Scale adaptability of filtering and unsupervised identification of measurement-while-drilling signals in fractured rock masses

1 Introduction

Joints, fractures, and weak discontinuities that are widely developed in fractured rock masses substantially alter rock-mass continuity and mechanical properties; their spatial distribution directly affects the stability of surrounding rock and the safety of support systems in tunnels, underground caverns, and mining excavations (Khani et al., 2013; Xing et al., 2018; Feng et al., 2022). Conventional methods, including core logging, borehole imaging, and geophysical exploration, can provide structural information, but they generally involve separate testing procedures, offer limited continuity, and are constrained by interpretation efficiency (Ferrero et al., 2009; Li et al., 2017). In recent years, measurement while drilling (MWD) has provided a new means of sensing lithology, strength, and structural anomalies in real time by continuously acquiring response parameters such as drilling pressure, rotational speed, torque, and penetration rate (Day-Lewis et al., 2017; Yue et al., 2004). Previous studies have shown that when a drill bit crosses a fracture or weak discontinuity, the local rock-breaking resistance and bit-rock contact state change, producing distinct anomalies in continuous MWD parameters (Tian et al., 2024; Wu et al., 2024; Long et al., 2025).

MWD parameters respond strongly to geological conditions, but raw signals are also affected by drilling conditions and equipment operating states (Khor et al., 2018). Mechanical vibration, drill rod transmission, hydraulic fluctuations, and sensor sampling introduce random disturbances into continuous sequences, resulting in nonstationarity, high-frequency fluctuations, and local spikes (Sun et al., 2025; Gao et al., 2025). The composite DPI proposed by Cao et al. (Cao and Feng, 2025) reduces the effects of variations in drilling pressure and rotational speed through parameter normalization. Nevertheless, DPI is calculated from raw monitoring signals, so high-frequency noise propagates into the DPI sequence. This problem is especially pronounced for small scale fractures with short response durations: their anomalies contain few valid samples, and their transient responses readily overlap mechanical disturbances, complicating the extraction of genuine fracture information (van Eldert et al., 2020).

To address random noise and nonstationary fluctuations in drilling signals, signal denoising has increasingly been used for drilling state monitoring and geological information extraction. Si et al. (Si et al., 2021) applied an improved empirical wavelet method to denoise deep-hole drilling signals and used the rotational frequency and its harmonics for condition monitoring. Other studies have employed empirical mode decomposition, the Hilbert–Huang transform, and low-pass filtering to separate trends from high-frequency noise in drilling-vibration signals and thereby improve the distinguishability of informative features (Wang et al., 2022). Huang et al. (Huang et al., 2025) further used a combined optimization strategy to process complex continuous wave drilling signals, demonstrating that appropriate signal preprocessing can substantially improve subsequent feature extraction. These studies indicate that denoising drilling signals is not merely a smoothing operation; the central task is to distinguish informative geological responses from non-geological disturbances while preserving local features that reflect changes in rock mass conditions.

This challenge is particularly important for MWD signals in fractured rock masses. A low pass filter controls the attenuation of high-frequency components through its cutoff frequency, fc. A lower cutoff frequency suppresses random fluctuations and concentrates the signal distribution, but it may also attenuate rapid local anomalies caused by fractures; a higher cutoff frequency preserves more of the original response but also retains more high-frequency noise (Ma et al., 2025; Deng et al., 2024). More importantly, fracture scale governs the time required for the drill bit to traverse the anomalous zone and the number of valid samples collected. Small scale fractures typically produce narrow, short-duration responses, whereas larger fractures produce anomalies over wider intervals. Fractures of different scales therefore exhibit different sensitivities to filtering. Existing MWD studies have focused primarily on relationships between drilling parameters and lithology, strength, or fractures (Xiao et al., 2025). By comparison, little attention has been paid to how the cutoff frequency affects preservation of fracture anomalies, sample distributions, and subsequent identification, and the scale adaptability of filtering parameters remains insufficiently understood (Xiao et al., 2024).

Accordingly, this study used digital drilling tests on a composite specimen containing predefined weak interlayers 5–50 mm thick and adopted DPI as the fracture descriptor to investigate how low pass filtering affects MWD signals and fracture identification. First, the frequency responses of least-squares finite impulse response (FIRLS), window designed finite impulse response (FIRWIN), Butterworth, and Type II Chebyshev filters were compared, and filtered datasets were constructed using cutoff frequencies of 0.1, 0.2, 0.4, and 0.8 Hz. The denoising performance at each filtering strength was then evaluated in terms of DPI dispersion, changes between adjacent samples, and local responses at representative fractures. Density based clustering was subsequently used to analyze the sample structure and identify fracture anomalies after filtering. Finally, the relationships among noise suppression, preservation of fracture features, and identification performance were examined across fracture scales to provide a basis for selecting appropriate filtering parameters for MWD signals in fractured rock masses. Building on the DPI framework of Cao et al. (Cao and Feng, 2025), this study focuses on the influence of cutoff frequency on fracture-response preservation and its scale-dependent filtering requirements.

2 Methodology

2.1 Mechanical basis of fracture-induced drilling responses

2.1.1 Structural characteristics of fractured rock masses

A fractured rock mass is a discontinuous geological medium composed of intact rock blocks, joints, fractures, bedding planes, and their infill materials. Discontinuities interrupt the otherwise continuous material structure and load-transfer paths of intact rock, producing pronounced spatial variations in strength, abrupt changes in stiffness, and incompatible deformation (Deere and Miller, 1966). Unlike intact rock, whose behavior is governed primarily by material properties, the engineering response of a fractured rock mass depends not only on the mechanical properties of the rock blocks but also on discontinuity spacing, aperture, persistence, infilling, and geometric configuration.

Discontinuity spacing and scale are important descriptors of rock-mass heterogeneity. According to the Standard for Engineering Classification of Rock Mass (GB/T 50218-2014) (Ministry of Housing and Urban-Rural Development of the People’s Republic of China et al., 2014), discontinuity spacing is divided into several development classes. In general, smaller spacing and a larger number of discontinuities produce smaller blocks and reduce the overall continuity and load-bearing capacity of the rock mass. During drilling, however, the effect of a discontinuity is governed not only by macroscopic integrity but also by the actual width of the anomalous zone traversed by the drill bit. Differences in the along-hole dimensions of fractures, weak interlayers, and broken zones alter both the duration of bit contact with the anomalous material and the corresponding number of data points.

Let b _*f* denote the equivalent width of a structural anomaly along the drilling direction and V the mean penetration rate within that interval. The theoretical time required for the drill bit to traverse the anomaly can be expressed as Equation 1:

t f = b f V (1)

For an MWD monitoring system with a sampling frequency f _*s*, the theoretical number of samples corresponding to the structural anomaly in the continuous drilling sequence is Equation 2:where t _*f* is the time required for the drill bit to traverse the structural anomaly; m _*f* is the theoretical number of samples corresponding to the anomaly; b _*f* is the equivalent width of the anomaly along the drilling direction; V is the mean penetration rate within the interval; and f _*s* is the sampling frequency.

m f = f s t f = f s b f V (2)

These equations show that fracture scale, penetration rate, and sampling frequency jointly determine the temporal extent and data volume of a structural anomaly in an MWD sequence. A small fracture is traversed quickly and corresponds to relatively few samples; its response therefore generally appears as a short local discontinuity or spike. As the scale of the anomaly increases, the drill bit remains in contact with the low-strength material or infill for longer, and the response may appear as a broader fluctuating interval or a sustained shift. Structural anomalies of different scales therefore exhibit distinct time-frequency characteristics in MWD signals.

Mechanical vibration, drill rod bouncing, and hydraulic fluctuations can likewise generate short duration, high frequency responses in MWD sequences, and their durations may be similar to those induced by small scale fractures. Consequently, valid responses from small fractures are more likely to overlap equipment noise, whereas sustained changes caused by larger structures are comparatively easier to separate from background fluctuations. Insufficient filtering may cause residual mechanical disturbances to be identified as fracture anomalies, whereas excessive filtering may attenuate short-duration responses from small-scale fractures.

2.1.2 Mechanical responses of drilling parameters

Drilling is a dynamic rock-breaking process involving continuous interaction between the drilling tool and the rock mass. Under drilling pressure F and rotational action N, the drill bit cuts, compresses, and fragments the rock at the bottom of the borehole; the resulting drilling state is influenced by rock strength, integrity, and discontinuities (Yue et al., 2004; Dias et al., 2020). When the bit advances through intact, relatively homogeneous rock, the bit rock contact state and rock breaking resistance remain comparatively stable, and response parameters such as penetration rate and torque fluctuate around characteristic background levels. Once the bit enters a fracture, weak interlayer, or locally broken zone, the confinement and local load-bearing capacity at the hole bottom change, altering both penetration efficiency and rotational resistance and producing local anomalies in the continuous MWD parameters (He et al., 2023).

The drilling response mechanism of fractured rock masses is illustrated in Figure 1. Cutting is relatively continuous in intact rock, and rotational speed N, torque M, and drilling pressure F exhibit comparatively stable background responses. When the bit moves from intact rock into a fracture or weak structural zone, continuity of the bit rock contact is disrupted and the local rock-breaking resistance decreases or changes abruptly, thereby altering the drilling response. As shown by the depth-dependent penetration-rate curves under different operating conditions in Figure 1b, the two curves have different background levels in the intact rock intervals but show clear local deviations at the same fracture position. Thus, penetration rate responds to changes in rock mass structure, whereas its absolute magnitude is also controlled by the drilling conditions. Fracture information is therefore expressed mainly as local anomalies superimposed on different background levels rather than as drilling parameter values within a fixed range.

Fracture induced drilling responses are not independent of equipment-related disturbances. Mechanical vibration, hydraulic fluctuations, and drill rod transmission also generate local high frequency variations in raw MWD signals. These random disturbances readily overlap valid responses from small scale fractures with short durations. Accordingly, rock mass characterization from drilling parameters requires both preservation of genuine fracture anomalies and attenuation of high-frequency components unrelated to geological structure, thereby providing reliable data for constructing drilling features and identifying fractures under different filtering conditions.

2.1.3 DPI-based characterization of fracture features

Penetration rate V is highly sensitive to changes in rock-mass structure, but it is also affected by operating parameters such as drilling pressure F and rotational speed N. Even under similar rock mass conditions, different operating conditions can substantially shift the overall penetration-rate level; penetration rate alone is therefore unsuitable as a unified structural descriptor across drilling conditions. To reduce the effect of operating-parameter variations on the drilling response, the Drilling Process Index (DPI), proposed by Cao et al. (Cao and Feng, 2025). On the basis of penetration rate, was introduced as Equation 3:where V is the penetration rate, F is the drilling pressure, N is the rotational speed, and α is a constant related to rock strength. The value α = 15.01was adopted from previous experimental calibration of the DPI under comparable drilling conditions (Cao et al., 2021).

D P I = α · V · F − 0.5 · N − 0.5 (3)

Once DPI has been calculated, the approximate distribution of fractured rock can be estimated using threshold values. For example, Cao et al. (Cao and Feng, 2025) reported that 0 < DPI ≤ 2 represents intact rock, whereas DPI > 2 indicates the presence of fractures (as shown in Table 1). Although this criterion has performed well in fracture identification, it was developed for data acquired at 1 Hz. Because sampling frequency affects the magnitude of DPI, a fixed threshold is not universally suitable for distinguishing intact and fractured rock. The present study therefore applies different filtering conditions to the DPI sequence to examine how filtering strength affects preservation of fracture anomalies and subsequent unsupervised identification.

TABLE 1. Relationship between DPI and rock-mass integrity.

2.2 Filtering methods for measurement-while-drilling signals

2.2.1 Noise components in measurement-while-drilling signals

The digital drilling monitoring system continuously acquires dynamic responses during drilling using multiple types of sensors. In addition to the informative geological response produced by bit rock interaction, the measured signals contain non-geological disturbances caused by rig vibration, hydraulic system fluctuations, drill-rod transmission, manual operation, and sensor sampling. Their combined effects make raw MWD signals distinctly nonstationary and randomly fluctuating, and some instantaneous anomalies have no direct correspondence to changes in rock-mass structure. Previous analyses of drilling data have shown that such disturbances increase parameter dispersion and interfere with subsequent extraction of structural features.

Representative fluctuations in the raw drilling parameters are shown in Figure 2. During drilling, current I, drilling pressure F, rotational speed N, and displacement D contain local fluctuations of varying intensity superimposed on their overall trends. The current and pressure sequences contain distinct instantaneous spikes and dense oscillations, whereas the displacement signal combines continuous periodic variation with local discontinuities; representative disturbed intervals are outlined by red boxes. Rotational speed varies less during steady drilling but still exhibits local disturbances caused by equipment adjustment and changes in operating state. These high frequency or abrupt variations propagate into drilling features calculated from the raw parameters, causing genuine fracture responses to overlap non-geological fluctuations in the continuous signal.

In unsupervised identification of fractured rock masses, high frequency disturbances directly change sample dispersion and local density in feature space. When the noise amplitude is large, fluctuations unrelated to rock-mass structure may appear as sparse, low density points and increase false identification of fracture anomalies. Stronger filtering suppresses random fluctuations and concentrates the data distribution, but excessive smoothing may attenuate short duration features associated with small scale fractures. Filtering parameters must therefore balance noise suppression against preservation of fracture features. The analyses below compare the effects of different filtering conditions on DPI characteristics, sample-density distributions, and unsupervised identification to clarify the scale dependent sensitivity of fractures to filtering.

2.2.2 Fundamentals of low-pass filtering

Digital filtering exploits differences in the frequency-domain distributions of signal components to selectively retain or attenuate components of a raw discrete sequence (Ah et al., 2001; Bédard et al., 2006). Let x[n] denote the raw signal acquired during drilling and h[n] the unit impulse response of the digital filter. The filtered output y[n] is given by their discrete convolution, was introduced as Equation 4:

y n = ∑ k = ‐ ∞ + ∞ h k x n ‐ k (4)

In the frequency domain, convolution is transformed into multiplication of the signal spectrum by the filter response, was introduced as Equation 5:where X(e ^*jω* ) and Y(e ^*jω* ) are the spectra of the unfiltered and filtered signals, respectively; H is the frequency response of the digital filter. By varying the gain of H across frequency bands, the retention of individual frequency components in the output signal can be controlled.

Y e j ω = H e j ω X e j ω (5)

Because MWD signals contain pronounced mechanical vibration and random high frequency disturbances, a low pass filter was used for signal processing. The filter passes the principal signal components below the cutoff frequency f _*c* while attenuating components above f _*c*. The magnitude response of an ideal low-pass filter can be expressed as Equation 6:

H f = 1 , f ≤ f c 0 , f > f c (6)

A practical digital filter cannot produce an instantaneous transition at the cutoff frequency; its frequency response instead comprises a passband, transition band, and stopband. For a discrete drilling signal sampled at f _*s*, the effective frequency range is bounded by the Nyquist frequency f _*s*/2. The cutoff frequency therefore directly determines which components of the raw signal are retained and which are attenuated.

For MWD signals in fractured rock masses, low-frequency components primarily represent the overall drilling trend and relatively persistent structural responses, whereas rig vibration and hydraulic fluctuations generally increase variability at higher frequencies. As the cutoff frequency decreases, high-frequency components are suppressed more strongly and the dispersion of the output signal decreases. Fracture responses also occupy characteristic frequency ranges, however, and short duration anomalies produced by small scale fractures contain relatively high frequency components; an excessively low cutoff frequency may therefore attenuate their local features.

2.2.3 Design of digital low-pass filters

Digital filter performance is governed primarily by filter type, cutoff frequency, and design parameters. Because informative low-frequency responses and high frequency disturbances overlap in MWD signals, the digital filtering procedure was organized into three steps filter-type selection, cutoff-frequency specification, and filter-parameter design as shown in Figure 3.

2.2.3.1 Filter-type selection

Digital filters are commonly classified as low pass, high pass, band pass, or band-stop according to their frequency selection characteristics. This study focuses on suppressing random high-frequency disturbances while retaining the principal responses that reflect changes in rock-mass structure; low-pass filtering was therefore selected. A low pass filter response typically comprises a passband, transition band, and stopband. The passband retains the target signal, the stopband attenuates high-frequency disturbances, and the transition band provides a continuous change in magnitude between them. Here, fpass and fstop denote the passband edge and stopband edge frequencies, respectively. In practical filter design, the cutoff frequency is commonly selected at the midpoint of the transition band and is calculated as Equation 7:

f c = f p a s s + f s t o p 2 (7)

2.2.3.2 Cutoff-frequency selection

The cutoff frequency f _*c* is a key parameter in low-pass filter design because it determines the range of frequency components retained from the raw MWD signal. At a high cutoff frequency, the filtered signal preserves more of the original fluctuations, but some high frequency noise is also retained. As the cutoff frequency decreases, high-frequency components are attenuated more strongly and the signal becomes smoother, although short-duration local responses caused by fractures may also weaken. Because fractures of different scales produce anomalies with different durations, their sensitivities to filtering are not identical. Multiple filtered datasets were therefore constructed at different cutoff frequencies, and their noise suppression and fracture-feature preservation were evaluated in conjunction with the subsequent unsupervised identification results.

2.2.3.3 Digital-filter parameter design

After the filter type and cutoff frequency were specified, four widely used digital low pass filters were compared: a least squares finite impulse response filter (FIRLS), a window-designed finite impulse response filter (FIRWIN), a Butterworth infinite impulse response filter, and a Type II Chebyshev infinite impulse response filter. FIRLS determines the coefficients by minimizing the error between the actual and target frequency responses. FIRWIN applies a window function to truncate the infinite impulse response of an ideal filter and thereby produces finite-length coefficients. The Butterworth filter has a smooth passband magnitude response, whereas the Type II Chebyshev filter permits equiripple behavior in the stopband to obtain a sharper transition. The filter used for subsequent MWD signal processing was selected by comparing passband preservation, transition-band attenuation, and stopband response.

2.3 Density-based unsupervised identification method

2.3.1 DBSCAN algorithm

Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is an unsupervised method that partitions data according to local sample density. It does not require the number of clusters to be specified in advance and can identify sparsely distributed anomalous samples while forming density-connected clusters (Ester et al., 1996). For a dataset D, the ε neighborhood centered on sample xi is defined as Equation 8:

N ε x i = x j ∈ D | d i s t x i , x j ≤ ε (8)

A point x _*i* is classified as a core point if Equation 9:

N ε x i ≥ M i n P t s (9)

In this case, x _*i* is defined as a core point. For the DPI sequences considered here, data from intact rock generally form a relatively concentrated high density region, whereas local anomalies caused by fractures change intersample distances and local density.

The DBSCAN procedure is shown in Figure 4. The input data are first standardized, and candidate values of the neighborhood radius ε are determined from the k-distance curve. MinPts is then specified, and points are classified as core, boundary, or noise points according to local density; density connected regions are progressively expanded to form clusters. Candidate parameter combinations are evaluated to determine the optimal pair (ε, minPts), which is then used to identify fracture anomalies (Han et al., 2006).

2.3.2 Evaluation metrics for fracture identification

To evaluate DBSCAN clustering under different filtering conditions, the Silhouette Coefficient (SC), Davies Bouldin Index (DB), and Calinski Harabasz Index (CH) were selected. SC measures within cluster compactness and between cluster separation; DB measures similarity among clusters; and CH evaluates the clustering structure by comparing between cluster and within cluster dispersion. These metrics are expressed as Equations 10–12: where a and b are the mean intracluster distance and the mean distance to the nearest neighboring cluster, respectively; K is the number of clusters; S _*i* is the within cluster dispersion of cluster i; M _*i*j is the distance between clusters i and j; B _*K* and W _*K* are the between cluster and within cluster dispersion matrices, respectively; and n is the total number of samples. In general, larger SC and CH values and a smaller DB value indicate a clearer clustering structure. The three metrics were used to evaluate clustering results consistently across filtering conditions and DBSCAN parameter combinations.

S C = b − a max a , b (10)

D B = 1 K ∑ i , j = 1 K max i ≠ j s i + s j ω i − ω j 2 (11)

C H = t r B k t r W k × n E − K K − 1 (12)

2.4 Coupled filtering clustering identification framework

The coupled filtering clustering identification framework developed in this study is shown in Figure 5. After the drilling data are input, the digital-filtering module sequentially selects the filter type, specifies the cutoff frequency, and performs signal denoising. Filtered datasets at different cutoff frequencies are then constructed from the same raw data. Because each filtering condition alters both attenuation of high frequency disturbances in the DPI sequence and preservation of fracture anomalies, the resulting datasets are analyzed independently during unsupervised identification to establish the relationship between filtering strength and clustering performance.

For each cutoff frequency, a unique neighborhood radius ε is determined from the elbow of the k-distance curve, and the corresponding clustering results are obtained by iterating over minPts. SC, DB, and CH are then used to evaluate the internal clustering structure and determine the corresponding DBSCAN parameters. The resulting anomaly distributions are subsequently compared among different filtering conditions to evaluate fracture-identification performance. The relationships among cutoff frequency, ε, minPts, and identification results are finally analyzed to clarify the influence of filtering strength on unsupervised identification.

3 Experimental program

3.1 Digital drilling tests

3.1.1 Digital drilling monitoring system

To acquire continuous drilling-tool responses, an XY-2B geological core drilling rig, which is widely used in hydraulic and hydropower engineering, was equipped with a digital drilling monitoring system for the tests. The system consists primarily of the drilling equipment, multiple sensors, a data-acquisition unit, and signal transmission modules, and it synchronously records the operating state and principal mechanical responses of the drilling tool. The rig provides multiple rotational speed settings and accommodates a 76 mm diameter borehole. Different drilling conditions can be established by adjusting drilling pressure and rotational speed.

The digital drilling monitoring system and sensor arrangement are shown in Figure 6. Figure 6a presents a schematic of the monitoring equipment, and Figure 6b shows the locations of the principal sensors at the front of the rig. The rotational speed sensor measures drill-rod rotation, the hydraulic sensor records drilling pressure, and the torque sensor measures the torque generated during rotary rock breaking. Figure 6c shows the complete system layout. The displacement sensor continuously records axial drill rod displacement, from which penetration rate is calculated using the time record, and the current sensor assists in monitoring equipment operating states. Signals from all sensors are transmitted to the data-acquisition unit for synchronous recording.

The sampling frequency can be set from 1 to 10 Hz according to the test requirements. After conversion, the acquired data are displayed in real time, stored, and processed. Synchronous acquisition of multiple parameters continuously records bit rock interaction and provides the raw data required for DPI calculation, signal processing under different filtering conditions, and unsupervised identification of fractured rock masses.

3.1.2 Preparation of composite fractured-rock specimens

To create calibration specimens with known fracture locations and scales, eight homogeneous rock blocks with different physical and mechanical properties were assembled. Each block was machined into a 500 mm × 500 mm × 500 mm cube. The specimen surfaces were intact and free of visible initial damage to minimize the additional influence of natural defects on the drilling response. The composite specimen was divided into left and right columns, designated L1-L4 and R1-R4, respectively; photographs and the spatial arrangement are shown in Figure 7.

M20 cement mortar was cast between adjacent rock blocks to form weak interlayers of different thicknesses, representing fractures or infilled discontinuities that may be encountered during drilling. The three interlayers on the left, p1, p2, and p3, were 5, 10, and 20 mm thick, respectively, whereas p4, p5, and p6 on the right were 30, 40, and 50 mm thick, respectively, as shown in Figure 7b. The blocks were positioned and cast sequentially; each overlying block was placed after the mortar had reached its design strength. The final composite specimen therefore contained multiscale structural anomalies with known locations and thicknesses, providing a controlled reference for comparing MWD responses and identification results before and after filtering.

3.2 Data acquisition and preprocessing

During the drilling tests, the digital monitoring system continuously and synchronously acquired drilling displacement, rotational speed N, drilling pressure F, and torque M and stored the complete MWD record using time stamps. Penetration rate V was calculated from displacement increments between consecutive sampling times, and DPI was then calculated using Equation 3, yielding a continuous sequence of raw operating parameters, drilling response parameters, and the composite descriptor. The complete drilling record included normal drilling, shutdowns, power head adjustments, and other operating states. Before subsequent signal analysis, valid drilling intervals were screened according to the rig operating state and synchronous variations in the monitored parameters. Data associated with shutdowns, power-head adjustments, and other intervals outside continuous active rock breaking were removed. The displacement records of successive drill-rod segments were then reconstructed continuously to maintain correspondence between the MWD parameters and actual drilling depth. This preprocessing reduced the influence of obvious operation-induced transients before DPI calculation, filtering, and clustering.

The overall statistical characteristics of the acquired data are summarized in Figure 8. Specifically, Figures 8a–e present the statistical intervals of penetration rate, rotational speed, drilling pressure, torque, and DPI, respectively, while Figure 8f provides the legend for the interval plots. Minimum–maximum ranges, mean ± standard deviation intervals, means, and medians were used to characterize the distributions of the left- and right-side specimens. As shown in Figures 8b,c, rotational speed and drilling pressure are relatively concentrated, whereas penetration rate, torque, and DPI in Figures 8a,d,e, respectively, span wider ranges, indicating greater dispersion of the response parameters with changing rock mass conditions. These data served as the basis for the subsequent filtering analysis. Multiple denoised datasets were then constructed using different cutoff frequencies to evaluate their effects on DPI characteristics and unsupervised identification.

3.3 Construction of datasets under different filtering conditions

Following the filtering method described in Section 2.2, the frequency responses of several digital low-pass filters were first compared. FIRLS, FIRWIN, Butterworth, and Type II Chebyshev (Cheby2) filters were evaluated with fpass = 0.06 Hz, fstop = 0.10 Hz, and fc = 0.08 Hz; their frequency responses are shown in Figure 9. All four filters retained low-frequency components and attenuated high-frequency components, but their response characteristics differed markedly. FIRLS and Cheby2 exhibited noticeable magnitude fluctuations over parts of the spectrum, whereas FIRWIN and Butterworth produced smoother response curves and achieved a better balance between passband preservation and high-frequency attenuation. This comparison provided an initial filter screening and a consistent basis for constructing datasets at different filtering strengths.

After the filter form was selected, DPI sequences from the left- and right-side specimens were filtered at cutoff frequencies of 0.1, 0.2, 0.4, and 0.8 Hz; the results are shown in Figure 10. As the cutoff frequency decreased, high-frequency fluctuations in DPI were progressively suppressed and the sequence became smoother. At 0.1 Hz, background fluctuations converged substantially, but rapid local changes at the fracture locations were also attenuated. As the cutoff frequency increased, the filtered DPI sequence approached the raw signal, preserving more of the local amplitude and morphology of fracture anomalies while also retaining more background high-frequency disturbance. Both specimens exhibited similar trends, confirming that cutoff frequency directly controls the balance between noise suppression and preservation of local anomalies in MWD signals.

Five DPI states were constructed: raw data and data filtered at 0.1, 0.2, 0.4, and 0.8 Hz. The left and right side specimens were analyzed independently. All datasets originated from the same raw drilling sequences and differed only in cutoff frequency, ensuring a consistent basis for comparison. Each DPI dataset was subsequently analyzed using DBSCAN, with clustering parameters determined independently. Comparisons of data distributions, clustering quality, and fracture-identification results across filtering conditions were then used to evaluate how filtering strength affected preservation of fracture features and unsupervised identification at different fracture scales.

3.4 Selection of DBSCAN parameters under different filtering conditions

Filtering at different cutoff frequencies changes both the amplitude of DPI fluctuations and the local sample-density distribution; a single set of DBSCAN parameters is therefore inappropriate for all filtered datasets. Following the method described in Section 2.3, k-distance curves were constructed independently for the raw data and the data filtered at 0.1, 0.2, 0.4, and 0.8 Hz. The corresponding neighborhood radius ε was identified from the elbow at which each curve transitioned from a gradual to a rapidly increasing segment. Both curve shape and elbow position varied with filtering strength, indicating that signal denoising also changes the distance structure on which DBSCAN operates.

After ε was determined for each dataset, minPts was varied iteratively and the corresponding clustering structures were evaluated using SC, DB, and CH. The parameters selected for each filtering condition are listed in Table 2. For the left-side specimen, ε values for the raw, 0.1, 0.2, 0.4, and 0.8 Hz datasets were 0.402, 0.0798, 0.0365, 0.189, and 0.123, respectively, and the corresponding minPts values were 18, 8, 6, 10, and 21. For the right-side specimen, the ε values were 0.377, 0.090, 0.163, 0.183, and 0.205, and minPts values were 14, 15, 13, 18, and 19. Each dataset was analyzed using its independently selected parameters, thereby minimizing the influence of fixed clustering parameters on comparisons among filtering conditions.

TABLE 2. DBSCAN parameters under different filtering conditions.

4 Results and discussion

4.1 Responses of drilling parameters and DPI under different rock-mass conditions

Before comparing the filtering conditions, the response patterns of the raw MWD parameters were examined. Rotational speed N and drilling pressure F were the principal operating control parameters; representative variations are shown in Figure 11. Both parameters maintained clear plateaus during steady drilling and exhibited only limited local fluctuation, indicating that the drilling conditions remained generally stable throughout the tests. Under the same control conditions, local changes in drilling response parameters can therefore be interpreted as changes in the bit rock interaction state. The stability of these control parameters within the retained drilling intervals also helps distinguish structural responses from obvious transients associated with changes in drilling operation.

Compared with the operating parameters, penetration rate V and torque M responded more strongly to changes in rock-mass structure, as shown in Figure 12. Within intact rock intervals, both parameters fluctuated around their respective background levels. When the drill bit crossed a fracture or weak structural zone, the local load bearing condition and rock breaking resistance changed, producing a sudden increase or pronounced fluctuation in penetration rate and varying shifts in torque. These results show that rock specimen conditions strongly affect both the magnitude and dispersion of penetration rate and torque. Thus, MWD parameters record local mechanical disturbances caused by fractured structures, although the raw responses also contain the effects of lithological differences, mechanical vibration, and random fluctuations.

4.2 Effects of filtering on measurement-while-drilling signal characteristics

Figure 13 shows the effects of cutoff frequency on the statistical characteristics of DPI and on local fracture responses. As shown in Figure 13a, filtering reduced the DPI standard deviation for both specimens, and dispersion generally decreased with cutoff frequency. For the left side specimen, the standard deviation decreased from 0.356 for the raw data to 0.296 at 0.1 Hz; for the right-side specimen, it decreased from 0.688 to 0.433. As the cutoff frequency increased to 0.8 Hz, the standard deviation for both specimens gradually approached the raw-data value. The mean absolute difference between adjacent samples in Figure 13b exhibited an even clearer trend, indicating that a low cutoff frequency strongly suppresses high frequency variation between consecutive samples, whereas a higher cutoff frequency preserves more of the original fluctuations.

The representative local fracture responses in Figures 13c,d further show that filtering attenuates fracture anomaly amplitudes while reducing background fluctuations. For the 5 mm fracture in the left-side specimen, the local discontinuity was markedly smoothed at 0.1 Hz, and the transient response at the fracture progressively recovered as the cutoff frequency increased. The 50 mm fracture in the right side specimen produced a larger anomaly over a wider interval and retained a distinct structural response even under stronger filtering. Filtering therefore affects fracture responses differently across scales.

Overall, selection of the cutoff frequency represents a tradeoff between noise suppression and preservation of structural anomalies. A lower cutoff frequency stabilizes the background signal but may attenuate local features from small scale fractures; a higher cutoff frequency preserves more of the structural response but also retains stronger high frequency disturbances.

4.3 Identification of fractured rock masses under different filtering conditions

Fractured-rock identification results under different filtering conditions are shown in Figure 14, and the corresponding metrics are listed in Table 3 and Table 4. The anomaly percentage (AP), boundary-point percentage (BP), and core point percentage (CP) describe, respectively, the number of anomalous samples relative to the known fracture samples, the proportion of boundary samples, and the retention of intact-rock core samples.

TABLE 3. Fracture-identification metrics for the left-side specimen under different filtering conditions.

TABLE 4. Fracture-identification metrics for the right-side specimen under different filtering conditions.

For the 5–20 mm fractures in the left side specimen, the intact-rock samples in the raw data formed a generally continuous dominant distribution, although some fracture anomalies remained mixed with background fluctuations and AP was only 76.92%. Filtering at 0.1 Hz substantially reduced background dispersion, but the strong smoothing divided different rock intervals into multiple independent density clusters and weakened some local structural responses. At 0.2 Hz, AP increased to 102.60%, indicating that the number of samples identified as anomalous slightly exceeded the number of samples corresponding to the predefined fracture intervals. However, the numbers of anomalous and boundary points in Figure 14e also increased markedly, DB rose to 1.292, and BP reached 1.15%. Thus, the increased number of anomalous samples did not improve identification quality. By contrast, at 0.4 Hz, anomalous points were concentrated near the predefined fracture depths, the dominant intact rock distribution remained continuous, and few boundary samples were present, with BP of only 0.31%. This condition achieved a better balance between background noise suppression and preservation of fracture anomalies. When the cutoff frequency increased to 0.8 Hz, more high-frequency fluctuations were retained and BP rose to 1.64%. Considering both spatial distributions and evaluation metrics, the left side specimen exhibited the best overall identification performance at 0.4 Hz.

The 30–50 mm fractures in the right-side specimen produced anomalies over wider drilling intervals, and the raw data already exhibited good structural separability. As shown in Figure 14b, intact rock samples formed a relatively continuous dominant density region, anomalous points were concentrated at the predefined structural positions, AP reached 97.87%, and BP was only 0.14%. Although filtering at 0.1 and 0.2 Hz substantially suppressed background high frequency fluctuations, it also markedly altered the original density structure, producing multiple independent clusters and many boundary samples. At 0.1 Hz, SC was only 0.364 and DB reached 1.708. As the cutoff frequency increased, the sample distribution progressively recovered its original structure. At 0.8 Hz, the dominant intact rock region became more continuous, the fracture locations remained distinct, SC increased to 0.687, DB decreased to 0.599-the best values among the right side datasets and AP remained 96.08%. Both the raw and 0.8 Hz data therefore produced good identification results for the right-side fractures. Filtering at 0.8 Hz slightly improved the overall clustering structure, but the improvement over the raw data was limited.

4.4 Scale adaptability of filtering parameters

The preceding results show that fracture scale affects not only the amplitude and duration of DPI anomalies but also the sensitivity of subsequent identification to filtering. The 5–20 mm fractures in the left-side specimen produced short duration local responses; in particular, the 5 mm fracture appeared primarily as a narrow transient anomaly that readily overlapped rig vibration and random high frequency fluctuations. Retaining the raw signal therefore increased background dispersion, whereas an excessively low cutoff frequency attenuated the valid fracture response. An appropriate bandwidth was required to balance these effects. At 0.4 Hz, the small scale fracture anomalies were clearly separated from the dominant intact rock region, indicating that moderate filtering is better suited to extracting such weak local anomalies.

As fracture scale increased, the bit remained in the anomalous material for longer and more samples were acquired; the DPI response consequently changed from a short local discontinuity to an anomalous interval of greater duration. According to the relationship among fracture scale, penetration rate, and sampling frequency established in Section 2.1.1, a large scale structure produces more samples with a consistent trend in the continuous MWD sequence and is therefore intrinsically easier to distinguish. The 30–50 mm fractures in the right-side specimen already formed clear low density anomalous regions in the unfiltered data, indicating much less dependence on denoising. Weak filtering at 0.8 Hz further improved the overall clustering metrics, but the resulting identification was broadly similar to that obtained from the raw data. In contrast, stronger filtering at 0.1 and 0.2 Hz changed the local sample-density structure without improving identification.

The scale adaptability of filtering parameters therefore reflects different denoising requirements across fracture scales. For small scale fractures with weak, short duration responses, moderate denoising increases the distinguishability of local anomalies from the background. For large scale fractures with stronger responses over wider intervals, the raw structural information is already sufficient, and filtering should primarily avoid disrupting the original density distribution. The objective of MWD signal filtering should therefore extend beyond simply reducing fluctuation: non-geological disturbances should be suppressed while the original structural characteristics of fracture responses are preserved to the greatest possible extent. A single fixed filtering parameter is consequently unsuitable across fracture scales; filtering should be selected according to both the response intensity and temporal extent of the target structure in the MWD sequence.

5 Conclusion

To address overlap between high-frequency disturbances and structural anomalies in MWD signals from fractured rock masses, this study developed a fractured rock identification framework integrating low-pass filtering and density based clustering. The effects of cutoff frequency on DPI characteristics, sample-density structure, and unsupervised identification were examined, and the scale adaptability of filtering conditions was evaluated. The principal conclusions are as follows:

• Under steady drilling conditions, rotational speed N and drilling pressure F remained generally stable, whereas penetration rate V and torque M were sensitive to fractures and weak structures. DPI reduced the influence of operating parameter differences, but the raw sequence retained high frequency disturbances caused by mechanical vibration and hydraulic fluctuations, which particularly interfered with local responses from small scale fractures.
• Cutoff frequency strongly affected both DPI smoothness and preservation of fracture features. As the cutoff frequency decreased, DPI dispersion and fluctuations between adjacent samples decreased markedly, but local fracture anomalies were also smoothed. The transient response of the 5 mm fracture was more sensitive to filtering, whereas the sustained anomaly associated with the 50 mm fracture remained distinct under stronger filtering.
• Filtering did not necessarily improve identification. For the 5–20 mm fractures in the left side specimen, anomaly locations matched the predefined fractures well at 0.4 Hz and the intact-rock distribution remained continuous, producing the best overall identification. The raw data for the 30–50 mm fractures in the right-side specimen were already sufficiently separable, and filtering at 0.8 Hz therefore provided only limited additional improvement, although SC increased to 0.687 and DB decreased to 0.599.
• Fracture scale governed the dependence of identification on filtering. Small scale fractures had short durations and few valid samples, so moderate filtering effectively reduced background disturbances. Large scale fractures produced broader, more distinct responses and were less dependent on filtering. Filtering parameters for MWD signals should therefore be selected according to the response scale of the target fracture while balancing noise suppression and preservation of structural features.

Overall, this study reveals the coupled relationships among fracture scale, MWD response, filtering strength, and unsupervised identification performance, providing a methodological basis for appropriate denoising and scale-adaptive identification of fractured rock masses in complex noise environments.

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Footnotes

Edited by: J. Gregory Shellnutt, National Taiwan Normal University, Taiwan

Reviewed by: Kimie Suzuki Morales, University of Chile, Chile

Xiuyang Liu, Chinese Academy of Sciences (CAS), China