Hurst Analysis Research Articles

The heart sound classification of congenital heart disease by using median EEMD-Hurst and threshold denoising method.

Heart sound signals are vital for the machine-assisted detection of congenital heart disease. However, the performance of diagnostic results is limited by noise during heart sound acquisition. A limitation of existing noise reduction schemes is that the pathological components of the signal are weak, which have the potential to be filtered out with the noise. In this research, a novel approach for classifying heart sounds based on median ensemble empirical mode decomposition (MEEMD), Hurst analysis, improved threshold denoising, and neural networks are presented. In decomposing the heart sound signal into several intrinsic mode functions (IMFs), mode mixing and mode splitting can be effectively suppressed by MEEMD. Hurst analysis is adopted for identifying the noisy content of IMFs. Then, the noise-dominated IMFs are denoised by an improved threshold function. Finally, the noise reduction signal is generated by reconstructing the processed components and the other components. A database of 5000 heart sounds from congenital heart disease and normal volunteers was constructed. The Mel spectral coefficients of the denoised signals were used as input vectors to the convolutional neural network for classification to verify the effectiveness of the preprocessing algorithm. An accuracy of 93.8%, a specificity of 93.1%, and a sensitivity of 94.6% were achieved for classifying the normal cases from abnormal one.

Identifying impending failure in heterogeneous materials: A study on acoustic emission time series

In the present paper, precursors to identify impending failure in heterogeneous materials are investigated by analyzing Acoustic Emission (AE) time series. Three main approaches are considered: (1) long-range correlations using the Hurst (H) analysis, (2) Natural Time (NT) analysis, and (3) a proposed Method of Critical Fluctuations-Based (MCF-B) approach. The above approaches are employed to data collected from an experimental AE test on a concrete cubic specimen subjected to an axial compression loading. The results indicate that: persistent long-range correlations tend towards near-random behavior prior to imminent failure; critical regions, characterized by the convergence of natural time parameters, show a direct correlation with imminent increments in the acoustic emission activity and the structure's collapse; the proposed MCF-B approach as precursor, is capable to identify critical states, being the results in agreement with those from NT and Hurst analysis.

Industrial production over the business cycle 1919–2022: R/S and wavelet hurst analysis of multifractality and Austrian business cycle theory

Industrial production over the business cycle 1919–2022: R/S and wavelet hurst analysis of multifractality and Austrian business cycle theory

Spatiotemporal patterns, sustainability, and primary drivers of NDVI-derived vegetation dynamics (2003-2022) in Nepal.

Understanding the vegetation dynamics and their drivers in Nepal has significant scientific reference value for implementing sustainable ecological policies. This study provides a comprehensive analysis of the spatio-temporal variations in vegetation cover in Nepal from 2003 to 2022 using MODIS NDVI data and explores the effects of climatic factors and anthropogenic activities on vegetation. Mann-Kendall test was used to assess the significant trend in NDVI and was integrated with the Hurst exponent to predict future trends. The driving factors of NDVI dynamics were analyzed using Pearson's correlation, partial derivative, and residual analysis methods. The results indicate that over the last 20 years, Nepal has experienced an increasing trend in NDVI at 0.0013 year-1, with 80% of the surface area (vegetation cover) showing an increasing vegetation trend (~ 28% with a significant increase in vegetation). Temperature influenced vegetation dynamics in the higher elevation areas, while precipitation and human interventions influenced the lower elevation areas. The Hurst exponent analysis predicts an improvement in the vegetation cover (greening) for a larger area compared to vegetation degradation (browning). A significantly increased area of NDVI residuals indicates a positive anthropogenic influence on vegetation cover. Anthropogenic activities have a higher relative contribution to NDVI variation followed by temperature and then precipitation. The results of residual trend and Hurst analysis in different regions of Nepal help identify degraded areas, both in the present and future. This information can assist relevant authorities in implementing appropriate policies for a sustainable ecological environment.

Analysis of Spatio-Temporal Evolution and Driving Factors of Eco-Environmental Quality during Highway Construction Based on RSEI

One essential part of transportation infrastructure is highways. The surrounding eco-environment is greatly impacted by the construction of highways. However, few studies have investigated changes in eco-environmental quality during highway construction, and the main impact areas of the construction have not been clarified. The highway from Sunit Right Banner to Huade (Inner Mongolia–Hebei border) was used as the study area. GEE was used to establish RSEI. During highway construction, Sen + M-K trend analysis, Hurst analysis, and Geodetector were employed to assess RSEI changes and driving factors. The results show the following: (1) An area of 1500 m around the highway is where the ecological impact of highway construction will be the greatest. (2) The curve of the annual mean of the RSEI from 2016 to 2021 is V-shaped. From northwest to southeast, there is an increasing trend in spatial distribution. (3) The largest environmental degradation during highway construction occurred during the first year of highway construction. (4) The factor detector results indicate that DEM, precipitation, distance from the administrative district, and FVC were the main RSEI drivers in the research region. The interaction detector’s findings show that the drivers’ combined influence on the RSEI was greater than that of their individual components. (5) Compared to the 2016–2021 trend, the proportion of future degraded areas in terms of eco-environmental quality will increase by 3.16%, while the proportion of improved areas will decrease by 2.99%.

Measuring solid particles in sand-carrying gas flow using multiscale vibration response statistics and deep learning algorithms

A method to quantitate sand particles in turbulent gas flow that combines the multiscale triaxial vibration response and deep learning algorithms is proposed. First, an optimized adaptive wavelet-empirical mode decomposition (EMD) denoising method is proposed based on multifrequency coherent and statistical analysis. Second, complex gas–solid turbulent flow information under multiple gas–particle coupling is characterized based on Hilbert-Huang transform (HHT), Hurst analysis, EMD entropy, etc. In addition, a deep learning algorithm that integrates multiscale flow information to determine sand content that includes two independent branches, a pure deep convolutional neural network (CNN) model driven by microscale triaxial response and a shallow long short-term memory (LSTM) network with regularization driven by mesoscale triaxial response, is proposed. Finally, a quantitative model to characterize sand-carrying turbulent gas flow based on the entropy weight effect of the triaxial vibration response is constructed as follows: Csand=A·p.∑i=xzSiQi. Experimental validation indicates that the proposed deep learning algorithm has recognition and prediction accuracy of 97.8% and 96.97% for sand particle size and the power spectrum, respectively, which are higher than those of the existing intelligent models to characterize sand information. Moreover, the quantitative sand content model based on the multiscale response and deep learning algorithm has a maximum error of only 1.56% under strong turbulence.

Flow regime identification using pressure fluctuation signals in an aerated vessel stirred

A novel method was proposed to determine the flow regime based on the bottom pressure fluctuations of the stirred tank. Statistical, Hurst, Shannon entropy and chaos analysis methods were used to analyze the pressure time series in an aerated stirred tank with a Rushton impeller, and the relationship between the characteristic parameters and the flow regimes was established. The results showed that the bubble motion in the loading regime was obviously stronger than that in the flooding regime, and the homogeneity of the system was rapidly improved. Compared with the first two stages, the chaotic extent of the complete dispersion regime was slightly weaker, and the benefit generated by continuously increasing the speed was limited at this time. In addition, considering the sensitivity of pressure pulsations to the gas–liquid dispersion state, the transition points of the three flow regimes were successfully identified by the standard deviation and the largest Lyapunov exponent. The data were well consistent with the measurements from the visual method and power method, with a maximum deviation of 16%. This demonstrated that it was a reliable non-invasive method for flow regime identification in gas–liquid stirred tanks.

Changes in Net Primary Productivity and Factor Detection in China’s Yellow River Basin from 2000 to 2019

Net primary productivity (NPP) is a main contributor to ecosystem carbon pools. It is crucial to monitor the spatial and temporal dynamics of NPP, as well as to assess the impacts of climate change and human activities to cope with global change. The dynamic of the NPP in China’s Yellow River Basin (YRB) from 2000 to 2019 and its influencing factors were analyzed by using trend and persistence tests and the GeoDetector method. The results show that the NPP had strong spatial heterogeneity, with a low NPP in the west and north, and a high NPP in the east and south. From 2000 to 2019, the NPP showed a statistically significant increase (at a mean of 5.5 g C m−2 yr−1, for a cumulative increase of 94.5 Tg C). A Hurst analysis showed that for the NPP in 76.3% of the YRB, the time series was anti-persistent. The spatial heterogeneity of the NPP in the YRB was mainly explained by precipitation and relative humidity (q value ranged from 0.24 to 0.44). However, the strength of the precipitation explained the decreased variation over time (q value decreased from 0.40 in 2000 to 0.26 in 2019). Interactions between the climate factors and human activities affected the NPP more strongly than individual factors. The results emphasize the importance of strengthening future research on the interaction between climate change and human activities. The results reveal the risk and optimal ranges of the driving factors and provide a quantification of the impacts of those factors regarding NPP. These findings can provide a scientific basis for vegetation restoration in the YRB.

Spatial-temporal evolution of vegetation coverage and its relationship with terrain and human factors in the upper reaches of Ganjiang River Basin, China

Vegetation coverage is an important indicator for evaluating regional environmental quality. Based on MODIS NDVI and DEM data collected for the upper reaches of the Ganjiang River Basin, China, this study used trend analysis, coefficient of variation, Hurst index, and linear regression to analyze the temporal and spatial evolution of vegetation coverage and its relationship with terrain factors in the basin during the years 2000–2020. The vegetation coverage in the study area showed a fluctuating increasing trend at a rate of 5%/10y, and an increasing trend with increasing elevation. The maximum vegetation coverage was identified in the elevation zone of 750–1,000 m, with an average of 83.54%. Vegetation coverage also showed an increasing trend with increasing slope. The maximum vegetation coverage was up to 82.22% in the slope zone of ≥25°. There were no significant differences among the distributions of vegetation coverage in different aspects because the terrain in the study area is not rugged enough to form barriers against sunlight. The vegetation coverage was relatively stable in the study area, with an average coefficient of variation of 14.8%. Hurst analysis showed that the anti-sustainability effect of vegetation change was stronger than that of sustainability, and weak anti-sustainability was dominant. The effects of human activities mainly concentrated in the areas of low elevation and small slopes less than 2°where cities and towns are located. The findings can provide a scientific basis for the management of regional ecosystems in the future.

Investigating the spatiotemporal changes and driving factors of nighttime light patterns in RCEP Countries based on remote sensed satellite images

The Regional Comprehensive Economic Partnership (RCEP) agreement signed in November 2020 is the world's largest and greatest potential free trade area. It was officially enforced on January 1, 2022, which attracted great worldwide attention. The RCEP advocates for the development of the low-carbon economy but lacks effective monitoring methods for socioeconomic conditions and carbon emissions . Nighttime light (NTL) images can objectively reflect socioeconomic status and carbon emission potential. However, most studies focused only on consistency correction for multi-source NTL data without deeply analyzing NTL dynamics. An in-depth analysis of the NTL change in the RCEP region is necessary and will strongly facilitate the strategic deployment of a low-carbon economy in RCEP countries. Sen's slope estimator, the Mann-Kendall trend test, the Mann-Kendall mutation test, and Hurst analysis were adopted to analyze the spatiotemporal changes of NTL in the past and future, and gray relational analysis was applied to explore driving factors. The results showed that (1) RCEP's NTL became brighter from 2000 to 2018, and the total NTL amount in 2018 was 3.27 times that in 2000. NTL in all countries except Japan showed an increasing trend to varying degrees, and this trend was more pronounced in developing countries. The maximum increase amount and growth rate were in China and Vietnam, respectively. (2) Areas where NTL showed an increasing trend in the past accounted for 76.67% of the NTL zones, and the areas where predicted to be brighter in the future accounted for 63.87%. These regions were generally clustered in developed urban zones. However, most Japanese cities have observed darkening trends. (3) The relational grade between NTL and all socioeconomic factors in the RECP region was greater than 0.6, and construction land expansion was the most direct and profound driver. Compared with that in developed countries, NTL in developing countries was more closely related to socioeconomic factors. Spatiotemporal Changes and Driving Factors in Nighttime Light for the RCEP Region. • Nighttime light (NTL) in the RCEP region became brighter from 2000 to 2018. • NTL in developed cities increased significantly and is expected to be brighter. • China led the lighting trend, while Japan's NTL declined. • Construction land expansion was the dominant driver of NTL changes in RCEP region. • Socioeconomic factors in developing countries more strongly promoted NTL increases.

Hurst analysis of dynamic networks.

The sequence of network snapshots with time stamps is an effective tool for describing system dynamics. First, this article constructs a multifractal analysis of a snapshot network, in which the Hurst integral is used to describe the fractal structure hidden in structural dynamics. Second, we adjusted the network model and conducted comparative analysis to clarify the meaning of the Hurst exponent and found that the snapshot network usually includes multiple fractal structures, such as local and global fractal structures. Finally, we discussed the fractal structure of two real network datasets. We found that the real snapshot network also includes rich dynamics, which can be distinguished by the Hurst exponent. In particular, the dynamics of financial networks includes multifractal structures. This article provides a perspective to study the dynamic networks, thereby indirectly describing the fractal characteristics of complex system dynamics.

Computerized lung sound based classification of asthma and chronic obstructive pulmonary disease (COPD)

Diagnostic ambiguity between chronic pulmonary diseases like asthma and Chronic Obstructive Pulmonary Disease (COPD) is very high, as they exhibit similar symptoms, which is the factor responsible for misdiagnosis, leading to heavy deaths every year. To prevent misdiagnosis, some useful work is highly required. This article presents the implementation of a computerized lung sound (LS) based method to classify asthma and COPD cases.The study is conducted on 80 asthma, 80 COPD and 80 healthy LSs.The LS denoising is carried out using empirical mode decomposition (EMD), Hurst analysis and spectral subtraction method. Wavelet entropy (WE) and wavelet packet energy (WPE) features of LS’s are extracted. Various classifiers like support vector machine (SVM), decision tree (DT), k-nearest neighbor (KNN) and discriminant analysis (DA) are accessed to classify healthy, COPD and asthma using WE and WPE features of LS to produce better outcomes. Using the proposed algorithm, the study discriminates between healthy, asthma and COPD cases based on LS with a considerable classification accuracy of 99.3% using the decision tree (DT) classifier. Thus, the study confirms the successful differentiation of asthma and COPD based on LS. Future endeavours will be based on the validation of this algorithm to distinguish the real-time LS data acquired from asthmatic and COPD patients.

THE EFFECT OF NOISE AND NONLINEAR NOISE REDUCTION METHODS ON THE FRACTAL DIMENSION OF CHAOTIC TIME SERIES

The fractal dimension (FD) of a signal is a useful measure for characterizing its complexity. The real signals are contaminated with noise, which leads to reduced efficiency of the fractal analysis. This paper investigates the effect of noise on the FD computation and the compares the fractal dimensions obtained from noise-reduced signals. To this aim, the FD of different continuous and discrete chaotic time series is computed in the case of noise-free and noisy signals, using Katz, Higuchi, and Leibovich and Toth algorithms. Also for further investigations, the result of Lyapunov and Hurst analysis is presented. It is observed that in the continuous-time systems, the fractal dimensions obtained from all algorithms have significant changes in the presence of noise. While for the discrete-time signals, the Katz and the Higuchi dimensions have more robustness to noise. Furthermore, the Lyapunov exponent is decreased, and the Hurst exponent is increased. Then, the noisy signals are filtered with four nonlinear noise-reduction methods. The fractal dimensions are calculated from each denoised signal, and the performances of the noise-reduction methods are compared. The results show that the Katz and the Higuchi methods have less percentage change in calculating the dimension of original and filtered signals than the Leibovich and Toth method. The analysis is also done on the real heart rate signals to expand the results to real processes.

Multi-step wind speed forecasting and Hurst analysis using novel hybrid secondary decomposition approach

Wind speed should be predicted in a sensitive and reliable manner for the effective use of wind energy in wind farms. However, the volatility and non-linearity features of wind make it difficult to do so. Hence, many researchers have focused on the development of reliable prediction models for wind speed. Aimed at this challenge, the present study proposes a hybrid model comprised of Ensemble Empirical Mode Decomposition Adaptive Noise (CEEMDAN), Local Mean Decomposition (LMD), Hurst and Back-propagation Neural Network (BPNN). This model is actualized as follows: First, wind speed time series is decomposed into its sub-components via CEEMDAN technique. The least irregular and unsystematic of the IMFs with the highest frequency obtained as a result of decomposition via CEEMDAN is subject to secondary decomposition using the LMD technique. The obtained components are subject to Hurst analysis to be transformed into micro, meso and macro scale series. These series are then applied on feedback artificial neural networks. The analysis results indicate that model proposed has a better performance than the compared traditional forecasting methods (EEMD-VDM-BPNN and EEMD-EWT-BPNN) with regard to prediction accuracy. The MAPE values obtained via the proposed hybrid model were observed to have decreased by 41.16% and 78.80% when compared with those obtained using traditional models.

Dynamic changes of vegetation coverage in China-Myanmar economic corridor over the past 20 years

The China-Myanmar Economic Corridor (CMEC) is a flagship project of the “Belt and Road” Initiative (BRI), which have made a major breakthrough from conceptual planning to actual construction in 2020, and subsequent construction activities will have a definite impact on local vegetation. To provide scientific support for vegetation conservation and sustainable development of the CMEC, statistical methods such as Morlet wavelet analysis, Mann-Kendall mutation test, Sen's slope estimator, Mann-Kendall trend test, and coefficient of variation were adopted to analyze the spatio-temporal changes in vegetation coverage; Hurst analysis was adopted to further predicted likely future development trends. The results suggested that: (1) The CMEC experienced an overall increasing Fractional Vegetation Cover (FVC) at a rate of 0.21%/yr from 2000 to 2019; 2005 was the mutation year when FVC changed from a slow increase to a significant increase. The FVC changes was mainly controlled by a 12-month oscillation period. The seasonal average FVC increase was slightly different, which were ranked in descending order, as winter (0.29%) > autumn (0.17%) > summer (0.14%) = spring (0.14%). The increasing trend in autumn and winter exceeded those in spring and summer, particularly after 2018. (2) The area with an increasing trend in FVC was five times of those with a decreasing trend (~49.40% VS ~ 9.97%). The former was mainly clustered in the Dehong Dai and Jingpo, China, central and southern part of sub-region Myanmar; whereas the latter primarily distributed in main urban zones such as Mangshi, Ruili, Mandalay, and Yangon. Above areas where FVC changes significantly were affected by human activities such as afforestation, agriculture and construction, and the fluctuation of FVC changes was strong in the short term. (3) Future changes in FVC indicated that ~ 88.08% of the CMEC will show a stable and positive trend, mainly agglomerated in forest and farmland zones. However, it is expected that vegetation coverage in main urban zones and several unused land zones formed by farmland degradation will experience further decrease, and the conservation of vegetation in these regions should be a focus during the construction of the CMEC.

Respiratory sound denoising using Empirical Mode Decomposition, Hurst analysis and Spectral Subtraction

Chronic pulmonary diseases, specifically Chronic Obstructive Pulmonary Disease (COPD), is in third position for causing deaths all over the globe. Misdiagnosis and higher health care cost is the reason behind the heavy loss of life every year. To detect such diseases, computerized respiratory sound based diagnosis is one of the non-invasive, economical, convenient and harmless procedures, which could be one of the solutions to this acute problem. But, this diagnostic method is often affected due to noise issues. This paper presents a new method to denoise the respiratory sound using empirical mode decomposition (EMD), Hurst analysis and spectral subtraction. Using this algorithm, the highest signal to noise ratio (SNR) acquired is 27.32 dB and the peak signal to noise ratio (PSNR) is 43.23 dB. The proposed denoising algorithm could be a significant approach for assisting clinicians to make clear interpretations from the respiratory sound. The future work will be based on the elimination of heart sound noises from the respiratory sound signal.

Multiscale dynamic distribution characteristics of dust collectors in wet scrubber based on image fields

ABSTRACT In order to reveal multiscale dynamic distribution characteristics of dust collectors in a wet scrubber, a method for scale decomposition of dust collectors based on Wigner–Ville distribution (WVD), empirical mode decomposition (EMD) and Hurst analysis of grayscale signals is reported. The WVD features of grayscale signals were used to observe the energy distribution details of dust collectors at different frequency bands and time periods. Then, the scale decomposition of dust collectors based on EMD and Hurst analysis of the grayscale signals was carried out. These analysis results showed that the motion behaviors of micro-, meso- and macro-scale subsets of dust collectors were determined: specifically, the single fractal features of micro-scale subsets conform to the motion characteristics of individual dust collectors. The dual fractal characteristics of meso-scale subsets denote the interactions among dust collector aggregations. Additionally, the fractal features of the macro-scale subsets reflect persistent liquid surface fluctuation behavior in wet scrubbers. Finally, the relative contribution of dust collectors at different scales to the effectiveness of dust removal was represented. This is not only an important innovation in the study of micro mechanism of wet dust removal but provides powerful theoretical support for technological innovations in wet scrubbers. Implications: The multiscale dynamic distribution characteristics of dust collectors in wet dust scrubber were explored, using a method for scale decomposition of dust collectors based on Wigner–Ville distribution, empirical mode decomposition and Hurst analysis of grayscale signals. The fractal characteristics of different scales of dust collectors are determined. Besides, the contribution of different scales of dust collectors to the effect of dust removal is quantized. Therefore, this research is very meaningful, which not only has important innovation in the study of micro mechanism of wet dust collectors but provides a powerful theoretical support for technological innovation of wet dust scrubbers.

Monitoring the hydrodynamics and critical variation of separation efficiency of cyclone separator via acoustic emission technique with multiple analysis methods

In this study, a non-invasive and environment-friendly acoustic emission (AE) technique, coupled with multiple analysis methods, was proposed to monitor the critical variation of separation efficiency of a cyclone separator by means of the gas-solid hydrodynamics. Acoustic energy analysis was used to reflect the characteristics of particle motion and particle-wall interaction. Shannon entropy analysis was adopted to reflect chaos and complexity of gas-solid two-phase motion. Multi-scale analysis (Hurst analysis and wavelet analysis) was used to obtain multi-scale characteristics inside the cyclone separator. To be specific, micro-scale collision behaviors of particle-particle and particle-wall, meso-scale interaction behavior between particle clusters and gas phase, and macro-scale interaction behavior (overall flow behavior). Furthermore, by comparison with the results of separation efficiency and pressure drop, the above-mentioned three methods based on AE technique can effectively reflect the critical variation of separation efficiency for cyclone separator.

Multi-scale characteristics and gas-solid interaction among multiple beds in a dual circulating fluidized bed reactor system

To investigate the gas-solid mixing and interaction among reactors of Dual Circulating Fluidized Bed Reactor (DCFBR), the detecting methods of acoustic emission and pressure fluctuation are employed to study the effects of operating parameters including riser gas velocity, bubbling bed gas velocity and pot-seal gas velocity on the gas-solid behavior and multi-scale characteristics of the DCFBR system. The experimental results demonstrate that gas disturbance makes bed particles fully mixed and the intensity of inter-particle mixing increases as gas disturbance intensifies. Meanwhile, inter-particle mixing can also cause changes in voidage. Therefore, gas and solid phases in the reactor have a mutual effect on each other. In addition, the particle circulation rate varies as the operating gas velocity changes, which in turn causes variations in both particle and bubble behaviors in the riser and the bubbling bed with particles and bubbles interacting with each other. By combining the methods of Hurst and fractal dimension analysis, the multi-scale variation of acoustic signals in the upper and lower parts of the riser under fast fluidization is obtained. As the results reveal, there are certain differences in particle clusters and bubble phase behaviors between the upper and lower parts of the riser. The larger the particle cluster size, the more uneven the flow inside the bed, indicating an intensified effect of the inter-granular particle cluster. Moreover, the size of particle cluster, which is related to particle concentration, increases as the concentration intensifies.

Denoising for satellite laser altimetry full-waveform data based on EMD-Hurst analysis

ABSTRACT Full-waveform decomposition is crucial for obtaining accurate satellite-ground distance, the accuracy of which is severely affected by noises. However, the traditional filters all depend on filtering parameters. This paper presents a new and adaptive method for denoising based on empirical mode decomposition (EMD) and Hurst analysis (EMD-Hurst). The noisy full-waveforms are first decomposed into their intrinsic mode functions (IMFs), and the Hurst exponent of each IMF is established by the detrended fluctuation analysis. The IMF is regarded as the high-frequency noise and is deleted if its Hurst exponent is ≤0.5. Both simulated and real full-waveforms were conducted to validate and evaluate the method by comparing with six other IMF selection methods via metrics like waveform decomposition consistency ratio (CR), average error of decomposition parameters, and ICESat/GLAS waveform-parameter product GLAH05. The comparisons show that: (1) under different SNR conditions, EMD-Hurst performs robustly and obtains a higher CR than other EMD based methods; (2) obtains the highest average CR and a relatively lower average error for the echo parameters; and (3) peak numbers and fitting accuracy for GLAH01 are more reasonable and precise than those of GLAH05, which could offer a good reference for the processing on future space-borne full-waveform data.