Compensation type displacement high-precision microwave measurement method

Abstract

The invention relates to the field of blade tip clearance measurement, in particular to a compensation type displacement high-precision microwave measurement method, by providing a new compensation technology, namely radar orthogonal signal equalization, the radar orthogonal signal equalization method firstly provides a mirror image congruence concept in an I / Q channel self-convolution track space, and the compensation type displacement high-precision microwave measurement method is provided. And a new view angle is provided for compensating amplitude and phase imbalance. The method comprises the following steps of: firstly, estimating a direct-current offset parameter by analyzing accumulated energy of a orthogonal channel; then, based on the mirror image congruence characteristic, an objective function used for compensating parameter estimation is formulated, amplitude-phase imbalance correction is achieved through multiple regression, the parameter estimation performance of the radar orthogonal signal equalization method has robustness for nonlinear modulation and high-order harmonics, and the method is superior to an existing method; and errors and nonlinearity of blade tip clearance measurement are significantly reduced.

Description

Technical Field

[0001] This application relates to the field of microwave echo signal measurement, and in particular to a compensated high-precision microwave measurement method for displacement. Background Technology

[0002] With the rapid development of the ultra-precision manufacturing industry, non-contact, high-precision real-time measurement of the relative distance or minute displacement between objects or between key points inside an object is a key technology to ensure product safety and performance in many fields such as industrial inspection, high-end manufacturing, and scientific research (such as semiconductor lithography, precision instrument calibration, and aerospace).

[0003] For example, in the aerospace field, blade tip clearance (BTC) is a key indicator for evaluating the performance and safety of rotating machinery, particularly in aero engines, water turbines, and nuclear turbines. Excessive BTC typically reduces energy conversion efficiency and impairs aerodynamic stability, while insufficient BTC may increase the risk of blade casing friction, thereby increasing failure risk and maintenance costs. Therefore, continuous BTC monitoring and control are crucial for improving operational efficiency and system safety. Accurate BTC monitoring and control rely on dynamic BTC measurement. Various sensors have been explored, with Doppler radar standing out due to its compact configuration and stability under harsh conditions. It achieves BTC monitoring through phase difference analysis between transmitted and received signals, demonstrating significant potential in BTC measurement.

[0004] However, front-end defects, particularly amplitude-phase imbalance and DC offset in the in-phase and quadrature (I / Q) channels, significantly affect measurement accuracy. Existing compensation methods can be broadly categorized into two types: (1) linear space-based methods, such as Gran-Schmidt (GS) projection and singular value decomposition (SVD), which rely on basic linear algebra techniques (e.g., projection, matrix decomposition). These methods offer moderate compensation accuracy and low computational complexity; (2) parametric compensation methods, including elliptic correction and its derivatives, as well as frequency domain methods. These methods leverage the fact that BTC and linear displacement have similar hardware-induced distortions. Both BTC and linear displacement are derived from the I / Q signals output by Doppler radar, enabling these methods to extract amplitude-phase imbalance and DC offset from linear displacement data based on blade tips. However, linear space-based techniques are limited by the nonlinear behavior of BTC information, leading to the loss of strict orthogonality in the I / Q channels and reducing the compensation effect. Therefore, an efficient compensation method is needed to compensate for the I / Q signals. Existing patent application CN108931223B provides a dynamic calibration system for a blade tip clearance measurement sensor. This system uses an optical probe mounted on the same side as the blade tip clearance measurement sensor to measure the change in distance between the sensor and the corresponding blade on the calibration disk during rotation, thus compensating for the signal. While this patent application can compensate for dynamic blade tip clearance, the additional optical probe undoubtedly increases the sensor's size, making it unsuitable for applications in confined spaces. Summary of the Invention

[0005] Based on this, in order to address the problem that the existing I / Q signal compensation effect is not ideal, resulting in insufficient accuracy in displacement measurement, this invention provides a compensated high-precision microwave displacement measurement method, which has the characteristic of high precision in displacement measurement.

[0006] The technical solution of this invention is as follows: a high-precision microwave measurement method for compensated displacement, comprising the following steps: First, estimating DC offset parameters by equalizing orthogonal signals from Doppler radar. Second, estimating amplitude and phase imbalance by using the Doppler radar orthogonal signal equalization method, thereby obtaining the amplitude and phase imbalance signal. Third, compensating for the amplitude and phase imbalance by characterizing and utilizing the mirror congruence properties of I / Q signals in the self-convolution trajectory space.

[0007] The aforementioned compensated displacement high-precision microwave measurement method addresses the issue that, in actual measurement environments, some non-ideals can distort the I / Q signals, thereby reducing the accuracy of relative distance or minute displacement estimation. This includes, but is not limited to, modeling the I / Q signals as: Furthermore, plane waves, especially high-frequency plane waves, exhibit significant energy attenuation in displacement measurements, such as BTC measurements, leading to nonlinear amplitude modulation. Multiple reflections between the radar and the blades further contribute to harmonic coupling. Therefore, the distorted I / Q signal can be described as: The method described above for estimating DC offset parameters using orthogonal signals from Doppler radar, where DC offset is represented by a zero-frequency constant in the signal, leads to a linear increase in accumulated energy over time. The accumulated energy of the I / Q signals can be calculated as follows: In the formula, and It can be expanded to: The trend of the accumulated energy is dominated by the integral of the DC offset, and a linear trend is approximated by linear regression: The estimated DC offset can be expressed as: The method described above, which compensates for amplitude and phase imbalance by characterizing and utilizing the mirror congruence properties of I / Q signals in the self-convolution trajectory space, constructs an analytic signal using Hilbert transform after removing the estimated DC offset. The self-convolution of analyzing I / Q signals can be described as: These signals define the trajectory coordinates in the self-convolution space as: and In the formula . The method described above, which uses the mirror congruence property of I / Q signals in the self-convolution trajectory space to achieve amplitude and phase imbalance compensation, defines a two-dimensional rotation matrix to estimate the amplitude and phase imbalance compensation parameters. To modulate direction These parameters are optimized by minimizing the following objective function: In the formula , ,and: By optimizing parameters and The compensation for the I / Q signals is as follows: The compensated tip clearance can be calculated as follows: The method for compensating for amplitude and phase imbalance by characterizing and utilizing the mirror congruence property of I / Q signals in the self-convolution trajectory space includes, but is not limited to, situations where the I / Q signals are completely orthogonal, have equal amplitudes, and a phase difference of . Under ideal conditions and It exhibits mirror congruence in the self-convolution space—a geometric symmetry that verifies correct phase and amplitude. This is relevant to Doppler radar I / Q signals. and When the DC offset is removed, they can be mapped to the self-convolution trajectory space, as shown below: In the formula It is a mapping operator. and These are the coordinates of the I / Q signals in the self-convolution trajectory space. and Satisfying Relationships The method described above for correcting signals with amplitude and phase imbalance by estimating the objective function through the development of compensation parameters includes, but is not limited to, gradient-based methods and evolutionary algorithms.

[0008] The beneficial effects of this invention are as follows: By proposing the "radar orthogonal signal equalization method" and the "mirror congruence property in the self-convolution trajectory space," this invention achieves high-precision compensation for amplitude imbalance, phase imbalance, and DC offset in I / Q signals, significantly improving the accuracy and stability of microwave displacement measurement. This method has strong robustness to nonlinear modulation and higher-order harmonics, maintains excellent performance in complex measurement environments, and requires no additional hardware, making it suitable for confined spaces and harsh working conditions. Experiments show that the repeatability error of the compensated measurement results is significantly reduced, and the confidence interval is better than that of laser sensors. It exhibits high consistency and reliability in precision measurements such as blade tip clearance, and can be widely applied in high-precision non-contact ranging fields such as aero-engines and precision manufacturing. Attached Figure Description

[0009] Figure 1This is a flowchart of an overall method for orthogonal equalization compensation measurement of microwave echo signals in one embodiment; Figure 2 This is a schematic diagram of the hardware structure of a Doppler radar BTC measurement system in one embodiment; Figure 3 (a) is a time-domain waveform of the simulated I / Q signal in one embodiment; Figure 3 (b) is an IQ trajectory diagram of the simulated I / Q signal in one embodiment; Figure 4 (a) is a trend graph of accumulated energy in one embodiment; Figure 4 (b) is an autoconvolutional graph of the I / Q signals in one embodiment; Figure 4 (c) is a rose-shaped self-convolution map of the I / Q signals in one embodiment; Figure 5 (a) is an I / Q signal diagram of a simulated signal with ROSE compensation in one embodiment; Figure 5 (b) is a linear displacement plot of the ROSE compensation for the analog signal in one embodiment; Figure 5 (c) is a diagram illustrating the index iteration process of ROSE compensation for analog signals in one embodiment; Figure 5 (d) is a graph of the absolute error of ROSE compensation for the analog signal in one embodiment; Figure 6 (a) is an I / Q signal diagram before compensation for dynamic BTC in another embodiment; Figure 6 (b) is a diagram of the I / Q signal after compensation for dynamic BTC in another embodiment; Figure 7 This is a schematic diagram of BTC localization and extraction measured by Doppler radar in another embodiment; Figure 8 (a) is a schematic diagram of the repeatability error of the laser and radar sensors in one embodiment; Figure 8 (b) is a schematic diagram of the relative error of dynamic BTC measured by ROSE compensation Doppler radar and laser displacement sensor in one embodiment. Detailed Implementation

[0010] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0011] The method of the present invention firstly estimates the DC offset parameters by equalizing the orthogonal signals of Doppler radar; secondly, it estimates the amplitude and phase imbalance by equalizing the orthogonal signals of Doppler radar, thereby obtaining the amplitude and phase imbalance signal; and thirdly, it achieves amplitude and phase imbalance compensation by characterizing and utilizing the mirror congruence properties of the I / Q signals in the self-convolution trajectory space.

[0012] Example 1 In this embodiment, as Figure 2 This is a schematic diagram of the hardware structure of a Doppler radar BTC measurement system. In this system, the antenna (Tx) transmits a continuous wave at a fixed frequency, and the signal reflected from the surface of the rotating blade is received by the receiving antenna (Rx). The measurement resolution is closely related to the carrier frequency. When there is a relative displacement between the Doppler radar and the blade, a Doppler frequency shift will appear in the received signal, resulting in a measurable phase difference. The transmitted and received signals are as follows: In the formula, and These are the transmitted signal and the received signal, respectively. and It is the gain of the transmitter and receiver. , and This indicates the amplitude, frequency, and initial phase of the carrier wave. It's a Doppler shift. It is the propagation delay, in close-range measurements. , , It is the relative velocity between the Doppler radar and the blade. It is the wavelength, the received signal after passing through components such as a low-noise amplifier (LNA), mixer, phase shifter, low-pass (LP) filter, and power amplifier (PA). Demodulated into a quadrature I / Q baseband signal: Then, the phase information embedded in the I / Q signals can be used to obtain BTC. As shown below: A new method called cumulative energy estimation is further introduced, whereby the DC offset, which is represented by a zero-frequency constant in the signal, causes the cumulative energy to increase linearly with time. The cumulative energy of the I / Q signal can be calculated as: In the formula, and It can be expanded to: The trend of accumulated energy is dominated by the integral of DC offset, and a linear trend is approximated by linear regression: In the formula These are the slope and the intercept, respectively. The estimated DC offset can be expressed as: After removing the estimated DC offset, an analytic signal is constructed using the Hilbert transform: In the formula This represents the Hilbert transform. The self-convolution of an analytic I / Q signal can be described as: In the formula, ∗ represents the convolution operator. These signals define the trajectory coordinates in the self-convolution space as: and In the formula . Furthermore, a two-dimensional rotation matrix is ​​defined. To modulate direction In the formula and These are the phase and amplitude factors, respectively. These parameters are optimized by minimizing the objective function: In the formula , ,and: In the formula express Norm, Evaluation trajectory and The degree of overlap between them also indicates that the trajectory has an extreme value. Evaluate and The consistency of direction between them, with an extreme value of 1. This can be achieved by optimizing the parameters. and The compensation for the I / Q signals is as follows: The compensated tip clearance can be calculated as follows: When the I / Q signals are perfectly orthogonal, have equal amplitudes, and a phase difference of , Under ideal conditions and It exhibits mirror congruence in the self-convolution space—a geometric symmetry that verifies correct phase and amplitude. This is relevant to Doppler radar I / Q signals. and When the DC offset is removed, they can be mapped to the self-convolution trajectory space, as shown below: In the formula It is a mapping operator. and These are the coordinates of the I / Q signals in the self-convolution trajectory space. and Satisfying Relationships Due to the amplitude and phase imbalance, DC offset, and nonlinear modulation of the Doppler radar, an analog signal is generated, such as... Figure 3 (a) and Figure 3 (b) shows the time-domain waveform and IQ trajectory of the analog I / Q signal.

[0013] Furthermore, the DC offset is estimated, the accumulated energy is calculated, and the trend of the accumulated energy is approximated by linear regression, such as... Figure 4 As shown in (a), the DC offset of the I / Q signals is determined based on the slope of the linear trend. The analytical trajectory and autoconvolution plot (with DC offset removed) of the I / Q signals are shown below. Figure 4 As shown in (b), DC offset can be effectively compensated. The self-convolution diagram resembles two signals, forming a "rose" shape, as shown... Figure 4 As shown in (c).

[0014] Further compensate the I / Q signals and use formula (13) to estimate the amplitude and phase imbalance parameters. Figure 5 (a) shows the compensated I / Q signals. Figure 5 (c) gives the iterative process of the two indices in equation (13), where the Euclidean distance (ED) and cosine similarity (CS) show obvious extreme values ​​within the parameter range. Figure 5(b) and (d) illustrate the compensation performance and corresponding absolute error for linear displacement changes, respectively. Table 1 shows a comparison of ROSE-compensated Doppler radar with other methods, such as GS, SVD, and piecewise elliptic correction (SEC), in terms of parameter estimation performance. Table 1 summarizes the absolute errors for different parameters and the time costs of different methods (n and m represent the orders of magnitude of the amplitude and phase factors in ROSE, respectively). Table 1 shows that the GS method accurately estimates the amplitude imbalance but has significant errors in estimating the phase imbalance. The SVD method lacks parameter estimation capabilities, and the accuracy of the SEC method is severely limited by harmonic coupling. In contrast, the ROSE method consistently demonstrates high accuracy in estimating I / Q imbalance parameters and DC offset in all scenarios.

[0015] Table 1 Example 2 To better understand the dynamic tip clearance compensation measurement method for Doppler radar orthogonal signal equalization in Example 1, a detailed explanation is provided below in conjunction with simulation experiments. The I / Q signals are obtained through an NI data acquisition system, with a sampling frequency of [frequency missing]. The Hz sliding travel speed is 2.34 mm / s. The initial blade tip clearance is 2 mm. Parameters extracted from ROSE are used to compensate for dynamic BTC. Figure 6 (a) and (b) show the waveforms of the I / Q signals before and after compensation. Compared with linear displacement, the I / Q signals corresponding to dynamic BTC exhibit more complex phase information. Parameters extracted by ROSE were used to compensate for dynamic BTC. The I / Q signals were sampled at 100 kHz, the distance between the Doppler radar and the blade tip was 5 mm, and the motor rotated at 100 RPM. Figure 7 The waveforms of the I / Q signals before and after compensation are displayed.

[0016] Furthermore, to better understand the repeatability of BTC measurements by the ROSE-compensated Doppler radar in Example 1, the following experiment was conducted: using the BTC of the first blade in the first revolution as a baseline, BTC fluctuations were recorded for three revolutions. Based on these fluctuations, the repeatability error of the Doppler radar measurement was calculated and compared with the repeatability error obtained by the laser displacement sensor, such as... Figure 8 As shown, from Figure 8 It is clear that the measurement results of the ROSE compensated Doppler radar are in excellent agreement with those of the laser displacement sensor. Figure 8The results show that the laser displacement sensor exhibits significant repeatability errors, particularly for the second blade, while the ROSE-compensated Doppler radar demonstrates excellent repeatability. Furthermore, to quantify the repeatability errors, the confidence intervals and widths of the laser and radar measurements at a 95% confidence level were calculated. As shown in Table 2, it can be observed that the radar typically exhibits a narrower confidence interval compared to the laser, indicating superior repeatability. This fully validates the accuracy and feasibility of the orthogonal equalization compensation-based high-precision displacement measurement method proposed in this application.

[0017] Table 2 The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0018] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method of high-precision microwave measurement of displacement with compensation, characterized in that, First, the first step is to estimate the DC offset parameter by the Doppler radar quadrature signal equalization; second, the second step is to estimate the amplitude and phase imbalance by the Doppler radar quadrature signal equalization method, so as to obtain the amplitude and phase imbalance signal; finally, the third step is to realize the amplitude and phase imbalance compensation by representing and utilizing the mirror congruence characteristics of the I / Q signal in the self-convolution trajectory space.

2. The method of claim 1, wherein the method is a compensated displacement high-precision microwave measurement method. The DC offset parameter is estimated by the Doppler radar quadrature signal equalization, including by introducing a new method called cumulative energy estimation, the DC offset appears as a zero-frequency constant in the signal, which causes the cumulative energy to increase linearly with time, the cumulative energy of the I / Q signal can be calculated as: wherein is the cumulative energy of the in-phase signal, is the cumulative energy of the quadrature signal, is the summation index, : in-phase component, Q : quadrature component; and can be extended to: wherein is a nonlinear amplitude modulation, is the gain of the second harmonic, ) is the noise, is the DC offset of the in-phase channel, is the DC offset of the quadrature channel, is the discretized in-phase signal, including distortion, is the discretized quadrature signal, including distortion, is the relative velocity between the Doppler radar and the blade, is the phase imbalance; The trend of the cumulative energy is dominated by the integral of the DC offset, and the linear trend is approximated by linear regression: wherein are the slope and intercept, respectively, is the linear trend of the in-phase cumulative energy, is the linear trend of the quadrature cumulative energy, is the estimated in-phase DC offset, is the estimated quadrature DC offset, , may be expressed as: .

3. The method of claim 1, wherein the method is a compensated displacement high-precision microwave measurement method. The method for estimating the amplitude and phase imbalance by the Doppler radar quadrature signal equalization, so as to obtain the amplitude and phase imbalance signal, includes using the Hilbert transform to construct the analytic signal after removing the estimated DC offset: wherein denotes the Hilbert transform, is the analytic signal of the in-phase signal, is the analytic signal of the quadrature signal, the auto-convolution of the analytic I / Q signal can be described as: where * denotes the convolution operator, is the imaginary unit, is the exponential function, is the autocorrelation of the in-phase analytic signal, is the autocorrelation of the quadrature analytic signal, is the transmitter gain, is the amplitude imbalance; is the receiver gain, is the carrier amplitude, these signals define the trajectory coordinates in the autocorrelation space as: And wherein is a set of coordinates of the in-phase signal in the auto-convolution trajectory space, is a set of coordinates of the quadrature signal in the auto-convolution trajectory space, is a coordinate of the th sampling point in the trajectory, is a coordinate of the th sampling point in the trajectory, is the total number of sampling points, is an amplitude constant, defined by .

4. The method of claim 1, wherein the method is a compensated displacement high-precision microwave measurement method. The method for obtaining the amplitude and phase imbalance signal by means of the Doppler radar quadrature signal equalization method for amplitude and phase imbalance estimation, further comprises defining a two-dimensional rotation matrix for estimating the amplitude and phase imbalance compensation parameters to modulate the direction of, the definition is as follows: where and are phase and amplitude factors, respectively, which are optimized by minimizing the following objective function: wherein , , , is the optimized parameter estimate, is the parameter value that minimizes the objective function, is the Euclidean distance sum between trajectories , is the cosine similarity between trajectories , is the constraint, is the Euclidean distance sum; and: wherein represents norm, is the dot product operator, evaluating the degree of coincidence between and , the trajectory having a maximum; evaluating and the consistency of the direction, the maximum being 1 ; by optimizing the parameters and , the compensation of the I / Q signal is as follows: wherein is the compensated in-phase signal, is the compensated quadrature signal, is the original in-phase signal vector, is the original quadrature signal vector, the compensated tip clearance can be calculated as In the formula, is the compensated tip clearance.

5. The method of claim 1, wherein the method is a compensated displacement high-precision microwave measurement method. By characterizing and exploiting the mirror congruence properties of I / Q signals in the self-convolution trajectory space, amplitude and phase imbalance compensation is achieved, including removing the DC offset from the Doppler radar I / Q signals and , which can then be mapped into the self-convolution trajectory space as follows: wherein is a mapping operator, and are, respectively, the coordinates of the I / Q signal in the self-convolution trajectory space, and are, respectively, the ideal in-phase signal and the ideal quadrature signal, and satisfy the relation: 。 6. The method of claim 5, wherein the method is a compensated displacement high-precision microwave measurement method. By characterizing and exploiting the mirror congruence property of I / Q signals in the autoconvolution trajectory space, amplitude and phase imbalance compensation is achieved. This method also includes, but is not limited to, the ideal condition that the I / Q signals are completely orthogonal, the amplitudes are equal, and the phase difference is , under which and mirror congruence, a kind of geometric symmetry, is exhibited in the autoconvolution space, which can verify the correct phase and amplitude.

7. The method of claim 1, wherein the method is a compensated displacement high-precision microwave measurement method. Further including that in the actual measurement environment, some non-idealities will bring distortion to the I / Q signal, thereby reducing the accuracy of the BTC estimation, including but not limited to the I / Q signal can be modeled as: wherein and denote the amplitude and phase imbalance, and are the DC offsets of the I / Q signals, respectively, and, in addition, plane waves, in particular high-frequency plane waves, exhibit a significant energy decay in displacement measurements, for example blade tip clearance (BTC) measurements, which leads to a non-linear amplitude modulation, and multiple reflections between the radar and the target can further lead to harmonic coupling, and, thus, the distorted I / Q signals can be described as: wherein is a nonlinear amplitude modulation, is a harmonic number, is a noise, is a gain of the mth harmonic.

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