Magnetofluid refractive index estimation method based on neural network space mapping

Abstract

The invention belongs to the technical field of optical fiber sensing, and relates to a magnetofluid refractive index estimation method based on neural network space mapping. The method aims at obtaining a high-precision magnetofluid refractive index estimation model, a fine model is established according to characteristic data of the change of the magnetofluid refractive index in a magnetic field and a temperature field and the data, and meanwhile, a coarse model is established by a Langevin function; and establishing an average error minimization optimization model among the magnetic field, the temperature field and the refractive index through a neural network space mapping technology, and searching an optimization weight by adopting a typical particle swarm algorithm so as to obtain an accurate magnetofluid refractive index estimation expression. The method provided by the invention has the advantages of high flexibility, high accuracy and easiness in implementation, so that the estimation method disclosed by the invention plays an important role in promoting research in fields related to magnetofluid and meeting application requirements.

Description

Technical Field

[0001] This invention belongs to the field of fiber optic sensing technology and relates to a method for estimating the refractive index of magnetohydrodynamic fluid based on neural network spatial mapping. Background Technology

[0002] Magnetofluids are innovative nanocomposite functional materials that possess both the magnetism of solid magnetic materials and the fluidity of liquid substances. Since their discovery, researchers have discovered many unique optical properties of magnetofluids, including birefringence, the Faraday effect, and tunable refractive index. Among these, the tunable refractive index of magnetofluids has facilitated the development of many novel photonic devices, including fiber optic modulators, magnetic field sensors, and fiber optic filters. In these applications, accurate estimation of the refractive index of magnetofluids is crucial, directly impacting the performance and efficiency of fiber optic equipment.

[0003] Traditional methods for estimating the refractive index of magnetohydrodynamics typically rely on a simple Langevin function fitting approach. This technique requires establishing a refractive index testing environment, acquiring refractive index data under different magnetic field strengths and temperatures, preprocessing the data, and then fitting it with the Langevin function to derive an expression for estimating the refractive index of the magnetohydrodynamics. However, the Langevin function uses a simple hyperbolic cosine function to describe the nonlinear relationship, which fails to adequately capture the complex relationships between the data, thus limiting the estimation accuracy.

[0004] Neural network spatial mapping technology possesses powerful nonlinear fitting, generalization, and adaptive capabilities, and has been successfully applied to nonlinear device modeling, yield estimation, and antenna gain estimation. It is reasonable to infer that using neural network spatial mapping technology for refractive index estimation will yield beneficial results, but related research has not yet been reported.

[0005] Therefore, this invention proposes a magnetohydrodynamic refractive index estimation method based on neural network spatial mapping. This method aims to obtain a high-precision magnetohydrodynamic refractive index estimation model. It is based on the characteristic data of the magnetohydrodynamic refractive index variation under magnetic and temperature fields, and a fine model is established based on this data. At the same time, a coarse model is established using the Langevin function. The average error minimization model between the magnetic field, temperature field and refractive index is established through neural network spatial mapping technology. A typical particle swarm optimization algorithm is used to find the optimal weights, thereby obtaining an accurate magnetohydrodynamic refractive index estimation expression.

[0006] The method proposed in this invention has the advantages of high flexibility, high accuracy and ease of implementation, and will play an important role in promoting research in the field of magnetohydrodynamics and meeting application needs. Summary of the Invention

[0007] The problem to be solved by this invention is to propose a magnetohydrodynamic refractive index estimation method based on neural network spatial mapping, which achieves high-precision estimation of magnetohydrodynamic refractive index with less training data under the combined effect of magnetic field and temperature field.

[0008] A method for estimating the refractive index of magnetohydrodynamic fluids based on neural network spatial mapping includes the following steps:

[0009] Step 1: Based on the principle of refractive index change of magnetofluids under magnetic and temperature fields, the refractive index of the magnetofluid is selected as the estimation object to accurately construct the refractive index expression n = f(H, T, H) based on physical properties. cn α) is the estimation target, where n represents the refractive index, f represents the functional relationship, H represents the magnetic field strength, T represents the temperature, and H cn α represents the critical magnetic field strength, and α represents the fitting parameter.

[0010] Step 2: Using measured or simulated data on the refractive index variation with magnetic field and temperature as a fine model, represent {([H]} in the form of data pairs. k T k ], n k , k∈D)}, where the index number k belongs to the index set D, H of the data. k T k n k These represent the data for the magnetic field, temperature, and refractive index corresponding to the k-th index number;

[0011] Step 3: Establish a coarse model based on the Langevin function, considering that the Langevin function has different parameters H under different temperature conditions. cn Given that α and β are proportional to temperature, we introduce a function H with respect to temperature. cn (T) and α(T), thus modifying the traditional Langevin formula to:

[0012]

[0013] Where, n s n represents the saturation value of the refractive index under high magnetic field strength, and n0 represents the initial refractive index when there is no magnetic field.

[0014] Step 4: Define the mapping function F using a multilayer perceptron. sm Based on the characteristics of the coarse model, a parallel multilayer perceptron structure is constructed, with H and T as inputs, and H′, T′, and H′ as inputs. cn With α′ as the output, each multilayer perceptron independently learns different features of the input, forming different mapping relationships, and corresponding to different mapping functions: H′=F 1 sm (H, T, ω)T′=F 2sm (H, T, ω), H′ cn =F 3 sm (T, ω), α′=F 4 sm (T, ω), where ω is the weight vector of the neural network;

[0015] Step 5: Construct a solution model for the refractive index of the magnetohydrodynamic fluid: n′=f(H′,T′,H′) cn , α′), specifically represented as: Where n′ represents the output refractive index variable;

[0016] Step 6: Based on the relationship between the output of the solved model and the detailed model, establish a model that minimizes the average error: Where, ω * For optimal weights, N represents the total number of data pairs in the detailed model;

[0017] Step 7: Select a typical particle swarm optimization algorithm to solve for the optimal weight ω * The particle swarm size, velocity, and optimization radius are initialized, and iterative optimization is performed. The maximum number of iterations is used as the termination condition to obtain the final optimization weight ω. * ;

[0018] Step 8: Substituting the optimal weights into the solution model for magnetohydrodynamic refractive index estimation, we obtain the expression for magnetohydrodynamic refractive index estimation: n = f(F 1 sm (H, T, ω) * ), F 2 sm (H, T, ω) * ), F 3 sm (T, ω) * ), F 4 sm (T, ω) * )). Attached Figure Description

[0019] Figure 1 This is a flowchart of the present invention.

[0020] Figure 2 A diagram of a parallel multilayer perceptron neural network.

[0021] Figure 3 Comparison chart of magnetohydrodynamic refractive index estimation models Detailed Implementation

[0022] The main purpose of this invention is to propose a method for estimating the refractive index of magnetohydrodynamics based on neural network spatial mapping. This method combines neural network spatial mapping technology with swarm intelligence optimization algorithm, and the obtained magnetohydrodynamic refractive index estimation model has high applicability and accuracy.

[0023] First, this invention combines the principle of refractive index change of magnetofluids under magnetic and temperature fields, selecting the refractive index of magnetofluids as the estimation object to accurately construct a refractive index expression n = f(H, T, H) based on physical properties. cn α) is the estimation target. Where n represents the refractive index, f represents the functional relationship, H represents the magnetic field strength, T represents the temperature, and H0 represents the magnetic field strength. cn α represents the critical magnetic field strength, and α represents the fitting parameter.

[0024] This invention uses measured data or simulation data as a detailed model, and represents {([H] in the form of data pairs}. k T k ], n k , k∈D)}, where D is the index set of the data.

[0025] This invention establishes a coarse model based on the Langevin function, and considers that the Langevin function has different parameters H under different temperature conditions. cn Given that these parameters, α and β, are proportional to temperature, we introduce a function H of these two parameters with respect to temperature. cn (T) and α(T) modify the traditional Langevin formula as follows:

[0026]

[0027] This invention defines the mapping function F based on multilayer sensing. sm Based on the characteristics of the coarse model, a parallel structure of two multilayer perceptrons is adopted, consisting of a primary mapping structure and a secondary mapping structure from left to right. For example... Figure 2 As shown, the parallel multilayer perceptron in this example has three layers, from bottom to top: the input layer, the hidden layer, and the output layer. The hidden layer on the left contains four neurons, and the hidden layer on the right contains three neurons. The left layer takes H and T from the fine model as inputs, and after mapping, obtains H′ and T′. The right layer takes T from the fine model as input, and after mapping, obtains H′. cn And α′, in this example, the sigmoid function is used as the activation function, and the mapping relationship between the input and output can be expressed as:

[0028]

[0029] Among them, ω = [ω1, ω2, ω3,...,ω 36 [ represents unknown weights].

[0030] Secondly, a solution model for the refractive index of a magnetohydrodynamic fluid is constructed. k =f(H′,T′,H′) cn , α′), where H′=F 1 sm (H, T, ω), T′=F 2 sm (H, T, ω), H′ cn =F 3 sm (T, ω), α′=F 4 sm (T, ω).

[0031] Based on the relationship between the output of the solution model and the detailed model, a model for minimizing the average error is established: Where, ω * For optimal weights, N represents the total number of data pairs in the detailed model.

[0032] To find the optimal weights, the weights in the network are adjusted using a typical particle swarm optimization algorithm to solve for the optimal weights ω. * Initialize the particle swarm size, velocity, and optimization radius, perform iterative optimization, and use the maximum number of iterations as the optimization termination condition to obtain the final optimization weight ω. * .

[0033] Substituting the optimal weights into the solution model for magnetohydrodynamic refractive index estimation, we obtain the expression for magnetohydrodynamic refractive index estimation:

[0034] n = f(F) 1 sm (H, T, ω) * ), F 2 sm (H, T, ω) * ), F 3 sm (T,ω* ) F 4 sm (T, ω) * At this point, the magnetohydrodynamic refractive index model has been completed.

[0035] The refractive index estimation method for magnetohydrodynamics based on neural network spatial mapping proposed in this invention has high accuracy, which is illustrated below with examples. For water-based Fe3O4 with a concentration of 0.85 emu / g, the refractive index estimation method of this invention is applied to obtain the optimal weight ω. * The specific values ​​are shown in Table 1. Finally, the refractive index estimation results for this example are as follows: Figure 3As shown: From top to bottom, the estimated refractive indices of three models at 281K, 288K, 297.3K, 313K, and 333K are displayed. The method proposed in this invention improves the accuracy of the estimated refractive index by 77.6% at 281K, 76.7% at 288K, 88.1% at 297.3K, 84.9% at 313K, and 97.0% at 333K compared to the coarse model. Therefore, the expression obtained by the method in this example can describe the refractive index variation very accurately.

[0036] Weight

[0037] <![CDATA[ω1]]> -1.0582 <![CDATA[ω 13 ]]> .0.0278 <![CDATA[ω 25 ]]> -1.3453 <![CDATA[ω2]]> -2.7049 <![CDATA[ω 14 ]]> 0.0197 <![CDATA[ω 26 ]]> -0.8374 <![CDATA[ω3]]> -1.7275 <![CDATA[ω 15 ]]> 2.6245 <![CDATA[ω 27 ]]> .1.2211 <![CDATA[ω4]]> 2.6537 <![CDATA[ω 16 ]]> -1.0148 <![CDATA[ω 28 ]]> -1.1268 <![CDATA[ω5]]> -0.6163 <![CDATA[ω 17 ]]> -2.7038 <![CDATA[ω 29 ]]> 1.3707 <![CDATA[ω6]]> 0.5447 <![CDATA[ω 18 ]]> 0.0828 <![CDATA[ω 30 ]]> 0.0734 <![CDATA[ω7]]> 1.4433 <![CDATA[ω 19 ]]> -1.4146 <![CDATA[ω 31 ]]> 2.5051 <![CDATA[ω8]]> -1.6287 <![CDATA[ω 20 ]]> -1.8678 <![CDATA[ω 32 ]]> -2.0382 <![CDATA[ω9]]> 1.426 <![CDATA[ω 21 ]]> -1.6759 <![CDATA[ω 33 ]]> -0.8214 <![CDATA[ω 10 ]]> .0.5810 <![CDATA[ω 22 ]]> 0.8642 <![CDATA[ω 34 ]]> 0.9931 <![CDATA[ω 11 ]]> 0.6567 <![CDATA[ω 23 ]]> 1.4541 <![CDATA[ω 35 ]]> 0.3299 <![CDATA[ω 12 ]]> 0.6896 <![CDATA[ω 24 ]]> 0.7693 <![CDATA[ω 36 ]]> -1.3400

[0038] Examples show that the refractive index estimation method for magnetofluids based on neural network spatial mapping proposed in this invention can achieve accurate calculation of the refractive index of magnetofluids. Therefore, the estimation method proposed in this invention has great practical significance in both practical applications and theoretical research.

Claims

1. A method for estimating the refractive index of magnetohydrodynamic fluids based on neural network spatial mapping, comprising the following steps: Step 1: Based on the principle of refractive index change of magnetofluids under magnetic and temperature fields, the refractive index of the magnetofluid is selected as the estimation object to accurately construct the refractive index expression n = f(H, T, H) based on physical properties. cn Let α be the target to be estimated, where n represents the refractive index, f represents the functional relationship, H represents the magnetic field strength, and T represents the temperature. cn α represents the critical magnetic field strength, and α represents the fitting parameter. Step 2: Using measured or simulated data on the refractive index variation with magnetic field and temperature as a fine model, represent {([H]} in the form of data pairs. k T k ], n k , k∈D)}, where the index number k belongs to the index set D, H of the data. k T k n k These represent the data for the magnetic field, temperature, and refractive index corresponding to the k-th index number; Step 3: Establish a coarse model based on the Langevin function, considering that the Langevin function has different parameters H under different temperature conditions. cn Given that α and β are proportional to temperature, we introduce a function H with respect to temperature. cn (T) and α(T), thus modifying the traditional Langevin formula to: Where, n s n represents the saturation value of the refractive index under high magnetic field strength, and n0 represents the initial refractive index when there is no magnetic field. Step 4: Define the mapping function F using a multilayer perceptron. sm Based on the characteristics of the coarse model, a parallel multilayer perceptron structure is constructed, with H and T as inputs, and H′, T′, and H′ as inputs. cn With α′ as the output, each multilayer perceptron independently learns different features of the input, forming different mapping relationships, and corresponding to different mapping functions: H′=F 1 sm (H, T, ω)T′=F 2 sm (H, T, ω), H′ cn =F 3 sm (T, ω), α′=F 4 sm (T, ω), where ω is the weight vector of the neural network; Step 5: Construct a solution model for the refractive index of the magnetohydrodynamic fluid: n′=f(H′,T′,H′) cn , α′), specifically represented as: Where n′ represents the output refractive index variable; Step 6: Based on the relationship between the output of the solved model and the detailed model, establish a model that minimizes the average error: Where, ω * For optimal weights, N represents the total number of data pairs in the detailed model; Step 7: Select a typical particle swarm optimization algorithm to solve for the optimal weight ω * The particle swarm size, velocity, and optimization radius are initialized, and iterative optimization is performed. The maximum number of iterations is used as the termination condition to obtain the final optimization weight ω. * ; Step 8: Substituting the optimal weights into the solution model for magnetohydrodynamic refractive index estimation, we obtain the expression for magnetohydrodynamic refractive index estimation: n = f(F 1 sm (H, T, ω) * ), F 2 sm (H, T, ω) * ), F 3 sm (T,ω * ), F 4 sm (T, ω) * )).

2. The magnetohydrodynamic refractive index estimation method based on neural network spatial mapping according to claim 1, characterized in that, In step 4, the mapping function F is defined using a multilayer perceptron. sm Based on the characteristics of the coarse model, the specific operation of constructing the parallel multilayer perceptron structure can be described as follows: The mapping structure is set as two parallel multilayer perceptron structures, divided into a primary mapping structure and a secondary mapping structure from left to right, and an input layer, a hidden layer, and an output layer from bottom to top. The left side uses H and T from the fine model as inputs, and obtains H′ and T′ through mapping; the right side uses T from the fine model as input, and obtains H′ through mapping. cn The mapping relationship between the coarse model and the fine model, α′ and α′, can be expressed as: The mapping function obtained by the main mapping structure for H′ is F. 1 sm The mapping function F of T′ is obtained through the master mapping structure. 2 sm H′ is obtained through the sub-mapping structure. cn The mapping function is F 3 sm The mapping function F obtained by the sub-mapping structure for α′ is 4 sm σ represents the activation function of the hidden layer neurons, n is the number of hidden layer neurons in the primary mapping structure, and k is the number of hidden layer neurons in the secondary mapping structure. The weights between the input layer and the hidden layer. The weights between the input layer and the hidden layer. This is the bias value.

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