Detection and analysis of acoustic characteristics for loose bolts on transmission towers

3.1. Acoustic-signal preprocessing method

Raw acoustic signals from continuous knocking inevitably contain sensor DC offset, low-frequency drift and random electronic noise, which degrade subsequent knocking-event detection and feature extraction. Standard preprocessing is therefore required: mono-channel conversion, mean removal and linear-trend elimination.

For stereo-collected signals, conversion to mono-channel is first performed to simplify analysis. Mean removal eliminates sensor DC offset and restores the signal baseline to zero, and linear-trend elimination removes slow linear drift induced by ambient-temperature variation and sensor-mounting-stress release.

3.2. Automatic detection of knocking moments

After preprocessing, time intervals of all knocking events need to be automatically detected to separately analyze signal features of knocking segments and silent segments. This study adopts a robust threshold method based on signal envelopes, which is insensitive to noise and effectively distinguishes knocking signals from background noise. First, the absolute-value envelope of the signal is computed and smoothed with a second-order Butterworth low-pass filter (cutoff 50 Hz) to suppress high-frequency glitches.

Threshold selection directly influences detection accuracy, and conventional mean-and-standard-deviation methods are susceptible to outliers. The threshold is therefore computed using the more robust median-absolute-deviation (MAD) approach. The definition of MAD is:

where $\text{median}(.)$ represents the median function. The detection threshold is set as:

where $k$ is the threshold coefficient, optimized from experimental data as $k=$5. This value guarantees high detection rates while minimizing false detections.

Samples where the envelope exceeds the threshold are marked as knocking intervals, and the rising and falling edges of each knocking event are located from the filtered envelope.

A single knock may produce multiple consecutive peaks and several adjacent short intervals, so closely-spaced intervals are merged when the gap between them is below 0.1 s. A total of 37 valid knocking events are detected after merging, consistent with the actual count and validating the detection accuracy.

4.1. Principle of spectrogram

Conventional frequency-domain analysis reflects only average frequency characteristics and cannot describe time-dependent variations, whereas bolt-looseness-induced friction and collision noise is distinctly transient, requiring time-frequency analysis. Continuous-knocking and exciter excitation are applied to the lower part of the first tower foot of the 2.2-m tower model, with sound data collected by a sound-source locator at 44 100 Hz.

The short-time Fourier transform (STFT) is a widely adopted time-frequency-analysis approach. Treating non-stationary signals as superpositions of short-time stationary segments, a finite-length window slides across the signal, and a Fourier transform is applied to each windowed segment to obtain the time-frequency distribution.

The definition of STFT is:

where $x\left(\tau \right)$ is the raw signal, $w\left(\tau \right)$ is the window function, $t$ is the time variable and $f$ is the frequency variable.

Window-function selection strongly affects STFT time- and frequency-resolution: shorter windows give higher time but lower frequency resolution, and vice versa. The Hamming window, with moderate main-lobe width and large sidelobe attenuation, is selected to suppress spectral leakage. For silent-segment signals, a window length of 8 820 points (0.2 s) with 75 % overlap gives 5 Hz and 50 ms resolution; for strongly transient knocking segments, a 1 024-point window (about 23.2 ms) with 50 % overlap achieves 43 Hz and 11.6 ms, balancing the two.

4.2. Analysis of knocking acoustic signals

Spectrograms are generated using the above parameters, with time on the horizontal axis, frequency on the vertical axis and color indicating power magnitude (brighter = higher power). Fig. 2(a) shows the silent segment between two adjacent knocks, Fig. 2(b) a single-knock segment and Fig. 2(c) the complete signal.

Fig. 2Spectrograms of three different situations

a) Spectrogram of signal between two adjacent impacts

b) Spectrogram of single hammer-impact signal

c) Spectrogram of complete audio record

The silent-segment spectrogram shows that, without external excitation, tower background noise concentrates in the 0-5 kHz band as low-intensity baseline features, decaying exponentially above 5 kHz. The band above 10 kHz contains no valid signals, with acoustic-power density below –100 dB/Hz. The tower thus emits no spontaneous acoustic radiation, and environmental noise causes no interference in the mid-high-frequency band, providing excellent signal-to-noise conditions for high-frequency-feature extraction.

The single-knock spectrogram illustrates the response of loose bolts under transient impact: knocking events occur within 30-80 ms, and responses cover a broadband 0-15 kHz range with clear pulse-decay behavior. The 0-5 kHz band is low-order global modal vibration with the highest power density, consistent with natural-vibration attenuation; the 5-10 kHz band relates to high-order local modes and elastic-wave scattering; and discrete striped signals emerge within 10-15 kHz. Such signals cannot be explained by linear-modal theory and originate from nonlinear acoustic radiation from micro-collision, tangential sliding and rough-surface friction at loose interfaces.

4.3. Analysis of steady-state-excitation acoustic signals

The spectrogram under 500 Hz steady-state excitation reveals unique features of loose bolts under continuous excitation. Besides bright lines at the 500 Hz fundamental and its 2nd-3rd harmonics, a continuous broadband-noise band spanning the full excitation duration appears in the 10-15 kHz band, radiated by persistent micro-sliding and friction at interfaces. This proves the 10 kHz component is a specific feature of bolt looseness, not of natural structural vibration or the excitation source.