Multi-factor error simultaneous decoupling method based on fiber bragg grating sensing

Abstract

The invention relates to the field of fiber shape sensing, and discloses a fiber grating sensing-based multi-factor error simultaneous decoupling method, which comprises the following steps of: S1, acquiring a spectral signal of a multi-core fiber grating; s2, determining an error source influencing the shape measurement of the fiber bragg grating through error analysis; s3, modeling error propagation by adopting a Monte Carlo method; s4, separating errors caused by temperature, torsion and bending from the wavelength drift data by adopting an error decoupling algorithm; s5, correcting the decoupled data by adopting an error compensation method; and S6, performing optical fiber shape reconstruction in combination with the corrected data to obtain three-dimensional shape information of the catheter. Through an accurate error decoupling method, the contribution of independently identifying and separating temperature, torsion and bending errors in the fiber bragg grating measurement process is realized, the interference of multiple error sources on the measurement result is effectively reduced, and the effects of improving the measurement precision and the shape reconstruction accuracy are achieved.

Description

Technical Field

[0001] The present invention relates to the field of optical fiber shape sensing, and particularly to a method for simultaneously decoupling multi-factor errors based on fiber Bragg grating sensing. Background Art

[0002] Interventional surgery, especially in the treatment of cardiovascular diseases, relies on fluoroscopy imaging technology to provide two-dimensional images to guide catheter operation. However, due to the lack of three-dimensional spatial information, the depth and shape of the catheter in complex vascular structures cannot be accurately presented, thus limiting the precision and safety of the surgery. However, when multi-core fiber Bragg gratings are used for shape sensing, different error sources will be introduced during the entire sensing process, including errors caused by the structural parameters of multi-core optical fibers, the surrounding environmental temperature, the number of gratings, and the reconstruction algorithm. These errors lead to a decrease in shape sensing accuracy. For cardiovascular interventional surgery, the accuracy requirement for shape sensing is relatively high, usually reaching the millimeter level. For some key shape information, the accuracy can even reach 0.01 mm. Reducing errors and improving sensing accuracy are problems that need to be solved currently. Therefore, it is of great significance to carry out research on the analysis and correction of shape sensing errors of multi-core fiber Bragg gratings.

[0003] The Monte-Carlo method is a general term for a class of statistical methods based on probability, mainly used to solve complex linear and non-linear statistical problems. By simulating the real measurement process through the uncertainty of random sampling, it can calculate the distribution of output variables based on the probability distribution of input variables, thereby determining the propagation law of uncertainty, and ensuring that the results obtained by simulation converge through a large number of sample experiments. Among them, the shape sensing error of multi-core fiber Bragg gratings is randomly generated during interventional surgery, meeting the usage conditions of the Monte-Carlo method.

[0004] At present, although there have been a large number of related studies on the method for decoupling shape sensing errors of multi-core fiber Bragg gratings, and it also has a certain effect on reducing the shape sensing errors of multi-core fibers, these methods only decouple single-factor errors in shape reconstruction and do not consider how to eliminate the coupling effect of multiple errors intertwined in shape reconstruction, resulting in a relatively low shape sensing accuracy of multi-core fibers and being difficult to meet the requirements of catheter shape reconstruction in interventional surgery. Summary of the Invention

[0005] Aiming at the deficiencies of the prior art, the present invention provides a method for simultaneously decoupling multi-factor errors based on fiber Bragg grating sensing, which solves the problem of measurement error interference caused by the combined action of multiple factors such as temperature, torsion, and bending during the fiber Bragg grating sensing process.

[0006] To achieve the above objectives, the present invention is realized through the following technical solutions: A method for simultaneously decoupling multi-factor errors based on fiber Bragg grating sensing, including the following steps:

[0007] S1. Collect the spectral signals of the multi-core fiber grating and obtain the wavelength drift data of the fiber grating;

[0008] S2. Through error analysis, determine the error sources affecting the fiber grating shape measurement, including temperature error, torsion error, and bending error;

[0009] S3. Use the Monte Carlo method to model the error propagation, construct an error transfer matrix, and describe the influence of temperature, torsion, and bending on the fiber grating strain measurement;

[0010] S4. Use an error decoupling algorithm to separate the errors caused by temperature, torsion, and bending from the wavelength drift data;

[0011] S5. Use an error compensation method to correct the decoupled data, including a temperature compensation method based on the temperature-strain relationship and a torsion error compensation method based on the Bishop framework;

[0012] S6. Combine the corrected data for fiber shape reconstruction to obtain the three-dimensional shape information of the catheter.

[0013] Preferably, in step S2, the temperature error is calculated through the temperature sensitivity parameter of the fiber grating, the torsion error is modeled through the strain distribution of the fiber grating, and the bending error is calculated through the distribution of the fiber grating along the length of the catheter.

[0014] Preferably, the Monte Carlo method in step S3 simulates the error propagation process based on a large number of random samples, obtains the influence of temperature, torsion, and bending on the wavelength drift of the fiber grating through statistical analysis, and calculates the error transfer matrix.

[0015] Preferably, the error decoupling algorithm in step S4 constructs a mathematical model containing temperature, torsion, and bending error factors, and based on the calculation of the error transfer matrix, separates the influence of different errors on the wavelength drift.

[0016] Preferably, the error decoupling model uses matrix calculation, where the relationship between the wavelength drift amount, temperature, torsion, and bending strain of the fiber grating is represented by a matrix, and the components of temperature, torsion, and bending errors are obtained through matrix operations.

[0017] Preferably, the temperature-strain vector matrix is [ε, T] T =[ε1, ε2, ε3, ε4, T] T , and the corresponding wavelength drift amount vector is Δλ = [Δλ1, Δλ2, Δλ3, Δλ4] T , expressed as:

[0018]

[0019] wherein, Δλ i , and are respectively the wavelength drift, strain sensitivity, and temperature sensitivity of the FBG in the i-th (i = 1, 2, 3) fiber core.

[0020] Preferably, the temperature compensation method in step S5 is calculated based on the influence of the temperature change measured by the fiber Bragg grating on the wavelength drift, and the strain error caused by temperature is corrected using temperature compensation parameters.

[0021] Preferably, the torsional error compensation method in step S5 is based on the Bishop frame model, and the torsional error is compensated by calculating the torsional strain correction matrix of the fiber Bragg grating in real time.

[0022] Preferably, the fiber shape reconstruction in step S6 adopts the curvature-bending conversion method, and based on the measurement data of multiple grating points arranged along the fiber, the three-dimensional shape information of the fiber is calculated by combining three-dimensional coordinate transformation.

[0023] Preferably, the real-time torsional compensation algorithm based on the Bishop frame model defines a correction matrix C to decouple the bending strain and torsional strain. The corrected attitude vector matrix W(s) embedded with the correction matrix C is expressed as:

[0024]

[0025] wherein, c1, c2, and c3 are respectively the coordinate correction coefficients of x, y, and z. Through the above decoupling method, the strain generated by temperature and torsion is separated from the bending strain, and the remaining strain is the pure bending strain.

[0026] The present invention provides a multi-factor error simultaneous decoupling method based on fiber Bragg grating sensing. It has the following beneficial effects:

[0027] 1. Through the precise error decoupling method of the present invention, it is realized to independently identify and separate the contributions of temperature, torsion, and bending errors during the fiber Bragg grating measurement process, effectively reducing the interference of multiple error sources on the measurement result, thereby improving the measurement accuracy and the accuracy of shape reconstruction.

[0028] 2. By introducing the error propagation modeling based on the Monte Carlo method, the present invention realizes more accurate quantification and modeling of errors in a complex environment, obtaining a more reliable error compensation basis, and providing higher-precision data support for error decoupling and shape reconstruction.

[0029] 3. The present invention compensates for errors by combining the sensitivity coefficients of temperature, torsion, and bending, effectively eliminating the interference of various environmental factors on the measurement results in an environment with dynamic temperature and strain changes, achieving stronger system adaptability and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 is a flowchart of the method of the present invention;

[0031] Figure 2 is a temperature distribution diagram of the present invention;

[0032] Figure 3 is a curve diagram showing the relationship between the twist angle and the fiber pitch and twist strain of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0033] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the present invention. 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 shall fall within the protection scope of the present invention.

[0034] Please refer to the attached Figure 1 , the present invention provides a multi-factor error simultaneous decoupling method based on fiber Bragg grating sensing, including the following steps:

[0035] S1. Collect the spectral signals of multi-core fiber Bragg gratings to obtain the wavelength drift data of the fiber Bragg gratings;

[0036] Specifically, first, the fiber Bragg grating sensing system can achieve high-precision measurement of the changes in fiber Bragg gratings through spectral signal collection and data processing. In the present invention, step S1 mainly involves collecting the spectral signals of multi-core fiber Bragg gratings to obtain the wavelength drift data of the fiber Bragg gratings. This step is the basis of the entire multi-factor error decoupling process and plays a key role in data acquisition and subsequent analysis. Under the influence of external environmental changes, the wavelength of the fiber Bragg grating will drift. Collecting these drift data helps subsequent decoupling and compensation of errors.

[0037] In this embodiment, sensing signals are collected through multi-core fiber Bragg gratings. Generally, fiber Bragg gratings are arranged in the target environment and may be subjected to different physical stresses, such as temperature changes, torsion, and bending. These stresses will cause changes in the wavelength of the fiber Bragg grating. Therefore, it is first necessary to collect the spectral signals of each fiber Bragg grating through precise spectral analysis equipment to obtain its wavelength drift information. For this purpose, a high-precision spectrometer device can be used for signal collection to ensure the accuracy of the data.

[0038] Specifically, in some embodiments, a fiber Bragg grating array configuration can be adopted, where multiple fiber Bragg grating sensing points are connected in parallel in a single optical fiber, thereby simultaneously monitoring the strain changes at multiple positions. Through such a design, the spatial resolution of the measurement can be improved, and more wavelength drift data can be obtained. During the acquisition process, the reflected wavelength of the fiber Bragg grating will shift when affected by external interference, and there is a quantitative relationship between this displacement and factors such as temperature, torsion, and bending.

[0039] S2. Through error analysis, determine the error sources affecting the measurement of the shape of the fiber Bragg grating, including temperature error, torsion error, and bending error;

[0040] Specifically, in step S1, we have completed the acquisition of the spectral signals of the multi-core fiber Bragg grating and obtained the relevant wavelength drift data. The next step S2 is to analyze the error sources based on these wavelength drift data, aiming to determine the main error factors affecting the measurement accuracy of the fiber Bragg grating and provide a basis for subsequent error decoupling and compensation.

[0041] In this embodiment, step S2 includes a detailed analysis of the error sources affecting the measurement accuracy of the fiber Bragg grating. Generally, the wavelength drift of the fiber Bragg grating may be interfered by multiple factors, and the most common error sources include temperature change, torsion error, and bending error. These errors not only affect the measurement accuracy of the fiber Bragg grating but may also cause deviations in the shape reconstruction results. Therefore, in this step, it is first necessary to identify and quantify the effects of these errors.

[0042] Specifically, the temperature error usually causes the wavelength drift of the fiber Bragg grating. This is because there is a direct relationship between the reflected wavelength of the fiber Bragg grating and temperature. The change in temperature causes the expansion or contraction of the optical fiber, thereby resulting in the drift of the reflected wavelength of the fiber Bragg grating. For this reason, in some embodiments, the temperature sensitivity coefficient (α T ) of the fiber Bragg grating is used to quantitatively describe the influence of temperature on the wavelength drift. The influence of the temperature error can be expressed by the following formula:

[0043] Δλ T =α T ·ΔT;

[0044] Where, Δλ T represents the wavelength drift caused by the temperature error, α T is the temperature sensitivity coefficient, and ΔT is the temperature change.

[0045] In terms of the torsion error, the fiber Bragg grating is usually affected by an external torsional force, resulting in the torsional deformation of the optical fiber, thereby causing wavelength drift. Specifically, the torsion sensitivity coefficient (α θ) can be used to quantitatively describe the influence of torsional error on wavelength drift. In one possible implementation, a mathematical model between torsional error and wavelength drift can be established by measuring the wavelength changes of fiber Bragg gratings at different torsional angles. The influence of torsional error on wavelength drift can be expressed by the following formula:

[0046] Δλ θ =α θ ·Δθ;

[0047] Where, Δλ θ represents the wavelength drift caused by torsional error, α θ is the torsional sensitivity coefficient, and Δθ is the change in torsional angle.

[0048] For bending error, the wavelength drift of fiber Bragg gratings may also be affected by bending force. Especially during the fiber laying process, the bending angle will cause changes in the strain distribution of fiber Bragg gratings. The influence of bending error can be quantitatively described by the bending sensitivity coefficient (α κ ) of the fiber Bragg grating. Specifically, in some embodiments, a model between bending error and wavelength drift is established through the relationship between the bending angle (Δκ) of the fiber Bragg grating and wavelength drift. The influence of bending error can be expressed as:

[0049] Δλ κ =α k ·Δκ;

[0050] Where, Δλ κ represents the wavelength drift caused by bending error, α κ is the bending sensitivity coefficient, and Δκ is the change in bending angle. Through the above analysis, the core task of step S2 is to determine and quantify the temperature, torsional and bending errors' influence on the wavelength drift of fiber Bragg gratings, and provide data support for error decoupling. As an option, the sensitivity coefficients of each error source can be determined experimentally and adjusted in combination with actual application conditions, so as to obtain more accurate error analysis results in different environments.

[0051] S3. Use the Monte Carlo method to model the error propagation, construct an error transfer matrix, and describe the influence of temperature, torsion, and bending on the strain measurement of fiber Bragg gratings;

[0052] Specifically, in step S2, we have completed the analysis of the error sources and clarified the influence of temperature, torsion, and bending errors on the wavelength drift of fiber Bragg gratings. The next step S3 is to model the error propagation process through the Monte Carlo method, construct an error transfer matrix, thereby describing the contribution of different error sources to the wavelength drift of fiber Bragg gratings, and providing data support for subsequent error decoupling. Through this process, we can more accurately simulate the influence of errors and lay a foundation for achieving high-precision error decoupling.

[0053] In this embodiment, step S3 uses the Monte Carlo method to model the error propagation process. Generally, the Monte Carlo method is a statistical simulation method based on random sampling, which can simulate the influence of various uncertain factors in the system through a large number of random experiments. In this technical solution, the Monte Carlo method is used to simulate the influence of temperature, torsion, and bending errors on wavelength drift. In some embodiments, the Monte Carlo simulation can also be combined with assumptions such as multivariate Gaussian distribution to better simulate the mutual correlation of error sources in actual situations. For example, there may be a certain correlation between temperature changes and bending errors, and by introducing a covariance matrix, the interaction between these error sources can be more accurately reflected.

[0054] As an option, the Monte Carlo method can also be combined with other numerical optimization methods to further improve the accuracy of the model. For example, the simulation results are fitted through optimization algorithms such as the least squares method to obtain a more accurate error transfer matrix, which is of great significance for high-precision error decoupling and subsequent shape reconstruction.

[0055] S4. Adopt an error decoupling algorithm to separate the errors caused by temperature, torsion, and bending from the wavelength drift data;

[0056] Specifically, in step S3, we have modeled the error propagation process through the Monte Carlo method, constructed an error transfer matrix, and obtained the specific influence relationship of factors such as temperature, torsion, and bending on wavelength drift. The next step S4 is to separate the contributions of different error sources from the wavelength drift data through an error decoupling algorithm. The key to this step is to independently extract temperature, torsion, and bending errors from the wavelength drift data of fiber Bragg gratings through a mathematical model, providing accurate input data for subsequent error compensation.

[0057] In this embodiment, the core task of step S4 is error decoupling. Generally, in the presence of multiple error sources, wavelength drift is the result of the combined action of multiple factors, which makes it very complex to separate the influence of each factor from the original signal. Therefore, in this step, we adopt an error decoupling algorithm and establish an error decoupling model to extract the influence of different error sources (such as temperature, torsion, bending) from the total wavelength drift.

[0058] As an option, the possible correlations between error sources can also be considered during the decoupling process. In some complex situations, the error sources are not completely independent but have a certain interaction. To handle this situation, a covariance matrix can be introduced to further correct the decoupling model to obtain more accurate error separation.

[0059] Specifically, in one possible implementation, the least squares method can be used to optimize the error decoupling model. In this way, by minimizing the difference between the actual measurement data and the model prediction results, the decoupling accuracy can be further improved. This method can not only effectively handle the correlations between error sources but also reduce the influence of noise on the decoupling results to a certain extent.

[0060] In some embodiments, to improve the efficiency and accuracy of decoupling, parallel computing technology can be combined. Especially when dealing with large-scale data processing, parallel algorithms can be used to accelerate the matrix operation process. This is particularly important for systems that require real-time or near-real-time decoupling in practical applications, which can significantly improve the response speed of the entire decoupling process.

[0061] S5. Adopt an error compensation method to correct the decoupled data, including a temperature compensation method based on the temperature-strain relationship and a torsional error compensation method based on the Bishop framework;

[0062] Specifically, in step S4, we have successfully separated the contributions of temperature, torsion, and bending errors through the error decoupling algorithm, providing independent data for subsequent error compensation. In step S5, we will use these decoupled data for error compensation to eliminate the influence of various errors on the final result, thereby improving the accuracy of fiber grating measurement. The error compensation process is a key step to ensure the accuracy of the final shape reconstruction. Through this process, we can make corresponding corrections to each factor according to the characteristics of different error sources, so that the measurement data is as close as possible to the true value.

[0063] In this embodiment, step S5 involves temperature and torsional error compensation for the decoupled data. Generally, temperature change is the main factor affecting the fiber grating measurement results. Especially in an environment with large temperature changes, the reflection wavelength of the fiber grating will be significantly affected.

[0064] In one possible implementation, the order of temperature compensation and torsional compensation can be flexibly adjusted according to the actual situation. If in a specific application scenario, the influence of a certain error source is more significant, the compensation for this error source can be given priority. However, in most cases, temperature error is usually considered to be the first to be compensated because temperature changes are common in the environment and usually have a greater impact.

[0065] As an option, the compensation process can also consider comprehensive multi-factor correction. For example, in addition to temperature and torsion, fiber Bragg gratings may also be affected by other factors (such as pressure, humidity, etc.). In some complex application scenarios, more error sources can be introduced for compensation to further improve the accuracy of measurement results.

[0066] Specifically, optimization algorithms such as the least squares method and genetic algorithms may be used in the error compensation process to further adjust the compensation parameters to ensure the optimization of the compensation effect. These optimization algorithms can automatically adjust the compensation coefficients through the analysis of multiple experimental results, thus achieving more accurate error correction.

[0067] S6. Reconstruct the fiber shape in combination with the corrected data to obtain the three-dimensional shape information of the catheter.

[0068] Specifically, in step S5, we have completed the compensation of temperature and torsion errors to ensure the accuracy of the fiber Bragg grating measurement data. The next step S6 involves the fiber shape reconstruction process, which reconstructs the three-dimensional shape of the fiber based on the error-compensated data. This process is the final step in the whole method, aiming to accurately reconstruct the actual shape information of the fiber according to the corrected data for further analysis or application.

[0069] In this embodiment, the core task of step S6 is to reconstruct the fiber shape using the compensated data. Generally, fiber shape reconstruction usually depends on the position information of the measurement points and the strain or displacement data distributed along the fiber axis. Specifically, the wavelength drift data after error compensation reflects the actual strain changes at each measurement point, and these strain data can be used to calculate the specific shape of the fiber in space.

[0070] Specifically, the fiber shape reconstruction can adopt the curvature-bending conversion method. This method is based on the strain values of each fiber Bragg grating measurement point, combined with parameters such as the elastic modulus and cross-sectional shape of the fiber, to perform shape calculation. Through this method, the curvature and bending degree of the fiber can be deduced from the strain data of a single fiber Bragg grating sensing point, thus reconstructing the three-dimensional shape of the fiber.

[0071] As an option, the fiber shape reconstruction can also be optimized by combining the finite element analysis (FEA) method. In this implementation, the fiber can be regarded as a series of small segments, and the strain of each small segment is modeled by the finite element analysis method to calculate the overall shape of the fiber. Through this method, fibers with complex shapes can be processed more efficiently and more accurate results can be provided.

[0072] Specifically, in some implementation manners, a node-based finite element model is adopted to locally reconstruct each part of the optical fiber. For example, a number of measurement nodes are set, and the shape changes between the nodes are deduced through the strain data of these nodes. Through the finite element solving process, the exact shape of the optical fiber can be obtained. The deformation amount of each node can be obtained through numerical calculation according to its local strain and bending relationship.

[0073] In addition, during the optical fiber shape reconstruction process, the mutual influence between fiber gratings can also be considered. In some complex applications, the fiber gratings may not be completely linearly distributed, but there is a certain non-uniformity. Therefore, the shape reconstruction algorithm can optimize the calculation of the optical fiber shape in combination with the actual layout of the fiber gratings.

[0074] In a possible implementation manner, an error correction term can also be introduced during the optical fiber shape reconstruction process. For example, in actual applications, if the distance between measurement points is relatively far, it may be necessary to correct the continuity of the optical fiber to avoid shape errors caused by discrete measurement points. For this purpose, a smoothing algorithm or a curve fitting method can be adopted to further optimize the reconstruction result.

[0075] Based on the above steps, embodiments of the technical solution of the present invention will be given below:

[0076] The present invention first analyzes the error sources in the shape reconstruction of multi-core optical fibers. There are errors introduced by multiple parameters during the shape reconstruction process, and the mathematical model is relatively complex. To simplify the analysis, the model is decomposed into analyzing the directly affected dependent variables by the independent variables introducing errors, as shown in Table 4-1.

[0077] Table 4-1 Independent variables introducing errors and corresponding dependent variables:

[0078]

[0079] When considering the surgical environment, the patient may show symptoms of hypothermia, and the body temperature drops by about 2.0 °C. Therefore, the influence of temperature disturbance on the reconstruction error in a small variable temperature environment (10 °C to 18 °C) is studied around the surgical environment. The method for analyzing the strain error introduced by FBG due to temperature disturbance using the Monte Carlo algorithm is as follows:

[0080] First, define the target distribution as a uniform distribution with a sample size of 106. Generate a sample distribution of 10 °C to 18 °C through the Monte Carlo method, and use this as a sample to analyze the influence of the wavelength drift caused by temperature disturbance on the strain. The sample distribution is as Figure 2 shown.

[0081] Then, calculate the wavelength drift caused by the core temperature perturbation ΔT. Based on the samples obtained in 2, set the FBG wavelength λB = 1550 nm, the temperature sensitivity kT = 10.0 pm / °C of the FBG, and the strain sensitivity kε = 1.2 pm / με, and obtain the wavelength drift and strain error introduced by temperature perturbation as shown in Table 4-2.

[0082] Table 4-2 Temperature distribution sample parameters:

[0083]

[0084] Multi-core fiber shape sensors are generally affected by torsion due to their high flexibility and the inherent torsion of the three-dimensional curve. The torsion phenomenon significantly reduces the accuracy of the shape sensor. Especially during the three-dimensional shape reconstruction process, the uncertainty of the bending direction and curvature generated will increase greatly.

[0085] Therefore, the Monte Carlo method is used to analyze the error introduced by fiber torsion. The relationship curves between the torsion angle and the fiber pitch and torsion strain are as Figure 3 shown. It can be seen from the figure that the torsion angle is approximately linearly related to the pitch and torsion strain, and the linearity degrees are 0.993 and 0.998 respectively.

[0086] Subsequently, a multi-factor error decoupling model is established to decouple temperature and torsion simultaneously. First of all, the key to compensation lies in quantifying and decoupling the effects of temperature and strain.

[0087] By establishing the mathematical relationship between temperature T and strain ε, the changes caused by temperature in FBG measurement can be accurately quantified and compensated in an environment with uneven temperature distribution. This can not only reduce the influence of temperature on the FBG bending strain response, but also significantly improve the accuracy and reliability of shape measurement.

[0088] Let the vector matrix of temperature-strain be [ε,T] T = [ε1, ε2, ε3, ε4, T] T , and the corresponding wavelength drift vector be Δλ = [Δλ1, Δλ2, Δλ3, Δλ4] T , which is expressed as:

[0089]

[0090] In the formula, Δλ i , and are the wavelength drift amount, strain sensitivity, and temperature sensitivity of the FBG in the i-th (i = 1, 2, 3) core respectively. By calibrating the strain and temperature of the sensor, a matrix for realizing strain-temperature decoupling in the algorithm can be deduced, thereby improving the reconstruction accuracy by reducing the cross-sensitivity effect.

[0091] Similarly, for torsional error correction, since the torsion related to torsion is not directly introduced into the shape reconstruction frame, the generated torsional strain cannot be characterized. Therefore, in combination with the Bishop frame, a Bishop algorithm for real-time torsion compensation is proposed. This method integrates Bishop and torsional variables into the algorithm framework, defines a correction matrix C, and decouples the bending strain and torsional strain. The corrected attitude vector matrix W(s) embedded with the correction matrix C is expressed as:

[0092]

[0093] In the formula, c1, c2, and c3 are the coordinate correction coefficients of x, y, and z respectively. Through the above decoupling method, the strains generated by temperature and torsion are separated from the bending strain, and the remaining strain is the pure bending strain.

[0094] Although the embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for simultaneously decoupling multi-factor errors based on fiber Bragg grating sensing, characterized in that, It includes the following steps: S1. Collect the spectral signals of multi-core fiber Bragg gratings and obtain the wavelength drift data of the fiber Bragg gratings; S2. Through error analysis, determine the error sources affecting the measurement of the shape of the fiber Bragg grating, including temperature error, torsion error, and bending error; S3. Use the Monte Carlo method to model the error propagation, construct an error transfer matrix, and describe the influence of temperature, torsion, and bending on the strain measurement of the fiber Bragg grating; S4. Use an error decoupling algorithm to separate the errors caused by temperature, torsion, and bending from the wavelength drift data; S5. Use an error compensation method to correct the decoupled data, including a temperature compensation method based on the temperature-strain relationship and a torsion error compensation method based on the Bishop framework; S6. Combine the corrected data to reconstruct the fiber shape and obtain the three-dimensional shape information of the catheter.

2. The multi-factor error simultaneous decoupling method based on fiber Bragg grating sensing according to claim 1, wherein In step S2, the temperature error is calculated through the temperature sensitivity parameter of the fiber Bragg grating, the torsion error is modeled through the strain distribution of the fiber Bragg grating, and the bending error is calculated through the distribution of the fiber Bragg grating along the length of the catheter.

3. A method for simultaneously decoupling multi-factor errors based on fiber Bragg grating sensing according to claim 1, characterized in that The Monte Carlo method in step S3 simulates the error propagation process based on a large number of random samples, obtains the influence of temperature, torsion, and bending on the wavelength drift of the fiber Bragg grating through statistical analysis, and calculates the error transfer matrix.

4. A multi-factor error simultaneous decoupling method based on fiber Bragg grating sensing according to claim 1, characterized in that The error decoupling algorithm in step S4 constructs a mathematical model containing temperature, torsion, and bending error factors, and separates the influence of different errors on the wavelength drift based on the calculation of the error transfer matrix.

5. A multi-factor error simultaneous decoupling method based on fiber Bragg grating sensing according to claim 4, characterized in that The error decoupling model uses matrix calculation, where the relationship between the wavelength drift amount, temperature, torsion, and bending strain of the fiber Bragg grating is represented by a matrix, and the components of temperature, torsion, and bending errors are obtained through matrix operations.

6. A method for simultaneously decoupling multi-factor errors based on fiber Bragg grating sensing according to claim 5, characterized in that, The vector matrix of temperature-strain is [ε, T] T = [ε1, ε2, ε3, ε4, T] T , and the corresponding vector of wavelength drift is Δλ = [Δλ1, Δλ2, Δλ3, Δλ4] T , which is expressed as: where Δλ i , and are the wavelength drift, strain sensitivity, and temperature sensitivity of the FBG in the i-th (i = 1, 2, 3) fiber core, respectively.

7. A multi-factor error simultaneous decoupling method based on fiber Bragg grating sensing according to claim 1, characterized in that The temperature compensation method in step S5 is calculated based on the influence of the temperature change measured by the fiber Bragg grating on the wavelength drift, and the temperature compensation parameter is used to correct the strain error caused by temperature.

8. A method for simultaneously decoupling multi-factor errors based on fiber Bragg grating sensing according to claim 1, characterized in that, The torsion error compensation method in step S5 is based on the Bishop framework model, and the torsion error is compensated by calculating the torsion strain correction matrix of the fiber Bragg grating in real time.

9. A method for simultaneously decoupling multi-factor errors based on fiber Bragg grating sensing according to claim 1, characterized in that The fiber shape reconstruction in step S6 uses a curvature-bending conversion method, and based on the measurement data of multiple grating points arranged along the fiber, combines three-dimensional coordinate transformation to calculate the three-dimensional shape information of the fiber.

10. A method for simultaneously decoupling multi-factor errors based on fiber Bragg grating sensing according to claim 8, characterized in that, The real-time torsion compensation algorithm based on the Bishop framework model defines a correction matrix C to achieve the decoupling of bending strain and torsion strain. The correction attitude vector matrix W(s) embedded with the correction matrix C is expressed as: In the formula, c1, c2, and c3 are the coordinate correction coefficients of x, y, and z respectively. Through the above decoupling method, the strain generated by temperature and torsion is separated from the bending strain, and the remaining strain is the pure bending strain.

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