Cobalt ion rejection rate prediction method based on artificial neural network

Abstract

The invention provides a cobalt ion rejection rate prediction method based on an artificial neural network, and the method comprises the steps: building a data set according to experimental data, and dividing the data set into a training set and a test set; establishing an artificial neural network model, wherein the artificial neural network model comprises an input layer, a hidden layer and an output layer; training parameter values are set, model training is carried out on the artificial neural network model according to the training set and the training parameter values, and model optimization parameters of the artificial neural network model are obtained; obtaining a model training evaluation result of the artificial neural network model based on the training set according to the model optimization parameters; performing model test on the model optimization parameters of the artificial neural network model according to the test set to obtain a model test evaluation result; comparing the model training evaluation result with the model test evaluation result to obtain a target neural network model; and predicting the cobalt ion rejection rate according to the target neural network model. The prediction precision of the cobalt ion rejection rate is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of nanofiltration membranes, and particularly to a method for predicting the rejection rate of cobalt ions based on an artificial neural network. Background Art

[0002] Currently, in the field of heavy metal wastewater treatment, nanofiltration (NF) membrane technology is widely used. Especially in the effective treatment of cobalt ions, the nanofiltration membrane has unique selective filtration ability, which can effectively separate cobalt ions in water from other ions and solutes, thus achieving efficient wastewater treatment. This technology utilizes the microscopic structure and surface chemical properties of the membrane, applying pressure to enable water molecules to pass through the membrane, while larger heavy metal ions are blocked, thereby achieving the effect of separation and purification.

[0003] Although nanofiltration (NF) technology has significant effects in treating cobalt ions, it still faces some challenges, especially the problem of concentration polarization. Concentration polarization refers to the phenomenon that solutes accumulate on the membrane surface during the filtration process, forming a high-concentration region. When cobalt ions in the wastewater are retained on the membrane surface, a high-concentration cobalt ion layer will be formed on the membrane surface, resulting in a significantly higher concentration of cobalt ions on the membrane surface than the average concentration in the solution. This concentration gradient increases the resistance of cobalt ions to diffuse towards the membrane surface, thereby reducing the diffusion rate of cobalt ions. Therefore, this leads to a decrease in the retention efficiency of cobalt ions, making the observed rejection rate lower than the inherent rejection rate of the membrane.

[0004] This application aims to apply an artificial neural network model to predict the rejection rate of cobalt ions during the nanofiltration process. By modeling and optimizing the input features that affect the retention of cobalt ions, it studies and solves the problem of inaccurate prediction values of traditional models. After using grid search for hyperparameter optimization, the dataset is retrained, and the trained artificial neural network model is verified on an unseen dataset to evaluate its prediction accuracy and stability.

[0005] The artificial neural network model proposed in this application has the potential to improve the treatment effect of heavy metal wastewater by improving the nanofiltration process, and has robustness and high efficiency in dealing with complex heavy metal wastewater, providing a new direction for optimizing nanofiltration technology. In the future, with the introduction of larger-scale datasets and testing in practical applications, this model is expected to further demonstrate its value in the field of heavy metal wastewater treatment. Summary of the Invention

[0006] The purpose of the embodiments of this application is to provide a method for predicting the rejection rate of cobalt ions based on an artificial neural network, including the following steps:

[0007] Obtain experimental data and establish a dataset based on the experimental data, where the dataset contains input parameters and output parameters.

[0008] The input parameters include pH value, cross-flow rate, feed concentration, and transmembrane pressure difference, and the output parameter includes the rejection rate of cobalt ions;

[0009] Group the data set into a training set and a test set;

[0010] Build an artificial neural network model, which includes an input layer, a hidden layer, and an output layer; where the input layer, hidden layer, and output layer are connected according to neurons;

[0011] Set the training parameter values, and train the artificial neural network model according to the training set and the training parameter values to obtain the model optimization parameters of the artificial neural network model;

[0012] And obtain the model training evaluation result of the artificial neural network model based on the training set according to the model optimization parameters; test the model optimization parameters of the artificial neural network model according to the test set to obtain the model test evaluation result;

[0013] Compare according to the model training evaluation result and the model test evaluation result to obtain the target neural network model;

[0014] And predict the rejection rate of cobalt ions according to the target neural network model.

[0015] Preferably, group the data set into a training set and a test set, specifically:

[0016] Set the data set grouping ratio and set the data set grouping method according to the random hypothesis rule;

[0017] Divide the data set into a training set and a test set according to the data set grouping ratio and the data set grouping method.

[0018] Preferably, build an artificial neural network model, which includes an input layer, a hidden layer, and an output layer; where the input layer, hidden layer, and output layer are connected according to neurons, specifically:

[0019] The input layer is used to input the input parameters of the data set;

[0020] The hidden layer is used to perform weighted summation processing on the input parameters from the input layer and obtain the output parameters corresponding to the input parameters;

[0021] The output layer is used to output the output parameters from the hidden layer.

[0022] Preferably, the input layer is used to input the input parameters of the data set, specifically:

[0023] The input layer is preset with a normalization processing algorithm;

[0024] The input layer standardizes the data parameters in the dataset according to the standardization processing algorithm.

[0025] Preferably, the hidden layer is used to perform weighted summation processing on the input parameters from the input layer and obtain output parameters corresponding to the input parameters, specifically:

[0026] The artificial neural network model is provided with an activation function and at least one hidden layer, the hidden layers are all set as fully connected layers, and the hidden layers contain a preset number of neurons;

[0027] The artificial neural network model assigns corresponding parameter weights to the input parameters according to the hidden layer;

[0028] Perform weighted processing on the input parameters according to the parameter weights corresponding to the input parameters, and sum up the weighted input parameters to obtain a summation result;

[0029] And use the summation result as the function input of the activation function of the artificial neural network model, and obtain the output parameters corresponding to the input parameters according to the function input and the activation function.

[0030] Preferably, set the training parameter values, and perform model training on the artificial neural network model according to the training set and the training parameter values to obtain the model optimization parameters of the artificial neural network model, specifically:

[0031] The training set includes a development set and a validation set;

[0032] Perform development training on the artificial neural network model according to the development set to obtain the coefficient of determination value corresponding to the development set, and obtain the model architecture parameters of the artificial neural network model according to the coefficient of determination value;

[0033] The model architecture parameters include the number of hidden layers of the artificial neural network model and the number of neurons in the hidden layers;

[0034] Perform validation training on the model architecture parameters of the artificial neural network model according to the validation set to obtain the mean square error corresponding to the validation set, and obtain the model iteration parameters of the artificial neural network model according to the mean square error;

[0035] The model iteration parameters include the number of iterations of the artificial neural network model;

[0036] Perform validation training on the model architecture parameters of the artificial neural network model according to the validation set to obtain the coefficient of determination value and the root mean square error corresponding to the validation set, and obtain the model activation function of the artificial neural network model according to the coefficient of determination value and the root mean square error;

[0037] Based on the model architecture parameters, model iteration parameters, and model activation function, the model optimization parameters of the artificial neural network model are constituted.

[0038] Preferably, by comparing the model training evaluation results and the model test evaluation results, a target neural network model is obtained, specifically:

[0039] The model training evaluation results include the training determination coefficient value and the training root mean square error of the artificial neural network on the training set;

[0040] The model test evaluation results include the test determination coefficient value and the test root mean square error of the artificial neural network on the test set;

[0041] Based on the comparison of the training determination coefficient value and the test determination coefficient value, and the training root mean square error and the test root mean square error, the target model optimization parameters are obtained;

[0042] And based on the target model optimization parameters, a target neural network model is obtained.

[0043] In summary, the beneficial effects of this application are as follows: By establishing an artificial neural network model and optimizing the input features and model parameters of the artificial neural network model, this application solves the problem of inaccurate prediction values of traditional models, significantly improves the prediction accuracy of the cobalt ion rejection rate; and through the verification and testing of the training set and the test set for the training and verification of the model parameters of the artificial neural network model, the prediction accuracy and stability of the artificial neural network model are evaluated and verified. Description of the Drawings

[0044] In order to more clearly illustrate the technical solutions of the embodiments of this application, some of the drawings in the embodiments of this application will be briefly described below. It should be understood that the following drawings only show some embodiments of this application, and therefore should not be considered as limiting the scope of this application.

[0045] Figure 1 It is a schematic flow chart of a cobalt ion rejection rate prediction method based on an artificial neural network provided by the present invention. Detailed Embodiments

[0046] The following combines the embodiments and Figure 1 makes a further detailed description of this application, but the implementation manners of this application are not limited to this.

[0047] Refer to Figure 1As shown in the figure, it is a schematic flowchart of a cobalt ion rejection rate prediction method based on an artificial neural network provided by an embodiment of the present application. In the embodiment of the present application, the application scenario is to predict the cobalt ion rejection rate through an artificial neural network model. The present application aims to apply an artificial neural network model to predict the rejection rate of cobalt ions in the nanofiltration process. By modeling and optimizing the input features affecting cobalt ion retention, the problem of inaccurate prediction values of traditional models is solved. After using grid search for hyperparameter optimization, the dataset is retrained, and the trained artificial neural network model is verified on an unseen dataset to evaluate its prediction accuracy and stability.

[0048] A cobalt ion rejection rate prediction method based on an artificial neural network includes the following steps:

[0049] Obtain experimental data and establish a dataset based on the experimental data, where the dataset contains input parameters and output parameters;

[0050] The input parameters include pH value, cross-flow rate, feed concentration, and transmembrane pressure difference, and the output parameter includes the cobalt ion rejection rate;

[0051] Group the dataset and divide the dataset into a training set and a test set;

[0052] Establish an artificial neural network model, which includes an input layer, a hidden layer, and an output layer; among them, the input layer, the hidden layer, and the output layer are connected according to neurons;

[0053] Set the training parameter values, and train the artificial neural network model according to the training set and the training parameter values to obtain the model optimization parameters of the artificial neural network model;

[0054] And obtain the model training evaluation result of the artificial neural network model based on the training set according to the model optimization parameters; test the model optimization parameters of the artificial neural network model according to the test set to obtain the model test evaluation result;

[0055] Compare according to the model training evaluation result and the model test evaluation result to obtain the target neural network model;

[0056] And predict the cobalt ion rejection rate according to the target neural network model.

[0057] Group the dataset and divide the dataset into a training set and a test set. Specifically:

[0058] Set the dataset grouping ratio and set the dataset grouping method according to the random hypothesis rule;

[0059] Divide the dataset into a training set and a test set according to the dataset grouping ratio and the dataset grouping method.

[0060] In some embodiments, the data set is divided into two groups: one for training, i.e., the training set; the other for testing, i.e., the test set. In practical applications, the data set grouping ratio is set to 7:3, specifically, 70% of the total data set is used as the training set for training and establishing a basic artificial neural network model; the remaining 30% is used as the test set for evaluating the performance of the model. The data set grouping method follows the "default" random hypothesis to ensure that the same grouping can be used for further optimization.

[0061] An artificial neural network model is established. The artificial neural network model includes an input layer, a hidden layer, and an output layer; among them, the input layer, the hidden layer, and the output layer are connected according to neurons. Specifically:

[0062] The input layer is used to input the input parameters of the data set;

[0063] The hidden layer is used to perform weighted summation processing on the input parameters from the input layer and obtain output parameters corresponding to the input parameters;

[0064] The output layer is used to output the output parameters from the hidden layer.

[0065] In some embodiments, the model includes an input layer, a hidden layer, and an output layer. The input layer, the hidden layer, and the output layer are interconnected through nodes called neurons.

[0066] The input layer is used to input the input parameters of the data set. Specifically:

[0067] The input layer is preset with a normalization processing algorithm;

[0068] The input layer normalizes the data parameters in the data set according to the normalization processing algorithm.

[0069] In some embodiments, the input parameters are passed to the input layer. Due to the different ranges of parameter values and the existence of categorical variables, these changes may lead to overfitting of the final trained model. To mitigate this potential error, the input parameters are normalized through a preset normalization processing algorithm; the normalization processing algorithm can be preset according to the actual input parameters. For example, the normalization processing algorithm can be preset as the min-max normalization algorithm, the Z-score normalization algorithm, or the eigenvector normalization algorithm, etc.

[0070] The hidden layer is used to perform weighted summation processing on the input parameters from the input layer and obtain output parameters corresponding to the input parameters. Specifically:

[0071] The artificial neural network model is provided with an activation function and at least one hidden layer. The hidden layers are all set as fully connected layers, and the hidden layers contain a preset number of neurons;

[0072] The artificial neural network model assigns corresponding parameter weights to the input parameters according to the hidden layer;

[0073] All the input parameters are weighted according to the corresponding parameter weights of the input parameters, and the weighted input parameters are summed up to obtain the summation result;

[0074] And the summation result is used as the function input of the activation function of the artificial neural network model, and the output parameters corresponding to the input parameters are obtained according to the function input and the activation function.

[0075] In some embodiments, the number of hidden layers is set within the common range of 1 to 6, and the number of neurons in each hidden layer is fixed within the range of 1 to 30. These limitations help to reduce the training time of the artificial neural network model; in addition, all hidden layers are fully connected layers, that is, the neurons in each layer are connected to all neurons in the next layer, so as to achieve the complete transmission of data and the full sharing of information.

[0076] Set the training parameter values, and train the artificial neural network model according to the training set and the training parameter values to obtain the model optimization parameters of the artificial neural network model. Specifically:

[0077] The training set includes a development set and a validation set;

[0078] The artificial neural network model is developed and trained according to the development set to obtain the coefficient of determination value corresponding to the development set, and the model architecture parameters of the artificial neural network model are obtained according to the coefficient of determination value;

[0079] The model architecture parameters include the number of hidden layers of the artificial neural network model and the number of neurons in the hidden layer;

[0080] The model architecture parameters of the artificial neural network model are verified and trained according to the validation set to obtain the mean square error corresponding to the validation set, and the model iteration parameters of the artificial neural network model are obtained according to the mean square error;

[0081] The model iteration parameters include the number of iterations of the artificial neural network model;

[0082] The model architecture parameters of the artificial neural network model are verified and trained according to the validation set to obtain the coefficient of determination value and the root mean square error corresponding to the validation set, and the model activation function of the artificial neural network model is obtained according to the coefficient of determination value and the root mean square error;

[0083] According to the model architecture parameters, the model iteration parameters and the model activation function, the model optimization parameters of the artificial neural network model are constituted.

[0084] In some embodiments, during the model training phase, the model may achieve a high accuracy rate, but perform poorly during the test evaluation phase, indicating that the artificial neural network model may be overfitted. Therefore, to improve accuracy and prevent overfitting, an additional parameter training value is introduced during the modeling process. Based on the parameter training value representing the regularization strength of the model, the introduction of the parameter training value aims to smooth the training process, prevent overfitting, and thus improve the accuracy of the model.

[0085] In some embodiments, the development and testing process of the artificial neural network model is divided into two main phases to ensure that the model's structure and parameter settings can effectively meet the prediction requirements. The first phase is the selection process of the number of hidden layers, the number of neurons in the hidden layer, and the activation function through the training set. These are the key factors affecting the model's performance. Subsequently, parameters such as the learning rate and the maximum number of iterations are adjusted through the validation set to achieve the stable convergence of the artificial neural network model and minimize the error. The second phase focuses on testing the generalization ability of the artificial neural network model on unseen data sets through the test set, and evaluating its applicability and prediction accuracy on new data.

[0086] In some embodiments, the coefficient of determination value of the training set increases with the increase in the number of neurons in each hidden layer. When the number of neurons exceeds 12, the performance approaches saturation regardless of the number of hidden layers. The test set results show that the best performance occurs when each hidden layer contains 12 - 20 neurons and the number of hidden layers is 5 or 6. At this time, the model exhibits strong generalization ability. On the contrary, too few or too many neurons will lead to a decline in performance. The former is due to insufficient model capacity, and the latter may be due to overfitting. According to the optimization criteria, configurations with a coefficient of determination value lower than 90% are considered sub-optimal configurations. Therefore, the number of hidden layers in the model architecture parameters of the artificial neural network model is set to 5, and the number of neurons in each hidden layer is set to 20. This model architecture parameter provides sufficient complexity in capturing the nonlinear relationship of the data, while avoiding the excessive computational burden and overfitting risk caused by too many layers and neurons. This model architecture parameter setting achieves a good balance between prediction accuracy and model efficiency.

[0087] In some embodiments, under repeated tests with different data partitions and random seed conditions, it is shown that the model using the "relu" activation function achieves excellent root mean square error of the coefficient of determination value on the validation set, showing higher prediction accuracy and lower error. Therefore, the model activation function is the "relu" activation function. "Relu" not only shows higher prediction accuracy but also has a faster convergence speed and better stability, thus supporting more efficient optimization in model training.

[0088] In some embodiments, during the process of adjusting the model architecture parameters on the validation set, the change of the mean square error gradually decreases and finally stabilizes as the number of iterations increases. The number of iterations when the mean square error stabilizes is used as the number of iterations in the model iteration parameters of the artificial neural network model.

[0089] Based on the comparison between the model training evaluation results and the model test evaluation results, the target neural network model is obtained, specifically:

[0090] The model training evaluation results include the training determination coefficient value and the training root mean square error of the artificial neural network on the training set;

[0091] The model test evaluation results include the test determination coefficient value and the test root mean square error of the artificial neural network on the test set;

[0092] Based on the comparison between the training determination coefficient value and the test determination coefficient value, and the training root mean square error and the test root mean square error, the target model optimization parameters are obtained;

[0093] And the target neural network model is obtained based on the target model optimization parameters.

[0094] In some embodiments, the training determination coefficient value of the model on the training set is 0.991, the test determination coefficient value on the test set is 0.962, the training root mean square error on the training set is 1.319, and the test root mean square error on the test set is 0.583. These results can prove the robustness and effectiveness of the model in predicting the cobalt ion rejection rate; and the target model parameters are that the number of hidden layers in the model architecture parameters is set to 5, the number of neurons in the hidden layers is set to 20, and the model activation function is "relu".

[0095] The above are only the preferred embodiments of the present invention. The protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the idea of the present invention belong to the protection scope of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A prediction method for cobalt ion rejection rate based on artificial neural network, characterized in that, Including: Obtain experimental data and establish a data set based on the experimental data, where the data set contains input parameters and output parameters; The input parameters include pH value, cross-flow rate, feed concentration, and transmembrane pressure difference, and the output parameter includes cobalt ion rejection rate; Group the data set and divide the data set into a training set and a test set; Establish an artificial neural network model, which includes an input layer, a hidden layer, and an output layer; where the input layer, hidden layer, and output layer are connected according to neurons; Set the training parameter values, and perform model training on the artificial neural network model according to the training set and the training parameter values to obtain the model optimization parameters of the artificial neural network model; And obtain the model training evaluation result of the artificial neural network model based on the training set according to the model optimization parameters; Perform model testing on the model optimization parameters of the artificial neural network model according to the test set to obtain the model testing evaluation result; Compare according to the model training evaluation result and the model testing evaluation result to obtain the target neural network model; And predict the cobalt ion rejection rate according to the target neural network model.

2. The cobalt ion rejection rate prediction method based on an artificial neural network according to claim 1, characterized in that Group the data set and divide the data set into a training set and a test set. Specifically: Set the data set grouping ratio and set the data set grouping method according to the random hypothesis rule; Divide the data set into a training set and a test set according to the data set grouping ratio and the data set grouping method.

3. The cobalt ion rejection rate prediction method based on artificial neural network according to claim 2, characterized in that, Establish an artificial neural network model, which includes an input layer, a hidden layer, and an output layer; where the input layer, hidden layer, and output layer are connected according to neurons. Specifically: The input layer is used to input the input parameters of the data set; The hidden layer is used to perform weighted summation processing on the input parameters from the input layer and obtain the output parameters corresponding to the input parameters; The output layer is used to output the output parameters from the hidden layer.

4. The cobalt ion rejection rate prediction method based on an artificial neural network according to claim 3, wherein The input layer is used to input the input parameters of the data set. Specifically: The input layer is preset with a normalization processing algorithm; The input layer performs normalization processing on the data parameters in the data set according to the normalization processing algorithm.

5. A method for predicting the cobalt ion rejection rate based on an artificial neural network according to claim 4, characterized in that, The hidden layer is used to perform weighted summation processing on the input parameters from the input layer and obtain the output parameters corresponding to the input parameters. Specifically: The artificial neural network model is provided with an activation function and at least one hidden layer. The hidden layers are all set as fully connected layers, and the hidden layers contain a preset number of neurons; The artificial neural network model assigns corresponding parameter weights to the input parameters according to the hidden layer; Perform weighted processing on all the input parameters according to the parameter weights corresponding to the input parameters, and perform summation calculation on the weighted input parameters to obtain the summation calculation result; And use the summation calculation result as the function input of the activation function of the artificial neural network model, and obtain the output parameters corresponding to the input parameters according to the function input and the activation function.

6. A cobalt ion rejection rate prediction method based on an artificial neural network according to claim 5, characterized in that, Set the training parameter values, and perform model training on the artificial neural network model according to the training set and the training parameter values to obtain the model optimization parameters of the artificial neural network model. Specifically: The training set includes a development set and a validation set; Develop and train an artificial neural network model based on the development set to obtain the coefficient of determination value corresponding to the development set, and obtain the model architecture parameters of the artificial neural network model based on the coefficient of determination value; The model architecture parameters include the number of hidden layers of the artificial neural network model and the number of neurons in the hidden layer; Verify and train the model architecture parameters of the artificial neural network model based on the validation set to obtain the mean squared error corresponding to the validation set, and obtain the model iteration parameters of the artificial neural network model based on the mean squared error; The model iteration parameters include the number of iterations of the artificial neural network model; Verify and train the model architecture parameters of the artificial neural network model based on the validation set to obtain the coefficient of determination value and root mean square error corresponding to the validation set, and obtain the model activation function of the artificial neural network model based on the coefficient of determination value and root mean square error; Based on the model architecture parameters, model iteration parameters, and model activation function, construct the model optimization parameters of the artificial neural network model.

7. A method for predicting the cobalt ion rejection rate based on an artificial neural network according to claim 6, characterized in that Compare the model training evaluation results and the model test evaluation results to obtain the target neural network model, specifically: The model training evaluation results include the training coefficient of determination value and training root mean square error of the artificial neural network on the training set; The model test evaluation results include the test coefficient of determination value and test root mean square error of the artificial neural network on the test set; Based on the comparison of the training coefficient of determination value and the test coefficient of determination value, and the training root mean square error and the test root mean square error, obtain the target model optimization parameters; And obtain the target neural network model based on the target model optimization parameters.

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