Accurate time delay estimation of target echo signals is a critical component of underwater target localization.In active sonar systems,echo signal processing is vulnerable to the effects of reverberation and noise in...Accurate time delay estimation of target echo signals is a critical component of underwater target localization.In active sonar systems,echo signal processing is vulnerable to the effects of reverberation and noise in the maritime environment.This paper proposes a novel method for estimating target time delay using multi-bright spot echoes,assuming the target’s size and depth are known.Aiming to effectively enhance the extraction of geometric features from the target echoes and mitigate the impact of reverberation and noise,the proposed approach employs the fractional order Fourier transform-frequency sliced wavelet transform to extract multi-bright spot echoes.Using the highlighting model theory and the target size information,an observation matrix is constructed to represent multi-angle incident signals and obtain the theoretical scattered echo signals from different angles.Aiming to accurately estimate the target’s time delay,waveform similarity coefficients and mean square error values between the theoretical return signals and received signals are computed across various incident angles and time delays.Simulation results show that,compared to the conventional matched filter,the proposed algorithm reduces the relative error by 65.9%-91.5%at a signal-to noise ratio of-25 dB,and by 66.7%-88.9%at a signal-to-reverberation ratio of−10 dB.This algorithm provides a new approach for the precise localization of submerged targets in shallow water environments.展开更多
Atmospheric aerosols are the primary contributors to environmental pollution.As such aerosols are micro-to nanosized particles invisible to the naked eye,it is necessary to utilize LiDAR technology for their detection...Atmospheric aerosols are the primary contributors to environmental pollution.As such aerosols are micro-to nanosized particles invisible to the naked eye,it is necessary to utilize LiDAR technology for their detection.The laser radar echo signal is vulnerable to background light and electronic thermal noise.While single-photon LiDAR can effectively reduce background light interference,electronic thermal noise remains a significant challenge,especially at long distances and in environments with a low signal-to-noise ratio(SNR).However,conventional denoising methods cannot achieve satisfactory results in this case.In this paper,a novel adaptive continuous threshold wavelet denoising algorithm is proposed to filter out the noise.The algorithm features an adaptive threshold and a continuous threshold function.The adaptive threshold is dynamically adjusted according to the wavelet decomposition level,and the continuous threshold function ensures continuity with lower constant error,thus optimizing the denoising process.Simulation results show that the proposed algorithm has excellent performance in improving SNR and reducing root mean square error(RMSE)compared with other algorithms.Experimental results show that denoising of an actual LiDAR echo signal results in a 4.37 dB improvement in SNR and a 39.5%reduction in RMSE.The proposed method significantly enhances the ability of single-photon LiDAR to detect weak signals.展开更多
The echo of the material level is non-stationary and contains many singularities.The echo contains false echoes and noise,which affects the detection of the material level signals,resulting in low accuracy of material...The echo of the material level is non-stationary and contains many singularities.The echo contains false echoes and noise,which affects the detection of the material level signals,resulting in low accuracy of material level measurement.A new method for detecting and correcting the material level signal is proposed,which is based on the generalized S-transform and singular value decomposition(GST-SVD).In this project,the change of material level is regarded as the low speed moving target.First,the generalized S-transform is performed on the echo signals.During the transformation process,the variation trend of window of the generalized S-transform is adjusted according to the frequency distribution characteristics of the material level echo signal,achieving the purpose of detecting the signal.Secondly,the SVD is used to reconstruct the time-frequency coefficient matrix.At last,the reconstructed time-frequency matrix performs an inverse transform.The experimental results show that the method can accurately detect the material level echo signal,and it can reserve the detailed characteristics of the signal while suppressing the noise,and reduce the false echo interference.Compared with other methods,the material level measurement error does not exceed 4.01%,and the material level measurement accuracy can reach 0.40%F.S.展开更多
Based on the scattering characteristic,the comparison of RCS(radar cross-section)at different positions of a target in the same direction of incidence can be obtained first by extruding or deleting part of the entity....Based on the scattering characteristic,the comparison of RCS(radar cross-section)at different positions of a target in the same direction of incidence can be obtained first by extruding or deleting part of the entity.A simulation method of aerial&space targets echo characteristics(A&STEC)is proposed that is universal to aerial and space targets.We utilize a fixed-wing UAV(unmanned aerial vehicle)and typical missiles in simulation.The echo signal modulation characteristic parameters are calculated theoretically by the atmospheric attenuation model,the finite element method and a MUMPS solver.The verification simulations show that this method can analyze the influence of the target shape,incident direction,detection position and detection frequency on echo waveform,intensity and energy distribution.The results show that the profile of echo waveform can invert the general shape of the target.The relationship between time and intensity can determine whether the target is moving towards or away from the detector in addition.These conclusions can provide a reference for the ballistic missile target tracking and the defense against UVA intrusion in theory.展开更多
The ultrasonic echo in liquid density measurement often suffers noise,which makes it difficult to obtain the useful echo waveform,resulting in low accuracy of density measurement.A denoising method based on improved v...The ultrasonic echo in liquid density measurement often suffers noise,which makes it difficult to obtain the useful echo waveform,resulting in low accuracy of density measurement.A denoising method based on improved variational mode decomposition(VMD)for noise echo signals is proposed.The number of decomposition layers of the traditional VMD is hard to determine,therefore,the center frequency similarity factor is firstly constructed and used as the judgment criterion to select the number of VMD decomposition layers adaptively;Secondly,VMD algorithm is used to decompose the echo signal into several modal components with a single modal component,and the useful echo components are extracted based on the features of the ultrasonic emission signal;Finally,the liquid density is calculated by extracting the amplitude and time of the echo from the modal components.The simulation results show that using the improved VMD to decompose the echo signal not only can improve the signal-to-noise ratio of the echo signal to 20.64 dB,but also can accurately obtain the echo information such as time and amplitude.Compared with the ensemble empirical mode decomposition(EEMD),this method effectively suppresses the modal aliasing,keeps the details of the signal to the maximum extent while suppressing noise,and improves the accuracy of the liquid density measurement.The density measurement accuracy can reach 0.21%of full scale.展开更多
Through analyzing the influence on echo signal by factors of kinematical parameters of airborne SAR platform and radar antenna direction, this letter, on the basis of classical SAR echo signal analogue algorithm, puts...Through analyzing the influence on echo signal by factors of kinematical parameters of airborne SAR platform and radar antenna direction, this letter, on the basis of classical SAR echo signal analogue algorithm, puts forward certain airborne SAR echo signal analogue algorithm of distance directional frequency domain pulse coherent accumulation, and goes through simulation. The simulation results have proved the effectiveness of this algorithm.展开更多
During high-intensity focused ultrasound(HIFU)treatment,the accurate identification of denatured biological tissue is an important practical problem.In this paper,a novel method based on the improved variational mode ...During high-intensity focused ultrasound(HIFU)treatment,the accurate identification of denatured biological tissue is an important practical problem.In this paper,a novel method based on the improved variational mode decomposition(IVMD)and autoregressive(AR)model was proposed,which identified denatured biological tissue according to the characteristics of ultrasonic scattered echo signals during HIFU treatment.Firstly,the IVMD method was proposed to solve the problem that the VMD reconstruction signal still has noise due to the limited number of intrinsic mode functions(IMF).The ultrasonic scattered echo signals were reconstructed by the IVMD to achieve denoising.Then,the AR model was introduced to improve the recognition rate of denatured biological tissues.The AR model order parameter was determined by the Akaike information criterion(AIC)and the characteristics of the AR coefficients were extracted.Finally,the optimal characteristics of the AR coefficients were selected according to the results of receiver operating characteristic(ROC).The experiments showed that the signal-to-noise ratio(SNR)and root mean square error(RMSE)of the reconstructed signal obtained by IVMD was better than those obtained by variational mode decomposition(VMD).The IVMD-AR method was applied to the actual ultrasonic scattered echo signals during HIFU treatment,and the support vectormachine(SVM)was used to identify the denatured biological tissue.The results show that compared with sample entropy,information entropy,and energy methods,the proposed IVMD-AR method can more effectively identify denatured biological tissue.The recognition rate of denatured biological tissue was higher,up to 93.0%.展开更多
In high intensity focused ultrasound(HIFU)treatment,it is crucial to accurately identify denatured and normal biological tissues.In this paper,a novel method based on compressed sensing(CS)and refined composite multi-...In high intensity focused ultrasound(HIFU)treatment,it is crucial to accurately identify denatured and normal biological tissues.In this paper,a novel method based on compressed sensing(CS)and refined composite multi-scale fuzzy entropy(RCMFE)is proposed.First,CS is used to denoise the HIFU echo signals.Then the multi-scale fuzzy entropy(MFE)and RCMFE of the denoised HIFU echo signals are calculated.This study analyzed 90 cases of HIFU echo signals,including 45 cases in normal status and 45 cases in denatured status,and the results show that although both MFE and RCMFE can be used to identify denatured tissues,the intra-class distance of RCMFE on each scale factor is smaller than MFE,and the inter-class distance is larger than MFE.Compared with MFE,RCMFE can calculate the complexity of the signal more accurately and improve the stability,compactness,and separability.When RCMFE is selected as the characteristic parameter,the RCMFE difference between denatured and normal biological tissues is more evident than that of MFE,which helps doctors evaluate the treatment effect more accurately.When the scale factor is selected as 16,the best distinguishing effect can be obtained.展开更多
The disguised covert detection method that imitates whale calls has received great attention in recent years because it can solve the traditional problem of the trade-off between long-range detection and covert detect...The disguised covert detection method that imitates whale calls has received great attention in recent years because it can solve the traditional problem of the trade-off between long-range detection and covert detection.However,under strong reverberation conditions,traditional echo signal processing methods based on matched filtering will be greatly disturbed.Based on this,a disguised sonar signal waveform design is proposed based on imitating whale calls and computationally efficient anti-reverberation echo signal processing method.Firstly,this article proposed a disguised sonar signal waveform design method based on imitating whale calls.This method uses linear frequency modulation(LFM)signals to replace LFM-like segments in real whale calls,and extracts the envelope of the real whale call’s LFM-like segment to modify the LFM signal.Secondly,this article proposed an echo signal processing method of fractional Fourier transform(FrFT)based on target echo locating of synchronization signals.This method uses the synchronization signal to locate the target echo,and determines the step-size interval of the FrFT based on the information carried by the synchronization signal.Compared with the traditional FrFT,this method effectively reduces the amount of calculation and also improves the anti-reverberation ability.Finally,the excellent performance of the proposed method is verified by simulation results.展开更多
Sand-dust storm is a type of disastrous weather, typically occurring in arid and semi-arid climates. This study selected a region in the hinterlands of the Taklimakan Desert, called the Tazhong region, as the experime...Sand-dust storm is a type of disastrous weather, typically occurring in arid and semi-arid climates. This study selected a region in the hinterlands of the Taklimakan Desert, called the Tazhong region, as the experimental area to quantitatively estimate the particle concentrations of sand-dust storms using the boundary layer wind-profiling radar. We thoroughly studied the radar echo signals and reflectivity factor features during the sand-dust storms. The results indicate that（1） under sand-dust storm conditions, boundary layer wind-profiling radar cannot capture the complete information regarding horizontal wind velocity and direction, but it can obtain the backscattering intensity of sand-dust storms; and（2） during sand-dust storms particle size distributions in the surface layer closely resemble log-normal distributions, with sand-dust particles sizes of 90–100 μm accounting for the maximum particle probability. Retrieved particle size distributions at heights of 600, 800, and 1000 m follow log-normal distributions, and the expected value of particle diameter decreases gradually with increasing height. From the perspective of orders of magnitude, the retrieved results for particle number concentrations and mass concentrations are consistent with previous aircraft-detected results, indicating that it is basically feasible to use boundary layer wind-profiling radar to quantitatively detect the particle concentrations of dust storms.展开更多
In this work,we introduce a novel framework to investigate ringdown gravitational waveforms in the presence of dynamical matter fields outside the horizon of a black hole.We systematically analyze two distinct scenari...In this work,we introduce a novel framework to investigate ringdown gravitational waveforms in the presence of dynamical matter fields outside the horizon of a black hole.We systematically analyze two distinct scenarios of dynamical matter fields:motion along geodesics and uniform motion with constant velocity.Our results reveal rich phenomena in the ringdown gravitational wave signals,including the suppression or enhancement of echoes,frequency shifts in the decay oscillations,and intricate modulations of the power-law tails.Notably,we demonstrate that subluminal moving potentials can produce irregular echo patterns and shift the dominant frequencies,offering potential new observational signatures beyond the already-known ringdown analyses.This study provides a new perspective for probing dynamic environments around black holes and offers a theoretical foundation for interpreting possible deviations in future gravitational wave detections.展开更多
基金Supported by the State Key Laboratory of Acoustics and Marine Information Chinese Academy of Sciences(SKL A202507).
文摘Accurate time delay estimation of target echo signals is a critical component of underwater target localization.In active sonar systems,echo signal processing is vulnerable to the effects of reverberation and noise in the maritime environment.This paper proposes a novel method for estimating target time delay using multi-bright spot echoes,assuming the target’s size and depth are known.Aiming to effectively enhance the extraction of geometric features from the target echoes and mitigate the impact of reverberation and noise,the proposed approach employs the fractional order Fourier transform-frequency sliced wavelet transform to extract multi-bright spot echoes.Using the highlighting model theory and the target size information,an observation matrix is constructed to represent multi-angle incident signals and obtain the theoretical scattered echo signals from different angles.Aiming to accurately estimate the target’s time delay,waveform similarity coefficients and mean square error values between the theoretical return signals and received signals are computed across various incident angles and time delays.Simulation results show that,compared to the conventional matched filter,the proposed algorithm reduces the relative error by 65.9%-91.5%at a signal-to noise ratio of-25 dB,and by 66.7%-88.9%at a signal-to-reverberation ratio of−10 dB.This algorithm provides a new approach for the precise localization of submerged targets in shallow water environments.
基金funded by the National Key R&D Program of China(Grant No.2022YFC3300705)the National Natural Science Foundation of China(Grant Nos.62203056,12202048,and 62201056).
文摘Atmospheric aerosols are the primary contributors to environmental pollution.As such aerosols are micro-to nanosized particles invisible to the naked eye,it is necessary to utilize LiDAR technology for their detection.The laser radar echo signal is vulnerable to background light and electronic thermal noise.While single-photon LiDAR can effectively reduce background light interference,electronic thermal noise remains a significant challenge,especially at long distances and in environments with a low signal-to-noise ratio(SNR).However,conventional denoising methods cannot achieve satisfactory results in this case.In this paper,a novel adaptive continuous threshold wavelet denoising algorithm is proposed to filter out the noise.The algorithm features an adaptive threshold and a continuous threshold function.The adaptive threshold is dynamically adjusted according to the wavelet decomposition level,and the continuous threshold function ensures continuity with lower constant error,thus optimizing the denoising process.Simulation results show that the proposed algorithm has excellent performance in improving SNR and reducing root mean square error(RMSE)compared with other algorithms.Experimental results show that denoising of an actual LiDAR echo signal results in a 4.37 dB improvement in SNR and a 39.5%reduction in RMSE.The proposed method significantly enhances the ability of single-photon LiDAR to detect weak signals.
基金National Natural Science Foundation of China(No.61761027)。
文摘The echo of the material level is non-stationary and contains many singularities.The echo contains false echoes and noise,which affects the detection of the material level signals,resulting in low accuracy of material level measurement.A new method for detecting and correcting the material level signal is proposed,which is based on the generalized S-transform and singular value decomposition(GST-SVD).In this project,the change of material level is regarded as the low speed moving target.First,the generalized S-transform is performed on the echo signals.During the transformation process,the variation trend of window of the generalized S-transform is adjusted according to the frequency distribution characteristics of the material level echo signal,achieving the purpose of detecting the signal.Secondly,the SVD is used to reconstruct the time-frequency coefficient matrix.At last,the reconstructed time-frequency matrix performs an inverse transform.The experimental results show that the method can accurately detect the material level echo signal,and it can reserve the detailed characteristics of the signal while suppressing the noise,and reduce the false echo interference.Compared with other methods,the material level measurement error does not exceed 4.01%,and the material level measurement accuracy can reach 0.40%F.S.
文摘Based on the scattering characteristic,the comparison of RCS(radar cross-section)at different positions of a target in the same direction of incidence can be obtained first by extruding or deleting part of the entity.A simulation method of aerial&space targets echo characteristics(A&STEC)is proposed that is universal to aerial and space targets.We utilize a fixed-wing UAV(unmanned aerial vehicle)and typical missiles in simulation.The echo signal modulation characteristic parameters are calculated theoretically by the atmospheric attenuation model,the finite element method and a MUMPS solver.The verification simulations show that this method can analyze the influence of the target shape,incident direction,detection position and detection frequency on echo waveform,intensity and energy distribution.The results show that the profile of echo waveform can invert the general shape of the target.The relationship between time and intensity can determine whether the target is moving towards or away from the detector in addition.These conclusions can provide a reference for the ballistic missile target tracking and the defense against UVA intrusion in theory.
文摘The ultrasonic echo in liquid density measurement often suffers noise,which makes it difficult to obtain the useful echo waveform,resulting in low accuracy of density measurement.A denoising method based on improved variational mode decomposition(VMD)for noise echo signals is proposed.The number of decomposition layers of the traditional VMD is hard to determine,therefore,the center frequency similarity factor is firstly constructed and used as the judgment criterion to select the number of VMD decomposition layers adaptively;Secondly,VMD algorithm is used to decompose the echo signal into several modal components with a single modal component,and the useful echo components are extracted based on the features of the ultrasonic emission signal;Finally,the liquid density is calculated by extracting the amplitude and time of the echo from the modal components.The simulation results show that using the improved VMD to decompose the echo signal not only can improve the signal-to-noise ratio of the echo signal to 20.64 dB,but also can accurately obtain the echo information such as time and amplitude.Compared with the ensemble empirical mode decomposition(EEMD),this method effectively suppresses the modal aliasing,keeps the details of the signal to the maximum extent while suppressing noise,and improves the accuracy of the liquid density measurement.The density measurement accuracy can reach 0.21%of full scale.
文摘Through analyzing the influence on echo signal by factors of kinematical parameters of airborne SAR platform and radar antenna direction, this letter, on the basis of classical SAR echo signal analogue algorithm, puts forward certain airborne SAR echo signal analogue algorithm of distance directional frequency domain pulse coherent accumulation, and goes through simulation. The simulation results have proved the effectiveness of this algorithm.
基金The authors thank the financial support of Natural Science Foundation of China(U2031112)Natural Science Foundation of Hunan Province(2021JJ30469)Natural Science Youth Foundation of Hunan Province(2020JJ5396).
文摘During high-intensity focused ultrasound(HIFU)treatment,the accurate identification of denatured biological tissue is an important practical problem.In this paper,a novel method based on the improved variational mode decomposition(IVMD)and autoregressive(AR)model was proposed,which identified denatured biological tissue according to the characteristics of ultrasonic scattered echo signals during HIFU treatment.Firstly,the IVMD method was proposed to solve the problem that the VMD reconstruction signal still has noise due to the limited number of intrinsic mode functions(IMF).The ultrasonic scattered echo signals were reconstructed by the IVMD to achieve denoising.Then,the AR model was introduced to improve the recognition rate of denatured biological tissues.The AR model order parameter was determined by the Akaike information criterion(AIC)and the characteristics of the AR coefficients were extracted.Finally,the optimal characteristics of the AR coefficients were selected according to the results of receiver operating characteristic(ROC).The experiments showed that the signal-to-noise ratio(SNR)and root mean square error(RMSE)of the reconstructed signal obtained by IVMD was better than those obtained by variational mode decomposition(VMD).The IVMD-AR method was applied to the actual ultrasonic scattered echo signals during HIFU treatment,and the support vectormachine(SVM)was used to identify the denatured biological tissue.The results show that compared with sample entropy,information entropy,and energy methods,the proposed IVMD-AR method can more effectively identify denatured biological tissue.The recognition rate of denatured biological tissue was higher,up to 93.0%.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11774088 and 11474090)。
文摘In high intensity focused ultrasound(HIFU)treatment,it is crucial to accurately identify denatured and normal biological tissues.In this paper,a novel method based on compressed sensing(CS)and refined composite multi-scale fuzzy entropy(RCMFE)is proposed.First,CS is used to denoise the HIFU echo signals.Then the multi-scale fuzzy entropy(MFE)and RCMFE of the denoised HIFU echo signals are calculated.This study analyzed 90 cases of HIFU echo signals,including 45 cases in normal status and 45 cases in denatured status,and the results show that although both MFE and RCMFE can be used to identify denatured tissues,the intra-class distance of RCMFE on each scale factor is smaller than MFE,and the inter-class distance is larger than MFE.Compared with MFE,RCMFE can calculate the complexity of the signal more accurately and improve the stability,compactness,and separability.When RCMFE is selected as the characteristic parameter,the RCMFE difference between denatured and normal biological tissues is more evident than that of MFE,which helps doctors evaluate the treatment effect more accurately.When the scale factor is selected as 16,the best distinguishing effect can be obtained.
基金National Natural Science Foundations of China under Grant(Nos.61971307,61905175,51775377)National Key Research and Development Plan Project(No.2020YFB2010800)+5 种基金Fok Ying Tung Education Foundation(No.171055)China Postdoctoral Science Foundation(No.2020M680878)Guangdong Province Key Research and Development Plan Project(No.2020B0404030001)Tianjin Science and Technology Plan Project(No.20YDTPJC01660)Foreign Affairs Committee of China Aviation Development Sichuan Gas Turbine Research Institute(Nos.GJCZ-2020-0040,GJCZ-2020-0041)Science and Technology on Underwater Information and Control Laboratory under Grant(No.6142218081811)。
文摘The disguised covert detection method that imitates whale calls has received great attention in recent years because it can solve the traditional problem of the trade-off between long-range detection and covert detection.However,under strong reverberation conditions,traditional echo signal processing methods based on matched filtering will be greatly disturbed.Based on this,a disguised sonar signal waveform design is proposed based on imitating whale calls and computationally efficient anti-reverberation echo signal processing method.Firstly,this article proposed a disguised sonar signal waveform design method based on imitating whale calls.This method uses linear frequency modulation(LFM)signals to replace LFM-like segments in real whale calls,and extracts the envelope of the real whale call’s LFM-like segment to modify the LFM signal.Secondly,this article proposed an echo signal processing method of fractional Fourier transform(FrFT)based on target echo locating of synchronization signals.This method uses the synchronization signal to locate the target echo,and determines the step-size interval of the FrFT based on the information carried by the synchronization signal.Compared with the traditional FrFT,this method effectively reduces the amount of calculation and also improves the anti-reverberation ability.Finally,the excellent performance of the proposed method is verified by simulation results.
基金supported by the National Natural Science Foundation of China (41775030, 41575008, 11302111, 11562017)the China Research Foundation for Desert Meteorology (SQJ2014003)the China Postdoctoral Science Foundation
文摘Sand-dust storm is a type of disastrous weather, typically occurring in arid and semi-arid climates. This study selected a region in the hinterlands of the Taklimakan Desert, called the Tazhong region, as the experimental area to quantitatively estimate the particle concentrations of sand-dust storms using the boundary layer wind-profiling radar. We thoroughly studied the radar echo signals and reflectivity factor features during the sand-dust storms. The results indicate that（1） under sand-dust storm conditions, boundary layer wind-profiling radar cannot capture the complete information regarding horizontal wind velocity and direction, but it can obtain the backscattering intensity of sand-dust storms; and（2） during sand-dust storms particle size distributions in the surface layer closely resemble log-normal distributions, with sand-dust particles sizes of 90–100 μm accounting for the maximum particle probability. Retrieved particle size distributions at heights of 600, 800, and 1000 m follow log-normal distributions, and the expected value of particle diameter decreases gradually with increasing height. From the perspective of orders of magnitude, the retrieved results for particle number concentrations and mass concentrations are consistent with previous aircraft-detected results, indicating that it is basically feasible to use boundary layer wind-profiling radar to quantitatively detect the particle concentrations of dust storms.
基金supported by the National Natural Science Foundation of China(Grant No.12175108)supported by Yantai University(Grant No.WL22B224.)。
文摘In this work,we introduce a novel framework to investigate ringdown gravitational waveforms in the presence of dynamical matter fields outside the horizon of a black hole.We systematically analyze two distinct scenarios of dynamical matter fields:motion along geodesics and uniform motion with constant velocity.Our results reveal rich phenomena in the ringdown gravitational wave signals,including the suppression or enhancement of echoes,frequency shifts in the decay oscillations,and intricate modulations of the power-law tails.Notably,we demonstrate that subluminal moving potentials can produce irregular echo patterns and shift the dominant frequencies,offering potential new observational signatures beyond the already-known ringdown analyses.This study provides a new perspective for probing dynamic environments around black holes and offers a theoretical foundation for interpreting possible deviations in future gravitational wave detections.
