Decoupling method based on fiber grating six-dimensional force sensor

Abstract

The application discloses a decoupling method based on a fiber grating six-dimensional force sensor and relates to the technical field of sensors.The method comprises the following steps: firstly, simulation data of a sensor strain path is obtained through finite element analysis; secondly, a cubic chaotic mapping is used to initialize a population of an improved sparrow search algorithm, a position of a discoverer is found through adaptive weight updating, a position of a follower is updated through a variable spiral strategy, a position of a scout is optimized through a warning mechanism, and initial weights and thresholds of a BP neural network are pre-screened; then, the optimization result is used as an initial value of the BP network, a Dropout algorithm is introduced to randomly discard neurons, an ADAM algorithm is combined to adaptively adjust a learning rate, and a first-order moment and a second-order moment estimation are used to perform gradient fine tuning on the weights and thresholds; and finally, the network is iterated and converged to obtain a high-precision decoupling model.The application solves the problems of traditional decoupling methods, such as easy falling into local optimization, slow convergence and large coupling interference, and significantly improves the measurement precision and anti-interference ability of the six-dimensional force sensor.

Description

Technical Field

[0001] This invention relates to the field of sensor technology, and in particular to a decoupling method for a six-dimensional force sensor based on a fiber Bragg grating. Background Technology

[0002] Six-dimensional force sensors are key sensors commonly used in industrial production control and robot motion. Their measurement range includes three torque components (Mx, My, and Mz) and three force components (Fx, Fy, and Fz). As sensors that measure the forces and torques experienced by a robot's end effector when it interacts with the external environment or grasps a workpiece, six-dimensional force and torque sensors provide force-sensing information for robot force and motion control, playing a crucial role in realizing robot intelligence. They enable precise measurement in force and motion control, thereby improving the robot's operational accuracy and intelligence level. Fiber Bragg gratings (FBGs) offer advantages such as immunity to electromagnetic interference and optical power fluctuations, small profile, and light weight, making them suitable for force measurement in harsh conditions such as severe vibration, strong electromagnetic interference, high temperature and humidity, and even underwater environments. This paper proposes a two-layer decoupling algorithm for an FBG six-dimensional force sensor that integrates ADAM and ISSA-BP. The improved Sparrow Search Algorithm (ISSA) is used to optimize the initial weights and biases of the BP neural network, and the validation set error is used as the fitness function. The parameters optimized by ISSA are then used as the initial values ​​of the BP network, and ADAM is used for training to achieve adaptive learning rate.

[0003] When using intelligent algorithms to decouple six-dimensional force sensors, commonly used algorithms include backpropagation (BP) neural network, extreme learning machine (ELM), and support vector regression (SVR). However, applying these algorithms to decouple six-dimensional force sensors during training can easily lead to problems such as oscillations, slow convergence, premature convergence, and getting trapped in local maxima, resulting in decoupling failures. This poses a challenge to research in this field, necessitating more intelligent and universal methods to address the interdimensional coupling problem of the sensor.

[0004] Existing six-dimensional force sensors based on fiber Bragg gratings generally suffer from high cross-sensitivity and high nonlinearity, with coupling interference between different dimensions affecting measurement accuracy and making calibration difficult. The least squares method assumes a linear relationship between the sensor's input and output, but due to the sensor's structural characteristics, the relationship is nonlinear, thus limiting its effectiveness. Decoupling methods based on backpropagation (BP) neural networks suffer from slow convergence, susceptibility to local minima, and weak generalization ability. Decoupling methods based on backpropagation (RBF) neural networks still rely on the validity and accuracy of calibration data for output accuracy, leading to decreased decoupling precision. SVR-based decoupling methods require extensive experimental data, making the algorithm computationally complex and inefficient. Summary of the Invention

[0005] The technical solution of this invention to solve the above-mentioned technical problems is to provide a decoupling method based on a fiber Bragg grating six-dimensional force sensor, comprising the following steps:

[0006] Step 1: Perform finite element analysis on the six-dimensional force sensor. In AnsysWorkbench, set 11 simulation paths corresponding to the FBG position, obtain the coordinates of the path endpoints and perform simulation. Record the strain signal in the calibration experiment as input data and the actual applied load as output data.

[0007] Step 2: Initialize the sparrow search algorithm population using cubic chaotic mapping, calculate and sort individual fitness values, and update the best and worst values; pre-screen the initial weights and thresholds of the BP neural network using the improved sparrow search algorithm;

[0008] Step 3: Using the weight threshold obtained in Step 2 as the initial value of the BP network, introduce the Dropout algorithm to randomly discard some neurons in each iteration, calculate the network error and adjust the weights;

[0009] Step 4: Adaptively adjust the learning rate using the ADAM algorithm, fine-tune the gradient of the weight thresholds, and update the formula as follows:

[0010]

[0011] In the formula: These are the first-order moment estimates before and after iteration, respectively; β1 is the exponentially weighted average parameter; dw i The gradient represents the weight w or the threshold θ;

[0012]

[0013] In the formula: These are the second-order moment estimates before and after iteration, respectively; β2 is the exponentially weighted average parameter. The squared gradient represents the weight w or the threshold θ;

[0014]

[0015]

[0016] In the formula: w i θ i The adjusted weights and thresholds; w i-1 θ i-1 , where is the weights and threshold to be trained; α is the learning rate; δ is a constant;

[0017] Step 5: Repeat steps 3 and 4 until the network converges to obtain the six-dimensional force sensor decoupling model.

[0018] Furthermore, in step two, the formula for the cubic chaotic mapping is:

[0019] y(n+1) = 4y(n) 3 -3y(n);

[0020] Where: n is the number of mappings, y(n)∈(-1,0)∪(0,1), and y(n) is the value of the nth mapping.

[0021] Furthermore, in step two, the sparrow search algorithm includes:

[0022] Introducing adaptive weights can improve the quality of the discoverer's individual position, enabling other individuals to converge to the optimal position more quickly and accelerating the convergence speed. The formula for adaptive weights is as follows:

[0023]

[0024] (a) Discoverer location is updated using adaptive weights:

[0025] The discoverer's updated location is:

[0026]

[0027] Where t represents the current iteration number, j = (1, 2, ..., d), X represents the position information of the first sparrow in dimension j in the t-th generation; α ∈ (0, 1) is a random number following a uniform distribution; iter max R2 represents the maximum number of iterations; R2∈(0,1) represents the warning value; ST∈[0.5,1] represents the safety threshold; Q is a random number that follows a normal distribution of [0,1]; L=1*d, and each element in it is 1; when R2<ST, the current environment is safe, and the discoverer continues to forage; when R2≥ST, the current environment is dangerous, and the discoverer will start chirping to send a danger signal to other sparrows, and the sparrow population will move to a safe area;

[0028] (b) Follower positions are updated using a variable spiral strategy:

[0029] A variable spiral position update strategy is introduced to make follower position updates more flexible. Various search paths are developed for position updates, balancing the algorithm's global and local search. The formula for the variable spiral position update strategy is as follows:

[0030]

[0031] in, This represents the worst-case position information of the discoverer in the j-th dimension during the t-th iteration. This represents the information that the discoverer is in the optimal position in dimension j during the (t+1)th iteration; A is a 1*d single-row multidimensional vector, and its internal elements are randomly selected to be 1 or -1. + =A T (AA T ) -1 ;when When the current follower is hungry, its fitness value is poor, and it needs to leave its current location to forage for food elsewhere; when When z is in the range of [-1, 1], it indicates that the follower at the current position has a good fitness value and can continue to forage in this area. z changes with the number of iterations and the size and amplitude of the spiral are dynamically adjusted according to the cosine function. k represents the coefficient of variation, k = 5. L represents a uniformly distributed random number in the range of [-1, 1].

[0032] (c) Update the location of the reconnaissance and early warning personnel using the following formula:

[0033]

[0034] in, The position information represents the global optimum; β is a parameter controlling the step size, which follows a normal distribution (mean 0, variance 1); K is a uniform random number in the range [-1, 1], used to control the sparrow's movement direction; f i f is the current fitness value of an individual sparrow. g and f w These represent the local optimum and worst fitness of the current population, respectively; ε is a very small constant used to prevent the denominator from being zero; when f i >f g When f indicates that the sparrow's foraging area is in a poor position and it is easily attacked; when f i =f g This indicates that some sparrows have sensed danger and need to move closer to their companions to reduce the risk of being caught.

[0035] The technical solution of this invention improves the initial sparrow search algorithm through a cubic chaotic mapping method and an adaptive spiral flight mechanism, enhancing the uniformity and randomness of population distribution and helping to strengthen the discoverer's exploration ability while avoiding premature convergence. It also achieves adaptive learning rate through the ADAM adaptive learning rate mechanism, fine-tuning the gradient of the initial weights generated by SSA to improve model convergence accuracy. Furthermore, by incorporating the improved sparrow search algorithm with ADAM, the BP neural network model is optimized, solving the problem of BP neural networks easily getting trapped in local minima and improving the decoupling accuracy of the six-dimensional force sensor. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0037] Figure 1 This is a flowchart of the decoupling method based on a six-dimensional force sensor using a fiber optic grating, as described in this invention.

[0038] Figure 2 The diagram shows the sensor structure and FBG distribution of the six-dimensional force sensor based on fiber optic grating described in this invention.

[0039] Figure 3 This is a diagram showing the decoupling results of the decoupling method based on a six-dimensional force sensor using a fiber optic grating as described in this invention.

[0040] Figure 4 The diagram shows the Type I and Type II errors of the decoupling method based on the fiber optic grating six-dimensional force sensor described in this invention.

[0041] Figure 5 This is a graph showing the average absolute percentage error of each dimension of the decoupling method based on a six-dimensional force sensor using a fiber optic grating as described in this invention.

[0042] Figure 6 This is a comparison of the convergence curves of the decoupling method based on a six-dimensional force sensor using a fiber optic grating as described in this invention.

[0043] The accompanying diagrams in the instruction manual illustrate: 11. Torque measuring layer; 21. Torque absorption layer; 31. Force measuring layer. Detailed Implementation

[0044] This invention proposes a decoupling method based on a fiber Bragg grating six-dimensional force sensor, aiming to improve the uniformity and randomness of population distribution.

[0045] The decoupling method based on a six-dimensional force sensor using a fiber optic grating proposed in this invention will be described below in specific embodiments:

[0046] In this embodiment, a decoupling method based on a fiber Bragg grating six-dimensional force sensor is described in the following flowchart. Figure 1 As shown, it includes the following steps:

[0047] Step 1: Perform finite element analysis on the six-dimensional force sensor. In AnsysWorkbench, set 11 simulation paths corresponding to the FBG position, obtain the coordinates of the path endpoints and perform simulation. Record the strain signal in the calibration experiment as input data and the actual applied load as output data.

[0048] Specifically, finite element analysis was performed on the six-dimensional force sensor using Ansys Workbench along a specified path to obtain strain data and curves at the designated locations. Based on the desired placement of the FBGs, the coordinates of the two endpoints on the line containing the FBGs were obtained, and the path settings were completed by inputting these coordinates. During the simulation, 11 simulation paths were defined based on the location and number of FBGs. The experimental data of the six-dimensional force sensor after calibration was recorded, with the sensor strain signal used as input data and the actual value applied to the six-dimensional force sensor as output data.

[0049] Step 2: Initialize the sparrow search algorithm population using cubic chaotic mapping, calculate and sort individual fitness values, and update the best and worst values; pre-screen the initial weights and thresholds of the BP neural network using the improved sparrow search algorithm;

[0050] Step 3: Using the weight threshold obtained in Step 2 as the initial value of the BP network, introduce the Dropout algorithm to randomly discard some neurons in each iteration, calculate the network error and adjust the weights;

[0051] Step 4: Adaptively adjust the learning rate using the ADAM algorithm, fine-tune the gradient of the weight thresholds, and update the formula as follows:

[0052]

[0053] In the formula: These are the first-order moment estimates before and after iteration, respectively; β1 is the exponentially weighted average parameter; dw i The gradient represents the weight w or the threshold θ;

[0054]

[0055] In the formula: These are the second-order moment estimates before and after iteration, respectively; β2 is the exponentially weighted average parameter. The squared gradient represents the weight w or the threshold θ;

[0056]

[0057]

[0058] In the formula: w i θ i The adjusted weights and thresholds; w i-1 θ i-1 , where is the weights and threshold to be trained; α is the learning rate; δ is a constant;

[0059] Step 5: Repeat steps 3 and 4 until the network converges to obtain the six-dimensional force sensor decoupling model.

[0060] Furthermore, in step two, the population is initialized using a cubic mapping, individual fitness values ​​are calculated and sorted, and the current best and worst values ​​are updated. The cubic chaotic mapping formula is:

[0061] y(n+1) = 4y(n) 3 -3y(n);

[0062] Where: n is the number of mappings, y(n)∈(-1,0)∪(0,1), and y(n) is the value of the nth mapping.

[0063] Furthermore, in step two, the sparrow search algorithm includes:

[0064] Introducing adaptive weights can improve the quality of the discoverer's individual position, enabling other individuals to converge to the optimal position more quickly and accelerating the convergence speed. The formula for adaptive weights is as follows:

[0065]

[0066] (a) Discoverer location is updated using adaptive weights:

[0067] The discoverer's updated location is:

[0068]

[0069] Where t represents the current iteration number, j = (1, 2, ..., d), X represents the position information of the first sparrow in dimension j in the t-th generation; α ∈ (0, 1) is a random number following a uniform distribution; iter max R2 represents the maximum number of iterations; R2∈(0,1) represents the warning value; ST∈[0.5,1] represents the safety threshold; Q is a random number that follows a normal distribution of [0,1]; L=1*d, and each element in it is 1; when R2<ST, the current environment is safe, and the discoverer continues to forage; when R2≥ST, the current environment is dangerous, and the discoverer will start chirping to send a danger signal to other sparrows, and the sparrow population will move to a safe area;

[0070] (b) Follower positions are updated using a variable spiral strategy:

[0071] A variable spiral position update strategy is introduced to make follower position updates more flexible. Various search paths are developed for position updates, balancing the algorithm's global and local search. The formula for the variable spiral position update strategy is as follows:

[0072]

[0073] in, This represents the worst-case position information of the discoverer in the j-th dimension during the t-th iteration. This represents the information that the discoverer is in the optimal position in dimension j during the (t+1)th iteration; A is a 1*d single-row multidimensional vector, and its internal elements are randomly selected to be 1 or -1. + =A T (AA T ) -1 ;when When the current follower is hungry, its fitness value is poor, and it needs to leave its current location to forage for food elsewhere; when When z is in the range of [-1, 1], it indicates that the follower at the current position has a good fitness value and can continue to forage in this area. z changes with the number of iterations and the size and amplitude of the spiral are dynamically adjusted according to the cosine function. k represents the coefficient of variation, k = 5. L represents a uniformly distributed random number in the range of [-1, 1].

[0074] (c) Update the location of the reconnaissance and early warning personnel using the following formula:

[0075]

[0076] in, The position information represents the global optimum; β is a parameter controlling the step size, which follows a normal distribution (mean 0, variance 1); K is a uniform random number in the range [-1, 1], used to control the sparrow's movement direction; f i f is the current fitness value of an individual sparrow. g and f w These represent the local optimum and worst fitness of the current population, respectively; ε is a very small constant used to prevent the denominator from being zero; when f i >f g When f indicates that the sparrow's foraging area is in a poor position and it is easily attacked; when f i =f g This indicates that some sparrows have sensed danger and need to move closer to their companions to reduce the risk of being caught.

[0077] The errors of a six-dimensional force sensor are divided into two types: Type I error and Type II error. Type I error refers to the degree of deviation between the actual force or torque applied to the sensor and the ideal force or torque applied. The formula is as follows:

[0078]

[0079] Where, ΔF i(max) F represents the maximum error between the output value of the decoupling algorithm model and the corresponding reference value in the i-direction. i(max) This represents the range value of force / torque in direction i.

[0080] Type II error, also known as static coupling rate, mainly reflects the degree of coupling between different dimensions, and its expression is shown in the following formula:

[0081]

[0082] Among them, F ij(max) F represents the maximum output force / torque obtained in the i direction when the load is mainly applied in the j direction. i(max) This represents the range value of force / torque in direction i.

[0083] Sensor structure and FBG distribution as follows Figure 2 As shown, the elastic structure can be divided into three layers from top to bottom: a torque measurement layer 11, a torque absorption layer 21, and a force measurement layer 31. The torque measurement layer adopts a modified Maltese cross structure. Four horizontal elastic beams and four longitudinal elastic beams are distributed around the central plate at uniform intervals of 90°, and the outer flange is connected to the central plate. The second layer is designed for torque absorption. When torque is applied to the sensor, the thin cylinder with a diameter smaller than that of the adjacent components will produce a large bending deformation to prevent the torque from being transmitted to the force measurement layer, thereby reducing the coupling between the force and torque response. The third layer is designed for force measurement; it adopts four vertical ribs as its basic structure, and the four vertical rib structure is more sensitive to force measurement. The number of fiber Bragg grating elements for sensing is 11, of which FBG1 to FBG6 measure the torque component, and FBG7 to FBG11 measure the force component. Three-dimensional force F x F y F z and three-dimensional torque M x M y M z It is obtained from the following formula.

[0084] Decoupling can be performed using MATLAB software, such as Figure 3 As shown, the horizontal axis represents the number of samples in the test set, and the vertical axis represents the load values. The blue line represents the actual load values, and the red line represents the predicted load values. From Figure 3 Overall, it can be seen that the six-dimensional decoupling model has a good regression effect.

[0085] When using LS linear decoupling, such as Figure 4 As shown, the decoupling effect is poor, with the maximum Type I and Type II errors after decoupling being 4.22% and 3.25%, respectively. The maximum Type I and Type II errors after nonlinear decoupling using a BP neural network are 2.14% and 1.53%, respectively. After decoupling the six-dimensional force sensor using the ADAM-ISSA-BP decoupling algorithm of this application, the maximum Type I and Type II errors of the sensor are 0.27% and 0.185%, respectively. The results indicate that the ADAM-ISSA-BP-based decoupling algorithm for the six-dimensional force sensor achieves ideal results, significantly improving the measurement accuracy and performance of the six-dimensional force sensor.

[0086] like Figure 5 As shown, the mean absolute percentage errors (MAS%) of ADAM-ISSA-BP across all dimensions are 1.92%, 1.30%, 1.40%, 1.13%, 0.64%, and 2.39%, respectively, which are significantly lower than the MAS%) of BP neural network and least squares method. The results indicate that the six-dimensional force sensor decoupling algorithm based on ADAM-ISSA-BP achieves better accuracy.

[0087] like Figure 6 As shown, when the training target error of the neural network is the same, the traditional BP neural network requires approximately 150 iterations, while the BP neural network optimized by ADAM-ISSA requires approximately 30 iterations, a significant reduction. The comparison results indicate that the BP neural network optimized by ADAM-ISSA requires significantly fewer iterations than the traditional BP neural network and has a faster convergence speed.

[0088] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A decoupling method based on a fiber Bragg grating six-dimensional force sensor, characterized in that, Includes the following steps: Step 1: Perform finite element analysis on the six-dimensional force sensor. In AnsysWorkbench, set 11 simulation paths corresponding to the FBG position, obtain the coordinates of the path endpoints and perform simulation. Record the strain signal in the calibration experiment as input data and the actual applied load as output data. Step 2: Initialize the sparrow search algorithm population using cubic chaotic mapping, calculate and sort individual fitness values, and update the best and worst values; pre-screen the initial weights and thresholds of the BP neural network using the improved sparrow search algorithm; Step 3: Using the weight threshold obtained in Step 2 as the initial value of the BP network, introduce the Dropout algorithm to randomly discard some neurons in each iteration, calculate the network error and adjust the weights; Step 4: Adaptively adjust the learning rate using the ADAM algorithm, fine-tune the gradient of the weight thresholds, and update the formula as follows: ； In the formula: , These are the first-order moment estimates before and after the iteration, respectively. The parameter for the exponentially weighted average; The gradient represents the weight w or the threshold θ; ； In the formula: , These are the second-order moment estimates before and after the iteration, respectively. The parameter for the exponentially weighted average; The squared gradient represents the weight w or the threshold θ; ； ； In the formula: , These are the adjusted weights and thresholds; , , where are the weights and thresholds to be trained; The learning rate; It is a constant; Step 5: Repeat steps 3 and 4 until the network converges to obtain the six-dimensional force sensor decoupling model.

2. The decoupling method based on a fiber Bragg grating six-dimensional force sensor according to claim 1, characterized in that, In step two, the formula for cubic chaos mapping is: ； Where: n is the number of mappings. , This is the value of the nth mapping.

3. The decoupling method based on a fiber Bragg grating six-dimensional force sensor according to claim 1, characterized in that, In step two, the sparrow search algorithm includes: (a) Discoverer location is updated using adaptive weights: The discoverer's updated location is: ； Where t represents the current iteration number, j=(1,2.…,d), and X represents the position information of the first sparrow in dimension j in the t-th generation; It is a random number that follows a uniform distribution; Indicates the maximum number of iterations; Indicates the warning value; This represents the safety threshold; Q is a random number that follows a normal distribution in the range [0,1]; L = 1*d, and each element in L is 1; when At that time, the environment was safe, and the finder continued to forage; when When the environment is dangerous, the early warning birds will start chirping to send a danger signal to other sparrows, and the sparrow population will move to a safe area. (b) Follower positions are updated using a variable spiral strategy: A variable spiral position update strategy is introduced to balance the global and local search of the algorithm; the formula for the variable spiral position update strategy is as follows: ； in, This represents the worst-case position information of the discoverer in the j-th dimension during the t-th iteration. This represents the information that the discoverer is in the optimal position in dimension j during the (t+1)th iteration; A is a 1*d single-row multidimensional vector, and its internal elements are randomly selected to be 1 or -1. ;when When the current follower is hungry, its fitness value is poor, and it needs to leave its current location to forage for food elsewhere; when When this value is 0, it indicates that the followers at the current position have a good fitness value, which can be determined by the parameter. The search continues within the defined search space, and z changes with the number of iterations. The size and amplitude of the spiral are dynamically adjusted according to the cosine function; k represents the coefficient of variation, k=5; L represents a uniformly distributed random number in the range [-1,1]. (c) Update the location of the reconnaissance and early warning personnel using the following formula: ； in, This represents the globally optimal location information; The parameters controlling the step size follow a normal distribution; A uniform random number within a certain range is used to control the sparrow's movement direction; This is the current fitness value of an individual sparrow. and These represent the local optimum and worst fitness of the current population, respectively. It is a very small constant used to prevent the denominator from being zero; when When this occurs, it indicates that the sparrow's foraging area is in a poor position and is easily attacked; when This indicates that some sparrows have sensed danger and need to move closer to their companions to reduce the risk of being caught.

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