Centroid Frequency Research Articles

Fracture Process Analysis and Acoustic Emission Response of Cemented Tailings Backfill with Different Sizes under Uniaxial Compression.

To investigate the effect of dimensional changes on the mechanical properties of cemented tailings backfill (CTB), uniaxial compression tests are performed on square CTBs of four different sizes. Combining digital image correlation (DIC) and acoustic emission (AE) methods, the fracture process and AE behavior characteristics of backfills with different sizes are analyzed. The results show that as the backfill size increases, its uniaxial compressive strength decreases, and its strength stabilizes gradually when it measures 100 mm. Under uniaxial compression loading, surface cracks on the smaller specimens evolve rapidly and aggressively, with no significant shedding area, whereas the larger specimens show plastic failure. The cracks expand and penetrate gradually, forming a large shedding area. As the specimen size increases, the backwards trend of the peak value of the ringing count relative to the peak value of the stress becomes increasingly evident. Combining the change law between the r value and the average frequency centroid, the sudden drop point of r value and the lowest value of average frequency centroid can be regarded as the precursor of macroscopic damage.

Abstract 13335: The Predictive Value of Paced Qrs Frequency Analysis in Achieving Left Bundle Branch Pacing

Introduction: Left bundle branch area pacing (LBp) is a newer technique to deliver more synchronous left ventricular activation. Several criteria have been proposed, but not fully validated, to confirm LBp during implantation of pacing lead. Hypothesis: We hypothesized that higher frequency content of the paced QRS complex may show predictive value of successful LBp. Methods: We evaluated 84 patients with ejection fraction >50%, who underwent LBB lead placement (n=42) using ≥1 current criteria and right ventricular midseptal (RVsp) lead placement (n=42) from 2000-22. Time frequency analysis (Matlab) was used to determine frequency content of paced QRS complex. Centroid Frequency (CF), which is the weighted average QRS frequency, was calculated. Unpaired t-test and Chi Square test were used for continuous and categorical variables, respectively. Multivariate analysis using logistic regression was used for variables with univariate p<0.20. Variables with significant multivariate comparison (p<0.05) underwent receiver operator curve analysis. Sensitivity and specificity for a CF ≥7.0 Hz for LBp was determined. Results: Baseline clinical characteristics are listed in Table 1. Patients in RVsp group had longer paced QRS duration (155.6 ± 28.0 vs 127.1 ± 17.2, p<0.002) compared to LBp group. Of all ECG leads, V2 gave greatest difference, with CF of LBp group at 8.8 ± 1.6 Hz vs 5.7 ± 0.7 Hz of RVsp group (fig 1). This difference was significant by both univariate (p<0.003) and multivariate (p<0.010) analysis. Predictive value of CF for successful LBB pacing in lead V2 was highest with an AUC of 0.98. Sensitivity and specificity were 88.1% and 97.6%, respectively. Conclusions: Spectral analysis predicts successful LBp with higher frequency content when compared to RVsp pacing. Given the limitations to the current criteria to confirm LBp, intraprocedural use of frequency content analysis of the paced QRS complex in patients may prove a useful means of identifying LBB capture

Q estimation based on the centroid frequency and standard deviation of frequency‐weighted‐exponential function

AbstractThe quality factor Q is a vital parameter for quantitatively describing the attenuation information of underground reservoirs, which is of great significance for hydrocarbon detection and reservoir characterization. A frequency‐weighted‐exponential (FWE) method utilizing the symmetry index and the characteristic frequency can obtain this parameter. Unfortunately, the constant symmetry index assumption of it reduces the accuracy of Q values under the non‐standard FWE shape. Selecting an optimal symmetry index is also a problem for this method. Hence, the basic idea of a novel Q estimation method is to substitute the symmetry index with the standard deviation of the source and attenuated wavelet spectrums. The added standard deviation varies with the degree of attenuation under different wavelet shapes, which can reduce the effects of the constant assumption. Meanwhile, it is simple to calculate this parameter directly from the spectrums. In this way, the proposed method has wider applicability to various wavelets. The synthetic records show the better performance of the novel method in improving the accuracy of Q values and the resistance to random noise than the FWE method. Furthermore, the results of matching wavelets exhibit the applicability of the proposed method in real data, and the quadratic spectrum simulation method improves the stability of the spectrums. Finally, real data experiments indicate the effectiveness of the proposed method after the above two processing means.

Impacts of anterior-posterior jaw disproportions on speech of dentofacial disharmony patients.

Articulation problems impact communication, development, and quality of life, and are diagnosed in 73-87% of patients with Class II Dentofacial Disharmony (DFD). We evaluated whether differences exist in stop (/t/ or/k/), fricative (/s/ or/ʃ/), and affricate (/tʃ/) consonant sounds of Class II DFD subjects, and whether extent of malocclusion correlates with severity of speech distortion. We hypothesized that Class II patients display milder distortions than Class III and anterior open bite (AOB), as Class II patients can posture into a Class I occlusion. Audio and orthodontic records were collected from DFD patients (N = 53-Class II, 102-Class III, 72-Controls) who were pursuing orthodontics and orthognathic surgery. A speech pathologist perceptually scored speech. Acoustic differences in recordings were measured using Spectral Moment Analysis. When Class II subjects were compared to controls, significant differences were found for the centroid frequency (M1) of the /s/ sound and the spectral spread (M2) of /t/, /tʃ/, and /s/ sounds, with pairwise significance for controls relative to Class II AOB and all Class II subjects. Class II AOB subjects had higher M1 and M2 values than patients with Class II closed bites and Class I controls for most sounds. When comparing across anterior-posterior (AP) groups, differences exist between controls, Class II and III DFD subjects for M1 of /t/, /tʃ/, and/ʃ/ and M2 for /t/, /tʃ/, /s/, and /ʃ/ sounds. Using linear regression, correlations between Class II and III severity and spectral measures were found for /t/ and /tʃ/ sounds. Class II and III patients have a higher prevalence of qualitative distortions and spectral changes in consonants compared to controls, but Class II spectral shifts are smaller and affect fewer sounds than in Class III and AOB cohorts. Linear correlations between AP discrepancy and spectral change suggest causation and that treatment may improve articulation problems.

Interval Q factor estimation based on an improved frequency shift method

To characterize seismic attenuation information quantitatively, the qualify factor Q is routinely used in seismic exploration. To obtain a more reliable Q value than the peak frequency shift (PFS) method, the improved frequency shift (IFS) method computes the peak frequency by the centroid frequency (CF) to improve the noise immunity. However, the IFS method assumes all wavelets are the standard Ricker shape and ignores the effect of attenuation on the wavelet, which greatly affects the accuracy of estimated Q values, especially in interlayer computations. Some analytical methods try to replace the original hypothesis with attenuated Ricker wavelets, but there are too many mathematical approximations, resulting in inaccurate analytical results. Here, a new formula is derived by matching the spectrums with the attenuated Ricker wavelets. The peak frequencies (PFs) of the reference and attenuated wavelet are calculated by the Gauss-Newton iteration method. Combined with fitted PFs, we derive another new formula to calculate the interval-Q value directly. With these modifications, the PFS improved (PFSI) method not only improves the accuracy of the Q factor but also has noise robustness. The synthetic data tests and field data application demonstrate the feasibility and effectiveness of the proposed method.

High energy millihertz quasi-periodic oscillations in 1A 0535 + 262 with Insight-HXMT challenge current models

ABSTRACT We studied the millihertz quasi-periodic oscillation (mHz QPO) in the 2020 outburst of the Be/X-ray binary 1A 0535 + 262 using Insight-HXMT data over a broad energy band. The mHz QPO is detected in the 27–120 keV energy band. The QPO centroid frequency is correlated with the source flux and evolves in the 35–95 mHz range during the outburst. The QPO is most significant in the 50–65 keV band, with a significance of ∼8σ, but is hardly detectable (<2σ) in the lowest (1–27 keV) and highest (>120 keV) energy bands. Notably, the detection of mHz QPO above 80 keV is the highest energy at which mHz QPOs have been detected so far. The fractional rms of the mHz QPO first increases and then decreases with energy, reaching the maximum amplitude at 50–65 keV. In addition, at the peak of the outburst, the mHz QPO shows a double-peak structure, with the difference between the two peaks being constant at ∼0.02 Hz, twice the spin frequency of the neutron star in this system. We discuss different scenarios explaining the generation of the mHz QPO, including the beat frequency model, the Keplerian frequency model, the model of two jets in opposite directions, and the precession of the neutron star, but find that none of them can explain the origin of the QPO well. We conclude that the variability of non-thermal radiation may account for the mHz QPO, but further theoretical studies are needed to reveal the physical mechanism.

Wavelet analysis of the transient QPOs in MAXI J1535−571 with Insight-HXMT

ABSTRACT Using wavelet analysis and power density spectrum, we investigate two transient quasi-periodic oscillations (QPOs) observed in MAXI J1535−571 observed with Insight-HXMT. The transient QPOs have a centroid frequency of ∼10 Hz with an FWHM ∼0.6 Hz, and an rms amplitude $\sim 14{{\ \rm per\ cent}}$. Energy spectra of QPO and non-QPO regimes are also separated and analysed, and the spectra become softer with higher Ecut in the non-QPO regime compared to the QPO regime. Our results suggest that the transient QPOs detected in MJD 58016 and 58017 are still the type-C QPO, and the source remains in its HIMS. The duration of all type-C QPO signals based on wavelet is positively correlated with the mean count rate above ∼10 keV, implying appearance of QPOs in different time-scales should be coupled with the corona. The transient QPO properties could be related to the jet or flares, perhaps the partial ejection of the corona is responsible for the disappearance of the type-C QPO.

Type-B QPOs in the black hole source H1743–322 and their association with Comptonization region and Jet

ABSTRACT The connection of type-B quasi-periodic oscillations (QPOs) to the hot flow in the inner accretion disc region is vaguely understood in black hole X-ray binaries. We performed spectral and timing studies of 23 observations where type-C and type-B QPOs with similar centroid frequencies (∼6 Hz) occurred. Their spectral differences were used to understand the production mechanism of type-B QPOs, along with the quasi-simultaneous radio observations. Based on the spectral results, we did not notice many variations in the Comptonization parameters and the inner disc radius during type-C and type-B QPOs. We found that the structure of the Comptonization region has to be different for observations associated with type-C and type-B QPOs based on the CompTT model. Radio flux density versus QPO width, soft to hard flux ratio, and QPO width versus inner disc temperature, were found to follow certain trends, suggesting that a jet could be responsible for the type-B QPOs in H1743–322. Further studies are required to uniquely constrain this scenario. In a case study where a gradual transition from type-C to type-B QPO was noticed, we found that the spectral changes could be explained by the presence of a jet or a vertically extended optically thick Comptonization region. The geometrical Lense–Thirring precession model with a hot flow and a jet in the inner region was incorporated to explain the spectral and timing variations.

Reliability and Usability Analysis of an Embedded System Capable of Evaluating Balance in Elderly Populations Based on a Modified Wii Balance Board.

This paper analyzes the reliability and usability of a portable electronic instrument that measures balance and balance impairment in older adults. The center of pressure (CoP) metrics are measured with a modified Wii Balance Board (mWBB) platform. In the intra- and inter-rater testing, 16 and 43 volunteers (mean 75.66 and standard deviation (SD) of 7.86 years and 72.61 (SD 7.86) years, respectively) collaborated. Five volunteer raters (5.1 (SD 3.69) years of experience) answered the System Usability Scale (SUS). The most reliable CoP index in the intra-examiner tests was the 95% power frequency in the medial-lateral displacement of the CoP with closed-eyes. It had excellent reliability with an intraclass correlation coefficient ICC = 0.948 (C.I. 0.862–0.982) and a Pearson’s correlation coefficient PCC = 0.966 (p < 0.001). The best index for the inter-rater reliability was the centroidal frequency in the anterior-posterior direction closed-eyes, which had an ICC (2,1) = 0.825. The mWBB also obtained a high usability score. These results support the mWBB as a reliable complementary tool for measuring balance in older adults. Additionally, it does not have the limitations of laboratory-grade systems and clinical screening instruments.

Estimation of Concrete Mechanical Properties by Acoustic Emission with Random Forest Algorithm

The concrete structures are damaged by environmental factors and external loads. To maintain such ages structures, it is necessary to properly determine the mechanical properties and accumulated damage level suffered by concrete using core tests. In this study, relationship between the stress level of damaged concrete under uniaxial compression test and acoustic emission (AE) parameters was investigated using clustering and regression analysis with random forests to identify the most important AE parameters. For clusters 1 and 3, R2 is higher, and RMSE and MAE are lower than for non-clustered cases. Therefore, cluster analysis can be expected to improve the accuracy of AE testing. Thus, the most important parameter is determined to be rise time, the secondly is detected the centroid frequency. These two parameters can be used to clarify compressive fracture behavior of damaged concrete.

Cross-well seismic attenuation tomography with correction for coupling effects at source and receiver positions in the Yutsubo geothermal field, Japan

Seismic attenuation is an important property in the geothermal field because it is related to fluid content and reservoir fractures. However, seismic attenuation analysis is easily affected by various factors that must be carefully treated. We investigated cross-well tomography data acquired in the Yutsubo geothermal field and revealed factors affecting the frequency response of data for attenuation tomography. The amplitude of the first arrival waveforms suggests the presence of effects from source coupling, and properties of the surrounding medium affect the radiation pattern and absolute amplitude values. Also, the amplitude and centroid frequencies of the first arrival waveforms show highly variable values along traces, and analysis using an autocorrelation function suggests that there are also effects due to receiver coupling. In this study, we developed a method to correct a coupling effect by assuming that wavefields inside the first Fresnel zone have the same amplitude and frequency character. Our approach uses neighboring traces inside the first Fresnel zone to estimate correction functions. By applying correction functions, the final attenuation tomography results showed a decrease in standard deviation, which indicates that applying a coupling correction increased the inversion stability. In addition, we investigated the interference of guided waves inside a low-velocity layer using finite-difference modeling. A comparison of synthetic and real data suggests the possibility of the phenomena in our data, which is not widely recognized in the geothermal field. We adopted an approach that excluded data having the potential of interference from those waves. Our attenuation tomography results extracted a high-attenuation zone where open fractures are thought to be distributed.

Language Accent Detection with CNN Using Sparse Data from a Crowd-Sourced Speech Archive

The problem of accent recognition has received a lot of attention with the development of Automatic Speech Recognition (ASR) systems. The crux of the problem is that conventional acoustic language models adapted to fit standard language corpora are unable to satisfy the recognition requirements for accented speech. In this research, we contribute to the accent recognition task for a group of up to nine European accents in English and try to provide some evidence in favor of specific hyperparameter choices for neural network models together with the search for the best input speech signal parameters to ameliorate the baseline accent recognition accuracy. Specifically, we used a CNN-based model trained on the audio features extracted from the Speech Accent Archive dataset, which is a crowd-sourced collection of accented speech recordings. We show that harnessing time–frequency and energy features (such as spectrogram, chromogram, spectral centroid, spectral rolloff, and fundamental frequency) to the Mel-frequency cepstral coefficients (MFCC) may increase the accuracy of the accent classification compared to the conventional feature sets of MFCC and/or raw spectrograms. Our experiments demonstrate that the most impact is brought about by amplitude mel-spectrograms on a linear scale fed into the model. Amplitude mel-spectrograms on a linear scale, which are the correlates of the audio signal energy, allow to produce state-of-the-art classification results and brings the recognition accuracy for English with Germanic, Romance and Slavic accents ranged from 0.964 to 0.987; thus, outperforming existing models of classifying accents which use the Speech Accent Archive. We also investigated how the speech rhythm affects the recognition accuracy. Based on our preliminary experiments, we used the audio recordings in their original form (i.e., with all the pauses preserved) for other accent classification experiments.

Finite element modelling of the Swiss plate geophone bedload monitoring system

ABSTRACT Drop experiments with quartz spheres in a flume setting were performed to investigate the dynamic signal response of the Swiss plate geophone bedload monitoring system for varying particle size, vertical impact velocity, and impact location. For a similar sphere impact set-up, the finite element method was used to determine the propagation characteristics of the stress wave in the structure of the monitoring system. The experimental and numerical results showed a qualitative and partially quantitative agreement in the changes in the number of signal impulses per particle mass, the amplitude, and the centroid frequency with increasing colliding sphere size. These parameters characterizing the geophone vibrations also showed qualitatively similar dependencies with increasing bedload size as field measurements show with natural particles and a theoretical model. The findings of this study contribute to the understanding of the signal response of the monitoring system, which may result in improving bedload grain size classifications.

Estimation method of coal channel Q value based on frequency shift phenomenon of transmitting channel wave

Currently, the transmitting channel wave technique mainly uses the attenuation coefficient of the channel wave total energy to explore the geological structure of the coal seam face. In the case of weak geophone coupling and intense geological anomaly, the channel wave energy will be attenuated severely, which significantly affects the stability and accuracy of the result. The Q value of the coal channel is a critical parameter to evaluate the energy attenuation characteristics of the channel wave. The Q value is typically estimated by using the attenuation coefficient of the body wave, but the special coal channel model hinders the estimation of the Q value of the coal seam. According to the linear attenuation characteristics of the centroid frequency of the transmitting channel wave, a new method was proposed to assess the quality factor (Q) of the coal channel by using the centroid frequency change of the channel wave signal. The expected frequency was calculated as its centroid frequency according to the energy ratio of each frequency point through the spectral analysis of the channel wave signal. Combined with the transmission tomography technology, the imaging of the coal seam face based on the transmitting channel wave Q value was established. According to the sudden change of the Q value of the coal channel near the geological structure of the coal seam face, a geological interpretation method based on the abnormal Q value was proposed. The two-dimensional numerical simulation demonstrated that the centroid frequency of the transmitting channel wave signal decayed linearly with the propagation distance and the geological structure increased the frequency shift. Furthermore, three-dimensional numerical simulation validated the feasibility and effectiveness of the Q value inversion method. Field Experimental results showed that the algorithm exhibited improved stability and accuracy. This work proposed a novel frequency-domain inversion method of the transmitting channel wave that directly uses the frequency shift characteristics of the channel wave to estimate the Q value of the coal channel, which offers a new strategy in the data processing of channel wave.

PySio: A New Python Toolbox for Physiological Signal Visualization and Feature Analysis.

In physiological signal analysis, identifying meaningful relationships and inherent patterns in signals can provide valuable information regarding subjects' physiological state and changes. Although MATLAB has been widely used in signal processing and feature analysis, Python has recently dethroned MATLAB with the rise of data science, machine learning and artificial intelligence. Hence, there is a compelling need for a Python package for physiological feature analysis and extraction to achieve compatibility with downstream models often trained in Python. Thus, we present a novel visualization and feature analysis Python toolbox, PySio, to enable rapid, efficient and user-friendly analysis of physiological signals. First, the user should import the signal-of-interest with the corresponding sampling rate. After importing, the user can either analyze the signal as it is, or can choose a specific region for more detailed analysis. PySio enables the user to (i) visualize and analyze the physiological signals (or user-selected segments of the signals) in time domain, (ii) study the signals (or user-selected segments of the signals) in frequency domain through discrete Fourier transform and spectrogram representations, and (iii) investigate and extract the most common time (energy, entropy, zero crossing rate and peaks) and frequency (spectral entropy, rolloff, centroid, spread, peaks and bandpower) domain features, all with one click. Clinical relevance- As the physiological signals originate directly from the underlying physiological events, proper analysis of the signal patterns can provide valuable information in personalized treatment and wearable technology applications.

Determination of QPO properties in the presence of strong broad-band noise: a case study on the data of MAXI J1820+070

ABSTRACT Accurate calculation of the phase lags of quasi-periodic oscillations (QPOs) will provide insight into their origin. In this paper, we investigate the phase lag correction method that has been applied to calculate the intrinsic phase lags of the QPOs in MAXI J1820+070. We find that the traditional additive model between broad-band noise (BBN) and QPOs in the time domain is rejected, but the convolution model is accepted. By introducing a convolution mechanism in the time domain, the Fourier cross-spectrum analysis shows that the phase lags between QPOs components in different energy bands will have a simple linear relationship with the phase lags between the total signals, so that the intrinsic phase lags of the QPOs can be obtained by linear correction. The power density spectrum (PDS) thus requires a multiplicative model to interpret the data. We briefly discuss a physical scenario for interpreting the convolution. In this scenario, the corona acts as a low-pass filter, Green’s function containing the noise is convolved with the QPOs to form the low-frequency part of the PDS, while the high-frequency part requires an additive component. We use a multiplicative PDS model to fit the data observed by the Insight-Hard X-ray Modulation Telescope (HXMT). The overall fitting results are similar compared to the traditional additive PDS model. Neither the width nor the centroid frequency of the QPOs obtained from each of the two PDS models was significantly different, except for the rms of the QPOs. Our work thus provides a new perspective on the coupling of noise and QPOs.

Analysis of Acoustic Emissions for Determination of the Mechanical Effects of Scratch Tests

Acoustic Emission (AE) is a promising technique for measuring tool wear online and in real time. In this work, scratch tests were conducted to better understand the “pre-wear” AE response based on loading conditions that were not sufficient to generate galling. The scratch tests used the same type of indenter against two different sheet materials: aluminum and steel. The results showed that AE parameters such as the mean frequency, Centroid frequency and Shannon entropy outperformed other frequency domain techniques by discriminating between the two sheet materials in scratch tests. From the literature, the frequency region of interest was expected to be sub 300 kHz. However, in this study, activity below this threshold was found to be noise, whereas distinct frequencies were found at much higher frequencies than expected. These results are compared against single grit “SG” tests of both mild steel- and nickel-based superalloys to allow comparison of the two test methods and materials used. This comparison showed that the SG tests excited the acoustic emission in ways in which the scratch tests did not. Another factor when using acoustic emissions to monitor sheet metal forming is the differences obtained in energy–frequency mapping, where many report the galling phenomena between a certain amplitude and frequency range. Such results are specific to the setup and the materials/geometries used. Further work presented here compares different scratch tests where energy–frequency mapping is different for different materials/geometries.

Frequency Characteristics of AE Caused by Bubble Motion in Plant's Vessels

Acoustic emission (AE) can be used to evaluate drought stress (water stress) in plants. Although bubble motion in plant vessels is suspected of being the source of AE generated by plants (burst-type AE), this has not yet been demonstrated experimentally. This study examined whether burst-type AE is caused by bubble motion by comparing the detected frequency with the theoretical frequency estimated based on a bubble motion equation. Four experimental treatments with different soil dry densities and water supply regimes were established, and the effect of the treatment conditions on AE characteristics was clarified. AE induced by water stress was extracted by focusing on the maximum amplitude and the centroid frequency calculated by wavelet transform analysis. The results showed that the measured frequency and the estimated frequency were almost equal, which demonstrates that the model agreed with the actual measurements and that the burst-type AE can be attributed to bubble motion. The AE induced by water stress had a smaller maximum amplitude and a higher centroid frequency than the AE detected during the water supply regime. Therefore, focusing on the centroid frequency may facilitate the extraction of AE induced by water stress.

Precise prediction of the collapse column based on channel wave spectral disparity characteristics and velocity tomography imaging

Abstract Collapse columns are complex geological anomalies that present safety hazards in coal mines. In practice, the boundaries and internal features are difficult to finely characterize. In this study, we use the Jeffrey divergence to reveal the spectral disparity when the channel wave seismic ray path encounters a collapse column. We use the forward mode and applications for verification. We find that the centroid peak frequency shifts toward lower frequencies, the frequency band narrows and the rays through a collapse column cause attenuation of energy. When a seismic ray path encounters a large collapse column, no channel wave appears in the seismic record, the dispersion curve velocity is greater than the velocity of a normal coal seam, the centroid peak frequency drops and the frequency band shrinks. When a seismic ray passes through the boundary of a collapse column, the dispersion curve shows two parallel velocity phases. When a seismic ray path passes through a small collapse column, the decrease in the centroid frequency becomes the only identifying feature. The proposed channel wave spectral disparity characteristic and velocity tomography imaging method can effectively identify small collapse columns and improve the accuracy and precision of the location of collapse column boundaries, with a position deviation of less than 10 m.

Vibration velocity and frequency characteristics of surrounding rock of adjacent tunnel under blasting excavation

The aim of this study is to improve the accuracy of response prediction and safety evaluation of blasting vibration of a deeply-buried tunnel group. For this purpose, the expression of frequency-domain and blasting vibration velocity spectra for the equivalent blasting load in multiple holes was derived through theoretical analysis, and propagation and attenuation of the primary frequency of blasting vibration of multiple cutting holes and caving holes in the infinite rock mass were explored. Response characteristics of vibration frequency spectra in rock surrounding of the adjacent tunnel induced by full-section blasting excavation of the tunnel under the high in situ stress were studied using the dynamic finite element method. The research indicates that blasting vibration waves have the greatest influences on the adjacent tunnel at the haunch in the side facing the blasting, where the vibration velocity is inversely proportional to the spacing between tunnels and directly proportional to the tunnel diameter. The centroid frequency increases with the increase of the spacing between tunnels and tunnel diameter. Furthermore, vibration velocity spectra at the most affected location (namely the haunch) in the side facing blasting of the adjacent tunnel under different conditions were derived. The coincidence of the theoretical formula was verified by comparing measured data of blasting of diversion tunnels in Pubugou Hydropower Station (Sichuan Province, China). The research results can provide theoretical guidance and reference for the prediction of blasting vibration response of similar projects in the future.