Towards Predictive Maintenance in an Aluminum Die-Casting Process Using Deep Learning Clustering and Dimensionality Reduction

Car manufacturing has several stages: Stamping (which creates the vehicle basic outer shell out of large rolls of sheet metal), Body Shop (which is devoted to welding and the assembly of the stamped panels from the previous stage), Painting of the car body, Assembly Line (where wiring, electronics, windows, seats, etc. are assembled), Powertrain Assembly (where engines and transmissions are installed), Quality Control and Testing, and finally Logistics and Delivery. In addition, all the components required in these stages need to be produced, such as engine blocks or gearboxes, before they can be assembled. Usually there are whole factories devoted to the production of an specific element, such as the engine block.

This work is focused on the die-casting process, where injection machines produce engine blocks from aluminum ingots, as can be seen in Figure 1. This work aims to build an intelligent system to support quality control for the die-casting process, by means of a degradation model, which can be used to warn the plant operator when the RUL of the system is close. After the die-casting process, the produced engine blocks are tested in the factory before they are delivered to the Powertrain Assembly stage.

Aluminum die-casting has several stages itself, which can be seen in Figure 2: the aluminum is melted in a Melting tower, and it goes directly to the Casting stage; afterwards, the engine blocks pass a Visual inspection; later on, each engine receives a Thermal treatment to avoid leakages, and the exceeding aluminum is removed in the Machining stage. Finally, to find potential liquid or gas leakages, each engine passes through the Leakage test. Engine blocks that do not pass this test are sent backwards to the Melting tower.

Filling the mold is a process which also has several stages: first, the aluminum is fed into the piston chamber. Second, there is a slow-speed phase, where the piston moves slowly to almost completely fill the mold. Third, there is the low pressure, high-speed phase to completely fill the mold. Fourth, compaction stage uses high pressure to remove air or any other gas from the mold. Later on, a vaccum valve is used to seal the mold. During all these phases, the piston speed and pressure must be carefully controlled, because it is critical to produce fine engine blocks. Finally, once the mold is open again, a layer of an oil-based solution is sprayed on both the engine block, and the mold. Then, there is a cooling stage.

In this study, the information used belongs to three of the four initial stages: slow-speed, high-speed, and compaction. All the data used from these stages are provided by the injection machine.

Each injection lasts less than 90 seconds, and in that span each injection device produces 2000 data for at least five measured signals for each piston: the space traveled, the current speed and its desired set point, and finally, the pressure exerted by the piston on the mold and its desired set point. Consequently, for each injection process, we have five time series made up of 2000 points each²²2Details about measurement units and scales are intentionally omitted due to confidentiality issues.. In addition, the injection machine provides a text file summarizing the injection process, and accordingly it labels each new engine block. If the generated label is not OK, then the engine block is rejected, but most of the generated engines are labeled as OK.

Figure 3(a) shows the evolution of the five measurements recorded for the relevant parts of one injection: the end of the slow speed, together with the fast speed, and the compaction stages, as described in Section 2.1. However, depending on the settings fixed by each plant operator, the time series had different parameters regarding the initial time point to be measured, and the sampling time for the data series. Hence, we were forced to subsample the original 2000 points to have the same number of points, with reference to the same time instant, for all the injections. Consequently, the time series were reduced to 158 points comprising the end of the slow-speed and the whole fast-speed stages for all the engine blocks. After analyzing those data, the size of the time series was later reduced to 56 points, available from the beginning of the fast-speed stage in the injection. Figure 3(b) shows the 56 points for the same injection as in Figure 3(a).

After training several Deep Learning configurations [7] only 20 time steps were considered as relevant to distinguish different behaviours. From these reduced data, only the real speed ($v\in ℝ$) and the real pressure ($p\in ℝ$), measurements were considered relevant. Additional features, related to the temporal evolution of these two measurements were included. Each feature will provide an additional 20 points time series for both $v$ and $p$.

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  the standard deviation (five points sliding window), $\sigma \in ℝ$,

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  relative speed: $\frac{x(t+1)-x(t)}{x(t)}$, $rs\in ℝ$,

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  curvature: $\frac{x(t+1)-2x(t)+x(t-1)}{{\left(1+{(x(t+1)-x(t))}^2\right)}^{3/2}}$, $c\in ℝ$,

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  third order difference: $x(t)-3x(t-1)+3x(t-2)-x(t-3)$, $tod\in ℝ$,

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  and lags of order 1 to 5: $x(t)-x(t-k),k=1,2,3,4,5$, $la{g}_k\in ℝ$.

As a result, the dataset is made up of 20 time series, made up of 20 time steps each, for each engine block: $x_i=\{v_i,{\sigma }_1,r{s}_1,c_1,to{d}_1,la{g}_{1_1},la{g}_{1_2},la{g}_{1_3},la{g}_{1_4},la{g}_{1_5},p_i,{\sigma }_2,r{s}_2,c_2,to{d}_2,la{g}_{2_1},la{g}_{2_2},la{g}_{2_3},la{g}_{2_4},la{g}_{2_5}\}$.

The dataset comprised data about engine blocks produced over a three-months span (mid-January to mid-April, 2023) by a single injection machine, and labeled as OK by the device. 20 pistons were used during that period of time, but the factory reported that four of them did not meet the expected lifespan standard, and were replaced due to unforeseen issues (the remaining 16 exhibited normal lifespans). A filtered dataset was established based on these 16 pistons, resulting in a total of 29158 engine blocks. The generated dataset has dimensions $N\times P\times F$, with $N$ representing the 29158 engine blocks, $P$ indicating the time points collected for each time series, 20, and $F$ representing the number of time series used for each block, 20.

An autoencoder is a deep neural network designed to learn an efficient representation of the input data, $𝐗$, by means of an Encoder, $E(𝐗)$, that extracts the inputs features to a latent representation, $𝐙$, and then uses a Decoder, $D$, which reconstructs $\widehat{𝐗}$ from the encoding $𝐙$, while minimizing a loss function $(L)$, which measures the difference between the input ($𝐗$) and the reconstructed output ($\widehat{𝐗}$). This can be expressed as follows:

The behavior of the autoencoder can be summarized as:

where $f$ and $g$ are activation functions, $W_e,W_d$ are weight matrices and $b_e,b_d$ are the biases.

A Dilated Convolutional Neural Network (DCNN) architecture [11] is employed to implement the autoencoder model for time-series clustering. This architecture leverages variations in the dilation parameter, which are determined by the length of the input time series. Specifically, the dilation increases exponentially: at a rate of 4 for series shorter than 50 data points, and at a rate of 2 for longer series.

Uniform Manifold Approximation and Projection (UMAP) [15] is a non-linear stochastic method based on graphs for dimensionality reduction. The algorithm is divided into two main steps. First, it constructs a fuzzy graph between the data points: it computes a k-nearest neighbor graph and then defines the probability that two points are connected. Next, it creates the low-dimensional embedding by minimizing a cross-entropy loss, which pulls points together or pushes them apart depending on their distances in the high-dimensional space. This optimization is performed using stochastic gradient descent.

Let $C$ be the set of all connections in the graph constructed from the high-dimensional space. Let $w_h(c)$ and $w_l(c)$ denote the weights of a connection $c$ in the high- and low-dimensional spaces, respectively. The cross-entropy is then computed as:

The objective is to minimize this function. The first term is minimized by increasing $w_l(c)$, meaning the points are close together in the low-dimensional space. The second term is minimized by decreasing $w_l(c)$, which pushes the corresponding points farther apart.

One major advantage of UMAP over other dimensionality reduction methods, such as t-SNE [21], is that, by saving the model parameters, we can obtain the latent representation in the low dimension space for each new block, without recomputing the UMAP model on the whole training set.

UMAP includes several hyperparameters, such as the number of neighbors, the distance metric used to construct the graph, the minimum allowed distance among points in the embedding, and the target dimensionality.

In this work, UMAP will be applied to the latent space $𝐙$ from the autoencoder, to reduce its initial dimensionality, which is 50.

Fuzzy c-means (FCM) [18, 5] is a clustering technique that allows the probabilistic assignment of an element to a set of clusters based on a minimization function. While there are several proposals for optimization criteria, the most popular to date is associated with the least square error function (6).

Where $N$ is the number of samples; $C$ is the number of clusters, $w_{ik}$ is the degree to which element $x_i$ belongs to the cluster $c_j$, $m$ is the fuzzy factor, strictly greater than one, and ${\Vert x_i-c_j\Vert }^2$ is understood as the euclidean distance that separates the element $x_i$ from the centroid of the cluster $c_j$. Optimization is subject to the constraint ${\sum }_{i=1}^C{w}_{ik}=1\forall k\in [1,\mathrm{\dots },N]$ and solved using Lagrange multipliers. It is worth mentioning that if $m$ tends to one, the optimal partition is increasingly closer to an exclusive partition (K-means), and when it tends to infinity the optimal partition approaches a matrix with all its values are equal to $1/C$. Usually $m$ takes values in the range between $[1-30]$.

In this work fuzzy c-means will be applied to the reduced space obtained after applying UMAP to the autoencoder latent space.

In order to plot the evolution of the cluster assignment obtained after applying fuzzy c-means for each new engine, which will be a really noisy value, LOWESS was selected to smooth the visualization.

LOWESS, which stands for Locally Weighted Scatterplot Smoothing [6], is a robust locally weighted regression method for smoothing scatterplots. Local regression is a nonparametric approach for estimating a regression function or a surface.

Let’s say that we have a collection of points $(x_i,y_i),i=1,\mathrm{\dots },n$, in a two dimensional space, in which the fitted value at $x_k$ is the value of a polynomial fit to the data using weighted least squares, where the weight for ($x_i$, $y_i$) is larger if $x_i$ is closer to $x_k$ and is smaller if it is not. This fitting procedure is used to deal with deviant points distorting the smoothed points.

In this work LOWESS was applied to the projection on a two, or three, dimensional space for the UMAP output after applying fuzzy c-means.

The methodology for obtaining the FPI that shows the evolution of piston head wear consists of three sequential stages, which are represented in Figure 4.

In the first stage, a DCNN-based autoencoder architecture is used to construct a latent representation of the input data. The autoencoder, using dilated convolutions, is trained to minimize the reconstruction error, thereby ensuring that the latent space effectively captures the most relevant features of the original high-dimensional dataset, including local and contextual patterns that might otherwise be lost with standard convolutional layers.

In the second stage, the dimensionality of the latent space generated by the autoencoder is further reduced using Uniform Manifold Approximation and Projection, which provides a compact and computationally tractable representation of the data while preserving its underlying topological structure. In this study, the UMAP projection will generate a three-dimensional region of high point density. The projection of the head piston for each newly generated engine block shifts from one end of the region to the other, as the number of injected blocks increases. Unfortunately, the displacement within the region is noisy, and there is no simple correlation between the location of the projection in one region and the degree of wear.

Finally, in the third stage, due to the noisy evolution of the piston head projection, fuzzy clustering is performed on the reduced latent space using the FCM algorithm. This step groups the engine blocks into distinct overlapping clusters. The trend of assignment of each component to different clusters, based on the probabilities provided by the FCM, can be used to define the Fuzzy Progression Index as follows:

Where $C$ is the number of clusters, $i=1$ is the cluster associated with the initial state, $i=C$ is the cluster representing the final state, and $w_i$ is the degree of membership to cluster $i$.

FPI is correlated to the remaining percentage of life of the piston head, but unfortunately it also presents a high variance. Therefore, LOWESS [6] method will be used to smooth the data in order to obtain the trend of the FPI. The resulting curve serves as an indicator of the piston life trend. Using the probabilistic nature of FCM assignments, the approach captures the gradual transition between health states.

Table 1 summarizes the parameter configurations explored for the DCNN, UMAP, and FCM techniques. For the FCM method, the values listed represent the various configurations tested during the optimization process, which aims to improve the accuracy and stability of the cluster assignments across the component data. By systematically adjusting these parameters, the model seeks to enhance the clarity of the clustering structure, ensuring that the transitions between health states are captured more effectively. This cluster representation can be used to obtain a more robust representation of the component’s behavior over time, providing a reliable foundation for subsequent analyses and decision-making processes. This idea will be explained in Section 5.

To validate the proposed approach, the dataset was partitioned into training and test subsets, following an 80-20% split, to ensure a fair comparison. The reader should notice that the split was made at the piston level, i.e. we used for training all the measurements from 80% of the available pistons, and 20% of the pistons were used for test, rather than doing a random 80-20% split of available measurements for each piston from the full set of pistons data. As a result, a $[13-3]$ piston split forms the basis for this work.

Several model configurations were explored for the training set. The upper part of Figure 5(a) shows the resulting structure of the latent space generated by the autoencoder in three dimensions for the training set; this structure can be interpreted as the characteristic life cycle of a piston.

Once the structure was fixed, various numbers of clusters were explored, ranging from five to twenty-five. This range was selected based on preliminary analyses, which indicated that fewer than five clusters failed to capture the necessary complexity of the system degradation patterns, while more than twenty-five clusters led to over-fitting and decreased generalization performance. From these experiments, the optimal number of clusters was determined to be 23, as this configuration achieved the best performance in the FCM method of FPI optimization. The criterion for optimizing the number of clusters was to minimize the prediction error at 15% of the remaining piston head life, along with the variance of these estimates in the training set. The reader should notice that, in the absence of failure models, the service life is estimated in terms of the percentage of the piston lifespan. In this case study, pistons from different manufacturers were used. Although all of them showed similar wear patterns over their service life, the expected lifespan is different among manufacturers. To obtain an estimate of the RUL in temporal terms, it would be necessary to know the average service life provided by each manufacturer for each type of piston.

The evolution of the piston head degradation over the piston life cycle for the training set is shown in the upper part of Figure 5(b), where different colors have been assigned to the clusters, temporally ordered: with the gray color representing the initial cluster, and the violet color representing the final cluster. As it can be seen in the lower part of both Figures 5(a) and 5(b), the results are very similar for the test dataset.

Using that fuzzy cluster results, the FPI values were generated for each engine block. Figure 6 shows the evolution of these FPI values (represented as points) generated by six pistons of the training set, and the LOWESS regression prediction for the pistons EOL.

To obtain an exponential data-based model, an exponential function for each piston in the training set was individually fit, and a threshold of this exponential function at the end of the lifetime was obtained. From these thresholds, the mean threshold and its variance were calculated. Next, the mean exponential function of the training set was computed. This was the function used as a model of the FPI in the testing phase. Subsequently, when evaluating the test set, a correction was applied to this mean exponential trend by incorporating the already observed residual values for each individually generated part and piston. This adjustment aims to refine the prediction by considering the previous piston behavior, which, in general, shows deviations that were not captured during the initial adjustment process. This adjustment improves the accuracy of the RUL estimation of the model through unobserved data.

Figure 7 presents the progressive estimation of the percentage of remaining parts for each of the test pistons at various points throughout their life cycle. The FPI value of each produced part is shown as a blue point, while the average trend for the exponential function derived from the training set is shown as a dotted red line. The dark blue line represents the corrected trend, obtained by adjusting the average exponential curve based on the residual values associated with each part for the current piston. Additionally, the orange and green vertical lines indicate the estimated range marking the end of the life cycle; specifically, these points correspond to the intersection of the corrected trend and the threshold value, considering both plus and minus one standard deviation. This visualization provides a clear and interpretable summary of the model’s performance, highlighting the variability inherent in the predictions and offering a practical estimation window for the remaining useful life of the components.

In particular, it is observed that each piston in the test set falls into one of the three possible estimation outcomes: underestimation, where the model predicts less remaining life than is actually present; overestimation, where the predicted remaining life exceeds the true value; and accurate prediction, where the estimation closely matches the actual remaining life. This variability highlights both the strengths and limitations of the proposed methodology, emphasizing the importance of understanding the conditions under which the model reliably performs versus when it tends to deviate. Such insights are critical for refining the approach and ensuring more consistent predictive performance across diverse operating scenarios.

In Table 2, the predicted threshold values for each chunk are presented, with the rows shaded in grey specifically highlighting the chunks that correspond to the actual EOL cycle for each piston in the test set.

Figure 7 and table 2 shows that only the third piston EOL is included in the estimated interval, while piston 1 lasts an additional 18% on the predicted Upper Threshold, and piston 2 lasts about 9% under the Lower Threshold. However, it is not easy to interpret these results as under or over estimations for the RUL. The data used for training and testing were not obtained in a controlled environment where the maximum acceptable RUL was pursued. These data come from standard factory operation where pistons are changed on a preventive maintenance agenda, that requires changing the piston head after a fixed number of operations. Moreover, the number of performed operations usually changes due to other operational criteria, such as the convenience of performing a programmed stop to change the piston head, or the detection of anomalies after the injection stage.

Even with these caveats, the proposed approach is considered as a potential valuable tool for plant operators and managers, to perform predictive maintenance of the piston head.