A neural network-based method for evaluating rheological properties of a magnetorheological fluid

Abstract

This invention provides a neural network-based method for evaluating the rheological properties of magnetorheological fluids, comprising the following steps: Step 1: Obtaining a magnetorheological fluid rheological dataset using experimental equipment, the dataset including input and output parameters; Step 2: Standardizing the magnetorheological fluid rheological dataset using the Z-score standardization method; Step 3: Dividing the collected magnetorheological fluid rheological dataset, establishing and training a BP neural network prediction model, and performing hyperparameter tuning on the BP neural network prediction model; Step 4: Evaluating the rheological properties of the magnetorheological fluid based on the trained BP neural network prediction model, and using evaluation indicators to assess the model and perform performance analysis based on the prediction results. This method addresses the difficulties in predicting the rheological properties of magnetorheological fluids and the poor applicability of parameterized models, enabling reliable performance prediction of magnetorheological fluids under complex environments and high shear conditions.

Description

Technical Field

[0001] This invention belongs to the field of predicting the rheological properties of magnetorheological fluids, and particularly relates to a method for evaluating the rheological properties of magnetorheological fluids based on neural networks. Background Technology

[0002] Magnetorheological fluids (MMRs), as controllable and reversible smart materials, exhibit rheological properties influenced by factors such as the amount of admixture A, temperature, and magnetic field strength. These factors are interconnected and mutually restrictive, making it difficult to establish a multi-condition evaluation method for the rheological properties of MMRs. Traditional evaluation methods are often limited by the amount of data and the parametric model structure under multiple factors, mostly involving the establishment of a parametric model followed by prediction. Since MMRs exhibit different fluid behaviors with and without a magnetic field, and different fluid behaviors correspond to different equation models, it is difficult to directly represent the actual situation of MMRs. Traditional methods suffer from the following drawbacks: poor model adaptability: MMRs exhibit non-Newtonian fluid characteristics under different magnetic fields, temperatures, and shear conditions, and a single parametric model cannot comprehensively and accurately describe their complex rheological behavior under multiple operating conditions; difficulty in modeling multi-factor coupling: significant interactions exist between multiple influencing factors, and traditional models often struggle to effectively capture their nonlinear and high-order coupling relationships; limited prediction accuracy: traditional methods have weak fitting capabilities to experimental data, especially in complex environments or extreme conditions, resulting in large prediction errors and failing to meet the requirements for high-precision engineering predictions. Summary of the Invention

[0003] The purpose of this invention is to provide a method for evaluating the rheological properties of magnetorheological fluids based on neural networks, so as to solve the problem that it is difficult to directly reflect the actual situation of magnetorheological fluids in the prior art.

[0004] To achieve the above objectives, the present invention adopts the following technical solution: A method for evaluating the rheological properties of magnetorheological fluids based on neural networks includes the following steps: Step 1: Obtain the magnetorheological fluid rheological data set according to the experimental equipment. The magnetorheological fluid rheological data set includes input parameters and output parameters; the input parameters include the amount of external dopant A added, temperature, magnetic field strength and shear rate, and the output parameter is shear stress. Step 2: The magnetorheological fluid rheological dataset is transformed into a distribution with a mean of 0 and a standard deviation of 1 using the Z-score normalization method; Step 3: Divide the preprocessed magnetorheological fluid rheological dataset into training set, validation set and test set in a ratio of 7:2:1. The training set has 2170 samples, the validation set has 620 samples and the test set has 310 samples. When dividing the dataset, a stratified sampling method is used for each magnetic field strength data to maintain the balance of the input parameter distribution in each subset. Step 4: Build and train the BP neural network prediction model, and perform hyperparameter tuning on the BP neural network prediction model; The BP neural network prediction model includes an input layer, at least one hidden layer, and an output layer. The BP neural network model is a multi-layer feedforward neural network with the characteristic of backpropagation. It adjusts the weights and biases from the hidden layer to the output layer and from the input layer to the hidden layer in turn, from the output layer to the hidden layer and finally to the input layer. Step 4: Evaluate the rheological properties of magnetorheological fluid based on the trained BP neural network prediction model, and use mean square error, mean absolute error, mean relative error and coefficient of determination as evaluation indicators to analyze and evaluate the performance of the model on the validation set and test set.

[0005] Furthermore, the Z-score standardization calculation formula in step two is as follows: in This represents the mean of the characteristic column. The standard deviation of the characteristic column is represented. For initial data, The data is standardized; the processed data has the characteristics of a mean of 0 and a standard deviation of 1.

[0006] Furthermore, in step three, the BP neural network model is tuned using a grid search method. The hyperparameters include the hidden layer structure, learning rate, activation function, and error threshold.

[0007] Furthermore, the optimal parameter combination for the grid search-based BP neural network model consists of two hidden layers: the first layer has 15 neurons, the second layer has 10 neurons, the learning rate is 0.001, the activation function is set to "tansig", and the error threshold is 10. -7 .

[0008] Furthermore, the stratified sampling method in step three is as follows: the data is stratified according to different magnetic field strength levels to ensure that the data at each magnetic field strength level is reasonably distributed in the training set, validation set, and test set.

[0009] Furthermore, the evaluation indicators in step four are MSE, MAE, MRE, and R. 2 The calculation formula is as follows: in For the true value, For predicted values, It is the average of the true values.

[0010] Furthermore, the calculated coefficient of determination R² for the test set is greater than 0.9995, and the coefficient of determination R² for the validation set is greater than 0.9993.

[0011] The beneficial effects of this invention are as follows: 1. This invention employs a backpropagation (BP) neural network for modeling. Through multi-layer nonlinear activation functions and a backpropagation mechanism, it can autonomously learn the complex mapping relationship between multiple factors (such as the amount of external additives, temperature, magnetic field strength, and shear rate) and shear stress, without relying on prior physical assumptions or simplified model structures. Compared to traditional parametric models (such as the Herschel-Bulkley model), this method exhibits a higher coefficient of determination (R²>0.999) and a lower prediction error (MSE<0.001) on the same dataset, significantly improving prediction accuracy and model adaptability under complex environments and high shear conditions.

[0012] 2. Traditional models often struggle to effectively describe the nonlinear coupling effects between multiple factors. This invention utilizes the hidden layer structure and activation function of a neural network to automatically extract high-order interaction information between features, achieving a comprehensive characterization of the rheological behavior of magnetorheological fluids. This method is not only applicable to single operating conditions but can also perform continuous predictions across temperature and magnetic field strengths, avoiding the shortcomings of traditional methods that require segmented modeling and improving the overall consistency and engineering applicability of the model.

[0013] 3. Through Z-score standardization, grid search hyperparameter tuning, and hierarchical partitioning of training, validation, and test sets, the neural network model constructed in this invention exhibits excellent generalization performance and stability. The model performs consistently on both the validation and test sets, with no significant overfitting observed. Furthermore, this method is relatively flexible in its requirements for data sample size; even with small sample conditions, the results can be further improved through transfer learning or data augmentation, making it suitable for magnetorheological fluid research scenarios where experimental costs are high and data acquisition is difficult. Attached Figure Description

[0014] Figure 1 This is the overall flowchart provided by the present invention; Figure 2 This is a neural network structure diagram provided in an embodiment of the present invention; Figure 3(a) is a graph showing the prediction effect of the validation set obtained by the embodiment of the present invention; Figure 3(b) is a test set prediction effect obtained by an embodiment of the present invention; Figure 3(c) is a graph showing the prediction effect of the total dataset obtained in the embodiment of the present invention; Figure 4(a) is a regression diagram of the training set provided in an embodiment of the present invention; Figure 4(b) is a regression diagram of the validation set provided in an embodiment of the present invention; Figure 4(c) is a regression diagram of the test set provided in an embodiment of the present invention. Detailed Implementation

[0015] To more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be further described in detail below with reference to the embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.

[0016] The application principle of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0017] Example 1: like Figure 1 As shown, this invention provides a method for evaluating the rheological properties of magnetorheological fluids based on neural networks, comprising the following steps: Step 1: Acquire rheological data of magnetorheological fluid The properties of magnetorheological fluids under complex environments were investigated to identify the multiple factors affecting their performance. This information was then used to determine the data needed to establish a predictive model for the rheological properties of magnetorheological fluids under complex environments, and a dataset of magnetorheological fluid rheological data was obtained based on experimental equipment.

[0018] This embodiment uses experimentally obtained rheological data of magnetorheological fluid, totaling 3100 samples. A high-temperature magnetorheological instrument (MCR 302e) was used to measure the rheological properties of the magnetorheological fluid. Experimental data on the shear rate and shear stress of the magnetorheological fluid under different operating conditions were recorded. The following factors were selected as the influence characteristics of the magnetorheological fluid's rheological properties: the addition amount of admixture A (%), temperature (°C), magnetic field strength (mT), and shear rate (1 / s), i.e., the input parameters; shear stress was selected as the dependent variable, i.e., the output parameter.

[0019] Step 2: Preprocessing the magnetorheological fluid rheological data The dataset showed no missing values, but the dimensionality of the features varied considerably. Z-score normalization was used to standardize the magnetorheological fluid rheological data. The specific calculation formula is as follows: in This represents the mean of the characteristic column. The standard deviation of the characteristic column is represented. For initial data, This is the standardized data. The processed data has the characteristics of a mean of 0 and a standard deviation of 1, which can effectively solve the problem of dimensions and preserve the distribution shape of the original data.

[0020] Step 3: Divide the collected magnetorheological fluid rheological data into datasets and establish a BP neural network prediction model.

[0021] (1) The magnetorheological fluid rheological data were divided into training set, validation set and test set in a ratio of 7:2:1, resulting in 2170 training set samples, 620 validation set samples and 310 test set samples.

[0022] (2) The magnetorheological fluid rheological data, after preprocessing, is used as the input parameters of the BP neural network model, and the model is trained using the training set. This is used to initially construct a BP neural network regression model. The BP neural network model is a multi-layered feedforward neural network. Its main characteristic is that the error propagates backward, from the output layer to the hidden layer, and finally to the input layer, adjusting the weights and biases from the hidden layer to the output layer, and from the input layer to the hidden layer; while the signal propagates forward. The input data is propagated and calculated through each layer of the neural network. In each layer, the neurons perform a weighted summation of the input and a nonlinear transformation through the activation function to obtain the output of that layer, which continues to be used as the input of the next layer. This process is repeated forward, eventually yielding the network's predicted output of the input data. The network's predicted output is compared with the actual data. This difference can be quantified using a loss function, with the commonly used loss function being the mean squared error.

[0023] in For the true value, For the output layer The predicted value of each neuron.

[0024] Set the parameter range, then input the dataset into the BP neural network model and use the grid search method to perform hyperparameter tuning to obtain the optimal parameter combination and model prediction evaluation index, as shown in Table 1.

[0025] Table 1 Optimal parameters and performance evaluation of the BP neural network model The grid search was performed 216 times. Only the top ten performing models are listed here. The model structure is shown in Table 1. The optimal parameter combination for the grid search-based BP neural network model is two hidden layers: the first layer has 15 neurons, the second layer has 10 neurons, the learning rate is 0.001, the activation function is set to "tansig", and the error threshold is 10. -7 . Figure 2 The diagram shows the neural network structure under optimal parameter conditions.

[0026] (3) The BP neural network prediction model was trained using the training set. During training, the weights and biases of the BP neural network were first set to small random values. For each sample in the training dataset, forward propagation was performed first to obtain the predicted output, then the loss was calculated, and backpropagation was performed to update the gradients of the weights and biases of each layer. Based on the obtained gradients, an optimization algorithm was used to update the weights and biases to reduce the loss function. By repeating the above process, after multiple iterations, the iteration stopped when the loss function converged to the preset number of training rounds. At this time, the mean square error of the validation set was only 0.000362, which shows that the model performed well and has certain guiding significance for the prediction of the rheological properties of magnetorheological fluids.

[0027] Step 4: Model Evaluation and Result Analysis Based on a trained BP neural network model, the evaluation metrics of the regression model can be used to assess the BP neural network model. We will now use a BP neural network regression model with optimal parameters to predict the target variable, shear stress. Specific evaluation metrics include MSE (mean squared error), MAE (mean absolute error), MRE (mean relative error), and R². 2 (Determination coefficient), the calculation formulas for each indicator are as follows:

[0028] in For the true value, For predicted values, It is the average of the true values.

[0029] As shown in Figures 3(a)-(c), the solid lines represent the actual data values ​​of the magnetorheological fluid under complex environments, and the dashed lines represent the model's predicted values ​​for the magnetorheological fluid data. The fitting effects on both the validation and test sets are good, indicating strong model generalization ability. Figure 3(c) shows the fitting results for all data, also demonstrating the model's good fitting effect. Figures 4(a)-(c) show the regression plots for the training, validation, and test sets. All three categories of data indicate excellent model fitting, with regression R values ​​close to 1, indicating a high linear correlation between predicted and actual values ​​and extremely small prediction errors. Meanwhile, the relevant indices for the test and validation sets obtained from the model operation are shown in Table 2. The model's MSE and MAE are close to 0, and the MRE is also close to 1. Furthermore, the coefficient of determination R for both the test and validation sets is high. 2 The values ​​were 0.9995 and 0.9993 respectively, which also showed that the model had good predictive ability.

[0030] Table 2 Evaluation metrics for the test set and validation set To verify the advantages of this invention, the Herschel-Bulkley model is used to simulate the rheological data of the magnetorheological fluid described above. The Herschel-Bulkley model can be used to describe shear-thinning or shear-thickening fluids with yield stress, and its specific mathematical form is as follows:

[0031] In the formula Indicates stress, This represents the static shear stress of a fluid. The flow index represents the fluid's flow properties. Represents shear strain. This represents the plasticity index of the fluid. The model can correlate the stress and strain of a fluid and can be adapted to different types of non-Newtonian fluids by adjusting the parameters.

[0032] In this invention, a programming language is also used to fit the aforementioned dataset, ensuring that the data partitioning and processing methods are consistent with the BP neural network model to guarantee comparability between the two models. The parameters of the Herschel-Bulkley model are determined by performing least-squares fitting on the model parameters of the experimental data. The fitting objective is to minimize the difference between the stress values ​​calculated by the model and the experimental measurements.

[0033] During the fitting process, a stratified sampling method was adopted for the magnetic field strength to ensure that the data under each magnetic field strength are reasonably distributed in the three subsets. At the same time, based on the physical properties of magnetorheological fluid, certain physical constraints were applied to the model parameters to finally obtain the predictive performance parameters of the model.

[0034] Based on the above dataset, the final prediction results of the Herschel-Bulkley model obtained in this invention are shown in Table 3. Here, piecewise fitting is performed according to temperature to obtain the yield stress, consistency index, and flow coefficient at the corresponding temperature. As shown in Table 3, the model's fitting effect is not ideal for each temperature. The model with the best fitting effect is the one at 70℃, with R0... 2 It is the highest, but still significantly smaller than the R of the BP neural network model. 2 .

[0035] Table 3. Fitting effect of the Herschel-Bulkley model In summary, compared with traditional evaluation methods for the rheological properties of magnetorheological fluids, the BP neural network model has stronger predictive performance, higher data efficiency, and greater adaptability, providing a reliable and efficient solution for engineering practice.

[0036] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for evaluating the rheological properties of magnetorheological fluids based on neural networks, characterized in that, Includes the following steps: Step 1: Obtain the magnetorheological fluid rheological data set according to the experimental equipment. The magnetorheological fluid rheological data set includes input parameters and output parameters; the input parameters include the amount of external dopant A added, temperature, magnetic field strength and shear rate, and the output parameter is shear stress. Step 2: The magnetorheological fluid rheological dataset is transformed into a distribution with a mean of 0 and a standard deviation of 1 using the Z-score normalization method; Step 3: Divide the preprocessed magnetorheological fluid rheological dataset into training set, validation set and test set in a ratio of 7:2:

1. The training set has 2170 samples, the validation set has 620 samples and the test set has 310 samples. When dividing the dataset, a stratified sampling method is used for each magnetic field strength data to maintain the balance of the input parameter distribution in each subset. Step 4: Build and train the BP neural network prediction model, and perform hyperparameter tuning on the BP neural network prediction model; The BP neural network prediction model includes an input layer, at least one hidden layer, and an output layer; Step 4: Evaluate the rheological properties of magnetorheological fluid based on the trained BP neural network prediction model, and use mean square error, mean absolute error, mean relative error and coefficient of determination as evaluation indicators to analyze and evaluate the performance of the model on the validation set and test set.

2. The method for evaluating the rheological properties of magnetorheological fluids based on neural networks according to claim 1, characterized in that, The Z-score standardization calculation formula in step two is as follows: in This represents the mean of the characteristic column. The standard deviation of the characteristic column is represented. For initial data, The data is standardized; the processed data has the characteristics of a mean of 0 and a standard deviation of 1.

3. The method for evaluating the rheological properties of magnetorheological fluids based on neural networks according to claim 1, characterized in that, In step three, the BP neural network model is tuned using a grid search method. The hyperparameters include the hidden layer structure, learning rate, activation function, and error threshold.

4. The method for evaluating the rheological properties of magnetorheological fluids based on neural networks as described in claim 3, characterized in that, The optimal parameter combination for the grid search-based backpropagation neural network model is two hidden layers: the first layer has 15 neurons and the second layer has 10 neurons, with a learning rate of 0.001, an activation function of "tansig", and an error threshold of 10. -7 .

5. The method for evaluating the rheological properties of magnetorheological fluids based on neural networks according to claim 1, characterized in that, The stratified sampling method in step three is as follows: the data is stratified according to different magnetic field strength levels to ensure that the data at each magnetic field strength level are reasonably distributed in the training set, validation set, and test set.

6. The method for evaluating the rheological properties of magnetorheological fluids based on neural networks according to claim 1, characterized in that, The evaluation indicators in step four are MSE, MAE, MRE, and R. 2 The calculation formula is as follows: in For the true value, For predicted values, It is the average of the true values.

7. The method for evaluating the rheological properties of magnetorheological fluids based on neural networks according to claim 6, characterized in that, The calculated coefficient of determination R² for the test set is greater than 0.9995, and the coefficient of determination R² for the validation set is greater than 0.9993.

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