3.1. Preprocessing

Before applying the sliding window strategy, the experiments use multi-channel field data recorded from tunnel drilling rigs that are preprocessed to ensure consistency and reliability for feature extraction. The raw signals are first time-aligned and screened to remove duplicated or invalid records, and missing values are handled by filling short gaps while discarding intervals with long gaps to avoid introducing artificial trends. When necessary, light noise suppression and mild outlier treatment are applied to reduce the influence of measurement fluctuations and sporadic spikes. To ensure that only stable drilling behaviors are analyzed, we extract the drilling timestamps from the recorded rig-state table and perform working-condition filtering in a rule-based manner: we retain the intervals where rig_state indicates drilling and auto_state is valid under drilling, remove pause periods using pause_continue, and retain only continuous segments with lengths no less than \(N_{\min}\). After this state-table-driven filtering, the remaining samples are partitioned into sliding windows for time-domain feature computation, and the extracted feature matrix is standardized to zero mean and unit variance prior to the PCA-based HI modeling (Eq. 9). The key state variables and their encodings used for the aforementioned rule-based filtering are summarized in Table 2.

3.2. Time-Domain Feature Extraction with Sliding Window

To capture the temporal evolution of the system behavior, a sliding window strategy is applied to partition the time-series data into overlapping segments ¹¹, thereby preserving the local dynamics while ensuring continuity. Within each window, the key time-domain statistical features are extracted for each sensor channel. Specifically, the mean value reflects the overall signal level; the standard deviation characterizes short-term fluctuations; and the linear slope, computed via least-squares regression, captures the local trend in the signal change. This process transforms the original multivariate time-series data into a structured feature matrix that serves as the basis for subsequent dimensionality reduction and degradation trend analysis ¹².

Let \(x(t)\) be a sensor signal (for example, pressure) sampled at fixed intervals. The time series is divided into windows of fixed length \(L\) with a step size \(S\). For the \(i\)-th window, the signal segment is

Each window becomes a unit for feature extraction. For each window \(x_i\), the following time-domain features are extracted: mean, standard deviation, and slope.

Assuming a time index \(t_{i} = j\), slope \(s_i\) is computed using linear regression as follows:

These computations are repeated for each selected signal channel (such as pressure and current), forming a multi-dimensional feature vector for each window ¹³. The extracted features reflect the localized trends and fluctuations of system variables that are sensitive to degradation phenomena such as pressure drops, control instability, or irregular flow patterns ¹⁴. These compact representations enable subsequent dimensionality reduction and unsupervised analysis.

3.3. Degradation Curves and Health Indicators

The health condition of electro-hydraulic equipment continuously evolves over its life cycle ¹⁵. Accurately describing the degradation trend is thus essential for health assessment and early warning. Following common practice, we normalize the time such that \(t \in [0, t_{n}]\). Here, \(t_n\) denotes the failure time and defines a normalized health trend \(f(t) \in [0, 1]\) with \(f(0) = 1\) and \(f(t_{n}) = 0\).

Commonly used degradation functions include linear, piecewise, and quadratic functions.

(1) Linear degradation

A linear trend assumes a constant degradation rate:

(2) Piecewise degradation

To represent a healthy plateau followed by a linear decline, we adopt a piecewise model with an (unknown) onset time \(t_j\):

(3) Quadratic degradation

Guided by the wear accumulation and damage propagation principles of the rotating/hydraulic components, we use a convex quadratic function to approximate the accelerating decline:

As illustrated in Fig. 5, Eq. 8 better reflects the empirical behavior we observe in the coal mine drilling rigs: indicators related to pump leakage and pressure loss degrade slowly at first and then enter a rapid acceleration phase near failure. Compared with Eqs. 6 and 7, the quadratic curve provides a more accurate description while avoiding explicit inflection point detection.

3.4. PCA-Based Health Index Construction

To provide a compact representation of the overall degradation state of the electro-hydraulic drive circuit, PCA is employed to reduce the dimensionality of multivariate time-domain features ¹⁷. Let \(\mathbf{X} \in \mathbb{R}^{N \times M}\) denote the feature matrix derived from \(N\) sliding windows, each containing \(M\) extracted statistical features ¹⁸. Prior to PCA, all features are standardized to zero mean and unit variance to eliminate the effects of differing physical units and scales.

PCA is then performed on standardized matrix \(\mathbf{Z}\).

The first principal component (PC1), which captures the dominant variance in the data, is selected as the HI.

The resulting \(HI(t)\) sequence reflects the temporal evolution of system performance and provides a quantitative basis for subsequent degradation interpretation and early anomaly detection ¹⁹.

3.5. Z-Score-Based Degradation Trend Interpretation

Although the HI captures the global degradation trend, feature-level interpretation is essential for linking system deterioration to specific physical components. To achieve this, Z-score normalization is used to quantify the statistical deviation of each time-domain feature from its global distribution. For the \(i\)-th window and feature \(j\), the Z-score is computed as follows:

The Z-score expresses deviations in units of standard deviation, enabling consistent comparisons across features with heterogeneous scales and physical units ²¹. Large positive or negative Z-scores highlight abnormal shifts in individual features, which can be traced to degradation mechanisms such as main pump leakage, control signal drift, or valve blockage. Monitoring the temporal profiles of Z-scores thus provides interpretable feature-level diagnostics and supports early warning and predictive maintenance, even in the absence of labeled fault data or clustering assumptions ²².

4.1. Feature Distribution and Global Operating Status

To analyze the degradation trend of the electro-hydraulic drive circuit, statistical features were first extracted from multi-channel sensor data using a sliding window approach. For each valid drilling segment, we computed three types of time-domain features, mean, standard deviation, and slope ²³, for each selected variable, including the pressure, speed, and control current signals. Consequently, a high-dimensional feature matrix was formed, where each row represented one windowed segment and each column corresponded to a specific signal feature ²⁴.

PCA was applied to synthesize the high-dimensional features into a unified degradation indicator ²⁵. The PC1 that captured the maximum variance direction of the data was selected as the HI. This index reflected the overall health state of the system over time. In our experiments, the PC1 explained \(r_{1} = 92.7\)% of the total variance, indicating that the dominant degradation-related variation was well captured by the HI.

The HI curve is plotted with respect to the window index, as illustrated in Fig. 6. A clear downward or fluctuating trend in the HI implied a possible degradation process, whereas a stable HI suggested normal operating conditions. The HI curve enabled trend tracking and provided a compact representation of the underlying system behavior. These observations demonstrated that the extracted features effectively captured relevant operational patterns and that the HI curve provided a meaningful basis for subsequent trend tracking and rule-based condition interpretation.

To further validate the effectiveness of the proposed PCA-HI, we computed Hotelling’s \(T^{2}\) statistic using the same PCA decomposition as a baseline indicator. Both indicators were standardized over the entire sequence to ensure comparability within the same coordinate system. Fig. 7 illustrates a comparison between the proposed PCA-HI and Hotelling’s \(T^{2}\), both standardized over the entire sequence. In the stable stage, the two curves remained close to zero without significant deviations. Once the degradation process began, both indicators started to increase; however, their behaviors differed considerably. The PCA-HI curve (blue) shows a clear and sharp increase, maintaining a relatively smooth trend throughout the degradation interval. In contrast, the \(T^{2}\) curve (orange) also increases but exhibits pronounced fluctuations and multiple transient spikes, making the underlying degradation trend less stable and more difficult to interpret. This observation confirmed that PCA-HI provided a more monotonic and interpretable trajectory, whereas \(T^{2}\) was more susceptible to noise. As confirmed from Table 5, PCA-HI outperformed \(T^{2}\) in terms of the end-stage slope and mean difference, indicating that PCA-HI was more suitable for degradation trend analysis and early fault warning.

4.2. Z-Score-Based Trend Explanation

A multivariate feature matrix was constructed to represent the evolving behavior of the electro-hydraulic system. However, owing to differences in feature magnitude and physical units (for example, MPa for pressure vs. mA for current), a direct comparison across features was not straightforward.

The validity of the proposed framework is exemplified in Tables 6 and 7 that present the statistical characteristics extracted from a typical sliding window in a degradation scenario. Several key indicators exhibited pronounced deviations, including a lower mean value of the main pump pressure, a positive slope in the oil return pressure, and an increasing trend in the propulsion valve current. These variations collectively reflected the atypical system behavior associated with the underlying deterioration. Tables 6 and 7 further characterize the temporal progression of degradation by comparing the feature statistics from the 16th and 18th sliding windows.

The comparison revealed progressive shifts across multiple signal channels, particularly in the hydraulic pressure, control current, and feeding speed. These gradual changes provided quantitative insights into the evolving health condition of the system and reinforced the effectiveness of the proposed feature-based degradation assessment strategy.

The global mean and standard deviation of each feature dimension, computed across all the sliding windows, are listed in Table 8. These statistical parameters were subsequently used to calculate the Z-scores, allowing the degree of deviation in each feature to be quantitatively assessed. A representative window was selected. The raw feature values obtained from this window are listed in Table 7. Considering the main pump pressure as an example, the current window mean was 10.845 MPa, whereas the global mean and standard deviation were 13.782 and 0.726 MPa, respectively. Applying the Z-score formula yields

In other words, these indicators suggested a systemic loss of pressure in the hydraulic supply line, consistent with the main pump leakage condition. This degradation was likely caused by internal wear or seal failure that gradually reduced the pressure output and affected the overall drilling performance.

By contrast, a different pattern was observed for the control current signals. The propulsion valve current in the window increased to 5.589 mA compared with its global mean of 5.081 mA (global std \(=\) 0.390), yielding

Additionally, the feeding valve current showed a positive Z-score of \(+\)0.62, whereas the corresponding standard deviation values were higher than the average, suggesting signal fluctuation or instability. This trend indicated an electronic control drift phenomenon in which the actuator current gradually deviated from normal owing to driver aging, sensor bias, or feedback loop degradation. The drift was slow and accumulative; hence, capturing it through traditional threshold alarms was difficult.

In summary, by combining global statistical baselines with local feature analysis using the Z-score transformation, two clear degradation patterns were identified, as shown in Fig. 8.

• Status 2: Main pump leakage. Significant negative deviations in both the main and sub-pump pressures, accompanied by negative slope trends.

• Status 3: Electronic control current drift, reflected by multiple control currents showing positive deviations in the mean and fluctuation levels.

This approach provided a fully unsupervised and feature-level interpretable solution for early-stage fault trend detection in electro-hydraulic drilling systems.