A microwave signal online correction and continuous displacement measurement method for dynamic rotating working conditions

Abstract

This invention relates to the field of microwave near-range displacement measurement technology, and more particularly to a method for online correction and continuous displacement measurement of microwave signals under dynamic rotating conditions. This method addresses the demodulation errors caused by amplitude imbalance, phase imbalance, and DC bias in the I / Q baseband signals under dynamic conditions, as well as the half-wavelength range limitation in phase difference ranging. It achieves online imbalance compensation by modeling the segmented boundaries of the I / Q signals and combining this with robust parameter estimation. Based on this, a complex signal is constructed for phase demodulation, and the phase folding effect is eliminated through phase rotation and cross-cycle displacement accumulation correction, achieving continuous displacement demodulation. This invention integrates signal correction and displacement measurement under dynamic motion conditions, breaking through the traditional half-wavelength limitation, improving measurement continuity and stability, and is suitable for measuring the gaps and displacements of rotating components.

Description

Technical Field

[0001] This invention relates to the field of microwave measurement technology, and in particular to a method for online correction and continuous displacement measurement based on I / Q signals, which is suitable for short-distance displacement and gap measurement under dynamic rotation conditions. Background Technology

[0002] In rotating machinery, turbine structures, compressor rotors, and high-speed moving components, the close-range clearance and displacement changes between components are key parameters reflecting operational safety and structural stability. To achieve online monitoring of these displacement parameters, microwave continuous wave-based phase difference ranging methods have gradually become an important technical means due to their advantages such as non-contact operation, strong anti-pollution capability, and applicability to high-temperature and high-speed conditions.

[0003] In a typical microwave displacement measurement system, the transmitter sends a continuous wave signal to the target. The echo is then mixed and demodulated to obtain the in-phase component (I) and the quadrature component (Q). Displacement demodulation is achieved by calculating the phase change of the complex signal. Under ideal conditions, the I / Q trajectory is distributed in a standard circular pattern on the complex plane, and the phase change corresponds linearly to the target displacement.

[0004] However, in real-world engineering environments, factors such as inconsistent amplitude gain of the RF link, positive cross-channel phase error, DC bias, and environmental reflection clutter can cause amplitude imbalance, phase shift, and DC drift in the I / Q signals. This degenerates the original circular trajectory into an eccentric ellipse, introducing phase error and reducing displacement demodulation accuracy. Existing technologies typically use static calibration to pre-estimate compensation parameters. However, under dynamic rotation conditions, as rotational speed fluctuates, attitude changes, and target surface characteristics alter, the imbalance parameters drift, rendering the static calibration results invalid and hindering online high-precision measurement.

[0005] On the other hand, phase difference-based ranging methods inherently have limitations on their unambiguous ranging range; their effective range is typically constrained by half the wavelength of the radio frequency signal. When the target displacement crosses half the wavelength, the phase folds back to its previous state. In certain intervals, phase jumps occur. Without cross-cycle processing, the displacement demodulation results will be discontinuous or even misjudged. This phase folding problem is particularly prominent in scenarios of continuous rotation or periodic motion. Although existing technologies offer compensation methods through phase unrolling or simple phase alignment, traditional unrolling algorithms cannot guarantee continuity when the displacement exceeds half a wavelength. This is especially true in the presence of noise disturbances or vibration interference, further increasing the risk of misjudgment and making it difficult to achieve stable continuous displacement reconstruction.

[0006] Therefore, there is an urgent need for a method that can achieve robust online correction of I / Q signals under dynamic rotation conditions and break through the half-wavelength limitation to achieve cross-cycle continuous displacement reconstruction, thereby improving the accuracy, stability and engineering applicability of short-distance displacement measurement. Summary of the Invention

[0007] To address the issues of signal distortion and range limitation in microwave displacement measurement systems under dynamic rotation conditions, a method for online microwave signal correction and continuous displacement measurement is provided.

[0008] Specifically, under dynamic motion conditions, non-ideal factors such as inconsistent RF link amplitudes, channel amplitude and phase errors, and DC drift cause eccentric deformation of the I / Q baseband signal trajectory, introducing displacement demodulation errors. Simultaneously, traditional phase difference-based ranging methods have a half-wavelength unambiguous range limitation; when the target displacement crosses half the wavelength, phase folding occurs, leading to discontinuous displacement demodulation. Existing static calibration methods struggle to adapt to the drift changes of unbalanced parameters under dynamic conditions, and traditional phase unfolding methods are difficult to reconstruct continuous displacement across cycles.

[0009] Therefore, the present invention aims to provide a method that can achieve robust online correction of I / Q signals under dynamic rotation conditions and break through the half-wavelength limitation to achieve continuous displacement measurement across cycles, thereby improving measurement accuracy, stability and engineering applicability.

[0010] To achieve the above objectives, this invention provides a method for online microwave signal correction and continuous displacement measurement under dynamic rotating conditions. The method first transmits a radio frequency (RF) signal to a moving target via a microwave continuous wave transmitting module. The RF signal is reflected by the target and received by a receiving module. The in-phase component is then obtained through local oscillator mixing and low-pass filtering. Orthogonal components .in, Represents a time variable.

[0011] Ideally, the in-phase component and the quadrature component satisfy the relationship of equal amplitude and orthogonal phase, and their mathematical model can be expressed as:

[0012]

[0013]

[0014] In the formula: The signal amplitude; Angular frequency; This is the initial phase; and These represent in-phase and positive traffic signals under ideal conditions. At this point, the complex plane trajectory exhibits a circular distribution centered at the origin.

[0015] However, under actual dynamic rotation conditions, due to factors such as inconsistent amplitude gain of the RF link, phase error of the quadrature path, and DC drift of the circuit, the in-phase component and the quadrature component usually satisfy the following imbalance model:

[0016]

[0017]

[0018] In the formula: The wavelength of the microwave carrier. The instantaneous displacement between the moving target and the sensor; and These are the amplitude scaling factors for the in-phase channel and the forward traffic channel, respectively; This is the initial phase; This refers to the phase imbalance quantity; and These are the DC bias values ​​for in-phase and positive cross-channels, respectively. and This is the actual measured signal. Due to the aforementioned imbalance factors, and An eccentric elliptical trajectory is formed on the complex plane, instead of satisfying the ideal circular distribution, which leads to systematic errors in the phase demodulation results.

[0019] To achieve subsequent displacement demodulation, this invention further constructs a complex signal:

[0020]

[0021] In the formula: For constructed complex signals; The imaginary unit; and These are the actual in-phase and quadrature signals, respectively. The phase information of the complex signal and the target displacement satisfy a linear mapping relationship. However, in the presence of amplitude imbalance and phase shift, this mapping relationship is distorted. Therefore, online correction and robust parameter estimation of the signal are required to restore the accurate correspondence between displacement and phase. The above dynamic signal acquisition and complex signal construction process provides the original data foundation for the segmented boundary modeling and robust imbalance parameter estimation.

[0022] To improve the stability of imbalance parameter estimation under dynamic rotating conditions, this invention addresses the issue of in-phase components... Orthogonal components The complex plane trajectory is segmented. Specifically, the continuous sampling sequence is divided into multiple local signal segments according to a preset segment length and sliding step size. Let the first segment be... The set of sampling point indices corresponding to each local signal segment is: Then the set of two-dimensional trajectory points within this segment can be represented as:

[0023]

[0024] In the formula, and The first The in-phase and quadrature components corresponding to each sampling point.

[0025] For the set of two-dimensional trajectory points The convex hull algorithm is used to extract the boundary point set. Specifically, it is first processed according to the in-phase components. The values ​​of the two-dimensional trajectory points are arranged in ascending order; when the values ​​of the in-phase components are the same, they are arranged according to the orthogonal components. The numerical values ​​are sorted. Then, based on the sorted 2D trajectory points, an upper convex hull and a lower convex hull are constructed respectively. Points located inside the convex hull are removed by determining the cross product direction, finally obtaining the set of convex hull vertices on the outer contour of the segmented trajectory. The set of convex hull vertices is used as the boundary point set corresponding to this segment.

[0026]

[0027] In the formula, For the first The set of boundary points for each local signal segment. These are the in-phase component coordinates and orthogonal component coordinates of the boundary point, respectively. Represents a set of points The set of vertices of the outer contour for convex hull extraction.

[0028] After obtaining the segment boundary points, each segment trajectory is represented as a general quadratic curve:

[0029]

[0030] In the formula: and These are segmented signal sample values; These are the parameters for the elliptic curve.

[0031] To achieve a stable solution for the ellipse parameters, the quadratic curve equation is transformed into matrix form, and a design matrix is ​​constructed. With the target vector Establish the normal equation:

[0032]

[0033]

[0034] In the formula: Let be the elliptic parameter vector; α is the regularization coefficient, used to suppress the influence of matrix ill-conditioning on the elliptic parameter solution results; The design matrix is ​​constructed from segmented sample data; The target vector; Representation matrix transpose; It is the identity matrix;

[0035] After performing the above ellipse fitting process on each segment, multiple sets of segmented parameter samples are obtained. To improve the robustness of the segmented parameter fusion process, this invention further performs a reliability assessment of the segmented ellipse parameter samples based on data distribution characteristics, specifically by estimating them using a local density function:

[0036]

[0037]

[0038] In the formula, For the first A sample of piecewise ellipse parameters The local density estimate; For the first The elliptic parameter vector obtained by segmenting the signal; The total number of sample parameters for the piecewise ellipse; Let be the number of nearest neighbor samples, and ; For the first in the parameter space A sample of piecewise ellipse parameters To its first The distance to the nearest neighbor sample; The dimension of the parameter space in which the ellipse parameter sample resides; for The volume constant of a unit sphere, or the dimension of the parameter space. The relevant preset normalization constants; For radius Dimensional neighborhood volume.

[0039] Based on the density estimation results, sample weights are defined and normalized.

[0040]

[0041]

[0042] In the formula: For the first The weights of each parameter sample; For normalized weights; This represents the number of sample segments for the parameter segmentation.

[0043] Subsequently, for each parameter component in the elliptic parameter vector The estimated values ​​of this parameter component in each segmented elliptic parameter sample are sorted by numerical value, and the corresponding weighted cumulative distribution function is constructed. The density-weighted median is then used as a robust estimate of this parameter component.

[0044]

[0045] In the formula: For sample values ​​where the cumulative normalized weight first reaches or exceeds 0.5; This results in robust parameter estimation. The density-weighted mechanism described above assigns higher weight to parameter samples from high-density clustered regions during the fusion process, while effectively suppressing the impact of low-density outliers on the final estimation results.

[0046] Obtaining robust elliptic parameters Then, calculate the amplitude-phase imbalance parameters and DC bias:

[0047]

[0048]

[0049]

[0050]

[0051] In the formula: Ellipse parameters for robust estimation; This indicates an imbalance in amplitude. This indicates a phase imbalance. and DC bias.

[0052] After obtaining the robust imbalance parameters, the original signal is subjected to combined amplitude and phase orthogonal compensation:

[0053]

[0054] In the formula: and For the original in-phase and quadrature signals, and This is the DC compensation amount. and This is the compensated signal.

[0055] After the amplitude-phase joint compensation is completed, a complex signal is constructed and phase demodulation is performed:

[0056]

[0057]

[0058]

[0059]

[0060] In the formula: It is the instantaneous phase; To unfold the phase; The wavelength of the microwave carrier. This represents the displacement demodulation result within a half-wavelength range. Through the above process, continuous displacement measurement can be achieved under conditions of a single cycle or displacement variation not exceeding half a wavelength.

[0061] Under dynamic rotation or periodic motion conditions, when the target displacement spans half a wavelength, phase folding occurs, leading to phase jumps between different periods. To achieve continuous displacement reconstruction across periods, this invention performs phase rotation compensation on signals of different periods. Specifically, for the first... For each displacement segment corresponding to a complex signal state, a recursive phase rotation transformation is applied:

[0062]

[0063]

[0064] In the formula: For the first The phase shift of each displacement segment relative to a preset uniform period; The signal is a complex signal after rotation; This represents the equivalent displacement. Through phase rotation, the cross-cycle phase folding phenomenon can be converted into an equivalent displacement, thereby achieving phase reference unification between cycles.

[0065] To further eliminate residual displacement offsets introduced by vibration disturbances or sampling errors between adjacent cycles, correlation matching or similarity alignment is performed on the displacement curves of adjacent cycles to obtain residual displacement correction amounts. And it is cumulatively corrected through a recursive method:

[0066]

[0067]

[0068] In the formula: For the first The cumulative displacement correction over the period; This is the residual displacement correction amount between adjacent periods; This yields the final continuous displacement result. By superimposing the corresponding cumulative correction values ​​on the displacement curves of each cycle and stitching them together sequentially, cross-cycle phase jumps can be converted into continuous displacement increments, enabling continuous displacement measurement beyond the half-wavelength limit.

[0069] Through the above-mentioned amplitude and phase compensation, phase expansion, and cross-cycle phase reconstruction and cumulative correction processes, this invention realizes the integrated processing of online signal correction and ultra-half-wavelength continuous displacement measurement under dynamic rotation conditions, thereby improving the continuity, stability and accuracy of displacement measurement.

[0070] Compared with the prior art, this application has at least the following beneficial effects:

[0071] First, this invention achieves online estimation of I / Q signal imbalance parameters under dynamic rotation conditions through segmented boundary modeling and robust parameter estimation mechanisms. Compared with traditional methods relying on static calibration parameters, this invention can adaptively update compensation parameters based on real-time acquired dynamic signals, avoiding parameter mismatch problems caused by speed fluctuations, attitude changes, or environmental disturbances, thereby improving stability and consistency under dynamic measurement conditions. Second, addressing the half-wavelength range limitation in phase difference ranging, this invention transforms cross-cycle phase folding into equivalent displacement translation through complex signal phase rotation and cross-cycle displacement accumulation correction mechanisms, achieving phase reference unification between different cycles. By recursively accumulating the residual displacement offset, periodic phase jumps are transformed into continuous displacement increments, thus breaking through the traditional half-wavelength limitation and achieving continuous displacement measurement over a range exceeding half a wavelength. Furthermore, this invention realizes an integrated processing flow for signal correction and displacement measurement, simultaneously completing parameter estimation and displacement demodulation during dynamic rotation, avoiding the traditional separate process of "calibration before measurement," and improving system real-time performance and engineering application feasibility. Attached Figure Description

[0072] To more clearly illustrate the technical solution of this application, the following is a brief description of the drawings used in the specification:

[0073] Figure 1 This is a schematic diagram of the process for estimating parameters based on piecewise geometric constraints and robust imbalance in an embodiment of the present invention;

[0074] Figure 2 This is a schematic diagram illustrating the principle of segmented boundary modeling in an embodiment of the present invention;

[0075] Figure 3 This is a schematic diagram illustrating the phase jump phenomenon analysis in an embodiment of the present invention;

[0076] Figure 4 This is a schematic diagram of the experimental setup of the 120GHz microwave measurement system in an embodiment of the present invention;

[0077] Figure 5 The diagram shows the fluctuations in the embodiments of the present invention, wherein (a) is a diagram showing the fluctuations of the piecewise ellipse fitting parameters, and (b) is a diagram showing the fluctuations of the unbalanced parameter sequence.

[0078] Figure 6 This is a schematic diagram of the ellipse fitting parameter density distribution and robust estimation results in an embodiment of the present invention;

[0079] Figure 7 This is a schematic diagram comparing the trajectories of the I / Q signals before and after correction in an embodiment of the present invention, where (a) is before correction of the rectangular blade, (b) is before correction of the curved blade, (c) is after correction of the rectangular blade, and (d) is after correction of the curved blade.

[0080] Figure 8 This is a schematic diagram of displacement extraction results in an embodiment of the present invention; (a) is a rectangular blade, and (b) is a curved blade;

[0081] Figure 9 This is a schematic diagram illustrating the demodulation displacement error and repeatability error statistics of the rectangular blade in an embodiment of the present invention;

[0082] Figure 10 This is a schematic diagram illustrating the demodulation displacement error and repeatability error statistics of the curved blade in an embodiment of the present invention;

[0083] Figure 11 This is a schematic diagram of the demodulation results of the ultra-half-wavelength continuous displacement in an embodiment of the present invention, where (a) is the continuous displacement variation curve of 12 blades, and (b) is the result of the demodulation displacement linearity analysis.

[0084] Table 1 shows the statistical results of displacement demodulation linearity of 12 blades under three independent repeated experiments in the embodiments of the present invention. Detailed Implementation

[0085] 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.

[0086] Example 1: Verification of Dynamic Online Correction and Half-Wavelength Shift Demodulation

[0087] In this embodiment, to verify the feasibility of the online microwave signal correction and continuous displacement measurement method for dynamic rotating conditions described in this invention, a 120GHz microwave measurement experimental platform was built, such as... Figure 4As shown. The experimental system mainly includes a rotating blade assembly, a three-dimensional micro-control platform, an electrically controlled displacement slide, a controller, a signal acquisition card, and a high-precision laser displacement sensor. The rotating blade is driven by a motor to achieve continuous rotation, used to simulate the operating state of an actual rotor blade under dynamic conditions. A microwave sensor emits a continuous wave signal and receives the echo reflected from the blade end face; the in-phase component is obtained after mixing and low-pass filtering. Orthogonal components The I / Q signals are acquired using an ADC data acquisition system at a sampling frequency of 100 kHz. A laser displacement sensor is used to provide high-precision reference displacement data.

[0088] In this embodiment, the electrically controlled slide moves the microwave sensor radially away from the blade end face at a constant speed of 1.68 mm / s, while continuously acquiring I / Q signals. Experiments were conducted on two end face morphologies: rectangular and curved blades, to simulate the changes in echo signals under different morphological conditions. Due to differences in end face morphology and the influence of dynamic vibration, the original I / Q signals satisfy the following imbalance model:

[0089]

[0090]

[0091] In the formula: The wavelength of the microwave carrier. The instantaneous displacement between the target and the sensor; It is a time variable; and These are the amplitude ratio coefficients for in-phase and positive traffic lanes, respectively; This is the initial phase; This refers to the phase imbalance quantity; and These represent the DC bias. Due to the aforementioned imbalance factors, the complex plane trajectory exhibits an eccentric elliptical distribution.

[0092] To achieve dynamic online correction, a sliding window segmentation strategy is used to process the acquired signal. Let the total length of the sampling sequence be... The segmented window length is The step size is , If the local sampling index is within the segment, then the first... The segment signal is represented as:

[0093]

[0094] Each segment corresponds to a local time window, with the window size being [step size]. Slide along the time series. To match the segment length with the signal periodicity, first define the base length. ,in Sampling frequency, The angular frequency; when the slide moves at a speed of During uniform motion, the phase term of the echo signal , can be obtained In this embodiment, when the sampling frequency is 100 kHz and the basic segment length is... Window length is The step size is .

[0095] Subsequently, convex hull boundary points are extracted from the complex plane point set within each segment to construct a segmented geometric constraint model. Let the first segment be... The set of sampling point indices corresponding to each local signal segment is: Then the set of two-dimensional trajectory points within this segment can be represented as:

[0096]

[0097] In the formula, and The first The in-phase and quadrature components corresponding to each sampling point.

[0098] In this embodiment, the Andrew monotonic chain algorithm is used to process the two-dimensional trajectory point set. Perform convex hull calculation and extract the vertices of the convex hull as the boundary point set. First, according to the in-phase components... The values ​​of the two-dimensional trajectory points are arranged in ascending order; when the values ​​of the in-phase components are the same, they are arranged according to the orthogonal components. The numerical values ​​are sorted. Then, based on the sorted 2D trajectory points, an upper convex hull and a lower convex hull are constructed respectively. Points located inside the convex hull are removed by determining the cross product direction, finally obtaining the set of convex hull vertices on the outer contour of the segmented trajectory. The set of convex hull vertices is used as the boundary point set corresponding to this segment.

[0099]

[0100] In the formula, For the first The set of boundary points for each local signal segment. These are the in-phase component coordinates and orthogonal component coordinates of the boundary point, respectively. Represents a set of points The set of vertices of the outer contour for convex hull extraction.

[0101] For each segment of the trajectory, an elliptic curve is used for fitting:

[0102]

[0103] Transform the above model into matrix form:

[0104]

[0105]

[0106] In the formula: The parameter vector of the ellipse; The design matrix is ​​constructed from segmented sample data; α is the regularization coefficient, used to suppress the influence of matrix ill-conditioning on the elliptic parameter solution results; The target vector; Representation matrix transpose; The identity matrix is ​​used. Statistical results in this embodiment show that the maximum RMSE of the piecewise ellipse fitting is 0.004 and the average RMSE is 0.001, indicating that piecewise modeling has good stability under dynamic conditions.

[0107] After obtaining the segmented elliptic parameter sequences, k-NN local density estimation is used to robustly fuse the segmented elliptic parameter samples. (Nearest neighbor number) Used to determine the neighborhood range in local density estimation, its value affects the smoothness of the local density estimation and its sensitivity to local clustering features of the samples. When When the value is small, the local density estimation is more sensitive to the local distribution structure of the parameter samples, but is easily affected by noise points or outlier segmented parameter samples; when When the value is larger, the local density estimation results are smoother and more robust to noise, but this may weaken the local clustering characteristics of the parameter samples. Therefore, The selection of a method needs to balance locality preservation and robustness.

[0108] In this embodiment, the total number of piecewise elliptic parameter samples is approximately Taking into account the number of piecewise elliptic parameter samples, sample distribution characteristics, experimental noise level, and the smoothness required for local density estimation, the nearest neighbor number in k-NN local density estimation is chosen to be [value missing]. .

[0109] The local density estimation specifically refers to:

[0110]

[0111]

[0112] In the formula, For the first A sample of piecewise ellipse parameters The local density estimate; For the first The elliptic parameter vector obtained by segmenting the signal; The total number of sample parameters for the piecewise ellipse; This represents the number of nearest neighbor samples; For the first in the parameter space A sample of piecewise ellipse parameters To its first The distance to the nearest neighbor sample; The dimension of the parameter space in which the ellipse parameter sample resides; for The volume constant of a unit sphere, or the dimension of the parameter space. The relevant preset normalization constants; For radius Dimensional neighborhood volume.

[0113] Define the sample weights as follows:

[0114]

[0115] The weights are then normalized.

[0116]

[0117] In the formula, Let be the weight of the i-th segmented elliptic parameter sample. For normalized weights.

[0118] Subsequently, density-weighted median estimation is performed on each parameter component a, b, c, d, and e in the elliptic parameter vector. Specifically, the estimated values ​​of the corresponding parameter components in each segment sample are sorted by numerical value, and a weighted cumulative distribution function is constructed based on the normalized weights of the corresponding samples. When the cumulative normalized weight first reaches or exceeds 0.5, the corresponding parameter component value is used as the robust estimate of that parameter component. The robust estimation results of the five parameter components a, b, c, d, and e constitute the globally robust elliptic parameter vector.

[0119] To verify the nearest neighbor number The impact of the selected values ​​on the robust parameter estimation results is further addressed in this embodiment, while keeping the rest of the processing flow and parameters unchanged. Comparative analysis was conducted, and different... The robust estimation results of the elliptic parameters under the given values ​​and the estimation results of the imbalance parameters derived from the elliptic parameters. The imbalance parameters include amplitude imbalance parameters. Phase imbalance parameters and DC bias compensation , .

[0120] In the comparative analysis, with The robust parameter estimates obtained at that time were used as a reference benchmark to calculate other parameters. The absolute change of the estimated values ​​of each imbalance parameter relative to the reference baseline under the given values. Experimental results show that, Within the range, robust parameter estimates vary. The changes exhibit a smooth and gradual characteristic, without any obvious abrupt changes or drastic fluctuations; the estimated values ​​of each imbalance parameter are relative to... The absolute changes in the reference results were all controlled within 0.005. This indicates that, given the sample size and noise level in this embodiment, the robust parameter estimation results are effective. The value does not show strong sensitivity. It can achieve a good trade-off between preserving local features and robust estimation.

[0121] The global robust elliptic parameters are obtained based on the density-weighted median above. Calculate the unbalance compensation parameters:

[0122]

[0123]

[0124] Then, amplitude and phase joint compensation is performed:

[0125]

[0126] In the formula: and This is the compensated signal.

[0127] Constructing a complex signal and performing displacement demodulation:

[0128]

[0129]

[0130] in, This indicates a phase unrolling operation. When the phase difference between adjacent sampling points is greater than π, 2π is subtracted from the subsequent phase sequence; when the phase difference between adjacent sampling points is less than -π, 2π is added to the subsequent phase sequence, thus obtaining a continuous unrolled phase.

[0131] Figure 8The displacement extraction results for rectangular and curved blades are shown. To verify the measurement accuracy, the microwave demodulation results were compared with the laser sensor measurement results. Statistical results over three consecutive rotation cycles show that the average absolute error for the rectangular blade condition is 1.611 μm, and the maximum absolute error is 4.77 μm. Repeatability testing was performed on 8 rotations, with a maximum repeatability error of 0.623 μm. For the curved blade condition, the average absolute error is 1.563 μm, the maximum absolute error is 4.041 μm, and the maximum repeatability error is 0.481 μm.

[0132] As can be seen from this embodiment, the method of the present invention can achieve robust online correction of I / Q signals and displacement demodulation within half a wavelength range under dynamic rotation conditions, and maintain stable measurement accuracy and repeatability under different end face morphology conditions.

[0133] Example 2: Verification of Continuous Shift Demodulation Beyond Half Wavelength

[0134] In this embodiment, to verify the feasibility of the cross-cycle phase reconstruction and ultra-half-wavelength continuous displacement measurement method described in this invention, a microwave sensor is continuously moved backward in the radial direction by an electrically controlled slide table to simulate the dynamic change process of the target displacement exceeding half a wavelength. During this process, the relative displacement between the target and the sensor exceeds half the carrier wavelength λ / 2, causing the displacement demodulation result based on the phase difference to exhibit periodic wrapping. If only a conventional phase unfolding method is used, erroneous unfolding can easily occur when there is noise, vibration disturbance, or sampling error in the signal, resulting in discontinuity in the cross-cycle displacement curve.

[0135] After completing the dynamic online correction in Example 1, construct the compensated complex signal:

[0136]

[0137] In the formula: and The in-phase and positive traffic lane signals after compensation; To compensate for complex signals; It is the imaginary unit.

[0138] When the displacement spans half a wavelength, the phase of the complex signal satisfies the periodic wrap-around characteristic. To achieve phase reference unification between different periods, in this embodiment, the phase reference is adjusted for the first period. For each displacement segment corresponding to a complex signal state, a recursive phase rotation transformation is applied:

[0139]

[0140] In the formula: For the first The phase shift of each displacement segment relative to a preset uniform period; The signal is a complex signal after rotation;

[0141] The phase shift and the equivalent displacement satisfy the following correspondence:

[0142]

[0143] In the formula: This corresponds to the equivalent displacement / translation amount; The wavelength is the microwave carrier wavelength. This phase rotation operation converts the cross-cycle phase folding phenomenon into an equivalent displacement, thereby achieving phase alignment between cycles.

[0144] To further eliminate residual displacement shifts caused by vibration disturbances or sampling errors between adjacent cycles, correlation matching analysis is performed on the displacement curves of adjacent cycles to obtain the residual displacement correction amount. And a recursive approach is used for cumulative correction:

[0145]

[0146] In the formula: For the first The cumulative displacement correction over the period; This is the residual displacement correction between adjacent periods; the initial conditions are set as follows: .

[0147] Finally, the first The periodic continuous displacement result is expressed as:

[0148]

[0149] In the formula: For the first Periodic original demodulation displacement; This is the corrected continuous displacement result.

[0150] Compared to the direct phase unwrapping method, the recursive coarse phase alignment in this embodiment does not simply rely on whether the phase difference between adjacent sampling points exceeds π to determine the phase jump. Instead, it first rotates the phase information of different BTC segments to a unified reference phase axis, and then performs recursive cumulative correction based on the residual offset between adjacent period displacement curves. Therefore, in the presence of noise disturbances, vibration interference, or local sampling errors, the impact of a single erroneous phase unwrapping on the reconstruction of subsequent period continuous displacements can be reduced.

[0151] Compared to simple fixed offset correction methods, this embodiment does not simply apply a preset fixed translation amount to each cycle. Instead, after coarse phase alignment is completed for each cycle or segment, the residual displacement correction amount is estimated based on the similarity relationship of the displacement curves of adjacent cycles, and cumulative compensation is performed through a recursive method. Therefore, the displacement jumps caused by cross-cycle phase folding can be converted into continuous displacement increments, reducing error accumulation during multi-cycle stitching.

[0152] In this embodiment, the displacement data of the 12 blades are phase aligned and cumulatively corrected to obtain a continuous displacement change curve, such as... Figure 11 As shown in (a). The results show that during the sensor retraction process, the displacement curves of all 12 blades exhibit a smooth and continuous trend, and no demodulation failure caused by phase jump occurs. Continuous displacement demodulation within a 5mm range is achieved under 120GHz system conditions.

[0153] To further verify the accuracy of the demodulation results, the demodulated relative displacements of the 12 blades were compared and analyzed with the actual displacements of the electrically controlled slide. Figure 11 As shown in (b), the results show that the demodulation displacement exhibits a good linear relationship with the increase of the number of cycles.

[0154] To eliminate the influence of random interference, three independent replicate experiments were conducted under the same experimental conditions, and the demodulation linearity of the 12 blades within a 5 mm travel range was statistically analyzed, as shown in Table 1. The statistical results show that the average linearity of the 12 blades in the three experiments was 99.932%, with the linearity of all blades in one experiment exceeding 99.950%.

[0155] Table 1:

[0156] ;

[0157] As can be seen from this embodiment, the cross-cycle phase rotation and displacement accumulation correction method of the present invention can effectively eliminate the phase folding effect generated during the displacement change of the super half wavelength, realize the phase reference unification and continuous displacement reconstruction between different cycles, and verify the ability of the method of the present invention to achieve integrated processing of signal correction and displacement measurement under long stroke and super half wavelength conditions.

[0158] 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 for online microwave signal correction and continuous displacement measurement under dynamic rotating conditions, characterized in that, Includes the following steps: Step S1, Signal Acquisition: Transmit a continuous microwave signal to the moving target and simultaneously receive the echo signal reflected back from the target; The received echo is mixed with the local oscillator signal and down-converted, then filtered to obtain the baseband in-phase component. Orthogonal components ; Step S2, Segmented Geometric Constraint Modeling: The complex plane trajectory formed by the in-phase component and the orthogonal component is segmented to obtain multiple local signal segments; for each local signal segment, the in-phase component and orthogonal component samples in the segment are used to form a two-dimensional trajectory point set, and the boundary point set is extracted from the two-dimensional trajectory point set based on the outer contour extraction algorithm. The segmented boundary model is constructed with the boundary point set to reduce the influence of internal dense points and abnormal disturbance points on the subsequent ellipse parameter estimation; Step S3, Robust Ellipse Parameter Estimation and Imbalance Parameter Determination: Based on the piecewise geometric constraint model, elliptical curve parameters are modeled for each segmented trajectory to obtain multiple segmented ellipse parameter samples; the reliability of the segmented ellipse parameter samples is evaluated based on local data distribution characteristics, and the segmented ellipse parameter samples are weighted and fused according to the reliability to obtain a global robust ellipse parameter estimate; then, the amplitude imbalance parameter, phase imbalance parameter, and DC bias compensation amount are determined based on the global robust ellipse parameter estimate. Step S4, Online signal compensation and displacement demodulation: Based on the robust imbalance parameters, the original signal is... , Perform a combined amplitude-phase orthogonal transform to obtain the correction signal. , And construct complex signals Displacement change information within half a wavelength range is obtained through phase calculation and phase expansion; Step S5, Demodulation of half-wavelength displacement: To address the phase folding phenomenon caused by continuous periodic motion, a phase translation transformation is applied to complex signals of different periods to ensure that each periodic displacement segment meets a unified phase reference; then, the residual translation between adjacent periodic displacement curves is estimated, and the residual translation is corrected by cross-period displacement accumulation to convert periodic phase jumps into continuous displacement increments, thereby obtaining continuous displacement measurement results that exceed the half-wavelength limit of the radio frequency signal.

2. The microwave signal online correction and continuous displacement measurement method according to claim 1, characterized in that, The in-phase and quadrature components satisfy the following mathematical model: In the formula, For microwave carrier wavelength, The instantaneous displacement between the target and the sensor. For time variables, , These are the amplitude scaling factors for the in-phase channel and the main traffic channel, respectively. For the initial phase, This is the phase imbalance quantity. , These are the DC bias values ​​for in-phase and positive-mode channels, respectively.

3. The microwave signal online correction and continuous displacement measurement method according to claim 1, characterized in that, The piecewise boundary model is represented by an ellipse: In the formula, , These are sample values ​​of in-phase and quadrature signals. These are the parameters for fitting the ellipse.

4. The microwave signal online correction and continuous displacement measurement method according to claim 1, characterized in that, The elliptic parameters are solved using regularized least squares, where a regularization term is introduced into the normal equation. , For regularization parameters, For identity matrix: In the formula, , The matrix is ​​designed, and α is the regularization coefficient, which is used to suppress the influence of matrix ill-conditioning on the solution of elliptic parameters; For the target vector, It is the identity matrix. Representation matrix The transpose of .

5. The method for online microwave signal correction and continuous displacement measurement according to claim 1, characterized in that, The confidence level of the parameter samples is estimated using a density function: In the formula, For the first A sample of piecewise ellipse parameters The local density estimate; For the first The elliptic parameter vector obtained by segmenting the signal; The total number of sample parameters for the piecewise ellipse; Let be the number of nearest neighbor samples, and ; For the first in the parameter space Ellipse parameter samples To its first The distance to the nearest neighbor sample; The dimension of the parameter space in which the ellipse parameter sample resides; for The volume constant of a unit sphere or the dimension of the parameter space The relevant preset normalization constants; For radius Dimensional neighborhood volume.

6. The microwave signal online correction and continuous displacement measurement method according to claim 1, characterized in that, To improve the robustness of the piecewise parameter fusion process, a reliability weighting mechanism based on local density is introduced for each piecewise elliptic parameter sample. This mechanism includes the following steps: First, based on the local density estimate... , define the first The weights of the piecewise elliptic parameter samples are: ; Secondly, the sample weights are normalized: ; Then, for each parameter component in the elliptic parameter vector The estimated values ​​of this parameter component in each segmented elliptic parameter sample are sorted by numerical value, and the corresponding weighted cumulative distribution function is constructed. The density-weighted median is then used as a robust estimate of this parameter component. ; In the formula, For sample weights, To normalize the weights, For samples whose cumulative weight first reaches 0.5, These are robust parameter estimates.

7. The method for online microwave signal correction and continuous displacement measurement according to claim 1, characterized in that, The elliptic parameters and the unbalance parameters satisfy the following: In the formula, For robust estimation of elliptic parameters, This is the amplitude imbalance coefficient. This is the phase imbalance quantity. This is the DC compensation amount.

8. The method for online microwave signal correction and continuous displacement measurement according to claim 1, characterized in that, The displacement demodulation formula is: In the formula, These are the corrected in-phase and quadrature signals. It is the arctangent function in the four quadrants; This indicates a phase unrolling operation. When the phase difference between adjacent sampling points is greater than π, 2π is subtracted from the subsequent phase sequence; when the phase difference between adjacent sampling points is less than -π, 2π is added to the subsequent phase sequence, thus obtaining a continuous unrolled phase.

9. The microwave signal online correction and continuous displacement measurement method according to claim 8, characterized in that, To achieve phase reference unification between different periods, a complex signal is constructed from the corrected in-phase and quadrature signals, and a phase rotation transformation and displacement translation are applied to the complex signal. The specific relationships are as follows: In the formula, The imaginary unit, The phase shift is determined by the difference between the current representative phase and the preset unified reference phase. This corresponds to the displacement / translation amount.

10. The method for online microwave signal correction and continuous displacement measurement according to claim 1, characterized in that, The cross-cycle displacement accumulation correction is achieved by accumulating the residual displacement offsets between adjacent cycles, specifically: In the formula, For the first Cumulative displacement of the period, The residual displacement correction between adjacent periods; the first The displacement curve obtained by periodic demodulation plus the corresponding cumulative correction amount The displacement curves of each cycle are spliced ​​together to convert the displacement discontinuity caused by the cross-cycle phase jump into a continuous displacement increment, thereby obtaining continuous displacement measurement results.

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