Millimeter wave radar displacement measurement method based on multi-linear frequency modulation signal adaptive phase unwrapping

Abstract

The invention relates to the technical field of displacement measurement, in particular to a millimeter-wave radar displacement measurement method based on multi-linear frequency modulation signal adaptive phase unwrapping, which comprises the following steps that: a millimeter-wave radar is arranged at a structural displacement monitoring position, and the millimeter-wave radar transmits a frequency modulation continuous wave signal and receives a reflection echo signal; the receiving signal and the transmitting signal are mixed to generate an intermediate frequency signal; fourier transform is carried out on the intermediate frequency signal to extract phase information, a distance spectrum is obtained, a target with the maximum reflection intensity is selected from the distance spectrum for displacement measurement, and a direction conversion factor beta is calculated according to the geometrical relationship between the radar and the target; the millimeter wave radar continuously emits linear frequency modulation signals at fixed time intervals, and phase information corresponding to each emission is extracted; carrying out unwrapping processing on the extracted phase information; and calculating the actual vibration displacement of the target structure based on the unwrapped phase information. According to the method, the phase winding problem is considered in phase change rate estimation, and the robustness to noise is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of displacement measurement, and particularly to a millimeter-wave radar displacement measurement method based on adaptive phase unwrapping of multi-linear frequency modulation signals. Background Art

[0002] The structural displacement response is a core parameter in structural health monitoring, which can reflect the overall performance of the structure, help to identify potential damages in advance, and prevent disaster risks. In the structural design codes of many countries, displacement is regarded as a key safety control index.

[0003] Especially in bridge engineering, displacement responses are widely used in load assessment, system identification, and the update and verification of finite element models. Therefore, carrying out high-precision and long-term stable displacement monitoring is of great significance for structural integrity assessment and safety operation guarantee.

[0004] The existing displacement monitoring methods are mainly divided into two categories: contact type and non-contact type. Contact type methods include sensors such as accelerometers, strain gauges, and Global Navigation Satellite System (GNSS), which have been widely used in bridge monitoring applications. Due to the mature technology, accelerometers and GNSS dominate in the existing systems. However, estimating displacement by integrating acceleration is prone to low-frequency drift errors, which affect the monitoring accuracy. Although GNSS has advantages in large-scale structure monitoring, its accuracy is difficult to meet the requirements of micro-vibration measurement of medium and small-sized structures.

[0005] With the development of sensing and information processing technologies, non-contact displacement monitoring technologies have received extensive attention, especially methods based on visual image processing and millimeter-wave radar interferometry. Visual methods have significant advantages such as obtaining full-field displacement information and supporting synchronous measurement of multiple targets. However, its long-term stability is easily affected by external environmental factors (such as light, temperature, humidity), which limits its application in complex working conditions. In contrast, millimeter-wave radar shows good application prospects in structural displacement monitoring due to its advantages such as long-distance measurement ability, strong environmental adaptability, miniaturization, and low power consumption. Especially due to its shorter wavelength and higher measurement resolution, millimeter-wave radar has become a promising alternative for realizing high-precision and non-contact displacement measurement. In addition, millimeter-wave radar can operate stably under harsh weather conditions such as rain and snow, further enhancing its practical value. However, millimeter-wave radar faces the problem of phase wrapping in practical applications. Since the phase value measured by the radar is limited within the range of [-π, π], when the phase caused by the actual displacement of the target structure exceeds this interval, a phase jump phenomenon will occur, affecting the accuracy of displacement calculation.

[0006] To solve the problem of phase wrapping, conventional methods usually assume that the phase change within consecutive sampling time steps is less than π, and correct the phase by adding or subtracting an integer multiple of 2π. In addition, additional sensors or technical means can be introduced to assist in phase unwrapping. For example, a combination of dual-frequency radar signals is used to generate virtual signals, effectively increasing the wavelength and thus enhancing the ambiguity resolution ability. Although the dual-frequency method has achieved certain results in improving the phase unwrapping performance, it has higher complexity in system design, signal processing, and calibration, and multi-frequency signal processing will bring additional computational burdens. Another approach is to fuse radar and accelerometer data to assist in unwrapping the phase through acceleration information. However, this method relies on the additional deployment of acceleration sensors, which not only increases the system cost but also poses higher requirements for synchronization and data fusion accuracy. Summary of the Invention

[0007] In view of the deficiencies in the prior art, the present invention provides a millimeter-wave radar displacement measurement method based on adaptive phase unwrapping of multi-linear frequency modulation signals.

[0008] To achieve the above object, the following technical solutions are provided:

[0009] A millimeter-wave radar displacement measurement method based on adaptive phase unwrapping of multi-linear frequency modulation signals, characterized by comprising the following steps:

[0010] Step 1: A millimeter-wave radar is arranged at the structural displacement monitoring position. The millimeter-wave radar transmits a frequency-modulated continuous wave (FMCW) signal and receives the reflected echo signal, and mixes the received signal with the transmitted signal to generate an intermediate-frequency signal;

[0011] Step 2: Perform Fourier transform on the intermediate-frequency signal to extract phase information, obtain a distance spectrum, select the target with the maximum reflection intensity in the distance spectrum for displacement measurement, and calculate the direction conversion factor β according to the geometric relationship between the radar and the target;

[0012] Step 3: The millimeter-wave radar continuously transmits linear frequency modulation signals at a fixed time interval, and extracts the phase information corresponding to each transmission; perform phase unwrapping processing on the extracted phase information;

[0013] Step 4: Based on the unwrapped phase information, calculate the actual vibration displacement of the target structure.

[0014] Specifically, in Step 2, the calculation of the direction conversion factor β is to compensate for the angular difference between the millimeter-wave radar displacement measurement direction and the actual vibration direction of the structure, and its value is calculated according to the geometric relationship between the radar and the selected target:

[0015]

[0016] Where D and L respectively represent the line-of-sight distance and the vertical distance between the radar and the selected target. D can be directly estimated by radar measurement, while L needs to be measured in advance using a laser rangefinder.

[0017] Preferably, in step three, the continuously transmitted chirp signal means that the millimeter-wave radar transmits a chirp signal sequence composed of a main chirp signal and N c sub-chirp signals at fixed time intervals.

[0018] Preferably, in step three, the extraction of the phase information corresponding to each transmission means performing a Fourier transform on the intermediate-frequency signals corresponding to the main chirp signal and the sub-chirp signals to obtain the phases of the selected target corresponding to all chirp signals, expressed as:

[0019]

[0020] In the formula, represents the phase corresponding to the main chirp signal, represents the phase corresponding to the sub-chirp signal.

[0021] Preferably, in step three, the specific steps of performing phase unwrapping on the extracted phase information are as follows:

[0022] Step 1: Compare the phase information of the main chirp signal and the sub-chirp signal, and add or subtract 2π according to the difference to ensure that the phase difference is less than π. The specific formula is as follows:

[0023]

[0024] Step 2: Let the unwrapped phase corresponding to the main chirp signal be Then the unwrapped phase corresponding to the sub-chirp signal is:

[0025]

[0026] Step 3: Assume that the phase changes linearly at a rate of v c T c within the time window of [kΔt, kΔt + N k , and the following equation can be constructed:

[0027]

[0028] Step 4: Use the least squares method to solve the phase change rate v k from Equation 5 and predict the phase at the next moment.

[0029]

[0030] In the formula, Δt represents the time interval;

[0031] Step 5: Denote the original phase corresponding to the main linear frequency modulation signal as Determine the unwrapped phase as:

[0032]

[0033] where N r is an integer, and its value is determined by minimizing the difference between and :

[0034]

[0035] Preferably, in Step 4, the actual vibration displacement of the target structure calculated refers to obtaining the structural displacement from the phase change after unwrapping based on the following formula:

[0036]

[0037] where f s is the starting frequency of the linear frequency modulation signal, is the initial phase of the main linear frequency modulation signal, represents the unwrapped phase of the main linear frequency modulation signal at the k-th time step.

[0038] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0039] 1. An adaptive phase unwrapping algorithm based on multi-linear frequency modulation signals is proposed to solve the phase wrapping problem of FMCW millimeter-wave radar.

[0040] 2. The phase wrapping problem is considered in the phase change rate estimation to improve the robustness to noise.

[0041] 3. The need for artificial experience thresholds or additional sensing data is eliminated, making it more suitable for engineering practical applications. Description of the Drawings

[0042] Figure 1 is a schematic diagram of phase wrapping caused by large-scale motion in an embodiment of the present invention;

[0043] Figure 2 is a schematic diagram of phase wrapping caused by the initial phase approaching the phase limit in an embodiment of the present invention;

[0044] Figure 3 is a schematic diagram of sensor setting and initial calibration in an embodiment of the present invention;

[0045] Figure 4 is a schematic diagram of the displacement measurement process using an FMCW radar in an embodiment of the present invention;

[0046] Figure 5 Schematic diagram of the basic principle of the phase unwrapping algorithm in the embodiment of the present invention;

[0047] Figure 6 Schematic diagram of the model configuration layout for experimental verification in the embodiment of the present invention;

[0048] Figure 7 Schematic diagram of the original phase result of the main linear frequency modulation signal in the embodiment of the present invention;

[0049] Figure 8 Schematic diagram of the displacement result estimated by the conventional method in the embodiment of the present invention;

[0050] Figure 9 Schematic diagram of the displacement result estimated by the method proposed in the present invention in the embodiment of the present invention;

[0051] Figure 10 Schematic diagram of the root mean square error of the displacement estimated by the conventional method under different excitation conditions in the embodiment of the present invention;

[0052] Figure 11 Schematic diagram of the root mean square error of the displacement estimated by the method proposed in the present invention under different excitation conditions in the embodiment of the present invention;

[0053] Figure 12 Schematic diagram of the estimated result of the phase change rate before phase unwrapping in the embodiment of the present invention;

[0054] Figure 13 Schematic diagram of the estimated result of the phase change rate after phase unwrapping in the embodiment of the present invention. Detailed implementation manners

[0055] The following combines the accompanying drawings to specifically illustrate the circuit structure, working principle, signal flow direction and the mutual relationship between each module involved in the present invention, so that those skilled in the art can implement the technical solutions of the various claims of the present invention according to the content of this embodiment. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0056] Embodiment 1

[0057] To accurately understand the technical basis of the present invention, the basic working principle of a frequency-modulated continuous-wave (FMCW) millimeter-wave radar is briefly introduced first: The FMCW radar measures the time of flight of electromagnetic waves by transmitting a frequency-modulated signal and receiving the target reflection signal, and combines the known propagation speed of electromagnetic waves to calculate the distance between the radar and the target. In the application of structural displacement monitoring, the FMCW radar usually estimates the small displacement of the target structure by measuring the change in signal phase. However, the original phase value directly extracted from the radar measurement is limited to the range of [-π, π]. Refer to Figure 1 , when the actual phase exceeds this range, a phase wrapping phenomenon will occur. Refer to Figure 2 , when the initial phase of the millimeter-wave radar is close to ±π, that is, close to the phase limit, even if the target mechanism undergoes a small displacement, it may trigger phase wrapping, resulting in distorted displacement estimation.

[0058] To solve the above limitations, according to an exemplary embodiment of the present invention, a millimeter-wave radar displacement measurement method based on multi-linear frequency-modulated signal adaptive phase unwrapping is provided. Figure 3 and Figure 4 schematically show an overview of a method for performing structural displacement estimation according to an exemplary embodiment of the present invention.

[0059] A millimeter-wave radar is deployed at the structural displacement monitoring position to be monitored. The radar first transmits a linear frequency-modulated signal and receives its reflection signal, generates an intermediate-frequency signal, and obtains a distance spectrum through Fourier transform; the target with the largest reflection intensity is selected in the distance spectrum for displacement measurement; the direction conversion factor β is calculated based on the geometric relationship between the radar and the target to compensate for the angular difference between the millimeter-wave radar displacement measurement direction and the actual vibration direction of the structure, and its value is calculated according to the geometric relationship between the radar and the selected target:

[0060]

[0061] where D and L respectively represent the line-of-sight distance and the vertical distance between the radar and the selected target. D can be directly estimated by radar measurement, while L needs to be measured in advance using a laser rangefinder;

[0062] Then, the millimeter-wave radar is used to transmit a linear frequency-modulated signal sequence composed of a main linear frequency-modulated signal and N c sub-linear frequency-modulated signals at fixed time intervals, perform Fourier transform on the intermediate-frequency signals corresponding to all linear frequency-modulated signals to obtain phase information; with the help of the phase information of the sub-linear frequency-modulated signals, the proposed phase unwrapping algorithm is used to unwrap the phase of the main linear frequency-modulated signal; finally, based on the unwrapped phase information of the main linear frequency-modulated signal, the actual vibration displacement of the target structure is calculated.

[0063] Figure 5Shows the basic principle of a detailed phase unwrapping algorithm, including the following steps:

[0064] 1. The millimeter-wave radar emits a sequence of chirp signals composed of a main chirp signal and N c sub-chirp signals at fixed time intervals. Then, the intermediate-frequency signals corresponding to the main chirp signal and the sub-chirp signals are subjected to Fourier transform to obtain the phases corresponding to all chirp signals for the selected target, expressed as:

[0065]

[0066] where represents the phase corresponding to the main chirp signal, and represents the phase corresponding to the sub-chirp signal.

[0067] 2. Compare the phase information of the main chirp signal and the sub-chirp signal, and add or subtract 2π according to the difference to ensure that the phase difference is less than π.

[0068]

[0069] 3. Let the unwrapped phase corresponding to the main chirp signal be Then the unwrapped phase corresponding to the sub-chirp signal is:

[0070]

[0071] 4. Assume that the phase changes linearly at a rate of v c T c within the time window of ]kΔt, kΔt + N k . The following equation can be constructed:

[0072]

[0073] 5. Use the least squares method to solve for the phase change rate v k . And predict the phase at the next moment:

[0074]

[0075] where Δt represents the time interval.

[0076] 6. Denote the original phase corresponding to the main chirp signal as Determine the unwrapped phase as:

[0077]

[0078] where N r is an integer, and its value is obtained by minimizing and Determined by the difference between:

[0079]

[0080] 7. Calculate the actual vibration displacement of the target structure, and obtain the structural displacement from the unwrapped phase change based on the following formula:

[0081]

[0082] In the formula, f s is the starting frequency of the chirp signal, is the initial phase of the main chirp signal, represents the unwrapped phase of the main chirp signal at the k-th time step.

[0083] Embodiment 2

[0084] Figures 6 to 13 Illustrates a method for estimating structural displacement according to an embodiment of the present invention and actual verification results using this method.

[0085] In actual tests, the structural displacement of a four-story building model was measured. The model was excited by an input signal with a duration of 325 seconds, which was a combination of actual bridge vibration signals (RBV) and sine signals with different frequencies, and this signal was input by a shaking table. Based on the data collected by the millimeter-wave radar, the structural displacements estimated according to the embodiments of the present invention (hereinafter referred to as "displacement of the proposed method") and the structural displacements estimated according to the conventional method (hereinafter referred to as "displacement of the conventional method") were calculated respectively. The conventional method assumes that the phase change within consecutive sampling time steps is less than π, and the phase is unwrapped by adding or subtracting an integer multiple of 2π.

[0086] Figure 6 Shows the equipment layout for experimental verification on the four-story building model. The millimeter-wave radar is installed on the top of the model, and the model realizes horizontal movement through a horizontal shaking table. The millimeter-wave radar selects a concrete wall about 1.318 meters away as the tracking target.

[0087] Figure 7 Shows the original phase of the main chirp signal, Figure 8 and Figure 9 Show the displacement of the proposed method and the displacement of the conventional method respectively.

[0088] Refer to Figure 7 , there is an obvious phase wrapping problem in the original phase of the main chirp signal, and all phases are limited between -π and π.

[0089] Refer to Figure 8, due to the fact that the conventional algorithm cannot accurately recover the phase in some time steps, the unwrapping error gradually accumulates, resulting in an obvious displacement estimation deviation, and its root mean square error (RMSE) is 22.10 mm.

[0090] Reference Figure 9 , the method described in the present invention can accurately recover the phase at each time step. Therefore, the displacement of this method is highly consistent with the true displacement measured by a laser Doppler vibrometer (LDV), and the RMSE is only 0.39 mm.

[0091] Figure 10 and Figure 11 respectively show the RMSE of the displacement of the conventional method and the proposed method under different excitations.

[0092] Reference Figure 10 , the RBV excitation contains both low-frequency and high-frequency components, resulting in sudden changes in displacement at some time steps, thus violating the premise assumption that the phase change between adjacent time steps relied on by the conventional method is less than π. Therefore, the conventional algorithm cannot correctly unwrap the phase when the displacement changes suddenly, and the error accumulates rapidly, resulting in a significant increase in RMSE (22.10 mm and 9.04 mm respectively). For low-frequency excitations (0.1 Hz and 0.3 Hz), since the displacement changes slowly, the phase change between adjacent time steps always satisfies the assumption condition. Therefore, the conventional algorithm can successfully achieve phase unwrapping, and the RMSEs are 0.25 mm and 0.36 mm respectively. However, under the 1 Hz excitation, the displacement changes faster, and the conventional algorithm fails in most time steps, with the RMSE exceeding 40 mm.

[0093] Reference Figure 11 , under the above five excitation conditions, the method proposed in the present invention has achieved high-precision displacement estimation, and the RMSE is always controlled within 0.6 mm.

[0094] Figure 12 and Figure 13 show the estimation results of the phase change rate before and after unwrapping.

[0095] Reference Figure 12 , without phase unwrapping, a total of 6258 outliers appear in the estimated phase change rate, and the outliers are widely distributed under five different excitation conditions.

[0096] Reference Figure 13 , with phase unwrapping, no outliers appear in the estimated phase change rate, fully demonstrating the necessity of phase unwrapping in the estimation of the phase change rate.

[0097] It is obvious to those skilled in the art that the present invention is not limited to the details of the above-described exemplary embodiments, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention. Therefore, in any aspect, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be embraced within the present invention. Any reference signs in the claims should not be construed as limiting the claims concerned.

Claims

1. A millimeter-wave radar displacement measurement method based on adaptive phase unwrapping of multi-linear frequency modulation signals, characterized in that It includes the following steps: Step 1: Deploy a millimeter-wave radar at the structural displacement monitoring position. The millimeter-wave radar emits a frequency-modulated continuous-wave signal and receives the reflected echo signal, and mixes the received signal with the transmitted signal to generate an intermediate-frequency signal; Step 2: Perform Fourier transform on the intermediate-frequency signal to extract phase information, obtain a distance spectrum, select the target with the maximum reflection intensity in the distance spectrum for displacement measurement, and calculate the direction conversion factor β according to the geometric relationship between the radar and the target; Step 3: The millimeter-wave radar continuously emits linear frequency-modulated signals at fixed time intervals, and extracts the phase information corresponding to each emission; perform phase unwrapping on the extracted phase information; Step 4: Calculate the actual vibration displacement of the target structure based on the unwrapped phase information.

2. The millimeter-wave radar displacement measurement method based on adaptive phase unwrapping of multi-linear frequency modulation signals according to claim 1, characterized in that: In Step 2, the calculation of the direction conversion factor β is to compensate for the angular difference between the millimeter-wave radar displacement measurement direction and the actual vibration direction of the structure, and its value is calculated according to the geometric relationship between the radar and the selected target: Where D and L respectively represent the line-of-sight distance and the vertical distance between the radar and the selected target. D can be directly estimated by the radar measurement, while L needs to be measured in advance using a laser rangefinder.

3. A millimeter-wave radar displacement measurement method based on adaptive phase unwrapping of multi-linear frequency modulation signals according to claim 2, characterized in that: In Step 3, the continuously transmitted linear frequency modulated signal means that the millimeter wave radar transmits a linear frequency modulated signal sequence composed of a main linear frequency modulated signal and N c sub-linear frequency modulated signals at fixed time intervals.

4. A millimeter-wave radar displacement measurement method based on adaptive phase unwrapping of multi-linear frequency modulation signals according to claim 3, characterized in that: In Step 3, the extraction of the phase information corresponding to each emission refers to performing Fourier transform on the intermediate-frequency signals corresponding to the main linear frequency-modulated signal and the sub-linear frequency-modulated signal, and obtaining the phases of the selected target corresponding to all linear frequency-modulated signals, expressed as: In the formula, represents the phase corresponding to the main chirp signal, represents the phase corresponding to the sub-chirp signal.

5. A millimeter-wave radar displacement measurement method based on adaptive phase unwrapping of multi-linear frequency modulation signals according to claim 4, characterized in that: In Step 3, the specific steps of performing phase unwrapping on the extracted phase information are as follows: Step 1: Compare the phase information of the main linear frequency-modulated signal and the sub-linear frequency-modulated signal, and add or subtract 2π according to the difference to ensure that the phase difference is less than π. The specific formula is as follows: Step 2. Assume that the unwrapped phase corresponding to the main linear frequency modulation signal is Then the unwrapped phase corresponding to the sub-linear frequency modulation signal is: Step 3. Assume that within the time window of [kΔt, kΔt + N c T c , the phase changes at a linear rate of v k . The following equation can be constructed: Step 4: Solve for the phase change rate v from Equation 5 using the least squares method k , and predict the phase at the next moment In the formula, Δt represents the time interval; Step 5, Denote the original phase corresponding to the main linear frequency modulation signal as Determine that the unwrapped phase is: where N r is an integer whose value is determined by minimizing the difference between and :

6. A millimeter-wave radar displacement measurement method based on adaptive phase unwrapping of multi-linear frequency modulation signals according to claim 5, characterized in that: In Step 4, the calculation of the actual vibration displacement of the target structure refers to obtaining the structural displacement from the unwrapped phase change based on the following formula: where f s is the starting frequency of the chirp signal, is the initial phase of the main chirp signal, represents the unwrapped phase of the main chirp signal at the k-th time step.

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