CN117782158A - Fiber optic gyroscope temperature drift compensation method based on improved GWO optimized SVM - Google Patents
Fiber optic gyroscope temperature drift compensation method based on improved GWO optimized SVM Download PDFInfo
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Abstract
The invention provides an improved GWO-based fiber optic gyroscope temperature drift compensation method for optimizing an SVM (support vector machine). The method models fiber optic gyroscope temperature drift by utilizing a support vector machine, optimizes nuclear parameters and penalty factors of the support vector machine by utilizing an improved gray wolf optimization algorithm, establishes an improved GWO-based SVM prediction model, trains the SVM prediction model by utilizing training set samples of fiber optic gyroscope output data to obtain an SVM prediction model with optimal nuclear parameters and penalty factors, and finally leads sample characteristics of a test set into the obtained SVM prediction model to obtain a data prediction value for temperature drift compensation. According to the method, a glowing-disturbance gray-wolf optimization algorithm is utilized to carry out iterative optimization on the nuclear parameters and the penalty factors of the support vector machine, balance between local optimization and global search is achieved, and good performance is achieved in terms of solving precision and convergence speed.
Description
Technical Field
The invention relates to the technical field of fiber-optic gyroscopes, in particular to a fiber-optic gyroscope temperature drift compensation method based on an improved GWO optimized support vector machine.
Background
The fiber optic gyroscope is used as a novel angle measuring device, is based on the optical Sagnac principle, has the advantages of high precision, compact structure, light weight, quick starting, wide dynamic range, impact resistance, high precision and the like compared with the traditional mechanical gyroscope, has no locking effect, and can accurately measure smaller angular velocity. The environmental temperature is an important factor affecting the precision characteristic of the fiber optic gyroscope, because the change of the environmental temperature affects the physical characteristics of components such as a fiber optic ring, an optical integrated device and the like of the fiber optic gyroscope, and the generated thermally-induced non-reciprocal phase delay can cause the fiber optic gyroscope to generate a non-negligible temperature drift error, thereby generating error drift on the output of the fiber optic gyroscope. For example, in the case of an optical fiber gyro having an output accuracy of ±0.01 (°)/h, if the temperature of the optical fiber ring changes by 10 ℃, the optical fiber gyro outputs a temperature drift error of 0.15 (°)/h. Therefore, it is necessary to suppress the gyro temperature drift error.
To suppress gyro temperature drift errors, many researchers have done a lot of work, mainly including hardware design and software modeling compensation. Compared with a temperature error suppression method of hardware design, the software modeling compensation method has the advantages of better flexibility, low cost and the like, and the effect is ideal. The common temperature compensation algorithm at present comprises an artificial neural network algorithm, a polynomial algorithm and the like. The artificial neural network algorithm has large calculated amount and is unfavorable for engineering application. The polynomial algorithm has simple structure and easy engineering realization, but has weak nonlinear compensation capability and poor compensation accuracy. The Support Vector Machine (SVM) has better generalization capability, can process more complex data, and has less overfitting risk. Meanwhile, the optimal values of the support vector machine are different for different data sets, and the parameters of the support vector machine need to be optimized.
Disclosure of Invention
In view of the above, the present invention provides a fiber optic gyroscope temperature drift compensation method based on an improved GWO optimized support vector machine.
The technical scheme of the invention is as follows: an optical fiber gyroscope temperature drift compensation method based on an improved GWO optimized support vector machine comprises the following steps:
s1, obtaining an output signal of an optical fiber gyro, and dividing the output signal of the optical fiber gyro into a training set and a testing set;
s2, introducing firefly disturbance into a gray wolf optimization algorithm (GWO), performing iterative optimization on the nuclear parameters and penalty factors of the support vector machine, and establishing a support vector machine prediction model based on an improvement GWO;
s3, training the support vector machine prediction model based on the improvement GWO in the step S2 by using the training set sample to obtain an optimal kernel parameter and penalty factor support vector machine prediction model;
s4, the test set sample obtained in the step S1 is guided into the improved GWO support vector machine prediction model trained in the step S3 to be predicted, and temperature drift compensation is performed.
Further, in step S1, the obtaining the output signal of the fiber optic gyroscope includes the following steps:
s11, placing the optical fiber gyroscope attached with the temperature sensor in an incubator to perform a temperature test, and obtaining temperature test data by changing the temperature environment of the optical fiber gyroscope, wherein the temperature test data comprise a temperature value, a temperature change rate, a temperature gradient, optical fiber gyroscope output data under the temperature value and corresponding time point data;
s12, constructing the following fiber-optic gyroscope temperature drift compensation model based on the temperature value and the time change rate of the temperature in the incubator:
wherein Δt is the temperature change; dT/dT is the rate of change of temperature;the temperature gradient is adopted, and the rest are coefficient parameters;
s13, acquiring real-time temperature data of the fiber optic gyroscope in actual working, and taking the real-time temperature data as input quantity of a temperature drift compensation model of the fiber optic gyroscope to acquire a required fiber optic gyroscope output data set; the real-time temperature data includes a temperature value and a rate of change of temperature in the operating environment over time.
Further, in step S1, the fiber-optic gyroscope output data set obtained in step S13 is represented by 8: the proportion of 2 is divided into a training set and a testing set, the training set is used as a learning sample of the model to carry out deep learning, and the testing set is used as a checking sample to verify the evaluation accuracy of the model.
Further, in order to improve the accuracy of training and prediction, in step S1, normalization processing is performed on the obtained output data of the fiber-optic gyroscope, and the calculation formula is as follows:
wherein x' is a normalized value, x is the original data, x min And x max Is the maximum and minimum of the sample data.
Further, in step 2, the Support Vector Machine (SVM) is a classification algorithm, which is based on the principle that two different classes of samples are divided by a hyperplane, and the calculation formula is as follows:
wherein ω is a weight value,b is the offset, which is the expression of the mapping function;
the objective function and constraint conditions are as follows:
s.t. 1-y i (ωx i +b)≤ε i
ε i ≥0 i＝1,2,…,n
wherein ε i For the relaxation factor, C is a penalty parameter in the support vector machine, s.t. represents a constraint condition;
further, in step S2, modeling the temperature drift of the fiber optic gyroscope by using a support vector machine, where the model is:
wherein sv is a support vector, a i Langerage operator, K (x i ,y i ) The method is as a kernel function:
the kernel function expression is:
wherein σ is a kernel parameter of the support vector machine.
Further, in step S2, a firefly disturbance is introduced into a wolf algorithm (GWO), and the kernel parameter σ and the penalty factor C of the support vector machine are iteratively optimized, which specifically includes the following steps:
s21, initializing parameters of a support vector machine model;
s22, initializing a sirius population by using a cat mapping chaotic strategy;
s23, calculating the fitness value of each gray wolf individual, and finding out the individual with the optimal fitness;
s24, carrying out position update by using a wolf optimization algorithm to obtain the wolf with the optimal position;
s25, disturbing the position of the wolf by adopting an attraction following strategy in a firefly optimization algorithm, comparing the wolf at the optimal position with the disturbed wolf, and determining the optimal position;
s26, judging whether the maximum iteration times are reached;
s27, deriving the optimal gray wolf position to obtain the optimal kernel parameters and penalty factors of the support vector machine.
In step S22, the expression of the cat mapping chaos is as follows:
wherein, (x) n ,y n ) And (x) n+1 ,y n+1 ) Respectively updating the positions of the initial population after two adjacent iterations; a, b, c, d are mapping coefficients and satisfy the relationship:
the social grades of the sirius population in the step S22 can be divided into alpha wolves, beta wolves, delta wolves and omega wolves, and alpha, beta and delta in the sirius optimization algorithm respectively represent a historical optimal solution, a superior solution and a suboptimal solution, and omega represents the rest individuals; in the process of algorithm evolution, alpha, beta and delta are responsible for locating the position of the prey, guiding other individuals to finish actions such as approaching, surrounding and attacking, and finally achieving the purpose of prey.
During hunting, the wolf surrounds the prey and its mathematical model is:
D＝|C·X P (t)-X(t)|
X(t+1)＝X P (t)-A·D
wherein t is the current iteration number, A and C are coefficients, X P And X is the position of the prey and the gray wolf, respectively. The calculation method of A and C is as follows:
A＝2a·r 1 -a
C＝2·r 2
wherein r is 1 、r 2 Is [0,1]]Random values in (a) are provided. a is a convergence factor, which is reduced from 2 in an iterative processAs little as 0.
The wolf recognizes the location of the prey and hunting, usually commanded by alpha wolves, beta wolves and delta wolves are also occasionally involved in hunting. The mathematical model of the individual gray wolves tracking the position of the prey is as follows:
D α ＝|C 1 ·X α -X|
D β ＝|C 2 ·X β -X|
D δ ＝|C 3 ·X δ -X|
wherein D is α ，D β And D δ Respectively representing the distances among alpha wolves, beta wolves and delta wolves and other individuals; x is X α 、X β And X δ Respectively representing the current positions of alpha wolves, beta wolves and delta wolves; c (C) 1 、C 2 And C 3 Is a random number, X is the current position of the individual wolf, and the position updating formula of the wolf is as follows:
X 1 ＝X α -A 1 ·(D α )
X 2 ＝X β -A 2 ·(D β )
X 3 ＝X δ -A 3 ·(D δ )
further, the principle of the firefly optimization algorithm is that, for a D-dimensional search space, assuming that the total number of fireflies in the population is N, the i-th (i=1, 2, …, N) -th position of the fireflies is expressed as:
X i ＝(x i1 ,x i2 ,…,x iD )；
the attractive force of fireflies is proportional to their luminous intensity and inversely proportional to the distance between fireflies. The formula of the attractive force of fireflies is as follows:
wherein beta is 0 Is the maximum attractive force, gamma is the light absorption coefficient, r i,j Is the Euclidean distance between firefly i and j;
in step S25, the firefly position is updated as follows:
wherein alpha epsilon [0,1] is a step factor; rand is a random factor, subject to normal distribution over [0,1 ].
Compared with the prior art, the invention has the following beneficial effects:
(1) The invention discloses an improved GWO optimized support vector machine-based fiber optic gyroscope temperature drift compensation method, which is used for generating an initial position of an individual by utilizing a cat mapping chaotic strategy, has better traversing uniformity and faster iteration speed, and has uniform chaotic sequence distribution generated between [0,1 ];
(2) The invention discloses an improved GWO-based fiber optic gyroscope temperature drift compensation method for optimizing a support vector machine, which is used for carrying out iterative optimization on a nuclear parameter and a penalty factor of the support vector machine by using a glowworm disturbance gray-wolf optimization algorithm, so that balance between local optimization and global search can be realized, and the method has good performance in terms of solving precision and convergence speed.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of a predictive model for optimizing a support vector machine based on improvement GWO.
Detailed Description
The invention will be further illustrated with reference to specific examples. It should be understood that the examples are illustrative of the present invention and are not intended to limit the scope of the present invention. Further, it is understood that various changes and modifications may be made by those skilled in the art after reading the teachings of the present invention, and such equivalents are intended to fall within the scope of the claims appended hereto.
As shown in fig. 1, the invention provides a fiber optic gyroscope temperature drift compensation method based on an improved GWO optimized SVM, which specifically comprises the following steps:
s1, obtaining an output signal of an optical fiber gyro, and dividing the output signal of the optical fiber gyro into a training set and a testing set;
s2, introducing firefly disturbance into a gray wolf optimization algorithm, performing iterative optimization on the nuclear parameters and penalty factors of the support vector machine, and establishing a support vector machine prediction model based on improvement GWO;
s3, training the support vector machine prediction model based on the improvement GWO in the step S2 by utilizing the training set sample obtained in the step S1 to obtain a support vector machine prediction model of the optimal nuclear parameter nuclear penalty factor;
s4, introducing the sample characteristics of the test set obtained in the step S1 into the improved GWO support vector machine prediction model trained in the step S3 to predict, and performing temperature drift compensation.
In step S1, the obtaining the output signal of the fiber optic gyroscope includes the following steps:
s11, placing the optical fiber gyroscope attached with the temperature sensor in an incubator to perform a temperature test, and obtaining temperature test data by changing the temperature environment of the optical fiber gyroscope, wherein the temperature test data comprise a temperature value, a temperature change rate, a temperature gradient, optical fiber gyroscope output data under the temperature value and corresponding time point data;
s12, constructing the following fiber-optic gyroscope temperature drift compensation model based on the temperature value and the time change rate of the temperature in the incubator:
wherein Δt is the temperature change; dT/dT is the rate of change of temperature;the temperature gradient is adopted, and the rest are coefficient parameters;
s13, acquiring real-time temperature data of the fiber optic gyroscope in actual working, wherein the real-time temperature data comprises the temperature value and the time-dependent change rate of the temperature in a working environment, and taking the real-time temperature data as the input quantity of the fiber optic gyroscope temperature drift compensation model to obtain a required fiber optic gyroscope output data set;
in this embodiment, the output data set of the fiber-optic gyroscope obtained in step S13 is divided into a training set and a test set according to a ratio of 8:2, the training set is used as a learning sample of the model to perform deep learning, and the test set is used as a test sample to verify the evaluation accuracy of the model.
In this embodiment, the obtained output data of the fiber optic gyroscope is normalized, and the calculation formula is as follows:
wherein x' is a normalized value, x is the original data, x min And x max Is the maximum and minimum of the sample data.
In step S2, modeling the temperature drift of the fiber optic gyroscope by using a support vector machine, where the model is:
wherein sv is a support vector, a i Langerage operator, K (x i ,y i ) The method is as a kernel function:
the kernel function expression is:
wherein σ is a kernel parameter of the support vector machine.
As shown in fig. 2, in step S2, firefly disturbance is introduced in GWO, and the kernel parameters and penalty factors of the support vector machine are iteratively optimized, including the following steps:
s21, initializing parameters of a support vector machine model;
s22, initializing a sirius population by using a cat mapping chaotic strategy;
s23, calculating the fitness value of each gray wolf individual, and finding out the individual with the optimal fitness;
s24, carrying out position update by using a wolf optimization algorithm to obtain the wolf with the optimal position;
s25, disturbing the position of the wolf by adopting an attraction following strategy in a firefly optimization algorithm, comparing the wolf at the optimal position with the disturbed wolf, and determining the optimal position;
s26, judging whether the maximum iteration times are reached;
s27, deriving the optimal gray wolf position to obtain the optimal kernel parameters and penalty factors of the support vector machine.
The firefly position in the step S25 is updated as follows:
wherein alpha epsilon [0,1] is a step factor; rand is a random factor, subject to normal distribution over [0,1 ].
The foregoing description is only of the preferred embodiments of the present invention and is not intended to limit the scope of the invention, and all equivalent structures or equivalent processes using the description and drawings are included in the scope of the invention.
Claims (7)
1. The optical fiber gyro temperature drift compensation method for optimizing the SVM based on the improvement GWO is characterized by comprising the following steps of:
s1, obtaining an output signal of an optical fiber gyro, and dividing the output signal of the optical fiber gyro into a training set and a testing set;
s2, introducing firefly disturbance into a gray wolf optimization algorithm, performing iterative optimization on the nuclear parameters and penalty factors of the support vector machine, and establishing a support vector machine prediction model based on improvement GWO;
s3, training the support vector machine prediction model based on the improvement GWO in the step S2 by utilizing the training set sample obtained in the step S1 to obtain a support vector machine prediction model of the optimal nuclear parameter nuclear penalty factor;
s4, the test set sample obtained in the step S1 is guided into the improved GWO support vector machine prediction model trained in the step S3 to be predicted, and temperature drift compensation is performed.
2. The method for compensating for temperature drift of a fiber optic gyroscope based on the improved GWO optimized SVM of claim 1, wherein in step S1, the obtaining of the output signal of the fiber optic gyroscope comprises the following steps:
s11, placing the optical fiber gyroscope attached with the temperature sensor in an incubator to perform a temperature test, and obtaining temperature test data by changing the temperature environment of the optical fiber gyroscope, wherein the temperature test data comprise a temperature value, a temperature change rate, a temperature gradient, optical fiber gyroscope output data under the temperature value and corresponding time point data;
s12, constructing the following fiber-optic gyroscope temperature drift compensation model based on the temperature value and the time change rate of the temperature in the incubator:
wherein Δt is the temperature change; dT/dT is the rate of change of temperature;the temperature gradient is adopted, and the rest are coefficient parameters;
s13, acquiring real-time temperature data of the fiber optic gyroscope in actual working, wherein the real-time temperature data comprise the temperature value and the time-dependent change rate of the temperature in the working environment, and acquiring an output data set of the fiber optic gyroscope by taking the real-time temperature data as the input quantity of the temperature drift compensation model of the fiber optic gyroscope.
3. The improved GWO optimized Support Vector Machine (SVM) -based fiber-optic gyroscope temperature drift compensation method according to claim 2, wherein in step S1, the fiber-optic gyroscope output dataset obtained in step S13 is divided into a training set and a test set in a ratio of 8:2, the training set is used as a learning sample of a model for deep learning, and the test set is used as a test sample for verifying the evaluation accuracy of the model.
4. The method according to claim 2, wherein in step S1, the obtained output data of the fiber-optic gyroscope is normalized, and the calculation formula is as follows:
wherein x' is a normalized value, x is the original data, x min And x max Is the maximum and minimum of the sample data.
5. The method according to claim 1, wherein in step S2, the fiber-optic gyroscope temperature drift is modeled by using a support vector machine, and the model is:
wherein sv is a support vector, a i Langerage operator, K (x i ,y i ) The method is as a kernel function:
the kernel function expression is:
wherein σ is a kernel parameter of the support vector machine.
6. The method of claim 5, wherein in step S2, firefly disturbance is introduced in GWO, and the kernel parameters and penalty factors of the support vector machine are iteratively optimized, comprising the steps of:
s21, initializing parameters of a support vector machine model;
s22, initializing a sirius population by using a cat mapping chaotic strategy;
s23, calculating the fitness value of each gray wolf individual, and finding out the individual with the optimal fitness;
s24, carrying out position update by using a wolf optimization algorithm to obtain the wolf with the optimal position;
s25, disturbing the position of the wolf by adopting an attraction following strategy in a firefly optimization algorithm, comparing the wolf at the optimal position with the disturbed wolf, and determining the optimal position;
s26, judging whether the maximum iteration times are reached;
s27, deriving the optimal gray wolf position to obtain the optimal kernel parameters and penalty factors of the support vector machine.
7. The method of claim 6, wherein in step S25, the firefly position is updated as:
wherein alpha epsilon [0,1] is a step factor; rand is a random factor, subject to normal distribution over [0,1 ].
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