Energy-based Method Research Articles

Serviceability performance of fiber-reinforced lightweight aggregate concrete beams with CFRP bars

Six lightweight aggregate concrete (LWC) beams reinforced with carbon fiber–reinforced polymer (CFRP) bars were tested under a four-point bending load with different steel fiber contents, reinforcement ratios, and clear span lengths to investigate their flexural behavior and serviceability performance. The test results showed that using steel fiber–reinforced lightweight aggregate concrete (SFLWC) and increasing the reinforcement ratio enhanced the serviceability performance of the beams. The incorporation of 0.6% by volume of steel fibers reduced the midspan deflection by 22.70%–36.87% at the same load level in service stage. At service load, all the CFRP-reinforced beams exhibited conservative deflections when compared to the deflection limits recommended by ACI 440.1 R and GB 50608, and satisfied the crack width limit of 0.7 mm. Comparing the measured maximum crack widths with the corresponding predictions revealed that the bond-dependent coefficient value of 1.4 specified in ACI 440.1 R was reasonable yet conservative. Moreover, an energy-based method was adopted to quantify the influence of the fibers on the beam stiffness. On this basis, a rational deflection model for SFLWC beams reinforced with CFRP bars was suggested.

Energy-based linear PCM audio recovery method of impaired MP4 file stored in dashboard camera memory

Sounds recorded by a dashboard camera presents essential evidence on a vehicle's driving condition for analyzing car accidents. In reality, when a direct impact of a vehicle equipped with a dashboard camera occurs, the power supply to the dashboard camera is abruptly terminated, and the digital video being recorded at that time may be incompletely stored; thus, there is no information such as the location or size to be read for the image and audio decoding. In this paper, we propose a method for recovering the linear pulse code modulation (PCM) audio from the impaired MP4 file partially stored in a video event data recorder (VEDR), known as a dashboard camera, during road vehicle accidents. This method is based on the principle of extracting an actual audio signal using the energy of each frame in the pseudo audio, which is generated from all data in the “mdat” area of the impaired MP4 file. For performance evaluation, the various video files with linear PCM audio format in the MP4 container were obtained through the different dashboard cameras. As the objective evaluation, we measured the audio recovery ratio, distance based on dynamic time warping (DTW) and comparison of the waveform and spectrogram. Moreover, the performance of the proposed method was evaluated using the multiple stimuli with a hidden reference and anchor (MUSHRA) test as the subjective assessment. As a result, it is shown from the evaluation that the proposed method can recover significantly better the linear PCM audio signal than the conventional methods from an impaired MP4 file.

Dynamic contact behavior of graphite-like carbon films on ductile substrate under nano/micro-scale impact

Coated components are often subjected to high strain rate and repetitive contact damage in practical service, so how to quickly evaluate the dynamic contact behavior of the thin protective coating is particularly important. Highly resolved single nano-impact and novel multiple micro-scale impact tests were used to investigate the dynamic hardness and fatigue failure of 0.55–1.52 μm thick graphite-like carbon (GLC) films on 316L stainless steel with varied thickness, respectively. By analyzing the impact depth and velocity before and after the indenter first contact with the sample, the dynamic hardness of GLC film/substrate system was obtained reasonably based on the energy approach in single nano-impact tests. Possible reasons for the higher dynamic hardness than quasi-static hardness include overestimation of the plastic absorbed energy W p and the strain rate sensitivity of materials. The thickest film/substrate system studied had a higher dynamic hardness than the thinner films due to its higher load carrying capability. Results with the multiple micro-impact technique showed that a GLC film with intermediate thickness (1.1 μm) was more resistant to the impact fatigue, while the thinnest film, 0.55 μm, exhibited more pronounced radial cracks under the indent and the thickest film , 1.52 μm, showed more significant edge ring cracks, these differences resulting from the combined action of stress distribution, film microstructure and mechanical properties . • Provide an energy-based method to evaluate the dynamic mechanical properties of thin films or film/substrate system. • Improve the understanding of impact failure of hard coatings deposited on ductile substrates by the novel micro-impact. • Investigate the influence of acceleration force on the dynamic contact behavior of hard coatings on ductile substrates. • Discuss the influence of film thickness on their dynamic contact behavior.

Energy-Based Interface Detection for Phase Change Processes of Monatomic Fluids in Nanoconfinements.

An energy-based liquid-vapor interface detection method is presented using molecular dynamics simulations of liquid menisci confined between two parallel plates under equilibrium and evaporation/condensation conditions. This method defines the liquid-vapor interface at the location where the average kinetic energy of atoms first exceeds the average potential energy imposed by all neighboring molecules. This definition naturally adapts to the location of the menisci relative to the walls and can properly model the behavior of the liquid adsorbed layers. Unlike the density cutoff methods frequently used in the literature that suffer from density layering effects, this new method gives smooth and continuous liquid-vapor interfaces in nanoconfinements. Surface tension values calculated from the equilibrium MD simulations match the Young-Laplace equation better when using the radius of curvatures calculated from this method. Overall, this energy-based liquid-vapor interface detection method can be used in studies of nanoscale phase change processes and other relevant applications.

Performance Assessment of an Energy–Based Approximation Method for the Dynamic Capacity of RC Frames Subjected to Sudden Column Removal Scenarios

The alternative load path method is widely used to assess the progressive collapse performance of reinforced concrete structures. As an alternative to an accurate non–linear dynamic analysis, an energy–based method (EBM) can also be adopted to approximately calculate the dynamic load–bearing capacity curve or the dynamic resistance based on a static capacity curve. However, dynamic effects cannot be explicitly taken into account in the EBM. The model uncertainty associated with the use of the EBM for evaluating the dynamic ultimate capacity of structural frames has not yet been quantified. Knowledge of this model uncertainty is however necessary when applying EBM as part of reliability calculations, for example, in relation to structural robustness quantification. Hence, this article focuses on the evaluation of the performance of the EBM and the quantification of its model uncertainty in the context of reliability–based assessments of progressive or disproportionate collapse. The influences of damping effects and different column removal scenarios are investigated. As a result, it is found that damping effects have a limited influence on the performance of the EBM. In the case of an external column removal scenario, the performance of the EBM is lower as the response is not a single deformation mode according to the results in the frequency domain. However, a good performance is found in the case of an internal column removal scenario in which the assumption of a single deformation mode is found to be sufficiently adequate. Probabilistic models for the model uncertainties related to the use of the EBM compared to direct dynamic analyses are proposed in relation to both the resistances and the associated displacements. Overall, the EBM shows to be an adequate approximation, resulting in a small bias and small standard deviation for its associated model uncertainty.

A physically-based method for predicting high temperature fatigue crack initiation in P91 welded steel

A methodology is presented for physically-based prediction of high temperature fatigue crack initiation in 9Cr steels, with a focus on material inhomogeneity due to welding-induced metallurgical transformations. A modified form of the Tanaka-Mura model for slip band formation under cyclically-softening conditions is implemented in conjunction with a physically-based unified cyclic viscoplasticity constitutive model. The physically-based constitutive model accounts for the key strengthening mechanisms, including precipitate hardening and hierarchical grain boundary strengthening, successfully predicting cyclic softening in 9Cr steels. A five-material, finite element model of a P91 cross-weld test specimen, calibrated using the physically-based yield strength and constitutive models, successfully predicts the measured detrimental effect of welding on high temperature low-cycle fatigue crack initiation for P91 cross weld tests, via the modified Tanaka-Mura model. A key finding of the current work is the requirement to adopt an energy-based Tanaka-Mura method to account for cyclic softening in 9Cr steels, with packet size as the critical length-scale for slip band formation. The work demonstrates the significant effect of highly flexible operation on the service life of welded connections.

Choosing Strategies to Deal with Artifactual EEG Data in Children with Cognitive Impairment.

Rett syndrome is a disease that involves acute cognitive impairment and, consequently, a complex and varied symptomatology. This study evaluates the EEG signals of twenty-nine patients and classify them according to the level of movement artifact. The main goal is to achieve an artifact rejection strategy that performs well in all signals, regardless of the artifact level. Two different methods have been studied: one based on the data distribution and the other based on the energy function, with entropy as its main component. The method based on the data distribution shows poor performance with signals containing high amplitude outliers. On the contrary, the method based on the energy function is more robust to outliers. As it does not depend on the data distribution, it is not affected by artifactual events. A double rejection strategy has been chosen, first on a motion signal (accelerometer or EEG low-pass filtered between 1 and 10 Hz) and then on the EEG signal. The results showed a higher performance when working combining both artifact rejection methods. The energy-based method, to isolate motion artifacts, and the data-distribution-based method, to eliminate the remaining lower amplitude artifacts were used. In conclusion, a new method that proves to be robust for all types of signals is designed.

A brittleness index evaluation method for weak-brittle rock by acoustic emission technique

Brittleness is a significant indicator of a series of engineering problems in the oil and gas community. However, the majority of brittleness evaluation methods focus on brittle rock, but few pay much attention to weak-brittle rock. In this study, an attempt has been made to study the relationship between released acoustic emission (AE) energy and brittleness during the fracture process of rock samples. An accumulative acoustic energy-based brittleness evaluation method was proposed according to the energy accumulation and dissipation in the pre-peak and post-peak stages. Moreover, the suitability and reliability of this method was verified by tri-axial compression tests on shale, tight sandstone, and glutenite. The experimental results indicate that both the complete stress vs. strain brittleness method and the accumulative acoustic energy-based brittleness method can reflect the effect of confining pressure, but deformation and failure characteristics that transition from brittle to weak-brittle behaviors with increasing confining pressure make the post-peak feature difficult to distinguish. Thus, the conventional complete stress vs. strain brittleness method fails to determine brittleness. However, the accumulative acoustic energy-based brittleness evaluation method is more sensitive to rock failure, even if the rock is weak-brittle or ductile, while acoustic energy can be directly monitored rather than calculated by a mathematical model. Thus, the accuracy of brittleness evaluation can be improved. The good match between the fracture morphology and accumulative acoustic energy-based brittleness results demonstrate that this novel method is more suitable for brittleness evaluation in weak-brittle or even ductile rock; therefore, this brittleness method can be efficiently used in deep formations under high-confining pressure, benefitting various engineering applications.

Comparison of different approaches to derive classical bonded force-field parameters for a transition metal cofactor: a case study for non-heme iron site of ectoine synthase

Computational investigations into the structure and function of metalloenzymes with transition metal cofactors require proper preparation of the model, which requires obtaining reliable force field parameters for the cofactor. Here, we present a test case where several methods were used to derive amber force field parameters for a bonded model of the Fe(II) cofactor of ectoine synthase. Moreover, the spin of the ground state of the cofactor was probed by DFT and post-HF methods, which consistently indicated the quintet state is lowest in energy and well separated from triplet and singlet. The performance of the obtained force field parameter sets, derived for the quintet spin state, was scrutinized and compared taking into account metrics focused on geometric features of the models as well as their energetics. The main conclusion of this study is that Hessian-based methods yield parameters which represent the geometry around the metal ion, but poorly reproduce energy variance with geometrical changes. On the other hand, the energy-based method yields parameters accurately reproducing energy-structure relationships, but with bad performance in geometry optimization. Preliminary tests show that admixing geometrical criteria to energy-based methods may allow to derive parameters with acceptable performance for both energy and geometry.

Phosphate binding sites prediction in phosphorylation-dependent protein-protein interactions.

Phosphate binding plays an important role in modulating protein-protein interactions, which are ubiquitous in various biological processes. Accurate prediction of phosphate binding sites is an important but challenging task. Small size and diversity of phosphate binding sites lead to a substantial challenge for developing accurate prediction methods. Here, we present the phosphate binding site predictor (PBSP), a novel and accurate approach to identifying phosphate binding sites from protein structures. PBSP combines an energy-based ligand-binding sites identification method with reverse focused docking using a phosphate probe. We show that PBSP outperforms not only general ligand binding sites predictors but also other existing phospholigand-specific binding sites predictors. It achieves ∼95% success rate for top 10 predicted sites with an average Matthews correlation coefficient value of 0.84 for successful predictions. PBSP can accurately predict phosphate binding modes, with average position error of 1.4 and 2.4 Å in bound and unbound datasets, respectively. Lastly, visual inspection of the predictions is conducted. Reasons for failed predictions are further analyzed and possible ways to improve the performance are provided. These results demonstrate a novel and accurate approach to phosphate binding sites identification in protein structures. The software and benchmark datasets are freely available at http://web.pkusz.edu.cn/wu/PBSP/. Supplementary data are available at Bioinformatics online.

Modified Time-Dependent Model for Flexural Capacity Assessment of Corroded RC Elements

The corrosion of embedded steel bars in concrete is one of the severe deterioration processes that can escalate the risk and reduce the durability and lifetime of concrete structures. Based on the literature, simultaneous corrosion of longitudinal and transverse bar is considered to estimate section capacity. In this research, a flexible multi-stage approach is proposed to differentiate between corrosion levels on longitudinal and transverse reinforcement based on their corrosion initiating time. The result indicated that the multi-stage approach provides higher capacity and curvature for the sections. A significant reduction in reinforced concrete (RC) sections’ ductility after corrosion of confining bars and before starting corrosion of longitudinal rebars was observed, which illustrates the importance of stirrups corrosion effects on the sections’ ductility. In the higher values of corrosion intensity, confined concrete’s ultimate strain tends to reach the unconfined state. Using the energy-based method of calculating ultimate concrete compressive strain instead of approximate methods, a higher value of curvature ductility of corroded RC cross-sections is obtained.

An Energy-Based Discrete Element Modeling Method Coupled with Time-Series Analysis for Investigating Deformations and Failures of Jointed Rock Slopes

The discrete element method (DEM) can be effectively used in investigations of the deformations and failures of jointed rock slopes. However, when to appropriately terminate the DEM iterative process is not clear. Recently, a displacement-based discrete element modeling method for jointed rock slopes was proposed to determine when the DEM iterative process is terminated, and it considers displacements that come from rock blocks located near the potential sliding surface that needs to be determined before the DEM modeling. In this paper, an energy-based discrete element modeling method combined with time-series analysis is proposed to investigate the deformations and failures of jointed rock slopes. The proposed method defines an energy-based criterion to determine when to terminate the DEM iterative process in analyzing the deformations and failures of jointed rock slopes. The novelty of the proposed energy-based method is that, it is more applicable than the displacement-based method because it does not need to determine the position of the potential sliding surface before DEM modeling. The proposed energy-based method is a generalized form of the displacement-based discrete element modeling method, and the proposed method considers not only the displacement of each block but also the weight of each block. Moreover, the computational cost of the proposed method is approximately the same as that of the displacement-based discrete element modeling method. To validate that the proposed energy-based method is effective, the proposed method is used to analyze a simple jointed rock slope; the result is compared to that achieved by using the displacement-based method, and the comparative results are basically consistent. The proposed energy-based method can be commonly used to analyze the deformations and failures of general rock slopes where it is difficult to determine the obvious potential sliding surface.

Theoretical determination of asymmetric rolling amplitude in irregular beam seas

A methodology for predicting the probability density function of roll motion for irregular beam seas is developed in the author’s previous research. In this paper, two methods for the prediction of the probability density function (PDF) of the rolling amplitude are examined. One of these methods is an approach based on a non-Gaussian PDF with the use of the equivalent linearization and the moment method, which has been used by Maki in the field of naval architecture. In the framework of this method, the instantaneous joint PDF of the roll and roll rate can be calculated. Thereby, the transformation from the joint PDF to the PDF of the total energy H is necessary. In this paper, the transformation from the joint PDF of instantaneous roll and rate to the PDF of H was conducted. The other method is the energy-based stochastic averaging method, whereby the PDF of the total energy H is determined from which the roll amplitude is calculated. It is noteworthy that the proposed theory aims to predict the PDF of the amplitude of the vessel due to wind or flooding. For such conditions, the restoring curve (GZ curve) has asymmetricity. To take into account this asymmetricity, a new theory for the transform of the PDF of the total energy H to the PDFof amplitude is proposed. The obtained theoretical results show almost complete agreement, and both of the two theoretical methods i.e., the energy-based stochastic averaging method and the non-Gaussian PDF method with the use of the equivalent linearization and moment method, show equivalent prediction performance even in the asymmetric condition.

Nonlinear thermoelastic fractional-order model of nonlocal plates: Application to postbuckling and bending response

This study presents a comprehensive frame-invariant fractional-order framework for the geometrically nonlinear bending and postbuckling analysis of nonlocal plates subject to combined thermal and mechanical loads. The fractional-order kinematic framework, unlike classical nonlocal formulations based on integer-order mechanics, is positive-definite and thermodynamically consistent. The positive-definite nature enables the application of variational principles to derive well-posed thermomechanical governing equations. A direct advantage of these theoretical advancements is reflected in the ability of the fractional-order approach to enable an energy-based asymptotic method obtained by extending the classical (local) Koiter’s approach. This method allows the analytical assessment of the impact of nonlocal interactions on the nature of the bifurcation and post-critical response of slender structures when subject to compressive loads. Further, the positive-definite nature of the fractional-order approach allows the development of an accurate fractional-order finite element method enabling the simulation of nonlocal structures subject to any combination of thermomechanical loads and boundary conditions. The above stated advantages are particularly important for a comprehensive and consistent analysis of nonlocal structures in the postbuckling regime. The theoretical framework is used to provide analytical and numerical insights on the effect of combined thermal and mechanical loads on the nonlinear response of nonlocal plates. Numerical results also demonstrate the high-level consistency of the framework when applied to the nonlinear thermoelastic analysis of nonlocal plates under different loading and boundary conditions.

Optimization layout of damping material using vibration energy-based finite element analysis method

It is essential to optimize the position and coverage of damping material to mitigate the vibration and noise in vehicles. Modal strain energy and genetic algorithms are traditionally used for damping material optimization, but these methods do not consider a specific loading position and loading case. Therefore, the optimization results do not include an actual working load case. This paper introduced an optimization method, including two steps for the damping material position and weight optimization. A specific and practical loading case was adopted. First, the damping position and its coverage area were calculated and optimized using the energy post-processing method. Second, the damping thickness and weight were treated as the optimization objective based on damping position and coverage optimization results, after which the structure-damping-cavity vibro-acoustic model was used for the response calculation. Two verification models, a box model, and an actual vehicle model were included in this paper to verify the efficacy of the technique. The optimization method proposed in this paper could visibly reduce the weight of the damping material while the noise level remained as initially planned. This method can easily be applied during the actual design process of the vehicle sound package, while the simulation results can be used as a reference in the optimization of the damping material.

Quantification of model uncertainties of the energy-based method for dynamic column removal scenarios

The Alternative Load Path (ALP) method is widely used to assess progressive collapse resistance of reinforced concrete (RC) structures by notional removal of one or more load-bearing elements. In general, a nonlinear time history analysis (NTHA) is needed to perform such an analysis if dynamic effects are explicitly taken into account. To avoid cumbersome nonlinear dynamic analyses, the energy-based method (EBM) is a promising technique to predict the maximum dynamic responses of a structural system. In this article, the accuracy and precision of the EBM is evaluated based on a validated finite element model of a tested RC slab subjected to a sudden column removal scenario, in particular in relation to the investigation of tensile membrane action (TMA). Influences of dynamic effects are evaluated, i.e. in relation to strain rate effects, damping, and the time duration of support removals. Strain rate effects are observed to have only slight influences on the dynamic responses. The strain rate dependency of reinforcement is found to have a more significant influence on the responses in TMA stage, although also to a limited extent. The magnitude of the load has a significant influence on the dynamic response, as do increasing damping ratios due to the corresponding significant energy dissipation. Finally, the dynamic response reduces with increasing time duration of the column removal. Based on the results of the stochastic analyses, the EBM is observed to perform well based on a comparison with the results of NTHA in both flexural and TMA stages. Furthermore, in relation to the analyzed case studies on reinforced concrete slabs, the model uncertainty of the responses obtained through the EBM compared with the NTHA is found to be represented well by a lognormal distribution with mean of 0.95 and a standard deviation of 0.20, for evaluating the loads of first rupture of reinforcement. Furthermore, a lognormal distribution with mean 0.96 and standard deviation 0.13 is found appropriate to represent the model uncertainty on ultimate load-bearing capacity predictions. Model uncertainties are also obtained with respect to the model predictions for displacements at the moment of the first rupture of reinforcement, displacements at the ultimate load-bearing capacities, and both loads and displacements at second load peaks.

Redesigned Filter Paper Method: Protocol and Assessment Using Reconstituted Samples

Abstract The soil-water retention curve defines a relationship between the water content of a soil and the corresponding pressure at which the soil-water-air is in equilibrium. In cases in which undisturbed sampling are not feasible, especially for nonplastic and low-plastic soil fabrics, reconstituted soil samples are required. A newly designed mold was devised for use with reconstituted soil samples and the filter paper test. The newly designed mold consisted of a #200 wire mesh that allows for three-dimensional vapor flow. Implementing this new apparatus in conjunction with an energy-based reconstitution protocol minimizes inconsistencies across the test specimen such that variabilities associated with the filter paper testing method can be isolated and calibration curves verified. Calibration procedures are assessed and results are presented based on axis translation and verified by tensiometer measurements. This redesigned filter paper test was then conducted over a range of nonplastic to low-plastic soils yielding comparable results with published field studies and data bases. It can be concluded from this investigation that the filter paper method, using an energy-based reconstitution method and a mesh mold, is comparable to non-filter paper testing methods and is preferable for some applications because of its simplicity and relative short testing times.

An energy-based method for assessing the equivalent static force of a vehicle collision with bridge columns

A new method is proposed to obtain the equivalent static forces of a vehicle collision with bridge columns. The method is based on energy-conservation and, conversely to other existing methods, does not require the use of complex models or experimental data to obtain time histories of impact. A simplified numerical model is also developed to generate data and compare the performance of the energy-conservation method against three other approaches (global average, local average, and equivalent displacement methods) and the AASHTO allowances. The simplified model is efficient and correctly captures the response for different impact velocities and column sizes. The impact velocity was shown to be positively related to the impact force and column displacement, and the size of the column is also positively related to the impact force but negatively with the column displacement. Results of equivalent static forces show that the global average and local average methods may not provide acceptable values for the equivalent impact force from the collision of vehicles with bridge columns, whereas the equivalent displacement and the proposed energy-based method provide adequate values. The latter approach, however, has the advantage of simplicity and convenience since it does not rely on any numerical/experimental model.

Gaussian orthogonal ensemble modeling of built-up systems containing general diffuse components and parametric uncertainty

Built-up vibro-acoustic systems may contain components whose vibration field is sensitive to uncertainty from small spatial variations in geometry, material properties, or boundary conditions, which have a wave scattering effect. Such components can be modeled as diffuse. Statistical energy analysis (SEA) and related approaches are frequently employed for analyzing built-up systems with diffuse components, but their scope is limited because subsystems must be weakly coupled, the displacement fields are not modeled but only the total energies, the joint response probability density function is not available, and the computational efficiency decreases when there is additional parametric uncertainty. Recently, a method of analysis was presented that overcomes those limitations. It is a computationally efficient Monte Carlo method in which the subsystem displacement fields rather than the total energies are modeled. The method relies on the fact that the undamped eigenvalues of a diffuse wave field conform to those of a Gaussian Orthogonal Ensemble (GOE) matrix, while the mode shapes are Gaussian random fields. In this paper, the method is generalized such that diffuse components that are not homogeneous and isotropic, and that have a non-constant modal density, can be analyzed. This is achieved by transforming the GOE eigenvalue spacings to conform to the modal density of a diffuse component, and by relating its mode shape correlation function to the Green’s function of the corresponding unbouded subsystem. Parametric uncertainty is included in a straightforward way. The accuracy and computational efficiency of this field-based method is investigated by comparison with the energy-based (hybrid deterministic-)SEA method and with a detailed Monte Carlo method, where the diffuse field assumption is not made and local random wave scatterers are explicitly modeled. It is found that the new approach is more accuracte than SEA and also more computationally efficient when there are several or many uncertain parameters.

Research on Sensitive Measuring Points for Vibration Fault of NC Turret Based on Energy Flow and Transfer Path

Some equipment fault measurement points are difficult to determine. Thus, this study proposes a method using energy flow and transfer path to select sensitive measurement points. Firstly, based on the energy flow theory of the shell, the energy flow is taken as the physical quantity to describe the energy transfer of the structure vibration, and the energy-based transfer path analysis method is established. Secondly, the simulation model of the finite element energy flow was established by focusing on the NC turret, and the vector image of the energy flow transfer path of the NC turret shell was created. For the relationship between the vector images of the experimental and simulation energy flows, the validity of the finite element energy flow simulation results is verified. Lastly, three abnormal areas of the NC turret shell are identified by comparing and analyzing the energy flow vector images of the NC turret in the healthy and fault states, taking the poor meshing fault of the grooves as an example. By choosing nine test points in the abnormal areas and calculating the distribution rate of the transfer paths between the test points to the joint surfaces of the fluted disc, the energy flow distribution rate of the different fault positions to the test points is obtained. Calculation results enabled us to identify three measuring points that can accurately distinguish the fault location for a typical fault mode. This research combined energy flow theory and transfer path analysis method to determine the vibration fault sensitive measuring points of NC equipment. The proposed method is practical in the field of fault diagnosis and has broad application prospects.