1. Introduction
High-temperature liquid metal flow technology is a core driver for the continued development of the nuclear, metallurgical, and related industries. For example, high-temperature liquid metal is used as an ideal coolant in fields such as nuclear reactors and aerospace engines [
1], and the precise acquisition of real-time flow and flow information is one of the key technologies to ensure safe control. In the casting industry, by accurately controlling the flow of liquid metal, not only can it effectively improve the quality of castings and prevent the production of defects such as rolled slag and billet cracks [
2], but also realize the fine regulation of grain growth. Therefore, the flow measurement of high-temperature liquid metal solution is of great significance in promoting the progress of related industrial fields [
3]. Currently, the flow control of high-temperature metal solutions in the industrial casting process mainly relies on the adjustment of various parameters by manual experience; however, in the face of liquid level fluctuations influenced by various factors, this method is difficult to maintain a stable flow rate. Metal solution, due to its high temperature, easy oxidation solidification, cooling solidification, ease to stick, and other characteristics, is injected into the mold cavity with rapid fluidity. At the same time, due to the harsh measurement environment and limited sensor installation space, conventional high-temperature liquid metal flow measurement techniques such as turbine flowmeter [
4], orifice plate flowmeter [
5], optical probe method [
6], and Coriolis flowmeter [
7] have limitations, mainly including limited practical applications, susceptibility to oxidation and corrosion, measurement space limitations, and the impact of external conditions; insufficient interference resistance and stability, especially in the noise environment, is prone to error; measurement accuracy is limited by the purity of the solution, flow rate and flow field complexity, and limited transmission and shooting area. Therefore, the online accurate flow measurement in the metal solution casting process is still a technical challenge. The accurate online measurement of solution flow in the industrial casting process for metal solutions is still a key issue to be solved.
The challenges of high-temperature liquid metal flow measurement technology have prompted researchers to explore soft measurement techniques. This technology solves spatial constraints and optimizes the operating conditions of high-temperature liquid metals by finding auxiliary variables related to flow and combining modern information processing techniques, such as deep learning models, to achieve online flow measurement. The selection of auxiliary variables in soft measurement methods is particularly important. It is necessary to choose process variables that have a strong correlation or causal relationship with the dominant variables, and follow the principles of sensitivity, specificity, and ease of access [
8]. For example, scholars such as Jagad PI derived mass flow by measuring substrate stress [
9]; Zhao YJ and others measured electrostatic induction charges using annular sensors, measured gas flow velocity using ultrasound, and derived smoke dust mass flow from friction current and gas velocity [
10]; and Jaiswal SK and others used a weighing method to indirectly measure water flow [
11]. Based on the actual industrial casting environment and metal solution characteristics, and drawing on previous researchers’ selection of auxiliary variables, three key variables related to outlet flow were identified: the impact force of the solution impacting the inclined plane, flow velocity, and mass. However, due to the fast flow velocity and easy oxidation of metal solutions, traditional methods of measuring flow through flow velocity or mass are difficult to achieve. Therefore, a soft measurement scheme for flow based on impact force is proposed: pressure sensors are installed at the bottom of the impact pipe at the outlet of the metal solution to collect the force of the solution impacting the inclined plane, thereby measuring the flow rate. This method takes into account the characteristics of metal solutions while satisfying the limiting conditions of the casting environment, making it practically operable.
The modeling of soft measurement technology is the core issue for achieving flow measurement, mainly including mechanism modeling and data-driven modeling. Mechanism modeling reveals the complex coupling relationship between parameters through physical or chemical equations [
12], while data-driven modeling establishes the mapping relationship between auxiliary variables and dominant variables through autonomous learning. Researchers will combine these two methods [
13] and strive to establish a precise correlation model between impact force and flow to promote the development of high-temperature liquid metal flow measurement technology. Since the relationship between impact force and flow is usually nonlinear, traditional methods may not accurately describe this relationship. The data-driven deep learning method has powerful feature extraction capabilities and can take into account the complex characteristics of the nonlinear, time-varying, and transient effects of the relationship between impact force and flow. The neural network based mainly on convolutional neural networks (CNN) and Long-Short Term Memory (LSTM) has more advantages in feature extraction and time series processing. CNN, with its convolutional layer as the core, can effectively extract sequence features and other data through convolutional operations, capturing local patterns and structures [
14]. Wang et al. improved on the basis of CNN (convolutional neural network). They designed a temporal convolutional network to estimate liquid volume flow, and this innovative method significantly improved the accuracy of flow estimation [
15]. At the same time, scholars such as Zhang improved the transient flow measurement method of gas–liquid two-phase flow by adjusting the parameters of the CNN network and utilizing its powerful feature extraction capabilities, achieving remarkable results [
16]. LSTM performs well in processing time series data. Through its unique memory unit structure, it can better learn the relationship between the front and back characteristics [
17] and capture long-term dependencies in fluid flow during flow measurement. Jin J et al. successfully used LSTM to analyze the vibration response of the metering plate, calculate the vibration level and roughness, and use them as input features. At the same time, they used the actual mass flow measured by the weighing sensor as the output feature of the LSTM prediction model. Experimental results showed that the deviation of their flow prediction was less than 6%, indicating the high accuracy of the model [
18]. In addition, Yan, L et al. also used LSTM to conduct a deep analysis of past water flow, weather, and other time series data, successfully predicting water flow for the next six hours [
19]. These CNN and LSTM models mostly extract data features from specifically filtered data, ignoring important information that may be contained in the original data. The CLCD model pays special attention to the information that may be filtered out in the original data during processing. By cleverly integrating this ignored information, the CLCD model not only enriches the data features but also enables the model to more comprehensively and deeply understand the inherent laws and structures of the data during the training process.
The above literature review shows that most current research mainly focuses on improving the accuracy and scope of the application of flow meters, but this still cannot meet the actual industrial needs. It is worth noting that in the field of metal solution measurement, no researchers have explored the use of impact force as an auxiliary variable. At the same time, the soft measurement modeling approach based on deep learning models has not yet been applied in the field of metal flow measurement. Therefore, the main contributions of this article are as follows:
- (1)
To address the problem of the limited measurement of high-temperature molten metal flow, a soft measurement method using impact force as an auxiliary variable is proposed to achieve the online accurate measurement of high-temperature liquid metal flow.
- (2)
Based on the theoretical foundation of fluid mechanics, a test platform is designed in combination with fluid simulation software to collect impact force sequences under different flow rates.
- (3)
Using the impact force sequence as input and the flow rate classification level as output, a CLCD deep learning model is constructed, achieving an accuracy rate of 90% with high stability in experimental results.
This article is divided into three chapters in total: The first chapter introduces the project background and significance, points out the defects of the existing high-temperature molten metal flow measurement technologies, and proposes a soft measurement method based on impact force. The second chapter first theoretically explains the relationship between impact force and flow rate, analyzes it using fluid simulation technology, and finally builds an experimental platform to collect data under different flow rates. The third chapter constructs the relationship between impact force and flow rate using the CLCD deep learning model, trains the experimental data, and verifies the effectiveness of the method.
3. Analysis of Test Results
Firstly, the simulation experiment platform is built, the frequency and time of the pump are adjusted, and the time series data of the water flow impact force is obtained through the pressure sensor. Subsequently, the impact force sequence is processed using the sliding window filtering technique to filter out the noise interference and make the data fluctuations stable and smooth while accelerating the data processing speed. In order to ensure the robustness of the model, adapt to the changes under different experimental conditions, and better adapt to the input requirements of the model, the WRP algorithm is used to normalize the length of the data, and the time series of the original length is cut into multiple copies of the data, each of which generates the elements of a new one of the time series according to the weight function.
Where the weight function f(x) is shown below:
The processed data are divided into a training set and test set in a 4:1 ratio, and input into the CNN-LSTM model for pre-training, and at the same time, the time series feature values of the original time series impact data are extracted, including maximum, minimum, mean, median, skewness, kurtosis, standard deviation, and variance. The output of the fully connected layer in the pre-training as well as the time series feature values are achieved through data splicing and stored in the feature layer of the network, which fuses the information from different sources, thus improving the generalization ability of the model. Finally, the feature layer is trained based on CNN to output the total traffic classification class. The whole process is shown in
Figure 11.
The CLCD model is not only capable of extracting features in the time domain and capturing the before-and-after temporal relationship, but also extracting time series eigenvalues of the original data, providing more information for the model, improving the model’s ability to understand the change in the impact force, integrating information from different sources, and improving the generalization ability so that it can accurately understand and classify the complex dynamic change in the impact force of the water flow under different frequency and time conditions. However, different parameters such as learning rate and the number of training times have a large impact on the classification accuracy of the CLCD model. According to
Figure 12, it can be seen that the maximum value is reached when the learning rate is 0.003 and the batch size is 400.
The CLCD model was trained with CNN, LSTM, and CNN-LSTM, and the results were evaluated in a comparative analysis. The excellent rate, good rate, and failure rate are used to represent the probability that the model training classification results are completely accurate, the probability that the classification error difference is within two classes, and the probability that the classification class is greater than two classes, respectively. The results are shown in
Figure 13 below.
CNN extracts the local features of the input data through the sliding operations of the convolutional kernel, and its advantage is that it can effectively capture the hierarchical features of the input data, and gradually extract the abstract and high-level features of the data through multiple convolutional and pooling layers, which is able to learn the fluctuation of the water impact force as well as the other feature changes in the processing of the water impact force data. The LSTM, through the gating mechanism, is able to learn inside the network and maintain long-term temporal dependencies, which is very critical for the time series data of water flow impact force, and is able to address the fact that the impact force may be affected by previous time points and there are long term dynamic patterns. So, it is well evident from the figure that the results of the individual model training of CNN and LSTM are not bad, and that the accuracy as well as the excellence rate of CNN-LSTM is higher than the effect of individual class prediction of CNN and LSTM.
However, the CLCD model incorporates the original data time series eigenvalues, and compared with the CNN-LSTM model, it makes up for the neglect of the time series information in the original data, helps to enrich the data characterization, and can accurately understand and categorize the complex dynamic changes in the water flow impact force under different frequency and time conditions, and it can be clearly seen through the experimental results that the CLCD model’s indexes are better than the other models and the classification effect is better.
In order to better analyze the training classification results of the CLCD model, the confusion matrix is plotted as in
Figure 14. More data were collected by adjusting the different speeds and running times of the pumps, but the small number of samples with a mass of more than 150 g led to the unsatisfactory performance of category 11 in terms of classification accuracy in the test dataset, which even reached 0%. However, it should be emphasized that despite the low accuracy of category 11, its error level is still effectively controlled within two levels, and thus still considered as an acceptable classification range. In addition, considering that in practical engineering applications, the flow rate is mainly concentrated between 60 g and 120 g, the accuracy of the CLCD model in this interval performs particularly well and fully meets the practical needs.
After training through the CLCD model, its accuracy and loss rate graphs are shown below in
Figure 15 and
Figure 16, with the increase in the number of training generation’s accuracy instantly reaching the highest value, and then gradually smoothing; the loss rate is also at the beginning of the drop below 0.5, and then fluctuates around 0.3.
In order to verify the stability of the flow classification prediction, 100 flow classification predictions were made for the model, and the accuracy of each classification was recorded in detail. As shown in
Figure 17, after statistical analysis, the accuracy error line was plotted, and its fluctuation range was stable between 0.86 and 0.87, showing that the model is highly stable.
4. Conclusions
In this paper, to solve problems such as unstable casting quality caused by the difficulty of controlling the flow in the casting process of high-temperature metal solution, according to the actual industrial environment, we propose to analyze and experimentally validate the soft measurement method for the flow process of high-temperature metal solution by taking the impact force as the observation variable to realize the online measurement of the flow. The CLCD deep learning model, which is mainly based on data, is adopted, and based on the fluid mechanics analysis and simulation results, the test platform is built to obtain the sample set of impact force sequences with different flow rates, and the model is trained with different flow size levels as output, with an accuracy rate of 90% and high stability. Due to the limitations of the test environment, room temperature water is used as an alternative to start the acquisition of the impact force training set, which is quite different from the actual metal solution in terms of density, fluidity, viscosity, and many other parameters, but the density of the liquid metal is usually several times that of the water, which means that the liquid metal has a greater mass under the same volume, and theoretically, it will also produce a greater impact force, and in terms of viscosity, although the viscosity of the liquid metal is 0.0022 kg/(m-s), which is slightly higher than the viscosity of water, it has good fluidity, so further test studies will be carried out subsequently for different metal solutions to verify the effectiveness of the method in this paper.