy current displacement sensor is proposed, a carrier signal of the sensor is designed by utilizing a digital output signal of a Field Programmable Gate Array (FPGA), and data processing is carried out on an output signal of a measuring circuit through software design of the FPGA. The external interference suffered by the sensor and the noise interference caused by hardware circuits such as A/D conversion can cause certain disturbance to the voltage measured by the detection measurement module, so that the noise interference needs to be filtered by digital filtering. The design adopts a moving average filtering method, the filtering method takes N sampling values obtained continuously as a queue, the length of the queue is fixed to N, new data are sampled each time and put into the tail of the queue, primary data (first-in first-out principle) of the original queue head are thrown out, the N data in the queue are subjected to arithmetic average operation, a new filtering result is obtained), the periodic interference is well inhibited, and the smoothness is high. But has the defects of low sensitivity, poor inhibition effect on the pulse interference which occurs occasionally, difficult elimination of sampling value deviation caused by the pulse interference, inapplicability to occasions with serious pulse interference and relatively waste of RAM.
Disclosure of Invention
The present invention aims to solve at least one of the technical problems in the related art to some extent.
To this end, a first object of the present invention is to propose a method for processing data of an eddy current sensor based on Kalman filtering.
A second object of the present invention is to propose an eddy current sensor data processing system based on Kalman filtering.
A third object of the present invention is to propose an electronic device.
A fourth object of the present invention is to propose a non-transitory computer readable storage medium.
To achieve the above objective, an embodiment of a first aspect of the present invention provides a method for processing data of an eddy current sensor based on Kalman filtering, including the following steps: step S1, carrying out digital detection on a voltage signal output by an eddy current sensor, and eliminating a high-frequency carrier signal in the voltage signal to obtain a measurement voltage signal actually required; step S2, carrying out phase detection on the voltage signal to determine the positive value and the negative value of the voltage signal; and step S3, carrying out fixed-point operation by using a Kalman filter according to the measured voltage signal and the positive and negative values, and carrying out filtering treatment on random noise.
The electric vortex sensor data processing method based on Kalman filtering can meet the requirements of engineering projects on speed and bottom signal processing, simultaneously can reduce occupied resources, flexibly perfects the functions of a system, and most importantly can improve the precision, realize the resolution of 100nm and obviously improve the precision of processing the electric vortex sensor data compared with the existing moving average filtering method.
In addition, the method for processing the data of the eddy current sensor based on Kalman filtering according to the embodiment of the invention can also have the following additional technical features:
further, in one embodiment of the invention, the Kalman filter comprises a time update equation responsible for timely forward estimating the values of the current state variable and the error covariance estimate to construct an a priori estimate for the next time state, and a measurement update equation responsible for feedback combining the a priori estimate with the new measured variable to construct an improved a posteriori estimate.
Further, in one embodiment of the present invention, the time update equation is:
wherein,for a priori state estimation, A is a state transition matrix, < >>For posterior state estimation at the previous time, B is the input control matrix, u k-1 For state control variables +.>For the prior covariance estimation value, Q is the process excitation noise covariance matrix;
the state update equation is:
wherein K is k In order for the kalman gain to be achieved,for a priori covariance estimate, H is the state variable to measurement conversion matrix, R is measurement noise covariance, ++>For posterior state estimation, A is the state transition matrix, < ->And a posterior covariance estimated value, wherein I is an identity matrix.
To achieve the above object, an embodiment of a second aspect of the present invention provides an eddy current sensor data processing system based on Kalman filtering, including: the digital detection module is used for carrying out digital detection on the voltage signal output by the eddy current sensor, eliminating the high-frequency carrier signal in the voltage signal and obtaining the actually required measurement voltage signal; the phase detection module is used for carrying out phase detection on the voltage signal so as to determine the positive value and the negative value of the voltage signal; and the digital filtering module is used for carrying out fixed-point operation by using a Kalman filter according to the measured voltage signal and the positive and negative values to carry out filtering processing on random noise.
The electric vortex sensor data processing system based on Kalman filtering can meet the requirements of engineering projects on speed and bottom signal processing, can flexibly improve the functions of the system, and can improve the precision, realize the resolution of 100nm and obviously improve the precision of processing the electric vortex sensor data compared with the traditional moving average filtering method.
In addition, the electric vortex sensor data processing system based on Kalman filtering according to the embodiment of the invention can also have the following additional technical features:
further, in one embodiment of the present invention, the Kalman filter is implemented by using an FPGA, where fixed-point operation is adopted in the FPGA, and fixed-point decimal is set by itself according to the actual situation.
Further, in one embodiment of the invention, the Kalman filter comprises a time update equation responsible for timely forward estimating the values of the current state variable and the error covariance estimate to construct an a priori estimate for the next time state, and a measurement update equation responsible for feedback combining the a priori estimate with the new measured variable to construct an improved a posteriori estimate.
Optionally, in an embodiment of the present invention, the time update equation is:
wherein,for a priori state estimation, A is a state transition matrix, < >>For posterior state estimation at the previous time, B is the input control matrix, u k-1 For state control variables +.>For the prior covariance estimation value, Q is the process excitation noise covariance matrix;
the state update equation is:
wherein K is k For the kalman gain at the current moment,for a priori covariance estimate, H is the state variable to measurement conversion matrix, R is measurement noise covariance, ++>For posterior state estimation, A is the state transition matrix, < ->For a priori state estimation, P k And I is an identity matrix for the posterior covariance estimation value.
To achieve the above object, an embodiment of a third aspect of the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, where the processor implements the above-mentioned Kalman filtering-based eddy current sensor data processing system when executing the computer program.
To achieve the above object, a fourth aspect of the present invention provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements a Kalman filtering based eddy current sensor data processing system as described above.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
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The foregoing and/or additional aspects and advantages of the invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings, in which:
FIG. 1 is a flow chart of a Kalman filtering-based eddy current sensor data processing method in accordance with one embodiment of the invention;
FIG. 2 is a specific process flow diagram of a Kalman filtering-based eddy current sensor data processing method, in accordance with one embodiment of the invention;
FIG. 3 is a schematic diagram of a time update and measurement update process according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of the implementation principle of a Kalman filtering algorithm based on an FPGA according to one embodiment of the invention;
FIG. 5 is a schematic diagram of a Kalman filtering-based eddy current sensor data processing system in accordance with one embodiment of the invention.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative and intended to explain the present invention and should not be construed as limiting the invention.
The method and the system for processing the data of the electric vortex sensor based on the Kalman filtering according to the embodiment of the invention are described below with reference to the accompanying drawings, and the method for processing the data of the electric vortex sensor based on the Kalman filtering according to the embodiment of the invention is described first with reference to the accompanying drawings.
FIG. 1 is a flow chart of a Kalman filtering-based eddy current sensor data processing method in accordance with one embodiment of the invention.
As shown in fig. 1, the method for processing the data of the eddy current sensor based on the Kalman filtering comprises the following steps:
in step S1, the voltage signal output by the eddy current sensor is digitally detected, and the high-frequency carrier signal in the voltage signal is eliminated, so as to obtain the actually required measurement voltage signal.
Specifically, as shown in fig. 2, the digital detection adopts a voltage-multiplying envelope detection mode to carry out digital design, and the working principle of the voltage-multiplying envelope detection is that the difference between the upper envelope and the lower envelope of the whole measurement signal is calculated by solving the upper envelope and the lower envelope of the whole measurement signal, so that the high-frequency carrier signal in the voltage signal can be eliminated, and the actually required measurement voltage signal is further solved, thereby realizing high-precision and high-precision voltage measurement.
In step S2, the voltage signal is subjected to phase detection to determine the positive and negative values of the voltage signal.
Specifically, the digital detection in step S1 cannot determine the phase information of the signal, and therefore it is necessary to design a phase detection module to determine the positive and negative values of the voltage signal. In differential measurement, the maximum displacement output signals of the rotor in both directions of the equilibrium position differ by 180 °. The main function of the phase detection is to judge whether the extreme value appears in the first half section or the second half section of the processing unit, and the output voltage can be set to be the maximum value minus the minimum value according to the situation, and the positive voltage is output.
In step S3, a fixed point operation is performed by using a Kalman filter to filter the random noise according to the measured voltage signal and the positive and negative values.
Because the external interference suffered by the electric vortex sensor and noise interference caused by hardware circuits such as A/D conversion and the like can bring certain disturbance to the voltage measured by the detection measurement module, the noise interference needs to be filtered by utilizing digital filtering.
Further, the principle of the Kalman filter is that a state space model of signals and noise is adopted by taking the minimum mean square error as an optimal estimation criterion, the estimation of state variables is updated by utilizing the estimated value of the previous moment and the observed value of the current moment, the estimated value of the current moment is obtained, and the algorithm makes the estimation meeting the minimum mean square error for the signals to be processed according to the established system equation and the observed equation.
The specific derivation formula is as follows:
kalman filtering is used to estimate the state variables of the discrete-time process. This discrete process time is described by the following discrete random differential equation:
x k ＝Ax k-1 +Bu k-1 +w k (1)
z k ＝Hx k +v k (2)
x k for state estimation, A is a state transition matrix, x k-1 For the previous state estimation, B is the input control matrix, u k-1 For state control variables, a random signal w k ,v k Is process excitation noise and observation noise, obeys the following distribution:q and R are the process excitation noise covariance matrix and the observation noise covariance matrix, respectively.
Handle(prior state estimation),>(posterior state estimation) while defining errors:
wherein e k In order to account for the posterior error,is a priori error.
Defining covariance:
P k ＝E[e k e k T ] (6)
wherein,for a priori covariance estimate, E is mathematical expectation, P k Is a posterior covariance estimate.
After which a Kalman filtered expression is constructed,
for posterior state estimation, ++>For a priori state estimation, K is referred to herein as Kalman gain, acting as a weight, z k For the measurement vector, H is the state variable to measurement conversion matrix.
The filter estimates the state of the process at a certain moment and then obtains feedback in the form of a (noisy) measured variable. The Kalman filter can therefore be divided into two parts: a time update equation and a measurement update equation. The time update equation is responsible for estimating the values of the current state variable and the error covariance estimate forward in time to construct a priori estimates for the next time state. The measurement update equation is responsible for feedback-that is, it combines the a priori estimates with the new measurement variables to construct an improved a posteriori estimate.
The time update equation is as follows:
wherein,for a priori state estimation, A is a state transition matrix, < >>For posterior state estimation at the previous time, B is the input control matrix, u k-1 For state control variables +.>For a priori covariance estimate, Q is the process excitation noise covariance matrix.
Note here thatIs the estimator and x in the discrete time difference equation mentioned earlier k Not a round.
The state update equation is as follows:
K k for the kalman gain at the current moment,for a priori covariance estimate, H is the state variable to measurement conversion matrix, R is measurement noise covariance, ++>For posterior state estimation, A is the state transition matrix, < ->For a priori state estimation, P k And I is an identity matrix for the posterior covariance estimation value.
Equation (11) is derived when the control amount U is 0, and P is used k Minimum to determine K k . The relationship of the time update equation and the state update equation is shown in fig. 3.
Furthermore, the Kalman filter directly filters the signal in a mathematical calculation mode, has no complex operation similar to the Fourier transform calculation, has simple thinking and speed superior to other filtering modes, and has small error value by adopting minimum mean square error estimation. The principle of the method for implementing the Kalman filter on the FPGA is shown in fig. 4, the important thing of the Kalman filter is that the Kalman filter is composed of 5 filtering equations, and the filtering equations are composed of simple operations of adding, subtracting, multiplying and dividing, so that the design of the Kalman filter becomes a combination of four operations, and when the adding and subtracting of the Kalman filtering equations are designed, a conversion of the IEEE 754 standard needs to be performed on each parameter and the value of a register, so as to improve the measurement resolution.
Next, it should be noted that, the FPGA has a floating point operation IP core, but needs to output data after several clock cycles, and the floating point operation IP core has a floating point operation defined by IEEE-754 standard, which has high precision and occupies very much resources.
There are two points in the fixed point decimal calculation, one is the use of an operator and one is the interception of an intermediate result. The fixed point decimal number needs to be quantized firstly when calculating, and is reflected to RTL, namely left shift and right shift, the right shift is divided into arithmetic right shift and logic right shift, the logic right shift is not considered with sign bit, and the sign bit is considered when calculating the arithmetic right shift, so that the complement operation must use the arithmetic right shift. The calculation after quantization corresponds to taking it as an integer, but this segment of binary is now a fixed point decimal representation, since the position of the decimal point is self-setting, the upper 8 bits being the integer part and the lower 8 bits being the decimal part. It is noted at this point that the result of the multiplication calculation also needs to be shifted to the right by 8 bits in order to ensure the alignment of the decimal points.
Further, in an embodiment of the present invention, the apparatus further includes a signal amplifying module, which amplifies the optimized voltage signal after the noise is processed by the Kalman filter, so as to facilitate subsequent applications.
In summary, the Kalman filtering-based data processing method for the eddy current sensor provided by the embodiment of the invention has the following advantages:
the precision and the speed are improved, and meanwhile, the method can be processed in the FPGA, so that the hardware circuit structure is avoided, the interference of the external environment is reduced, and the distortion and zero drift caused by the design of hardware circuit parameters are reduced;
the floating point operation in the FPGA has the defects of large delay and large resource occupation, and meanwhile, more clock cycles are needed to finish one operation, so that fewer logic units are occupied after fixed point operation is changed, and one operation can be finished with fewer clock cycles;
the method for realizing the Kalman filter by using the FPGA can not only meet the requirements of engineering projects on speed and bottom signal processing, but also flexibly improve the functions of the system, and most importantly, can improve the precision, realize the resolution of 100nm, and obviously improve the precision of processing the data of the eddy current sensor compared with the existing moving average filtering method.
Next, an eddy current sensor data processing system based on Kalman filtering according to an embodiment of the present invention will be described with reference to the accompanying drawings.
FIG. 5 is a schematic diagram of a Kalman filtering-based eddy current sensor data processing system in accordance with one embodiment of the invention.
As shown in fig. 5, the system 10 includes: a digital detection module 100, a phase detection module 200 and a digital filtering module 300.
The digital detection module 100 is configured to digitally detect a voltage signal output by the eddy current sensor, and eliminate a high-frequency carrier signal in the voltage signal, so as to obtain a actually required measurement voltage signal. The phase detection module 200 is configured to perform phase detection on the voltage signal to determine a positive value and a negative value of the voltage signal. The digital filtering module 300 is configured to perform fixed-point operation on random noise by using a Kalman filter according to the measured voltage signal and positive and negative values.
Further, in one embodiment of the present invention, the Kalman filter is implemented by using an FPGA, where fixed-point operation is adopted in the FPGA, and fixed-point decimal is set by itself according to the actual situation.
Further, in one embodiment of the invention, the Kalman filter comprises a time update equation responsible for timely forward calculation of the values of the current state variable and the error covariance estimate to construct an a priori estimate for the next time state, and a measurement update equation responsible for feedback combining the a priori estimate with the new measured variable to construct an improved a posteriori estimate.
Further, in one embodiment of the invention, the time update equation is:
wherein,for a priori state estimation, A is a state transition matrix, < >>For posterior state estimation at the previous time, B is the input control matrix, u k-1 For state control variables +.>For the prior covariance estimation value, Q is the process excitation noise covariance matrix;
the state update equation is:
wherein K is k For the kalman gain at the current moment,for a priori covariance estimate, H is the state changeConversion matrix from quantity to measurement, R is measurement noise covariance, +.>For posterior state estimation, A is the state transition matrix, < ->For a priori state estimation, P k And I is an identity matrix for the posterior covariance estimation value.
It should be noted that the foregoing explanation of the embodiment of the method for processing data of an eddy current sensor based on Kalman filtering is also applicable to the system for processing data of an eddy current sensor based on Kalman filtering in the embodiment of the present invention, and the implementation principle is similar and will not be repeated here.
The electric vortex sensor data processing system based on Kalman filtering provided by the embodiment of the invention has the following advantages:
the precision and the speed are improved, and meanwhile, the method can be processed in the FPGA, so that the hardware circuit structure is avoided, the interference of the external environment is reduced, and the distortion and zero drift caused by the design of hardware circuit parameters are reduced;
the floating point operation in the FPGA has the defects of large delay and large resource occupation, and meanwhile, more clock cycles are needed to finish one operation, so that fewer logic units are occupied after fixed point operation is changed, and one operation can be finished with fewer clock cycles;
the method for realizing the Kalman filter by using the FPGA can not only meet the requirements of engineering projects on speed and bottom signal processing, but also flexibly improve the functions of the system, and most importantly, can improve the precision, realize the resolution of 100nm, and obviously improve the precision of processing the data of the eddy current sensor compared with the existing moving average filtering method.
In order to implement the above embodiment, the present invention further provides an electronic device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor, where the processor implements the method for processing data of an eddy current sensor based on Kalman filtering according to the above embodiment when executing the computer program.
In order to implement the above-mentioned embodiments, the present invention also proposes a non-transitory computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements the method for processing data of an eddy current sensor based on Kalman filtering as in the previous embodiments.
Furthermore, the terms "first," "second," and the like, are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include at least one such feature. In the description of the present invention, the meaning of "plurality" means at least two, for example, two, three, etc., unless specifically defined otherwise.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, the different embodiments or examples described in this specification and the features of the different embodiments or examples may be combined and combined by those skilled in the art without contradiction.
While embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the invention, and that variations, modifications, alternatives and variations may be made to the above embodiments by one of ordinary skill in the art within the scope of the invention.
Claims (4)
1. The electric vortex sensor data processing method based on Kalman filtering is characterized by comprising the following steps of:
step S1, digital detection is carried out on a voltage signal output by an eddy current sensor, the digital detection is digitally designed by adopting a voltage doubling envelope detection mode, the difference between the upper envelope and the lower envelope of the whole measurement signal is calculated by solving the upper envelope and the lower envelope of the whole measurement signal, and a high-frequency carrier signal in the voltage signal is eliminated to obtain an actually required measurement voltage signal;
step S2, carrying out phase detection on the voltage signal, and judging whether an extremum exists in the first half section or the second half section of the processing unit so as to determine the positive value and the negative value of the voltage signal;
step S3, according to the measured voltage signal and the positive and negative values, performing fixed-point operation by using a Kalman filter to perform filtering processing on random noise;
realizing a Kalman filter by using an FPGA, wherein fixed-point operation is adopted in the FPGA, and fixed-point decimal is set automatically according to actual conditions;
the Kalman filter comprises a time update equation and a measurement update equation, wherein the time update equation is responsible for timely calculating the values of the current state variable and the error covariance estimate forward so as to construct a priori estimate for the next time state, the measurement update equation is responsible for feedback, and the priori estimate and a new measurement variable are combined to construct an improved posterior estimate;
the time update equation is:
wherein,for a priori state estimation, A is a state transition matrix, < >>Is in front ofA posterior state estimation at a moment, B is an input control matrix, u k-1 For state control variables +.>For the prior covariance estimation value, Q is the process excitation noise covariance matrix, P k-1 A posterior covariance estimated value of a previous moment;
the state update equation is:
wherein K is k For the kalman gain at the current moment,for a priori covariance estimate, H is the state variable to measurement conversion matrix, R is measurement noise covariance, ++>For posterior state estimation, A is the state transition matrix, < ->For a priori state estimation, P k And I is an identity matrix for the posterior covariance estimation value.
2. An eddy current sensor data processing system based on Kalman filtering, comprising:
the digital detection module is used for carrying out digital detection on the voltage signal output by the electric vortex sensor, the digital detection adopts a voltage doubling envelope detection mode for digital design, the difference between the upper envelope and the lower envelope of the whole measurement signal is calculated by solving the upper envelope and the lower envelope of the whole measurement signal, and a high-frequency carrier signal in the voltage signal is eliminated to obtain an actually required measurement voltage signal;
the phase detection module is used for carrying out phase detection on the voltage signal and judging whether an extremum appears in the first half section or the second half section of the processing unit so as to determine the positive value and the negative value of the voltage signal;
the digital filtering module is used for carrying out fixed-point operation on random noise by utilizing a Kalman filter according to the measured voltage signal and the positive and negative values;
realizing a Kalman filter by using an FPGA, wherein fixed-point operation is adopted in the FPGA, and fixed-point decimal is set automatically according to actual conditions;
the Kalman filter comprises a time update equation and a measurement update equation, wherein the time update equation is responsible for timely calculating the values of the current state variable and the error covariance estimate forward so as to construct a priori estimate for the next time state, the measurement update equation is responsible for feedback, and the priori estimate and a new measurement variable are combined to construct an improved posterior estimate;
the time update equation is:
wherein,for a priori state estimation, A is a state transition matrix, < >>For posterior state estimation at the previous time, B is the input control matrix, u k-1 For state controlVariable (I)>For the prior covariance estimation value, Q is the process excitation noise covariance matrix, P k-1 A posterior covariance estimated value of a previous moment;
the state update equation is:
wherein K is k For the kalman gain at the current moment,for a priori covariance estimate, H is the state variable to measurement conversion matrix, R is measurement noise covariance, ++>For posterior state estimation, A is the state transition matrix, < ->For a priori state estimation, P k And I is an identity matrix for the posterior covariance estimation value.
3. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the Kalman filter based eddy current sensor data processing method as recited in claim 1 when the computer program is executed by the processor.
4. A non-transitory computer readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the Kalman filtering based eddy current sensor data processing method as claimed in claim 1.
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