Understanding how rock slopes respond to blasting loads is crucial for maintaining excavation safety and slope stability.Nevertheless,the spatiotemporal evolution,nonlinear dependence on blasting parameters,and predic...Understanding how rock slopes respond to blasting loads is crucial for maintaining excavation safety and slope stability.Nevertheless,the spatiotemporal evolution,nonlinear dependence on blasting parameters,and predictive behavior of dominant frequency responses in slope vibrations remain insufficiently understood and quantified.This study combines time-frequency analysis with machine learning to explore how the dominant frequency(f_(d))evolves in slopes under blasting.Continuous Wavelet Transform(CWT)was employed to characterize the temporal-frequency evolution of vibration signals,revealing that the dominant frequency exhibits strong spatial dependence and nonlinear variability influenced by blasting parameters and rock mass structures.Three machine learning models,namely Back Propagation Neural Network(BP),Support Vector Machine(SVM),and Random Forest(RF),were developed to predict f_(d) based on 1,000 monitoring samples obtained from numerical and field simulations.Among them,the RF model achieved the highest prediction accuracy,with mean absolute percentage errors(MAPE)below 15%,demonstrating strong robustness and generalization capability.Our analysis shows that external excitation factors,especially the loading frequency(f_(d)),mainly control the frequency response,while internal controlling factors,such as spatial position,lithological variation,and mechanical heterogeneity,modulate localized frequency amplification and energy redistribution.The results reveal that f_(d) tends to decrease with elevation and distance from the blasting source,whereas structural planes and weathered zones induce high-frequency amplification due to scattering and modal coupling effects.This study offers a new framework combining time-frequency analysis and machine learning to measure the nonlinear interaction between blasting and rock mass response,offering new insights for dynamic stability evaluation and hazard mitigation in complex rock slope systems.展开更多
Functionally graded material(FGM)plates are widely used in various engineering structures owing to their tailor-made mechanical properties,whereas cracked homogeneous plates constitute a canonical setting in fracture ...Functionally graded material(FGM)plates are widely used in various engineering structures owing to their tailor-made mechanical properties,whereas cracked homogeneous plates constitute a canonical setting in fracture mechanics analysis.These two classes of problems respectively embody material non-uniformity and geometric discontinuity,thereby imposing more stringent requirements on numerical methods in terms of high-order field continuity and accurate defect representation.Based on the classical Kirchhoff-Love plate theory,a numerical manifold method(MLS-NMM)incorporating moving least squares(MLS)interpolation is developed for bending analysis of FGM plates and fracture simulation of homogeneous plates with defects.The method constructs an H^(2)-regular approximation with high-order continuous weighting functions and,combined with the separation of mathematical and physical covers,establishes a unified framework that accurately handles material gradients and cracks without mesh reconstruction.For the crack tip,a singular physical cover incorporating the Williams asymptotic field is introduced to achieve local enrichment,enabling the natural capture of displacement discontinuity and stress singularity.Stress intensity factors are extracted using the interaction integral method,and the dimensionless J-integral shows a maximum relative error below 1.2%compared with the reference solution.Numerical results indicate that MLS-NMM exhibits excellent convergence performance:using 676 mathematical nodes,the nondimensional central deflection of both FGM and homogeneous plates agrees with reference solutions with a maximum relative error below 0.81%,and no shear locking occurs.A systematic analysis reveals that for a simply supported on all four edges(SSSS)FGM square plate with a/h=10,the nondimensional central deflection increases by 212%as the gradient index nrises from 0 to 5.For a homogeneous plate containing a central crack with c/a=0.6,the nondimensional central deflection increases by approximately 46%compared with the intact plate.Under weak boundary constraints(e.g.,SFSF),the deformation is markedly amplified,with the deflection reaching more than three times that under strong constraints(SCSC).The proposed method provides an efficient,reconstruction-free numerical tool for high-accuracy bending and fracture analyses of FGM and cracked thin-plate structures.展开更多
A novel method of Doppler frequency extraction is proposed for Doppler radar scoring systems. The idea is that the time-frequency map can show how the Doppler frequency varies along the time-line, so the Doppler frequ...A novel method of Doppler frequency extraction is proposed for Doppler radar scoring systems. The idea is that the time-frequency map can show how the Doppler frequency varies along the time-line, so the Doppler frequency extraction becomes curve detection in the image-view. A set of morphological operations are used to implement curve detection. And a map fusion scheme is presented to eliminate the influence of strong direct current （DC） component of echo signal during curve detection. The radar real-life data are used to illustrate the performance of the new approach. Experimental results show that the proposed method can overcome the shortcomings of piecewise-processing-based FFT method and can improve the measuring precision of miss distance.展开更多
The conventional linear time-frequency analysis method cannot achieve high resolution and energy focusing in the time and frequency dimensions at the same time,especially in the low frequency region.In order to improv...The conventional linear time-frequency analysis method cannot achieve high resolution and energy focusing in the time and frequency dimensions at the same time,especially in the low frequency region.In order to improve the resolution of the linear time-frequency analysis method in the low-frequency region,we have proposed a W transform method,in which the instantaneous frequency is introduced as a parameter into the linear transformation,and the analysis time window is constructed which matches the instantaneous frequency of the seismic data.In this paper,the W transform method is compared with the Wigner-Ville distribution(WVD),a typical nonlinear time-frequency analysis method.The WVD method that shows the energy distribution in the time-frequency domain clearly indicates the gravitational center of time and the gravitational center of frequency of a wavelet,while the time-frequency spectrum of the W transform also has a clear gravitational center of energy focusing,because the instantaneous frequency corresponding to any time position is introduced as the transformation parameter.Therefore,the W transform can be benchmarked directly by the WVD method.We summarize the development of the W transform and three improved methods in recent years,and elaborate on the evolution of the standard W transform,the chirp-modulated W transform,the fractional-order W transform,and the linear canonical W transform.Through three application examples of W transform in fluvial sand body identification and reservoir prediction,it is verified that W transform can improve the resolution and energy focusing of time-frequency spectra.展开更多
Focused on the non-statlonarity and real-time analysis of signal in flutter test with progression variable speed （FTPVS）, a new method of recursive time-frequency analysis is presented. The time-varying system is tr...Focused on the non-statlonarity and real-time analysis of signal in flutter test with progression variable speed （FTPVS）, a new method of recursive time-frequency analysis is presented. The time-varying system is tracked on-line by building a time-varying parameter model, and then the relevant parameter spectrum can be obtained. The feasibility and advantages of the method are examined by digital simulation. The results of FTPVS at low-speed wind-tunnel promise the engineering application perspective of the method.展开更多
With the continuous improvement of Synthetic Aperture Radar(SAR) resolution, interpreting the small targets like aircraft in SAR images becomes possible and turn out to be a hot spot in SAR application research. Howev...With the continuous improvement of Synthetic Aperture Radar(SAR) resolution, interpreting the small targets like aircraft in SAR images becomes possible and turn out to be a hot spot in SAR application research. However, due to the complexity of SAR imaging mechanism, interpreting targets in SAR images is a tough problem. This paper presents a new aircraft interpretation method based on the joint time-frequency analysis and multi-dimensional contrasting of basic structures. Moreover, SAR data acquisition experiment is designed for interpreting the aircraft. Analyzing the experiment data with our method, the result shows that the proposed method largely makes use of the SAR data information. The reasonable results can provide some auxiliary support for the SAR images manual interpretation.展开更多
The local wave method is a very good time-frequency method for nonstationaryvibration signal analysis. But the interfering noise has a big influence on the accuracy oftime-frequency analysis. The wavelet packet de-noi...The local wave method is a very good time-frequency method for nonstationaryvibration signal analysis. But the interfering noise has a big influence on the accuracy oftime-frequency analysis. The wavelet packet de-noising method can eliminate the interference ofnoise and improve the signal-noise-ratio. This paper uses the local wave method to decompose thede-noising signal and perform a time-frequency analysis. We can get better characteristics. Finally,an example of wavelet packet de-noising and a local wave time-frequency spectrum application ofdiesel engine surface vibration signal is put forward.展开更多
Rock slope instability is a prevalent geological hazard that imposes significant adverse impacts on engineering activities.Although existing studies have focused on homogeneous rock slopes,the theoretical models for q...Rock slope instability is a prevalent geological hazard that imposes significant adverse impacts on engineering activities.Although existing studies have focused on homogeneous rock slopes,the theoretical models for quantifying the stability of softhard interbedded anti-inclined slopes remain underdeveloped,primarily due to the complex force transfer mechanisms involved.This study proposed a novel theoretical model for the stability analysis of soft-hard interbedded anti-inclined slopes under rainfall conditions.The framework models stratified rock layers as layered cantilever beams with material heterogeneity.Based on the principle of deformation compatibility,it comprehensively accounted for interlayer force transfer and strength degradation resulting from differential deformations among rock layers.Furthermore,it integrated the critical instability length induced by the self-weight of rock layers to determine the fracture depth.The proposed method was validated against engineering case studies and physical model tests,with error falling within an acceptable range.Compared to existing theoretical methods,the proposed method provided a more realistic representation of the slope's stress field.The analysis results demonstrate that rainfall not only reduces the inclination angle of the failure surface but also leads to an approximate 30%decrease in the safety factor.The proposed theoretical model is particularly useful for quickly calculating the stability of soft-hard interbedded anti-inclined rock slope under rainfall conditions,compared to complex and time-consuming numerical simulation calculations.展开更多
Uncertain parameters are widespread in engineering systems.This study investigates the modal analysis of a fluid-conveying pipe subjected to elastic supports with unknown-but-bound parameters.The governing equation fo...Uncertain parameters are widespread in engineering systems.This study investigates the modal analysis of a fluid-conveying pipe subjected to elastic supports with unknown-but-bound parameters.The governing equation for the elastically supported fluid-conveying pipe is transformed into ordinary differential equations using the Galerkin truncation method.The Chebyshev interval approach,integrated with the assumed mode method is then used to investigate the effects of uncertainties of support stiffness,fluid speed,and pipe length on the natural frequencies and mode shapes of the pipe.Additionally,both symmetrical and asymmetrical support stiffnesses are discussed.The accuracy and effectiveness of the Chebyshev interval approach are verified through comparison with the Monte Carlo method.The results reveal that,for the same deviation coefficient,uncertainties in symmetrical support stiffness have a greater impact on the first four natural frequencies than those of the asymmetrical one.There may be significant differences in the sensitivity of natural frequencies and mode shapes of the same order to uncertain parameters.Notably,mode shapes susceptible to uncertain parameters exhibit wider fluctuation intervals near the elastic supports,requiring more attention.展开更多
This study aims to establish an integrated sensitivity analysis framework for optimization and design of the dynamic performance of mechanical systems such as tracked vehicles,by combining the direct differentiation m...This study aims to establish an integrated sensitivity analysis framework for optimization and design of the dynamic performance of mechanical systems such as tracked vehicles,by combining the direct differentiation method(DDM)with the linear multibody system transfer matrix method(linear MSTMM).The rigid-flexible coupled multibody system dynamics model of a tracked vehicle is established using the linear MSTMM and validated through the modal test.Building upon the existing DDM-based eigenvalue sensitivity analysis method within the linear MSTMM,the DDM is embedded into it to enable programmable and efficient computation of dynamic response sensitivities for mechanical systems.The proposed approach is used to quantitatively evaluate the sensitivities of both natural vibration characteristics(e.g.,natural frequencies and mode shapes)and transient dynamic responses of the tracked vehicle with respect to system parameters,successfully identifying critical structural parameters.Compared to conventional finite difference methods,the developed methodology eliminates sensitivity to perturbation step sizes.The contributions of this work lie in establishing a unified theoretical foundation and analysis framework for guiding dynamics optimization and design of mechanical systems,and extending the applicability of the linear MSTMM to sensitivity analysis of transient dynamic responses.展开更多
The probabilistic stability evolution analysis of reservoir bank slopes is a crucial aspect of risk assessment,with core challenges including the consideration of deformation mechanisms and accurate determination of m...The probabilistic stability evolution analysis of reservoir bank slopes is a crucial aspect of risk assessment,with core challenges including the consideration of deformation mechanisms and accurate determination of mechanical parameters.In this study,a novel time-varying reliability analysis framework based on sequential Bayesian updating of mechanical parameters is proposed.The inverse parameters account for damage time-dependent behavior,incorporating water effect and a strain-driven softening-hardening process that depends on sliding states.The likelihood function is enhanced to simultaneously consider observation error,surrogate model prediction error,and model structural error,with the introduction of physical penalty.Exploration of the high-dimensional parameter space is achieved via the Hamiltonian Monte Carlo(HMC)method and the physics knowledge-based time-dependent deformation surrogate model.The time-varying reliability analysis of the slope is performed using the multi-grid method.Taking a reservoir bank slope as a case study,the sequential updating of 12 mechanical parameters is conducted based on deformation time series from 16 monitoring points,thereby validating the proposed framework.The results indicate that the proposed framework effectively captures the posterior distribution of mechanical parameters,with the case slope remaining in a critically stable state after overall sliding,showing a high failure probability.Introducing model structural error can reduce parameter compensation,and a reasonable sequential updating step size can improve inversion accuracy.展开更多
The accurate mechanical analysis of thick-walled pressure vessel structures composed of advanced materials,such as hyperelastic and functionally graded materials(FGMs),is critical for ensuring their safety and optimiz...The accurate mechanical analysis of thick-walled pressure vessel structures composed of advanced materials,such as hyperelastic and functionally graded materials(FGMs),is critical for ensuring their safety and optimizing their design.However,conventional numerical methods can face challenges with the non-linearities inherent in hyperelasticity and the complex spatial variations in FGMs.This paper presents a novel hybrid numerical approach combining Physics-Informed Neural Networks(PINNs)with Finite Element Method(FEM)derived data for the robust analysis of thick-walled,axisymmetric,heterogeneous,hyperelastic pressure vessels with elliptical geometries.A PINN framework incorporating neo-Hookean constitutive relations is developed in MATLAB.To enhance training efficiency and accuracy,the PINN’s loss function is augmented with displacement data obtained from high-fidelity FEM simulations performed in ANSYS.The methodology is rigorously validated by comparing PINN-predicted displacement and von Mises stress fields against ANSYS benchmarks for various scenarios of FGMconfigurations(with material properties varying according to a power law)subjected to internal and external pressurization.The results demonstrate excellent agreement between the proposed hybrid PINN-FEMapproach and conventional FEMsolutions across all test cases,accurately capturing complex deformation patterns and stress concentrations.This study highlights the potential of data-augmented PINNs as an effective and accurate computational tool for tackling complex solid mechanics problems involving non-linearmaterials and significant heterogeneity,offering a promising avenue for future research in engineering design and analysis.展开更多
This article presents a micro-structure tensor enhanced elasto-plastic finite element(FE)method to address strength anisotropy in three-dimensional(3D)soil slope stability analysis.The gravity increase method(GIM)is e...This article presents a micro-structure tensor enhanced elasto-plastic finite element(FE)method to address strength anisotropy in three-dimensional(3D)soil slope stability analysis.The gravity increase method(GIM)is employed to analyze the stability of 3D anisotropic soil slopes.The accuracy of the proposed method is first verified against the data in the literature.We then simulate the 3D soil slope with a straight slope surface and the convex and concave slope surfaces with a 90turning corner to study the 3D effect on slope stability and the failure mechanism under anisotropy conditions.Based on our numerical results,the end effect significantly impacts the failure mechanism and safety factor.Anisotropy degree notably affects the safety factor,with higher degrees leading to deeper landslides.For concave slopes,they can be approximated by straight slopes with suitable boundary conditions to assess their stability.Furthermore,a case study of the Saint-Alban test embankment A in Quebec,Canada,is provided to demonstrate the applicability of the proposed FE model.展开更多
With Beijing Huilongguan Sports and Cultural Park as the research object,this study was conducted to investigate public service satisfaction in the park by the Importance-Performance Analysis(IPA)method.A questionnair...With Beijing Huilongguan Sports and Cultural Park as the research object,this study was conducted to investigate public service satisfaction in the park by the Importance-Performance Analysis(IPA)method.A questionnaire covering six dimensions,including public transportation,sanitation and environment,and supporting facility construction,was designed.A total of 208 valid samples were collected,and SPSS was employed for reliability and validity tests as well as IPA analysis.The findings were as follows:①Visitors were generally quite satisfied with the overall public services in Huilongguan Sports and Cultural Park.②The highest satisfaction levels were observed in sanitation and environment services and the sports and cultural atmosphere,while lower satisfaction was noted for supporting facility construction and public information services.③The advantage enhancement zone includes sanitation and environment services and sports and cultural atmosphere;and the continuous maintenance zone includes public transportation services and security management amd maintenance;the subsequent opportunity zone includes supporting facility construction and public information services;and there are no dimensions in the urgent improvement zone.The study recommends strengthening the service connotations from three aspects:enhancing facilities with sports as the core,optimizing services with a people-centered approach,and upgrading the information platform through technological efficiency.Additionally,a multi-stakeholder collaborative mechanism involving the government in coordinating policy resources,the operator in improving implementation efficiency,and the public participating in supervision and evaluation is proposed to drive the enhancement of public service quality at Huilongguan Sports and Cultural Park.展开更多
To study the uncertainty quantification of resonant states in open quantum systems,we developed a Bayesian framework by integrating a reduced basis method(RBM)emulator with the Gamow coupled-channel(GCC)approach.The R...To study the uncertainty quantification of resonant states in open quantum systems,we developed a Bayesian framework by integrating a reduced basis method(RBM)emulator with the Gamow coupled-channel(GCC)approach.The RBM,constructed via eigenvector continuation and trained on both bound and resonant configurations,enables the fast and accurate emulation of resonance properties across the parameter space.To identify the physical resonant states from the emulator’s output,we introduce an overlap-based selection technique that effectively isolates true solutions from background artifacts.By applying this framework to unbound nucleus ^(6)Be,we quantified the model uncertainty in the predicted complex energies.The results demonstrate relative errors of 17.48%in the real part and 8.24%in the imaginary part,while achieving a speedup of four orders of magnitude compared with the full GCC calculations.To further investigate the asymptotic behavior of the resonant-state wavefunctions within the RBM framework,we employed a Lippmann–Schwinger(L–S)-based correction scheme.This approach not only improves the consistency between eigenvalues and wavefunctions but also enables a seamless extension from real-space training data to the complex energy plane.By bridging the gap between bound-state and continuum regimes,the L–S correction significantly enhances the emulator’s capability to accurately capture continuum structures in open quantum systems.展开更多
Objective:This study aims to explore the benefit analysis of the same disease in different departments of public hospitals under the DIP payment method.Methods:This study is a retrospective analysis that selected clin...Objective:This study aims to explore the benefit analysis of the same disease in different departments of public hospitals under the DIP payment method.Methods:This study is a retrospective analysis that selected clinical data from patients who received treatment in the Department of Orthopedics and the Department of Acupuncture and Moxibustion at our hospital from January 1,2023,to December 31,2023.The study compared the costs of medications,examinations,treatments,laboratory tests,nursing and other expenses,and total treatment costs between the two departments.It analyzed the cost structure of the two departments and proposed further improvement suggestions.Results:The study results indicated that the total costs in the Department of Acupuncture and Moxibustion were significantly higher than those in the Department of Orthopedics.Among medication costs,the total medication costs in the Department of Orthopedics were higher than those in the Department of Acupuncture and Moxibustion,with costs for Western medicine,proprietary Chinese medicine,and herbal medicine all being higher(p<0.05).Regarding examination costs,consultation fees in the Department of Orthopedics were lower than those in the Department of Acupuncture and Moxibustion,while examination costs were higher(p<0.05).In terms of treatment costs,orthopedic treatment and surgical fees were higher than those in the Department of Acupuncture and Moxibustion(p<0.05).For laboratory test costs,orthopedic laboratory fees were significantly higher than those in the Department of Acupuncture and Moxibustion(p<0.05).Among nursing and other expenses,orthopedic blood transfusion,bed fees,and other expenses were higher than those in the Department of Acupuncture and Moxibustion,while nursing fees were lower(p<0.05).Conclusion:Treatment fees in the Department of Acupuncture and Moxibustion are the core and account for a relatively high proportion of the total costs.The benefits generated by the Department of Orthopedics are primarily derived from medication,examination,and laboratory fees,aligning with the characteristics of combining diagnosis,medication,and surgical intervention in orthopedic treatment.Consultation fees,nursing fees,and bed fees in the Department of Acupuncture and Moxibustion are higher than those in the Department of Orthopedics,indicating a longer treatment cycle in acupuncture,which warrants clinical attention.展开更多
The incremental capacity analysis(ICA)technique is notably limited by its sensitivity to variations in charging conditions,which constrains its practical applicability in real-world scenarios.This paper introduces an ...The incremental capacity analysis(ICA)technique is notably limited by its sensitivity to variations in charging conditions,which constrains its practical applicability in real-world scenarios.This paper introduces an ICA-compensation technique to address this limitation and propose a generalized framework for assessing the state of health(SOH)of batteries based on ICA that is applicable under differing charging conditions.This novel approach calculates the voltage profile under quasi-static conditions by subtracting the voltage increase attributable to the additional polarization effects at high currents from the measured voltage profile.This approach's efficacy is contingent upon precisely acquiring the equivalent impedance.To obtain the equivalent impedance throughout the batteries'lifespan while minimizing testing costs,this study employs a current interrupt technique in conjunction with a long short-term memory(LSTM)network to develop a predictive model for equivalent impedance.Following the derivation of ICA curves using voltage profiles under quasi-static conditions,the research explores two scenarios for SOH estimation:one utilizing only incremental capacity(IC)features and the other incorporating both IC features and IC sampling.A genetic algorithm-optimized backpropagation neural network(GABPNN)is employed for the SOH estimation.The proposed generalized framework is validated using independent training and test datasets.Variable test conditions are applied for the test set to rigorously evaluate the methodology under challenging conditions.These evaluation results demonstrate that the proposed framework achieves an estimation accuracy of 1.04%for RMSE and 0.90%for MAPE across a spectrum of charging rates ranging from 0.1 C to 1 C and starting SOCs between 0%and 70%,which constitutes a major advancement compared to established ICA methods.It also significantly enhances the applicability of conventional ICA techniques in varying charging conditions and negates the necessity for separate testing protocols for each charging scenario.展开更多
This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-...This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-oped using the material point method.To reduce the computational cost of Monte Carlo simulations,response surface models are created as surrogate models for the material point system to approximate its dynamic behavior.An adaptive randomized greedy algorithm is employed to construct a sparse polynomial chaos expansion model with a fixed order,effectively balancing the accuracy and computational efficiency of the surrogate model.Based on the sparse polynomial chaos expansion,sensitivity analysis is conducted using the global finite difference and Sobol methods.Several examples of structural dynamics are provided to demonstrate the effectiveness of the proposed method in addressing structural dynamics problems.展开更多
To address the deficiency in loss diagnostic methods for turbines working at off-design angles of attack,a novel loss decomposition method suitable for cascade flow with large separation is proposed.The method propose...To address the deficiency in loss diagnostic methods for turbines working at off-design angles of attack,a novel loss decomposition method suitable for cascade flow with large separation is proposed.The method proposed has the following advantages over existing methods:(A)It enables refined loss decomposition for cascade flows,capable of identifying the spatial range of specific regions such as shear layers and backflow regions,thereby obtaining the loss characteristics of these regions.(B)The region identification criteria in this method have clear physical meanings,rather than relying on arbitrary area division.(C)The method has good applicability and is suitable for cascade flows under various angles of attack.Validation shows that this method achieves satisfactory results.Based on this method,the loss mechanisms of a low-pressure turbine cascade at a low Reynolds number of 4.3×10^(4)and angles of attack of-5°,-20°,and-45°are investigated using Large Eddy Simulations(LESs).Entropy analysis quantitatively demonstrates significant differences in the composition of losses among flow regions,due to their different flow characteristics.From the perspective of flow regions,wake loss dominates total loss,while loss in backflow region is negligible.Furthermore,the variation mechanisms of loss with incidence differ among different flow regions.展开更多
Li transient concentration distribution in spherical active material particles can affect the maximum power density and the safe operating regime of the electric vehicles(EVs). On one hand, the quasiexact/exact soluti...Li transient concentration distribution in spherical active material particles can affect the maximum power density and the safe operating regime of the electric vehicles(EVs). On one hand, the quasiexact/exact solution obtained in the time/frequency domain is time-consuming and just as a reference value for approximate solutions;on the other hand, calculation errors and application range of approximate solutions not only rely on approximate algorithms but also on discharge modes. For the purpose to track the transient dynamics for Li solid-phase diffusion in spherical active particles with a tolerable error range and for a wide applicable range, it is necessary to choose optimal approximate algorithms in terms of discharge modes and the nature of active material particles. In this study, approximation methods,such as diffusion length method, polynomial profile approximation method, Padé approximation method,pseudo steady state method, eigenfunction-based Galerkin collocation method, and separation of variables method for solving Li solid-phase diffusion in spherical active particles are compared from calculation fundamentals to algorithm implementation. Furthermore, these approximate solutions are quantitatively compared to the quasi-exact/exact solution in the time/frequency domain under typical discharge modes, i.e., start-up, slow-down, and speed-up. The results obtained from the viewpoint of time-frequency analysis offer a theoretical foundation on how to track Li transient concentration profile in spherical active particles with a high precision and for a wide application range. In turn, optimal solutions of Li solid diffusion equations for spherical active particles can improve the reliability in predicting safe operating regime and estimating maximum power for automotive batteries.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.52379098,52274075)the Project of Xingliao Talents Program(XLYC2203008)the Science and Technology Program Project of Liaoning Province(2025JH2/101900011).
文摘Understanding how rock slopes respond to blasting loads is crucial for maintaining excavation safety and slope stability.Nevertheless,the spatiotemporal evolution,nonlinear dependence on blasting parameters,and predictive behavior of dominant frequency responses in slope vibrations remain insufficiently understood and quantified.This study combines time-frequency analysis with machine learning to explore how the dominant frequency(f_(d))evolves in slopes under blasting.Continuous Wavelet Transform(CWT)was employed to characterize the temporal-frequency evolution of vibration signals,revealing that the dominant frequency exhibits strong spatial dependence and nonlinear variability influenced by blasting parameters and rock mass structures.Three machine learning models,namely Back Propagation Neural Network(BP),Support Vector Machine(SVM),and Random Forest(RF),were developed to predict f_(d) based on 1,000 monitoring samples obtained from numerical and field simulations.Among them,the RF model achieved the highest prediction accuracy,with mean absolute percentage errors(MAPE)below 15%,demonstrating strong robustness and generalization capability.Our analysis shows that external excitation factors,especially the loading frequency(f_(d)),mainly control the frequency response,while internal controlling factors,such as spatial position,lithological variation,and mechanical heterogeneity,modulate localized frequency amplification and energy redistribution.The results reveal that f_(d) tends to decrease with elevation and distance from the blasting source,whereas structural planes and weathered zones induce high-frequency amplification due to scattering and modal coupling effects.This study offers a new framework combining time-frequency analysis and machine learning to measure the nonlinear interaction between blasting and rock mass response,offering new insights for dynamic stability evaluation and hazard mitigation in complex rock slope systems.
基金supported by Beijing Natural Science Foundation(L233025)。
文摘Functionally graded material(FGM)plates are widely used in various engineering structures owing to their tailor-made mechanical properties,whereas cracked homogeneous plates constitute a canonical setting in fracture mechanics analysis.These two classes of problems respectively embody material non-uniformity and geometric discontinuity,thereby imposing more stringent requirements on numerical methods in terms of high-order field continuity and accurate defect representation.Based on the classical Kirchhoff-Love plate theory,a numerical manifold method(MLS-NMM)incorporating moving least squares(MLS)interpolation is developed for bending analysis of FGM plates and fracture simulation of homogeneous plates with defects.The method constructs an H^(2)-regular approximation with high-order continuous weighting functions and,combined with the separation of mathematical and physical covers,establishes a unified framework that accurately handles material gradients and cracks without mesh reconstruction.For the crack tip,a singular physical cover incorporating the Williams asymptotic field is introduced to achieve local enrichment,enabling the natural capture of displacement discontinuity and stress singularity.Stress intensity factors are extracted using the interaction integral method,and the dimensionless J-integral shows a maximum relative error below 1.2%compared with the reference solution.Numerical results indicate that MLS-NMM exhibits excellent convergence performance:using 676 mathematical nodes,the nondimensional central deflection of both FGM and homogeneous plates agrees with reference solutions with a maximum relative error below 0.81%,and no shear locking occurs.A systematic analysis reveals that for a simply supported on all four edges(SSSS)FGM square plate with a/h=10,the nondimensional central deflection increases by 212%as the gradient index nrises from 0 to 5.For a homogeneous plate containing a central crack with c/a=0.6,the nondimensional central deflection increases by approximately 46%compared with the intact plate.Under weak boundary constraints(e.g.,SFSF),the deformation is markedly amplified,with the deflection reaching more than three times that under strong constraints(SCSC).The proposed method provides an efficient,reconstruction-free numerical tool for high-accuracy bending and fracture analyses of FGM and cracked thin-plate structures.
基金the Ministerial Level Advanced Research Foundation(020045089)
文摘A novel method of Doppler frequency extraction is proposed for Doppler radar scoring systems. The idea is that the time-frequency map can show how the Doppler frequency varies along the time-line, so the Doppler frequency extraction becomes curve detection in the image-view. A set of morphological operations are used to implement curve detection. And a map fusion scheme is presented to eliminate the influence of strong direct current （DC） component of echo signal during curve detection. The radar real-life data are used to illustrate the performance of the new approach. Experimental results show that the proposed method can overcome the shortcomings of piecewise-processing-based FFT method and can improve the measuring precision of miss distance.
基金Supported by the National Science Foundation of China(42055402)。
文摘The conventional linear time-frequency analysis method cannot achieve high resolution and energy focusing in the time and frequency dimensions at the same time,especially in the low frequency region.In order to improve the resolution of the linear time-frequency analysis method in the low-frequency region,we have proposed a W transform method,in which the instantaneous frequency is introduced as a parameter into the linear transformation,and the analysis time window is constructed which matches the instantaneous frequency of the seismic data.In this paper,the W transform method is compared with the Wigner-Ville distribution(WVD),a typical nonlinear time-frequency analysis method.The WVD method that shows the energy distribution in the time-frequency domain clearly indicates the gravitational center of time and the gravitational center of frequency of a wavelet,while the time-frequency spectrum of the W transform also has a clear gravitational center of energy focusing,because the instantaneous frequency corresponding to any time position is introduced as the transformation parameter.Therefore,the W transform can be benchmarked directly by the WVD method.We summarize the development of the W transform and three improved methods in recent years,and elaborate on the evolution of the standard W transform,the chirp-modulated W transform,the fractional-order W transform,and the linear canonical W transform.Through three application examples of W transform in fluvial sand body identification and reservoir prediction,it is verified that W transform can improve the resolution and energy focusing of time-frequency spectra.
文摘Focused on the non-statlonarity and real-time analysis of signal in flutter test with progression variable speed （FTPVS）, a new method of recursive time-frequency analysis is presented. The time-varying system is tracked on-line by building a time-varying parameter model, and then the relevant parameter spectrum can be obtained. The feasibility and advantages of the method are examined by digital simulation. The results of FTPVS at low-speed wind-tunnel promise the engineering application perspective of the method.
文摘With the continuous improvement of Synthetic Aperture Radar(SAR) resolution, interpreting the small targets like aircraft in SAR images becomes possible and turn out to be a hot spot in SAR application research. However, due to the complexity of SAR imaging mechanism, interpreting targets in SAR images is a tough problem. This paper presents a new aircraft interpretation method based on the joint time-frequency analysis and multi-dimensional contrasting of basic structures. Moreover, SAR data acquisition experiment is designed for interpreting the aircraft. Analyzing the experiment data with our method, the result shows that the proposed method largely makes use of the SAR data information. The reasonable results can provide some auxiliary support for the SAR images manual interpretation.
文摘The local wave method is a very good time-frequency method for nonstationaryvibration signal analysis. But the interfering noise has a big influence on the accuracy oftime-frequency analysis. The wavelet packet de-noising method can eliminate the interference ofnoise and improve the signal-noise-ratio. This paper uses the local wave method to decompose thede-noising signal and perform a time-frequency analysis. We can get better characteristics. Finally,an example of wavelet packet de-noising and a local wave time-frequency spectrum application ofdiesel engine surface vibration signal is put forward.
基金supported by the Chongqing Water Conservancy Science and Technology Project(grant number:CQSLK-202329)the Natural Science Foundation of Chongqing,China(grant number:CSTB2022NSCQ-MSX0991)+1 种基金the National Natural Science Foundation of China(grant number:52378327)the Chongqing Natural Science Foundation Innovation Development Joint Fund(grant number:CSTB2022NSCQ-LZX0049)。
文摘Rock slope instability is a prevalent geological hazard that imposes significant adverse impacts on engineering activities.Although existing studies have focused on homogeneous rock slopes,the theoretical models for quantifying the stability of softhard interbedded anti-inclined slopes remain underdeveloped,primarily due to the complex force transfer mechanisms involved.This study proposed a novel theoretical model for the stability analysis of soft-hard interbedded anti-inclined slopes under rainfall conditions.The framework models stratified rock layers as layered cantilever beams with material heterogeneity.Based on the principle of deformation compatibility,it comprehensively accounted for interlayer force transfer and strength degradation resulting from differential deformations among rock layers.Furthermore,it integrated the critical instability length induced by the self-weight of rock layers to determine the fracture depth.The proposed method was validated against engineering case studies and physical model tests,with error falling within an acceptable range.Compared to existing theoretical methods,the proposed method provided a more realistic representation of the slope's stress field.The analysis results demonstrate that rainfall not only reduces the inclination angle of the failure surface but also leads to an approximate 30%decrease in the safety factor.The proposed theoretical model is particularly useful for quickly calculating the stability of soft-hard interbedded anti-inclined rock slope under rainfall conditions,compared to complex and time-consuming numerical simulation calculations.
基金supported by the National Natural Science Foundation of China(Grant Nos.12272211,12072181,and 12121002).
文摘Uncertain parameters are widespread in engineering systems.This study investigates the modal analysis of a fluid-conveying pipe subjected to elastic supports with unknown-but-bound parameters.The governing equation for the elastically supported fluid-conveying pipe is transformed into ordinary differential equations using the Galerkin truncation method.The Chebyshev interval approach,integrated with the assumed mode method is then used to investigate the effects of uncertainties of support stiffness,fluid speed,and pipe length on the natural frequencies and mode shapes of the pipe.Additionally,both symmetrical and asymmetrical support stiffnesses are discussed.The accuracy and effectiveness of the Chebyshev interval approach are verified through comparison with the Monte Carlo method.The results reveal that,for the same deviation coefficient,uncertainties in symmetrical support stiffness have a greater impact on the first four natural frequencies than those of the asymmetrical one.There may be significant differences in the sensitivity of natural frequencies and mode shapes of the same order to uncertain parameters.Notably,mode shapes susceptible to uncertain parameters exhibit wider fluctuation intervals near the elastic supports,requiring more attention.
基金supported by the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20241443)the Jiangsu Funding Program for Excellent Postdoctoral Talent(Grant No.2024ZB072)the National Natural Science Foundation of China(Grant No.92266201).
文摘This study aims to establish an integrated sensitivity analysis framework for optimization and design of the dynamic performance of mechanical systems such as tracked vehicles,by combining the direct differentiation method(DDM)with the linear multibody system transfer matrix method(linear MSTMM).The rigid-flexible coupled multibody system dynamics model of a tracked vehicle is established using the linear MSTMM and validated through the modal test.Building upon the existing DDM-based eigenvalue sensitivity analysis method within the linear MSTMM,the DDM is embedded into it to enable programmable and efficient computation of dynamic response sensitivities for mechanical systems.The proposed approach is used to quantitatively evaluate the sensitivities of both natural vibration characteristics(e.g.,natural frequencies and mode shapes)and transient dynamic responses of the tracked vehicle with respect to system parameters,successfully identifying critical structural parameters.Compared to conventional finite difference methods,the developed methodology eliminates sensitivity to perturbation step sizes.The contributions of this work lie in establishing a unified theoretical foundation and analysis framework for guiding dynamics optimization and design of mechanical systems,and extending the applicability of the linear MSTMM to sensitivity analysis of transient dynamic responses.
基金supported by the National Natural Science Foundation of China(Grant No.41961134032).
文摘The probabilistic stability evolution analysis of reservoir bank slopes is a crucial aspect of risk assessment,with core challenges including the consideration of deformation mechanisms and accurate determination of mechanical parameters.In this study,a novel time-varying reliability analysis framework based on sequential Bayesian updating of mechanical parameters is proposed.The inverse parameters account for damage time-dependent behavior,incorporating water effect and a strain-driven softening-hardening process that depends on sliding states.The likelihood function is enhanced to simultaneously consider observation error,surrogate model prediction error,and model structural error,with the introduction of physical penalty.Exploration of the high-dimensional parameter space is achieved via the Hamiltonian Monte Carlo(HMC)method and the physics knowledge-based time-dependent deformation surrogate model.The time-varying reliability analysis of the slope is performed using the multi-grid method.Taking a reservoir bank slope as a case study,the sequential updating of 12 mechanical parameters is conducted based on deformation time series from 16 monitoring points,thereby validating the proposed framework.The results indicate that the proposed framework effectively captures the posterior distribution of mechanical parameters,with the case slope remaining in a critically stable state after overall sliding,showing a high failure probability.Introducing model structural error can reduce parameter compensation,and a reasonable sequential updating step size can improve inversion accuracy.
文摘The accurate mechanical analysis of thick-walled pressure vessel structures composed of advanced materials,such as hyperelastic and functionally graded materials(FGMs),is critical for ensuring their safety and optimizing their design.However,conventional numerical methods can face challenges with the non-linearities inherent in hyperelasticity and the complex spatial variations in FGMs.This paper presents a novel hybrid numerical approach combining Physics-Informed Neural Networks(PINNs)with Finite Element Method(FEM)derived data for the robust analysis of thick-walled,axisymmetric,heterogeneous,hyperelastic pressure vessels with elliptical geometries.A PINN framework incorporating neo-Hookean constitutive relations is developed in MATLAB.To enhance training efficiency and accuracy,the PINN’s loss function is augmented with displacement data obtained from high-fidelity FEM simulations performed in ANSYS.The methodology is rigorously validated by comparing PINN-predicted displacement and von Mises stress fields against ANSYS benchmarks for various scenarios of FGMconfigurations(with material properties varying according to a power law)subjected to internal and external pressurization.The results demonstrate excellent agreement between the proposed hybrid PINN-FEMapproach and conventional FEMsolutions across all test cases,accurately capturing complex deformation patterns and stress concentrations.This study highlights the potential of data-augmented PINNs as an effective and accurate computational tool for tackling complex solid mechanics problems involving non-linearmaterials and significant heterogeneity,offering a promising avenue for future research in engineering design and analysis.
基金supported by the National Natural Science Foundation of China(Grant Nos.51890912,51979025 and 52011530189).
文摘This article presents a micro-structure tensor enhanced elasto-plastic finite element(FE)method to address strength anisotropy in three-dimensional(3D)soil slope stability analysis.The gravity increase method(GIM)is employed to analyze the stability of 3D anisotropic soil slopes.The accuracy of the proposed method is first verified against the data in the literature.We then simulate the 3D soil slope with a straight slope surface and the convex and concave slope surfaces with a 90turning corner to study the 3D effect on slope stability and the failure mechanism under anisotropy conditions.Based on our numerical results,the end effect significantly impacts the failure mechanism and safety factor.Anisotropy degree notably affects the safety factor,with higher degrees leading to deeper landslides.For concave slopes,they can be approximated by straight slopes with suitable boundary conditions to assess their stability.Furthermore,a case study of the Saint-Alban test embankment A in Quebec,Canada,is provided to demonstrate the applicability of the proposed FE model.
基金Sponsored by The Youth Project of National Social Science Foundation of China(21CTY007)Special Fund for Basic Scientific Research Business Expenses of Central Universities(2024DAWH008).
文摘With Beijing Huilongguan Sports and Cultural Park as the research object,this study was conducted to investigate public service satisfaction in the park by the Importance-Performance Analysis(IPA)method.A questionnaire covering six dimensions,including public transportation,sanitation and environment,and supporting facility construction,was designed.A total of 208 valid samples were collected,and SPSS was employed for reliability and validity tests as well as IPA analysis.The findings were as follows:①Visitors were generally quite satisfied with the overall public services in Huilongguan Sports and Cultural Park.②The highest satisfaction levels were observed in sanitation and environment services and the sports and cultural atmosphere,while lower satisfaction was noted for supporting facility construction and public information services.③The advantage enhancement zone includes sanitation and environment services and sports and cultural atmosphere;and the continuous maintenance zone includes public transportation services and security management amd maintenance;the subsequent opportunity zone includes supporting facility construction and public information services;and there are no dimensions in the urgent improvement zone.The study recommends strengthening the service connotations from three aspects:enhancing facilities with sports as the core,optimizing services with a people-centered approach,and upgrading the information platform through technological efficiency.Additionally,a multi-stakeholder collaborative mechanism involving the government in coordinating policy resources,the operator in improving implementation efficiency,and the public participating in supervision and evaluation is proposed to drive the enhancement of public service quality at Huilongguan Sports and Cultural Park.
基金supported by the National Key Research and Development Program(MOST 2023YFA1606404 and MOST 2022YFA1602303)the National Natural Science Foundation of China(Nos.12347106,12147101,and 12447122)the China Postdoctoral Science Foundation(No.2024M760489).
文摘To study the uncertainty quantification of resonant states in open quantum systems,we developed a Bayesian framework by integrating a reduced basis method(RBM)emulator with the Gamow coupled-channel(GCC)approach.The RBM,constructed via eigenvector continuation and trained on both bound and resonant configurations,enables the fast and accurate emulation of resonance properties across the parameter space.To identify the physical resonant states from the emulator’s output,we introduce an overlap-based selection technique that effectively isolates true solutions from background artifacts.By applying this framework to unbound nucleus ^(6)Be,we quantified the model uncertainty in the predicted complex energies.The results demonstrate relative errors of 17.48%in the real part and 8.24%in the imaginary part,while achieving a speedup of four orders of magnitude compared with the full GCC calculations.To further investigate the asymptotic behavior of the resonant-state wavefunctions within the RBM framework,we employed a Lippmann–Schwinger(L–S)-based correction scheme.This approach not only improves the consistency between eigenvalues and wavefunctions but also enables a seamless extension from real-space training data to the complex energy plane.By bridging the gap between bound-state and continuum regimes,the L–S correction significantly enhances the emulator’s capability to accurately capture continuum structures in open quantum systems.
文摘Objective:This study aims to explore the benefit analysis of the same disease in different departments of public hospitals under the DIP payment method.Methods:This study is a retrospective analysis that selected clinical data from patients who received treatment in the Department of Orthopedics and the Department of Acupuncture and Moxibustion at our hospital from January 1,2023,to December 31,2023.The study compared the costs of medications,examinations,treatments,laboratory tests,nursing and other expenses,and total treatment costs between the two departments.It analyzed the cost structure of the two departments and proposed further improvement suggestions.Results:The study results indicated that the total costs in the Department of Acupuncture and Moxibustion were significantly higher than those in the Department of Orthopedics.Among medication costs,the total medication costs in the Department of Orthopedics were higher than those in the Department of Acupuncture and Moxibustion,with costs for Western medicine,proprietary Chinese medicine,and herbal medicine all being higher(p<0.05).Regarding examination costs,consultation fees in the Department of Orthopedics were lower than those in the Department of Acupuncture and Moxibustion,while examination costs were higher(p<0.05).In terms of treatment costs,orthopedic treatment and surgical fees were higher than those in the Department of Acupuncture and Moxibustion(p<0.05).For laboratory test costs,orthopedic laboratory fees were significantly higher than those in the Department of Acupuncture and Moxibustion(p<0.05).Among nursing and other expenses,orthopedic blood transfusion,bed fees,and other expenses were higher than those in the Department of Acupuncture and Moxibustion,while nursing fees were lower(p<0.05).Conclusion:Treatment fees in the Department of Acupuncture and Moxibustion are the core and account for a relatively high proportion of the total costs.The benefits generated by the Department of Orthopedics are primarily derived from medication,examination,and laboratory fees,aligning with the characteristics of combining diagnosis,medication,and surgical intervention in orthopedic treatment.Consultation fees,nursing fees,and bed fees in the Department of Acupuncture and Moxibustion are higher than those in the Department of Orthopedics,indicating a longer treatment cycle in acupuncture,which warrants clinical attention.
基金funded by the Bavarian State Ministry of ScienceResearch and Art(Grant number:H.2-F1116.WE/52/2)。
文摘The incremental capacity analysis(ICA)technique is notably limited by its sensitivity to variations in charging conditions,which constrains its practical applicability in real-world scenarios.This paper introduces an ICA-compensation technique to address this limitation and propose a generalized framework for assessing the state of health(SOH)of batteries based on ICA that is applicable under differing charging conditions.This novel approach calculates the voltage profile under quasi-static conditions by subtracting the voltage increase attributable to the additional polarization effects at high currents from the measured voltage profile.This approach's efficacy is contingent upon precisely acquiring the equivalent impedance.To obtain the equivalent impedance throughout the batteries'lifespan while minimizing testing costs,this study employs a current interrupt technique in conjunction with a long short-term memory(LSTM)network to develop a predictive model for equivalent impedance.Following the derivation of ICA curves using voltage profiles under quasi-static conditions,the research explores two scenarios for SOH estimation:one utilizing only incremental capacity(IC)features and the other incorporating both IC features and IC sampling.A genetic algorithm-optimized backpropagation neural network(GABPNN)is employed for the SOH estimation.The proposed generalized framework is validated using independent training and test datasets.Variable test conditions are applied for the test set to rigorously evaluate the methodology under challenging conditions.These evaluation results demonstrate that the proposed framework achieves an estimation accuracy of 1.04%for RMSE and 0.90%for MAPE across a spectrum of charging rates ranging from 0.1 C to 1 C and starting SOCs between 0%and 70%,which constitutes a major advancement compared to established ICA methods.It also significantly enhances the applicability of conventional ICA techniques in varying charging conditions and negates the necessity for separate testing protocols for each charging scenario.
基金support from the National Natural Science Foundation of China(Grant Nos.52174123&52274222).
文摘This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-oped using the material point method.To reduce the computational cost of Monte Carlo simulations,response surface models are created as surrogate models for the material point system to approximate its dynamic behavior.An adaptive randomized greedy algorithm is employed to construct a sparse polynomial chaos expansion model with a fixed order,effectively balancing the accuracy and computational efficiency of the surrogate model.Based on the sparse polynomial chaos expansion,sensitivity analysis is conducted using the global finite difference and Sobol methods.Several examples of structural dynamics are provided to demonstrate the effectiveness of the proposed method in addressing structural dynamics problems.
基金co-supported by the National Natural Science Foundation of China(No.52176033)the National Science and Technology Major Project,China(No.J2019-II-0012-0032)the Science Center for Gas Turbine Project,China(No.P2022-B-II-009-001)。
文摘To address the deficiency in loss diagnostic methods for turbines working at off-design angles of attack,a novel loss decomposition method suitable for cascade flow with large separation is proposed.The method proposed has the following advantages over existing methods:(A)It enables refined loss decomposition for cascade flows,capable of identifying the spatial range of specific regions such as shear layers and backflow regions,thereby obtaining the loss characteristics of these regions.(B)The region identification criteria in this method have clear physical meanings,rather than relying on arbitrary area division.(C)The method has good applicability and is suitable for cascade flows under various angles of attack.Validation shows that this method achieves satisfactory results.Based on this method,the loss mechanisms of a low-pressure turbine cascade at a low Reynolds number of 4.3×10^(4)and angles of attack of-5°,-20°,and-45°are investigated using Large Eddy Simulations(LESs).Entropy analysis quantitatively demonstrates significant differences in the composition of losses among flow regions,due to their different flow characteristics.From the perspective of flow regions,wake loss dominates total loss,while loss in backflow region is negligible.Furthermore,the variation mechanisms of loss with incidence differ among different flow regions.
基金the financial support from the National Science Foundation of China(22078190 and 12002196)the National Key Research and Development Program of China(2020YFB1505802)。
文摘Li transient concentration distribution in spherical active material particles can affect the maximum power density and the safe operating regime of the electric vehicles(EVs). On one hand, the quasiexact/exact solution obtained in the time/frequency domain is time-consuming and just as a reference value for approximate solutions;on the other hand, calculation errors and application range of approximate solutions not only rely on approximate algorithms but also on discharge modes. For the purpose to track the transient dynamics for Li solid-phase diffusion in spherical active particles with a tolerable error range and for a wide applicable range, it is necessary to choose optimal approximate algorithms in terms of discharge modes and the nature of active material particles. In this study, approximation methods,such as diffusion length method, polynomial profile approximation method, Padé approximation method,pseudo steady state method, eigenfunction-based Galerkin collocation method, and separation of variables method for solving Li solid-phase diffusion in spherical active particles are compared from calculation fundamentals to algorithm implementation. Furthermore, these approximate solutions are quantitatively compared to the quasi-exact/exact solution in the time/frequency domain under typical discharge modes, i.e., start-up, slow-down, and speed-up. The results obtained from the viewpoint of time-frequency analysis offer a theoretical foundation on how to track Li transient concentration profile in spherical active particles with a high precision and for a wide application range. In turn, optimal solutions of Li solid diffusion equations for spherical active particles can improve the reliability in predicting safe operating regime and estimating maximum power for automotive batteries.
