Interior Void Classification in Liquid Metal Using Multi-Frequency Magnetic Induction Tomography With a Machine Learning Approach

Identification of gas bubble, void detection and porosity estimation are important factors in many liquid metal processes. In steel casting, the importance of flow condition and phase distribution in crucial parts, such as submerged entry nozzle (SEN) and mould raises the needs to observe the phenomena. Cross-section of flow shapes can be visualised using the magnetic induction tomography (MIT) technique. However, the inversion procedure in the image reconstruction has either limited resolution or involving post-processing stages degrading its real-time capability. Additionally, when quantifying the void fraction or porosity, the image may not be required. This work proposes an interior void classifier based on multi-frequency mutual induction measurements with eutectic alloy GaInSn as a cold liquid metal model contained in a 3D printed plastic miniature of an SEN. The sensors consist of eight coils arranged in a circle encapsulating the column, providing combinatorial detection on conductive surface and depth. The datasets are induced voltage collections of several non-metallic inclusions (NMI) patterns in liquid metal static test and used to train a machine learning model. The model architectures are a fully connected neural network (FCNN) for 1D; and a convolutional neural network (CNN) for 2D data. The classifier using 1D data has been trained to provide 95% accuracy on this dataset. On the other hand, CNN classification using multi-dimensional data produces 96% of test accuracy. Refined with representative flow scenarios, the trained model could be deployed for an intelligent online control system of the liquid metal process.

porous metal. Liquid metal is also used for cooling a nuclear reactor [3], [4]. In the liquid metal-cooled reactor, it is desired to detect and characterize the voids due to their influence on heat exchange.
Magnetic induction tomography (MIT) system produces mutual induction values as boundary measurements which are then transformed into a cross-sectional image of conductivity distribution. This capability is further enriched by employing frequency-sweep on each measurement resulting in spatiospectral information. The structure of a conductive body can be explored using the aforementioned spectroscopy [5]. However, spatial resolution is limited especially for recovering small and dispersed interior non-conductive disturbances. Exhaustive algorithm or post-processing is the usual treatments, still, they could not satisfy demands from some industrial applications.
The advancement in artificial intelligence (AI) is accelerated by the availability of data generated from potent sectors. Since the algorithm shows its capability for image interpretation, its implementation progressively finds the broad area of medical, industrial and informatics [6], [7]. This trend also applies in tomography technology [8], [9], where the data and/or the resulting image can be exploited to obtain conclusive outputs. Machine learning (ML) utilised in tomography research has mainly been for the reconstruction scheme [10], [11], image enhancement [12], [13], and various post-processing mechanisms [14], [15]. Those methods are rarely directly targeting primary information embedded in the measurement data. Bypassing the complexity of tomographic image reconstruction, the detection based on raw data will reduce the computational resources in the deployment phase [16]. Moreover, end-to-end learning of spatio-temporal feature from raw tomography sensor data was assessed to be an efficient scheme [17].
Key parameters in multiphase flow were predicted from multiple sensors reading using a deep-learning method [18]. The model demonstrated generalisation capability for potential field measurement. The work presented in [19] took a direct approach to map the relationship between measurements from electrical capacitance tomography (ECT) sensors and hydrodynamics parameters of flow patterns in a fluidised bed. Although the reconstruction process was still conducted to infer the process parameters, it experimentally collected training samples offline and then the model was used for online monitoring to estimate solid concentration and bubble diameter.
Previously, in cold miniaturised static model experiments, we investigate common two-phase liquid-gas flow scenarios such as full-stream, stratified, bubbly, and annular. These basic flow shapes have been reconstructed with conventional MIT [20]. Accordingly, adaptation of AI become more common in the metallurgy sector [21], [22]. ML approaches for analysing the continuous casting process was surveyed in [23]. Thus, data-driven method and system are prospective for field implementation to extract useful information in helping production. This work attempts to produce a classification of liquid metal inner structure based on multi-frequency mutual induction measurements data.

II. MACHINE LEARNING METHOD USING
MUTUAL INDUCTION DATA Among several techniques in employing ML for classification problems reviewed in [24], the following work trains the network from scratch while adjusting an efficient architecture for the given problem and dataset.
For dense layer, where each input feature is assigned a vector of weights that connects to activation output, this operation applies [25]: here, W i and b i are weights and biases at ith layer respectively. The layer's input is x, and the resulting linear activation z i is transformed by a non-linear activation function f i . There are various activation functions such as sigmoid or hyperbolic tangent. In order to start the approach based on experimental sensing data, the Rectified Linear Unit (ReLU) will be used. On the other hand, convolutional neural network (CNN) conducts: where n is the index of the feature map, K i n is the nth filter kernel, and * is the convolution operator. In order to reduce the computation cost, the CNN layer is usually accompanied by a pooling layer for sub-sampling the feature map. Max operation finds the maximum value.
The performance is evaluated using accuracy, i.e. ratio of correctly classified samples vs all available samples [22]: where c m,n are the elements of the confusion matrix. The network is also trained to minimise the loss between prediction and true labels.
Mutual induction measurements are conducted using a twoport method with LCR meter and additional switching module (Keysight Technologies) for sequentially selecting a pair out of an 8-coil array at a time. This measurement system has a signal-to-noise ratio (SNR) between 60-90 dB, where measurement at low-frequency opposite-coil has the lowest SNR; and high-frequency adjacent-coil has the highest SNR. The detailed configuration was described in [26]. For the following work (see Fig. 1), all 28 (pair-combination) mutual induction coils are measured and swept from 100 Hz to 100 kHz (logarithmic scale with 28 points).
Pixelated data vector was commonly used as either main or additional input for improving traditional image classification performances [27]. This form of pseudo-image can be built from an array of sensors' reading on the first axis and another measurement dimension on the second axis. An example of a classifier model which is built on limited training images was reported by [28]. Nevertheless, this dataset will be a valuable framework in developing tomographic sensing interpretation using ML [29], [30].

III. FCNN CLASSIFIER
In the FCNN classifier, the data are built from mutual induction measurement between every coil pair. There are eight coils so that C 8 2 gives 28 data of mutual combination. This is observed at multiple frequency points.
The measurement data structure in (6) details frequency point f with ith mutual induction value. For instance, m 1,1 is mutual induction between coil-1 and coil-2 at the first frequency point, m 1,28 is mutual induction between coil-7 and coil-8 at the first frequency point, m 28,1 is mutual induction between coil-1 and coil-2 at the last frequency point, and m 28,28 is mutual induction between coil-7 and coil-8 at the last frequency point. Particularly, the phase-shift between the driving signal from transmitting-coil and the detected signal at receiving-coil is taken to represent the sensing information. The measurement is relative values against the reference where liquid metal is full (without any inclusion). θ are phase-shift values for an investigated case, whereas θ 0 are phase-shift values for a reference condition. By this definition, the studied data are 28 of θ = θ − θ 0 values at 28 frequency points.
Equation (7) is applied on each frequency point for all 28 phase-difference values, thus val( f ) is the value at frequency f . As a result, a normalised one-dimensional data plot is obtained as shown in Fig. 2. Previous work [5] used the same normalisation so that the measurement data can be treated as an indicator for structural characteristic of metallic materials.  A wood (balsa) occupies a single grid in the liquid metal (GaInSn) column. Five classes are studied: 1 wood (central grid), 2 woods (East-West), 3 woods (East-centre-West), 4 woods (North-South East-West), and 5 woods (North-South centre East-West), as shown in Fig. 3. Each case is measured in separate sessions and accompanied by the respective reference measurement. Datasets are created and labelled for five classes, and split into training (80%) and test (20%) data. The validation set is a quarter amount of the training data and randomly chosen during the training process. Figure 4 shows the FCNN architecture. Keras model Sequential is constructed consisting of hidden dense layers with 32 neurons. Dropout regularisation layers with a rate of 0.2 are added in an attempt to prevent overfitting. Vector of "logits" scores for each class are then converted into probability using a Softmax function. Loss function Sparse Categorical Crossentropy takes a vector of logits and a "True" index and returns a scalar loss for each example. The model is compiled using optimiser ADAptive with Momentum (Adam), utilising "accuracy" metrics to measure the loss and the accuracy of the model. This model will then be fitted adjusting parameters to minimise the loss. The total number of parameters (param) is 2149, all of which are trainable. Model summary is described in Table I. Figure 5 shows training and validation accuracy-loss along 250 epochs. At the beginning (1s 28ms/step) train loss is 1.6931, train accuracy is 0.2200, validation loss is 1.6403, and validation accuracy is 0.2000; at the end (0s 5ms/step) train loss is 0.4075, train accuracy is 0.8800, validation loss is 0.3122, and validation accuracy is 0.9599. Performance is checked on test set, giving: test loss 0.31 and test accuracy 0.95.
Examples of prediction on woods/voids are depicted in Fig. 6. Ten test data are fed into the model, and the prediction bar chart is shown accordingly. The chart shows how confident the model decides that the data corresponds to each class. The confusion matrix is shown in Fig. 7. The map represents tests, where each case has ten predictions. The classifier has a good accuracy, although four-woods case produce prediction errors. Experimentally, 4woods and 5woods are only differentiated by a central inclusion which is inherently difficult to measure.
IV. CNN CLASSIFIER Two-dimensional data in the form of multi-frequency mutual coil combination are constructed as pseudo-image. The data arrangement follows the structure in (6). This makes a 2D analysis approach is suitable, such as applying a CNN model.
Mutual coil pairs measurements lie on the horizontal axis; whereas frequency points on the vertical axis.  Mutual inductance combinations are 28 (from eight coils), so to shape the image into 2D form, the same number of frequency points is set to 28. The measurement frequency is swept in logarithmic fashion from 100 Hz up to 100 kHz. An example of a pseudo-image is shown in Fig 8. The pseudo-image is 28×28 pixels and the values are scaled between [0 1]. Each value represents θ which is a phasedifference measurement of a liquid metal case (θ ), against a free-space (air) background reference (θ 0 ). In addition to cases depicted in Fig. 3, up to nine inclusions are given, and a full liquid metal (no inclusion) condition is incorporated. Therefore, there are ten classes to investigate. Datasets are split into training (80%) and test (20%) data. The validation set is a quarter amount of the training data and randomly chosen during the training process.
Sequential layers consist of Conv2D, MaxPooling2D, and Dense are stacked for the model, as illustrated in Fig. 9. The diagram gives the information about the input shape, which is a pseudo-image in 2D 28 × 28 pixels and one 'colour' channel. Subsequent layers are convolution and pooling before the tensor is flattened for the traditional dense neural network. Finally, the last layer provides a number of outputs according   to the prediction classes. Table II describes the architecture in detail, where total (trainable) parameters are 93322. Figure 10 shows training and validation accuracy-loss along 250 epochs. Performance is checked on test set, giving: test loss 0.18 and test accuracy 0.96. Examples of prediction cases are depicted in Fig. 11 where confidence percentage is shown at the bottom of each illustration.
The confusion matrix is mapped in Fig. 12. For clarity, the labels associated with inclusion numbers are presented on the axes. Almost all test samples are predicted accurately, except for the full case (no inclusion) where the classifier mispredicts symmetrically distributed of one and five voids/woods (NMI).

V. DISCUSSION
In this study, we define the classification based on the number of voids. It is possible to define the classification in different ways depending on the application. The accuracy of the classifier, on the one hand, depends on the algorithm and training strategies and the other hand depends on the accuracy of the MIT data. With an interest in the interior region of the liquid metal, the accuracy of the MIT setup for low-frequency data will be an important factor.
We intend to provide a prospect of the study for liquid metal processing where void or NMI determination is crucial. As far as our literature survey is concerned at the time this work is written, there have been no published reports that attempt to quantify voids in liquid metal using ML technique based on experimental data. The ML approach we develop provides a potent sensing method to address some issues on detecting and characterising the two-phase liquid metalgas system. Although our case study is for steel-casting where the investigation of bubble distribution in metal flow is desired, this approach would also apply in a wide area of implementation involving liquid metal such as reactor coolant and functional material processing.
For liquid metal fast breeder reactors, real-time radiography is used to image the system [33]. Basic research has been conducted in using neutron radiography for observing liquid metal two-phase flows in vessels. Using the technique reported in [34], radial void fraction profiles were obtained. Also, the follow-up research by authors [35] clarified the basic characteristics of the flow. They visualised the liquid metal two-phase flow and measured its void fraction using neutron radiography and conductivity probe, respectively. The radiography method was used earlier utilising a tracer particle [36]. However, it requires the attenuation of rays caused by the liquid metal being less than 1/e, and particle size larger than one digitised image element size. The other known method is invasive. Report by [37] discloses a probe insertion for detecting gas bubbles in liquid metals. A recent technique, optical fibre sensors were used and tested in a well-controlled lab-scale and a pilot-scale reactor [38].
Porous metal is another engineering material product that is formed in the liquid phase. Its processing method involves bubble generation where pore growth is one of the parameters of interest [39]. Although several modelling methods for liquid metal foam processing have been established [40], experimental observations are still limited. The difficulty in investigating opaque system such as metallic foam is acknowledged. In [41], X-ray tomoscopy was used to clarify the liquid metal's dynamic phenomena, one of which is bubble arrangements.
Generally, alloy casting suffers from inclusions such as dissolved gases. A technique was demonstrated to assess the metal quality by visualising gas content, albeit only a single dissolved gas in the aluminium alloy was tested by [42]. An online liquid metal cleanliness analyzing system is used for quality assurance of inclusion sensitive products. The commercial system [43] is based on the electric sensing zone.
From the above prior methods, further training data could be gathered to refine our initial model. The simplified experimental data is aimed as a starter to demonstrate the ML approach for liquid metal interior investigation. Additionally, computational fluid dynamics (CFD) simulation would also be used to provide training and validation input. We hope that our proposed method, once escalated to field test could offer an alternative to capture local and quantitative information relevant to operating condition.

VI. CONCLUSION
The work proposes a liquid metal flow condition classifier focused on the interior voidage. Measurement datasets are multi-frequency mutual induction sensing of several wood inclusion variations inside liquid metal GaInSn. The 1D classifier architecture is a multi-layered fully connected neural network (FCNN). After 250 epochs, this model produces a training loss of 0.40, training accuracy 0.88; whereas test accuracy is 95%. The 2D classifier architecture is based on a convolutional neural network (CNN). After 250 epochs, this model produces a training loss of 0.15, training accuracy 0.95; whereas test accuracy is 96%. The number of woods, or nonmetallic inclusions (NMI), classification can be further translated into other quantification such as interior void fraction. This framework provides a prospect for a data-driven liquid metal processing system.