Fiber bragg grating three-dimensional force sensor decoupling method based on improved BES-ELM

Abstract

The invention relates to a fiber bragg grating three-dimensional force sensor decoupling method based on an improved BES-ELM, and belongs to the technical field of sensors. The method comprises the following steps: carrying out a calibration experiment on a fiber bragg grating three-dimensional force sensor to obtain a plurality of experimental data; introducing an eagle search optimization algorithm, improving the eagle search optimization algorithm based on a cosine adaptive strategy, optimizing the weight and bias of an extreme learning machine based on experimental data and the improved eagle search algorithm, and obtaining an improved BES-ELM decoupling three-dimensional force sensor model; and decoupling the fiber bragg grating three-dimensional force sensor based on the improved BES-ELM decoupling three-dimensional force sensor model. According to the method, the model decoupling precision is improved, premature falling into local optimum is avoided, the global exploration capability is improved, the population diversity is enhanced, the local extremum is escaped, and the convergence speed is increased.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of sensors, and particularly relates to a decoupling method for a fiber Bragg grating three-dimensional force sensor based on improved BES-ELM. BACKGROUND

[0002] With the continuous development of science and technology, three-dimensional force sensors are increasingly widely used in various fields, and particularly play a crucial role in key fields such as robotics, aerospace, and medical devices. Compared with traditional electromagnetic three-dimensional force sensors such as resistance or piezoelectric types, three-dimensional force sensors based on fiber Bragg gratings (FBG) have many unique advantages, including anti-electromagnetic interference capability, electromagnetic insulation, high and low temperature resistance, center wavelength without temperature drift, high measurement accuracy, and long-term use reliability. Due to the influence of the structure or processing errors of the sensor itself, the output of a certain measurement dimension will be affected by the changes in other dimensions, resulting in inter-dimension coupling and affecting the accuracy of the sensor. Therefore, it is of great significance to study a reasonable and effective decoupling method for improving the accuracy of the sensor.

[0003] Currently, three-dimensional force sensor decoupling mainly includes nonlinear decoupling (such as BP neural network, support vector regression, etc.) and linear decoupling (such as least squares method). Using the least squares method for linear decoupling is difficult to depict the inherent complex nonlinear relationship of the elastomer structure, resulting in significant errors at the range boundary and under complex loads. Although the decoupling method based on back propagation (BP) neural network has nonlinear fitting capability, it has problems such as slow convergence speed, easy to fall into local optimum, and strong dependence on super parameters. While the traditional ELM has a fast learning speed, the input weight and hidden layer bias are randomly generated, resulting in unstable network performance, large fluctuation in generalization ability, and great randomness in the accuracy of the decoupling model. When using common optimization algorithms (such as PSO, GA) to optimize the ELM parameters, there are problems such as premature convergence, insufficient global search capability, and easy to fall into local optimum, which makes it difficult to find the best parameter combination of ELM, and restricts the application of ELM in high-precision and high-stability decoupling. SUMMARY

[0004] The purpose of the present application is to provide a decoupling method for a fiber Bragg grating three-dimensional force sensor based on improved BES-ELM, to solve the problems of low precision, poor stability, and slow convergence of existing decoupling methods.

[0005] In order to achieve the above-mentioned purpose, the technical solutions of the present application are as follows: The present application relates to a decoupling method for a fiber Bragg grating three-dimensional force sensor based on improved BES-ELM, which comprises the following steps: S1. Calibrating the fiber Bragg grating three-dimensional force sensor to obtain a plurality of experimental data; S2. Introducing the bald eagle search optimization algorithm, improving the bald eagle search optimization algorithm based on the cosine adaptive strategy, optimizing the weights and biases of the extreme learning machine based on experimental data and the improved bald eagle search algorithm, and obtaining the improved BES-ELM decoupling three-dimensional force sensor model; S3. Decoupling the fiber grating three-dimensional force sensor based on the improved BES-ELM decoupling three-dimensional force sensor model.

[0006] Preferably, the specific steps of S1 for calibrating the fiber grating three-dimensional force sensor are: S1.1. Place the three-dimensional force sensor in a zero load state and record the initial center wavelength of each fiber grating; S1.2. For each measurement direction, gradually apply load and then gradually unload, and record the center wavelength of each fiber grating in three measurement directions after each loading or unloading, and obtain the wavelength drift of each fiber grating in three measurement directions after each loading or unloading by subtracting the initial center wavelength, and use it as experimental data; S1.3. Repeat steps S1.1-S1.2 until the expected number of experimental data is obtained.

[0007] Preferably, the improvement of the bald eagle search optimization algorithm based on the cosine adaptive strategy refers to the improvement of the selection space stage in the bald eagle search optimization algorithm, specifically introducing a cosine adaptive strategy to adaptively control the factor, and then updating the position of the bald eagle individual to obtain the optimal search space; The update formula of the position of the bald eagle individual is: , Wherein, is the newly generated position of the th bald eagle individual, , and are the prey position, the average position and the original position of the th bald eagle individual, is the control factor, is a random number; The adaptive formula of the control factor is: , Wherein, is the adaptive control factor, and represent the maximum and minimum values of the control factor in the traditional bald eagle search optimization algorithm, represents the current iteration number, represents the maximum iteration number.

[0008] Preferably, the original position of the individual bald eagle is obtained through a Logistic chaotic mapping, and the mapping formula is: , in, For the number of mappings, and The first Second and third Secondary mapping value, For control parameters, and .

[0009] Preferably, step S2 further optimizes the vulture search algorithm using an adaptive t-distribution, where the probability density function of the t-distribution is: , in, This is the standardized sample statistic. Let be the probability density function. For degrees of freedom, It is the Gamma function; After further optimizing the bald eagle search algorithm using an adaptive t-distribution, the update formula for the individual bald eagle's position is: , in, To further optimize the t-distribution, the th The location where a new individual bald eagle is generated. The distribution operator corresponding to the degrees of freedom that adjust with the number of iterations.

[0010] Preferably, in step S2, the experimental data is divided into a training set and a test set. The training set is used to optimize the weights and biases of the extreme learning machine, and the test set is used to evaluate the decoupling performance of the improved BES-ELM decoupled three-dimensional force sensor model.

[0011] Preferably, the evaluation of the decoupling performance of the improved BES-ELM decoupled three-dimensional force sensor model is represented by the combined error and coupling error, as follows: , , in, Indicates the overall error. Indicates coupling error. express The maximum difference between the standard force value actually applied and the actual measured force value in the direction. express When a force is applied in one direction and no force is applied in other directions. The maximum force value measured in the direction, representing representing The direction can apply the full-scale value of force.

[0012] Compared with the prior art, the technical scheme provided by the application has the following beneficial effects: 1. The improved BES-ELM-based optical fiber grating three-dimensional force sensor decoupling method introduces a cosine adaptive control factor, thereby updating the vulture individual position, and can dynamically adjust the search step according to the iteration process, enhances global exploration in the early iteration stage, and gradually shifts to local fine development in the later stage, realizes the balance optimization of exploration and development, obtains the optimal search space, helps to find the best weight and bias parameter combination of the extreme learning machine, and thereby improves the precision of model decoupling.

[0013] 2. The improved BES-ELM-based optical fiber grating three-dimensional force sensor decoupling method uses Logistic chaotic mapping to initialize the population, can utilize the ergodicity and randomness of the chaotic system, make the initial solution more uniform and diverse in the search space, thereby avoid the algorithm from falling into local optimum too early, and improve the global exploration ability.

[0014] 3. The improved BES-ELM-based optical fiber grating three-dimensional force sensor decoupling method also combines an adaptive t-distribution variation strategy, can apply disturbance to the individual position in the later stage of the algorithm, the tail characteristics change with the adjustment of the degree of freedom, and has the local concentration of Gaussian distribution and the jumping of Cauchy distribution, thereby effectively enhancing the population diversity, escaping from local extreme value, and accelerating the convergence speed. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 The flowchart of the improved BES-ELM-based optical fiber grating three-dimensional force sensor decoupling method; Figure 2 The curve graph of the cosine adaptive control factor changing with the number of iterations; Figure 3 The optimal fitness change curve in the training process of the improved BES-ELM Figure 4 Comparison of type I errors of different decoupling methods; Figure 5 Comparison of type II errors of different decoupling methods. DETAILED DESCRIPTION

[0016] In order to further understand the content of the application, the application will be described in detail in combination with the embodiments, and the following embodiments are used to illustrate the application, but not to limit the scope of the application.

[0017] Refer to the drawings Figure 1As shown, the present application relates to a fiber grating three-dimensional force sensor decoupling method based on improved BES-ELM, which comprises the following steps: S1. Calibrating the fiber grating three-dimensional force sensor, obtaining a plurality of experimental data, specifically: S1.1. Place the three-dimensional force sensor in a zero load state for five minutes, and record the initial center wavelength of each fiber grating through the demodulation system; S1.2. For each measurement direction, gradually apply a load at intervals of 10N in the range of 0N to 100N and then gradually unload, and this cycle is repeated five times, and the center wavelength of each fiber grating in three measurement directions after each loading or unloading is recorded in real time. Subtract the initial center wavelength from the obtained center wavelength to obtain the wavelength drift of each fiber grating in three measurement directions after each loading or unloading, and use it as experimental data; S1.3. Repeat steps S1.1-S1.2 until the expected number of experimental data is obtained, and 300 groups of data are obtained in this embodiment, each group of data containing the applied load and the wavelength drift of each FBG.

[0018] S2. Introduce the bald eagle search optimization algorithm, improve the bald eagle search optimization algorithm based on the cosine adaptive strategy, use 240 groups of data as the training set, optimize the weights and biases of the extreme learning machine based on the training set and the improved bald eagle search algorithm, and obtain the improved BES-ELM decoupling three-dimensional force sensor model: The bald eagle search optimization algorithm includes three stages, namely: selection space stage, search space stage and diving stage, and the improvement of the bald eagle search optimization algorithm based on the cosine adaptive strategy refers to the improvement of the selection space stage of the bald eagle search optimization algorithm. Specifically, the cosine adaptive strategy is introduced to adaptively control the factor, and then the position of the bald eagle individual is updated to obtain the optimal search space.

[0019] The original position of the bald eagle individual is obtained through the Logistic chaotic mapping, and the initial position of the bald eagle is an important factor affecting the performance of the algorithm. It not only relates to the positioning of the global optimal solution, but also has a significant impact on the convergence speed and accuracy. The Logistic chaotic mapping initialization can improve the diversity and ergodicity of the population, avoid premature convergence of the population to the local optimum, enhance the global search ability of the algorithm, and improve the convergence speed and accuracy of the algorithm. The mapping formula for initializing the original position of the bald eagle through the Logistic chaotic mapping is: , Wherein, is the number of mappings, and are the th and th mapping values, As control parameters, they directly determine the dynamic behavior of the system, and Within [0,4], when 0≤ When 1 < 1, the system tends to die out; when 1 ≤ 1, the system tends to die out. When <3, it tends to reach a stable equilibrium; when 3≤ A periodic doubling bifurcation occurs when the value is less than 3.57, and when the value is less than or equal to 3.57. When the value is ≤4, it enters a chaotic state (extremely sensitive to initial values). When the value is greater than 4, the system will escape the [0,1] interval. In this invention, μ is set to 4. The mapping value obtained in this process corresponds to the original position of each individual bald eagle.

[0020] During the spatial selection phase, the entire bald eagle population will search based on historical experience: each bald eagle will refer to the best location it has found in the past and perform a random search around that location in its neighborhood. This strategy aims to use the information already available to efficiently explore the area where potential better solutions are located.

[0021] The calculation of an individual bald eagle's new location follows the formula below: , in, It is the first The location where a new individual bald eagle is generated. , and These are the prey position, average position, and first The original location of the individual bald eagle. It is a control factor for positional changes, a constant within the interval [1.5, 2]. It is a random number within the interval [0, 1]. Control factor in the original algorithm The fixed value limits the algorithm's adaptability at different optimization stages. Therefore, a cosine adaptive strategy is introduced. During the iteration process, the curve smoothly changes within a preset range according to a cosine curve. This non-linear change mode can better simulate the natural optimization process. In the early stages of iteration, the larger... The value enhances the population's global exploration capabilities, helping the algorithm quickly scan the entire search space; in the mid-term, smaller values... The value facilitates fine-grained local search and improves convergence accuracy; however, in the later stages, A moderate increase in the value helps to escape potential local optima and avoid premature convergence. In this invention, the control factor... The adaptive formula is: , in, The adaptive control factor, and Let represent the maximum and minimum values ​​of the control factor in the traditional vulture search optimization algorithm, respectively. Indicates the current iteration number. This indicates the maximum number of iterations.

[0022] Cosine adaptive control factor The curves showing how the number of iterations changes are as follows: Figure 2 As shown.

[0023] Furthermore, this invention employs an adaptive t-distribution to further optimize the vulture search algorithm, where the probability density function of the t-distribution is: , in, This is a standardized sample statistic used to measure the magnitude of the difference in means relative to the standard error. Let be the probability density function. The degree of freedom determines the shape of the distribution, which is equal to the sample size minus 1. The smaller the value, the thicker the tails. This is the Gamma function, used to standardize the density function to ensure the total probability is 1; When degrees of freedom When the number of degrees of freedom is 1, the distribution corresponds to the Cauchy distribution; while when the number of degrees of freedom is 1, the distribution corresponds to the Cauchy distribution. As the value approaches infinity, it degenerates into a Gaussian distribution. The Cauchy and Gaussian distributions can be considered two special cases of this distribution. To alleviate the problem of the vulture search algorithm easily getting trapped in local optima in the later stages of iteration, this distribution is introduced to randomly perturb the vulture's position, thereby enhancing its global exploration ability. After further optimizing the vulture search algorithm using an adaptive t-distribution, the update formula for the vulture's position is: , in, To further optimize the t-distribution, the th The location where a new individual bald eagle is generated. The distribution operator corresponding to the degrees of freedom that adjust with the number of iterations; In the early stages of algorithm iteration When the value is small, the distribution is closer to the Cauchy distribution. The larger the perturbation amplitude, the more it helps enhance the algorithm's global exploration capability. As the iteration progresses to later stages... As it gradually increases, the distribution approaches a Gaussian distribution, at which point... The reduced perturbation helps improve the algorithm's local mining capability, thereby accelerating the convergence speed. In the middle stage of the algorithm iteration, the distribution is in a transitional state from Cauchy distribution to Gaussian distribution, possessing the characteristics of both distributions, and can achieve an effective balance between global search and local search.

[0024] Search Space Phase: Once the vulture identifies a potential prey area, it switches to a spiral flight mode to accelerate the detailed search of the target area. This spiral optimization strategy has a dual advantage: on the one hand, it significantly speeds up the algorithm's convergence process; on the other hand, due to its powerful local exploration capabilities, it increases the likelihood of locking onto the global optimum. The specific formula is as follows: (1), (2), (3), (4), In formula (1), Indicates the first Adjacent positions of individual bald eagles and These represent the standardized perturbation components, controlling the direction and magnitude of individual adjustments relative to neighboring individuals and the group mean, respectively. Formula (2) is used to normalize the polar coordinate components. and This indicates that the original component values ​​are calculated based on polar coordinates. and These are all individuals in the current population. and The absolute maximum value of the component, the purpose of normalization is to make and The value is scaled to a stable range (usually [-1, 1]) to avoid the position update step size getting out of control due to the value being too large or too small, thus ensuring the stability and convergence of the search process; Formula (3) transforms the polar coordinate system into a Cartesian coordinate system to generate the spiral motion trajectory, where, It is the angle in polar coordinates, which determines the direction of rotation of the spiral; The radius in polar coordinates determines the size and tightness of the spiral. Through this transformation, the algorithm can simulate the spiraling descent behavior of a vulture in three-dimensional space. This movement pattern can effectively balance the breadth (through angle changes) and depth (through radius changes) of the search in mathematics. Formula (4) generates unique spiral search parameters for each eagle. Wherein, In the calculation, It is an important control constant, with a value range of [5, 10]. It directly affects the magnitude of the angle change; a larger value... The value will produce a larger angular change, increasing the randomness of the exploration; for the radius Its value is determined by the angle. Add a random perturbation term constituted, here is another control constant, taking values in the range [0.5, 2], which adjusts the random fluctuation range of the spiral radius, denotes a random number uniformly distributed on the interval [0, 1). The combination of these parameters makes each eagle's search path have a certain randomness while maintaining the overall characteristics of spiral motion.

[0025] Dive phase: In the dive hunting phase, all the eagles start from the current optimal position in the search space and launch a dive along a specific trajectory towards the target prey position. This dynamic process is accurately simulated by the polar equation, which is mathematically expressed as follows: (5), (6), (7), (8), In formula (5), denotes the lateral position adjustment weight generated based on the hyperbolic sine function (sinh), which is used to control the random amplitude and direction of individual movement towards the group mean, helping the algorithm to perform lateral search and exploration, denotes the longitudinal position adjustment weight generated based on the hyperbolic cosine function (cosh), which is used to control the random amplitude and direction of individual movement towards the global optimal solution, simulating the process of the eagle diving towards the prey, denotes the mean guidance coefficient, which is used to adjust the influence of the group average position on individual update, enhancing the global exploration ability of the algorithm in the search space, denotes the optimal solution guidance coefficient, which is used to adjust the attraction strength of the current optimal solution to individual update, enhancing the local development ability of the algorithm and promoting the convergence of individuals towards the optimal solution, and take values in the range [1, 2]; The function of formula (6) is similar to the search space phase, which is to normalize the polar coordinate components and used in the dive phase, ensuring that the values of and are within a controllable range, thereby stabilizing the position update step size in the dive phase and preventing "over-dive" due to excessively large values, which may miss the optimal solution; Formula (7) uses hyperbolic functions instead of standard trigonometric functions to calculate polar coordinate components. The characteristic of hyperbolic functions is that the function value increases exponentially when the independent variable increases. This mathematical characteristic can better simulate the natural phenomenon that the speed of a vulture increases and the position changes rapidly when it dives, so that the algorithm can quickly and directly converge to the vicinity of the optimal solution in the final stage. In formula (8), the angle The generation method and search space stage are the same, but the radius... The calculation is simplified to be directly equal to the angle. This simplification makes the dive trajectory more direct and predictable, reduces unnecessary random fluctuations, and conforms to the "precise and fast" behavioral characteristics of the dive phase, which helps the algorithm to achieve final convergence stably and efficiently.

[0026] The aforementioned search space phase and dive phase are existing technologies and are not the subject of this application.

[0027] Repeat this step until the maximum number of iterations is reached. Use the final result as the weights and biases of the ELM to obtain the decoupled model of the fiber grating three-dimensional force sensor. Figure 3 It can be seen that when the number of iterations reaches 96, the optimal fitness reaches the maximum value of 0.9999278954, thus achieving the optimal fitness.

[0028] To comprehensively evaluate the performance of the three-dimensional force sensor, it is necessary to establish accuracy indicators for its measurements. The remaining 60 sets of data are used as a test set to evaluate the decoupling performance of the improved BES-ELM decoupled three-dimensional force sensor model. This performance is typically represented by combined error (or Type I error) and coupling error (or Type II error). , , in, Indicates the overall error. Indicates coupling error. express The maximum difference between the standard force value actually applied and the actual measured force value in the direction. express When a force is applied in one direction and no force is applied in other directions. The maximum force value measured in the direction, Indicate The full-scale value of the direction to which force can be applied.

[0029] Combined with appendix Figure 4 and attached Figure 5As shown, the least squares (LS) method exhibits the largest decoupling error in both types of errors, particularly in the Type II errors of 17.34% and 13.7% in the Fy and Fz directions, respectively, significantly higher than other methods. This indicates that LS has limited ability to handle nonlinear coupling relationships between variables, exhibits weak generalization, and is prone to significant systematic biases. The improved BES-ELM algorithm, on the other hand, has a maximum Type I error of 0.87% and a maximum Type II error of 0.49%, outperforming the other three methods in both types of errors in each direction. This demonstrates that the improved BES-ELM algorithm achieves ideal decoupling performance and significantly improves the measurement accuracy and performance of the fiber optic grating three-dimensional force sensor.

[0030] S3. Decoupling of fiber optic grating three-dimensional force sensor based on improved BES-ELM decoupling three-dimensional force sensor model.

[0031] The present invention has been described in detail above with reference to the embodiments, but the content described is only a preferred embodiment of the present invention and should not be considered as limiting the scope of the present invention. All equivalent changes and improvements made in accordance with the scope of the present invention should still fall within the patent coverage of the present invention.

Claims

1. A decoupling method for a fiber optic grating three-dimensional force sensor based on an improved BES-ELM, characterized in that: It includes the following steps: S1. A calibration experiment was conducted on the fiber optic grating three-dimensional force sensor to obtain some experimental data; S2. Introduce the Bald Eagle Search optimization algorithm, improve the Bald Eagle Search optimization algorithm based on the cosine adaptive strategy, optimize the weights and biases of the Extreme Learning Machine based on experimental data and the improved Bald Eagle Search algorithm, and obtain the improved BES-ELM decoupled three-dimensional force sensor model. S3. Decoupling of fiber optic grating three-dimensional force sensor based on improved BES-ELM decoupling three-dimensional force sensor model.

2. The decoupling method for a fiber optic grating three-dimensional force sensor based on an improved BES-ELM according to claim 1, characterized in that: The specific steps for the calibration experiment of the fiber optic grating three-dimensional force sensor in step S1 are as follows: S1.

1. Place the three-dimensional force sensor in a zero-load state and record the initial center wavelength of each fiber grating; S1.

2. For each measurement direction, load is applied step by step and then unloaded step by step. The center wavelength of each fiber grating in the three measurement directions is recorded in real time after each loading or unloading. The obtained center wavelength is subtracted from the initial center wavelength to obtain the wavelength drift of each fiber grating in the three measurement directions after each loading or unloading, and this is used as experimental data. S1.

3. Repeat steps S1.1-S1.2 until the expected amount of experimental data is obtained.

3. The decoupling method for a fiber optic grating three-dimensional force sensor based on an improved BES-ELM according to claim 1, characterized in that: The improvement of the bald eagle search optimization algorithm based on the cosine adaptive strategy in S2 refers to the improvement of the selection space stage in the bald eagle search optimization algorithm. Specifically, it introduces the cosine adaptive strategy adaptive control factor to update the position of individual bald eagles and obtain the optimal search space. The formula for updating the location of individual bald eagles is as follows: ， in, It is the first The location where a new individual bald eagle is generated. , and These are the prey position, average position, and first The original location of the individual bald eagle. It is a control factor. It is a random number; The control factor The adaptive formula is: ， in, The adaptive control factor, and Let represent the maximum and minimum values ​​of the control factor in the traditional vulture search optimization algorithm, respectively. Indicates the current iteration number. This indicates the maximum number of iterations.

4. The decoupling method for a fiber optic grating three-dimensional force sensor based on an improved BES-ELM according to claim 3, characterized in that: The original positions of the individual bald eagles were obtained through a Logistic chaotic mapping, with the following formula: ， in, For the number of mappings, and The first Second and third Secondary mapping value, For control parameters, and .

5. The decoupling method for a fiber optic grating three-dimensional force sensor based on an improved BES-ELM according to claim 3, characterized in that: S2 further optimizes the vulture search algorithm using an adaptive t-distribution, where the probability density function of the t-distribution is: ， in, This is the standardized sample statistic. Let be the probability density function. For degrees of freedom, It is the Gamma function; After further optimizing the bald eagle search algorithm using an adaptive t-distribution, the update formula for the individual bald eagle's position is: ， in, To further optimize the t-distribution, the th The location where a new individual bald eagle is generated. The distribution operator corresponding to the degrees of freedom that adjust with the number of iterations.

6. The decoupling method for a three-dimensional force sensor based on an improved BES-ELM fiber optic grating according to claim 1, characterized in that: In step S2, the experimental data is divided into a training set and a test set. The training set is used to optimize the weights and biases of the extreme learning machine, and the test set is used to evaluate the decoupling performance of the improved BES-ELM decoupled three-dimensional force sensor model.

7. The decoupling method for a fiber optic grating three-dimensional force sensor based on an improved BES-ELM according to claim 6, characterized in that: The evaluation of the decoupling performance of the improved BES-ELM decoupled three-dimensional force sensor model is represented by the combined error and coupling error, as follows: ， ， in, Indicates the overall error. Indicates coupling error. express The maximum difference between the standard force value actually applied and the actual measured force value in the direction. express When a force is applied in one direction and no force is applied in other directions. The maximum force value measured in the direction, Indicate The full-scale value of the direction to which force can be applied.

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