Domain-based Method Research Articles

Finite domain solution of a hydraulic fracture in a permeable rock

In this work, we present a domain-based algorithm to simulate the propagation of a plane-strain hydraulic fracture in a zero-toughness permeable elastic medium. The algorithm utilizes a domain-based method to solve the elasticity equations and integrates a multi-scale tip asymptote, which is particular to hydraulic fractures, into this framework. This integration is key to accurately model the energy dissipation and the fluid leak-off in the fracture tip region. The algorithm combines a 2D finite volume method (FVM) for solving the elasticity equation with a 1D FVM for solving the nonlinear lubrication equation. Incorporating the far-field asymptotics and using a moving-mesh scheme reduces the computational burden while improving the accuracy of the scheme. The paper concludes with an analysis of the numerical results. This study demonstrates the potential of this domain-based approach for modeling hydraulic fractures in poroelastic media.

Deep learning-based low-dose CT simulator for non-linear reconstruction methods.

Computer algorithms that simulate lower-doses computed tomography (CT) images from clinical-dose images are widely available. However, most operate in the projection domain and assume access to the reconstruction method. Access to commercial reconstruction methods may often not be available in medical research, making image-domain noise simulation methods useful. However, the introduction of non-linear reconstruction methods, such as iterative and deep learning-based reconstruction, makes noise insertion in the image domain intractable, as it is not possible to determine the noise textures analytically. To develop a deep learning-based image-domain method to generate low-dose CT images from clinical-dose CT (CDCT) images for non-linear reconstruction methods. We propose a fully image domain-based method, utilizing a series of three convolutional neural networks (CNNs), which, respectively, denoise CDCT images, predict the standard deviation map of the low-dose image, and generate the noise power spectra (NPS) of local patches throughout the low-dose image. All three models have U-net-based architectures and are partly or fully three-dimensional. As a use case for this study and with no loss of generality, we use paired low-dose and clinical-dose brain CT scans. A dataset of paired scans was retrospectively obtained. All images were acquired with a wide-area detector clinical system and reconstructed using its standard clinical iterative algorithm. Each pair was registered using rigid registration to correct for motion between acquisitions. The data was randomly partitioned into training ( samples), validation ( samples), and test ( samples) sets. The performance of each of these three CNNs was validated separately. For the denoising CNN, the local standard deviation decrease, and bias were determined. For the standard deviation map CNN, the real and estimated standard deviations were compared locally. Finally, for the NPS CNN, the NPS of the synthetic and real low-dose noise were compared inside and outside the skull. Two proof-of-concept denoising studies were performed to determine if the performance of a CNN- or a gradient-based denoising filter on the synthetic low-dose data versus real data differed. The denoising network had a median decrease in noise in the cerebrospinal fluid by a factor of and introduced a median bias of HU. The network for standard deviation map estimation had a median error of HU. The noise power spectrum estimation network was able to capture the anisotropic and shift-variant nature of the noise structure by showing good agreement between the synthetic and real low-dose noise and their corresponding power spectra. The two proof of concept denoising studies showed only minimal difference in standard deviation improvement ratio between the synthetic and real low-dose CT images with the median difference between the two being 0.0 and +0.05 for the CNN- and gradient-based filter, respectively. The proposed method demonstrated good performance in generating synthetic low-dose brain CT scans without access to the projection data or to the reconstruction method. This method can generate multiple low-dose image realizations from one clinical-dose image, so it is useful for validation, optimization, and repeatability studies of image-processing algorithms.

External validation and diagnostic value of the Elderly Functional Index version 2.0 for assessing functional status and frailty in older Danish patients with gastrointestinal cancer receiving chemotherapy: A prospective, clinical study

IntroductionPatient perspectives on functioning are often overlooked in oncology practice. This study externally validates the ELderly Functional Index (ELFI), a patient-reported measure for assessing multidimensional functioning, in older patients with gastrointestinal cancer receiving chemotherapy. The study compares ELFI scoring methods, evaluates its diagnostic value with geriatric oncology tools, and proposes a cut-off point for clinical use. Materials and MethodsDanish patients aged ≥70 years with gastrointestinal cancer undergoing chemotherapy from a prospective, observational study were included. Two ELFI scoring methods, item-based and domain-based, were compared. Internal consistency reliability, validity, and correlations between ELFI, its component scales, and measures of functioning/frailty (including Eastern Cooperative Oncology Group Performance Status [ECOG-PS], Geriatric-8 [G8], Vulnerable Elders Survey-13 [VES-13], Timed-Up-and-Go [TUG], and 30-s chair stand test [30CST]) were investigated. Sensitivity and specificity analyses evaluated the ability of ELFI to predict frailty outcomes and identified frailty thresholds. Receiver operating characteristic analyses assessed the diagnostic ability of ELFI, alongside other measures, for oncological outcomes and frailty differentiation. Equipercentile equating methods enabled ECOG-PS, ELFI, and G8 mapping. ResultsOne hundred fifty-four patients (median age 73.5 years, range 70–85) undergoing curative- or palliative-intent chemotherapy (49%) were included. ELFI demonstrated good internal consistency (Cronbach's alpha = 0.82) and acceptable convergent, structural, and discriminant validity. ELFI showed moderate to very strong correlations with its component scales (r = 0.40–0.93), and weaker correlations with frailty measures (r = 0.02–0.60). ELFI score < 80 indicated frailty risk, with almost fivefold risk of ECOG-PS 2 at follow-up (odds ratio[OR] = 4.8, 95% confidence interval [CI] 1.4–15.9), and predicted G8, VES-13, TUG, and 30CST frailty at follow-up, not completing planned chemotherapy (OR = 3.1; 95%CI 1.5–6.2), mono-therapy (OR = 3.5; 95%CI 1.5–8.1), initial dose reduction (OR = 4.9; 95%CI 2.0–12.1), and shorter overall survival (hazard ratio = 2.0, 95%CI 1.4–3.0). A preliminary crosswalk between ECOG-PS, ELFI, and G8 was established. DiscussionELFI was validated as a concise patient-reported measure of functional status in older patients with cancer and its relationship to frailty. ELFI demonstrated comparable predictive ability to other tools for oncological outcomes. Both scoring methods yielded similar results, with the domain-based method (ELFI v2.0) endorsed for consistency. ELFI v2.0 score of 80 was suggested as the frailty threshold in this population, supporting its clinical utility.

Application of pressure-sensitive paint for explosive blast measurements

This study demonstrates the application of fast response pressure-sensitive paint (PSP) to explosively driven blast wave testing. A sprayable polymer ceramic fast response PSP was applied to an aluminium disc before being coated with platinum porphyrin compound as the active luminophore. The disc was then exposed to a blast wave and the response was measured using a high-speed video camera. The PSP measured the transit of the incident shock wave clearly, albeit with a slight response delay following the instantaneous change in pressure. A time domain-based method for improving temporal response, whilst considering both spatial and temporal effects, is described. This study clearly demonstrates that the spatial distribution of a blast wave on a surface may be captured by PSP technology. Integrated parameters such as impulse can correctly be characterised using this method. This technology offers an enhanced and more efficient way of characterising blast.

Using Computer Technique for Developing Method for Vibration Damage Estimation Under Combined Random and Deterministic Loading

Abstract This paper is focusses on developing a novel method for vibration damage estimation for military helicopters, fighter aircrafts and any other aircraft exposed to combined stochastic and deterministic loading. The first stage of the research focused on frequency domain damage prediction, which is the legacy method proposed by Bishop and developed by Sweitzer, Schlesinger, Woodward, Kerr, Murthy, Datta and, Atkins. The mentioned frequency domain-based method is used in commercial software, e.g., MSC CAE Fatigue. Frequency domain damage prediction is based on superposition of spectral moments and Dirlik method of Rainflow Cycle Counting algorithm in frequency domain. The first phase of the research showed the legacy algorithm based on transfer function developed using FEM (Finite Element Method) method in Abaqus environment and is very conservative. The second stage of the research aims to develop a novel method which allowing for more robust and accurate damage estimation. For this purpose, the Monte Carlo method for retrieving random signal in the time domain from signal in frequency domain was used. To obtain the system transfer function, – the 1 g load harmonic system response was obtained using FEM analysis. It was subsequently scaled linearly by the PSD input curve for random loading and sine wave, or sine sweep function for deterministic loading to calculate the cumulative system response of the linear system. The research allows the development of a novel method to precisely estimate vibration damage using combined time and frequency domains approach, based on effective frequency domain FEM analysis of the linear system. The new proposed method can be also used for precise replication of test conditions via considering signal clipping and frequency resolution used for real testing.

A single-image human body reconstruction method combining normal recovery and frequency domain completion

&lt;p&gt;&lt;span lang="EN-US"&gt;Reconstructing a 3D human body from a single image is convenient and efficient, but it faces challenges when the face is heavily occluded or the person is wearing loose clothing. In this paper, we propose a frequency domain-based method for completing missing parts of the human body using manifold harmonics and frequency domain analysis. Our approach involves linear interpolation of the incomplete 3D human body obtained through normal integration. The interpolated points are then projected onto the appropriate dimension of the frequency domain space using manifold harmonic bases. Through Laplacian mesh editing, the interpolated points are replaced, resulting in a refined and complete 3D human body. Our method surpasses the limitations of template human bodies and marching cubes algorithms, enabling more detailed feature reconstruction. By locally completing the body in a low-dimensional frequency domain space, our method avoids over smoothing and bulging issues, effectively filling the missing regions while maintaining mesh smoothness consistency. Experimental results demonstrate the effectiveness and superiority of our frequency domain-based completion method for accurate and detailed 3D human body reconstruction from single images.&lt;/span&gt;&lt;/p&gt;

Capacity Analysis of Holographic MIMO Channels With Practical Constraints

Holographic Multiple-Input and Multiple-Output (MIMO) is envisioned as a promising technology to realize unprecedented spectral efficiency by integrating a large number of antennas into a compact space. Most research on holographic MIMO is based on isotropic scattering environments, and the antenna gain is assumed to be unlimited by deployment space. However, the channel might not satisfy isotropic scattering because of generalized angle distributions, and the antenna gain is limited by the array aperture in reality. In this letter, we aim to analyze the holographic MIMO channel capacity under practical angle distribution and array aperture constraints. First, we calculate the spectral density for generalized angle distributions by introducing a wavenumber domain-based method. And then, the capacity under generalized angle distributions is analyzed and two different aperture schemes are considered. Finally, numerical results show that the capacity is obviously affected by angle distribution at high signal-to-noise ratio (SNR) but hardly affected at low SNR, and the capacity will not increase infinitely with antenna density due to the array aperture constraint.

Acceleration Based Condition Monitoring of Steel Bridges

This paper presents a frequency domain-based method for continuous health monitoring of steel truss bridge, based on the power spectral density and frequency analysis of the recorded acceleration response time histories at the selected node points of a bridge under regular operational conditions. This method is also implemented on a railway steel truss bridge connecting the mainland India to Rameswaram, named the Pamban bridge. The measured acceleration response time histories at some selected nodes on the bridge were parameterized into 4 power spectral density and frequency-based parameters. Also, the frequency analysis of the acceleration response time histories was done. The continuous variation of these parameters with measurement points was observed for about a year to investigate the suitability of these parameters to detect, locate damages in a railway steel truss bridge, and find their severity. Then, the consistency of damages detected by the variation of these parameters and the damages expected based on strain measurements and visual inspections made on the bridge was examined to evaluate the suitability of these parameters for the level 3 damage detection. The same is documented and performance of the parameters discussed.

Computational Systems Biology of Alfalfa - Bacterial Blight Host-Pathogen Interactions: Uncovering the Complex Molecular Networks for Developing Durable Disease Resistant Crop.

Medicago sativa (also known as alfalfa), a forage legume, is widely cultivated due to its high yield and high-value hay crop production. Infectious diseases are a major threat to the crops, owing to huge economic losses to the agriculture industry, worldwide. The protein-protein interactions (PPIs) between the pathogens and their hosts play a critical role in understanding the molecular basis of pathogenesis. Pseudomonas syringae pv. syringae ALF3 suppresses the plant’s innate immune response by secreting type III effector proteins into the host cell, causing bacterial stem blight in alfalfa. The alfalfa-P. syringae system has little information available for PPIs. Thus, to understand the infection mechanism, we elucidated the genome-scale host-pathogen interactions (HPIs) between alfalfa and P. syringae using two computational approaches: interolog-based and domain-based method. A total of ∼14 M putative PPIs were predicted between 50,629 alfalfa proteins and 2,932 P. syringae proteins by combining these approaches. Additionally, ∼0.7 M consensus PPIs were also predicted. The functional analysis revealed that P. syringae proteins are highly involved in nucleotide binding activity (GO:0000166), intracellular organelle (GO:0043229), and translation (GO:0006412) while alfalfa proteins are involved in cellular response to chemical stimulus (GO:0070887), oxidoreductase activity (GO:0016614), and Golgi apparatus (GO:0005794). According to subcellular localization predictions, most of the pathogen proteins targeted host proteins within the cytoplasm and nucleus. In addition, we discovered a slew of new virulence effectors in the predicted HPIs. The current research describes an integrated approach for deciphering genome-scale host-pathogen PPIs between alfalfa and P. syringae, allowing the researchers to better understand the pathogen’s infection mechanism and develop pathogen-resistant lines.

Machine Learning-Based Detection of Graphene Defects with Atomic Precision

HighlightsA machine learning-based approach is developed to predict the unknown defect locations by thermal vibration topographies of graphene sheets.Two prediction strategies are developed: an atom-based method which constructs data by atom indices, and a domain-based method which constructs data by domain discretization.Our machine learning model can achieve approximately a 90% prediction accuracy on the reserved data for testing, indicating a promising extrapolation into unseen future graphene configurations.

A Novel Approach for Continuous Health Status Monitoring and Automatic Detection of Infection Incidences in People With Type 1 Diabetes Using Machine Learning Algorithms (Part 2): A Personalized Digital Infectious Disease Detection Mechanism.

BackgroundSemisupervised and unsupervised anomaly detection methods have been widely used in various applications to detect anomalous objects from a given data set. Specifically, these methods are popular in the medical domain because of their suitability for applications where there is a lack of a sufficient data set for the other classes. Infection incidence often brings prolonged hyperglycemia and frequent insulin injections in people with type 1 diabetes, which are significant anomalies. Despite these potentials, there have been very few studies that focused on detecting infection incidences in individuals with type 1 diabetes using a dedicated personalized health model.ObjectiveThis study aims to develop a personalized health model that can automatically detect the incidence of infection in people with type 1 diabetes using blood glucose levels and insulin-to-carbohydrate ratio as input variables. The model is expected to detect deviations from the norm because of infection incidences considering elevated blood glucose levels coupled with unusual changes in the insulin-to-carbohydrate ratio.MethodsThree groups of one-class classifiers were trained on target data sets (regular days) and tested on a data set containing both the target and the nontarget (infection days). For comparison, two unsupervised models were also tested. The data set consists of high-precision self-recorded data collected from three real subjects with type 1 diabetes incorporating blood glucose, insulin, diet, and events of infection. The models were evaluated on two groups of data: raw and filtered data and compared based on their performance, computational time, and number of samples required.ResultsThe one-class classifiers achieved excellent performance. In comparison, the unsupervised models suffered from performance degradation mainly because of the atypical nature of the data. Among the one-class classifiers, the boundary and domain-based method produced a better description of the data. Regarding the computational time, nearest neighbor, support vector data description, and self-organizing map took considerable training time, which typically increased as the sample size increased, and only local outlier factor and connectivity-based outlier factor took considerable testing time.ConclusionsWe demonstrated the applicability of one-class classifiers and unsupervised models for the detection of infection incidence in people with type 1 diabetes. In this patient group, detecting infection can provide an opportunity to devise tailored services and also to detect potential public health threats. The proposed approaches achieved excellent performance; in particular, the boundary and domain-based method performed better. Among the respective groups, particular models such as one-class support vector machine, K-nearest neighbor, and K-means achieved excellent performance in all the sample sizes and infection cases. Overall, we foresee that the results could encourage researchers to examine beyond the presented features into other additional features of the self-recorded data, for example, continuous glucose monitoring features and physical activity data, on a large scale.

NDDSA: A network- and domain-based method for predicting drug-side effect associations

Finding side effects of drugs, before reaching the animal and clinical test, can decrease the cost and time of developing new drugs. Also, a lot of side effects are reported after going to market and using it by patients (post-marketing). There are some systems to report these events but most of the time, side effects stay hidden. Thus, a lot of computational methods have been developed to predict the side effects of drugs before reaching the clinical test or going to market. These methods are based on different features of drugs like chemical or biological features. Most of these methods can just complete the side effect list of approved drugs or require a great deal of biological information about the drugs. So, it is impossible to find the side effects of a new drug candidate very early. In this paper, we propose a network and domain-based algorithm (NDDSA) that can predict the side effects of new drug candidates by assigning a score to each side effect. Unlike other methods, it needs just the chemical formula of the new drug. We show that NDDSA performs better than the best present method in case of predicting ADRs for a new drug and has acceptable results in case of predicting potential side effects for approved drugs, while it is much faster than the other methods.

In silico prediction of host-pathogen protein interactions in melioidosis pathogen Burkholderia pseudomallei and human reveals novel virulence factors and their targets.

The aerobic, Gram-negative motile bacillus, Burkholderia pseudomallei is a facultative intracellular bacterium causing melioidosis, a critical disease of public health importance, which is widely endemic in the tropics and subtropical regions of the world. Melioidosis is associated with high case fatality rates in animals and humans; even with treatment, its mortality is 20-50%. It also infects plants and is designated as a biothreat agent. B. pseudomallei is pathogenic due to its ability to invade, resist factors in serum and survive intracellularly. Despite its importance, to date only a few effector proteins have been functionally characterized, and there is not much information regarding the host-pathogen protein-protein interactions (PPI) of this system, which are important to studying infection mechanisms and thereby develop prevention measures. We explored two computational approaches, the homology-based interolog and the domain-based method, to predict genome-scale host-pathogen interactions (HPIs) between two different strains of B. pseudomallei (prototypical, and highly virulent) and human. In total, 76335 common HPIs (between the two strains) were predicted involving 8264 human and 1753 B. pseudomallei proteins. Among the unique PPIs, 14131 non-redundant HPIs were found to be unique between the prototypical strain and human, compared to 3043 non-redundant HPIs between the highly virulent strain and human. The protein hubs analysis showed that most B. pseudomallei proteins formed a hub with human dnaK complex proteins associated with tuberculosis, a disease similar in symptoms to melioidosis. In addition, drug-binding and carbohydrate-binding mechanisms were found overrepresented within the host-pathogen network, and metabolic pathways were frequently activated according to the pathway enrichment. Subcellular localization analysis showed that most of the pathogen proteins are targeting human proteins inside cytoplasm and nucleus. We also discovered the host targets of the drug-related pathogen proteins and proteins that form T3SS and T6SS in B. pseudomallei. Additionally, a comparison between the unique PPI patterns present in the prototypical and highly virulent strains was performed. The current study is the first report on developing a genome-scale host-pathogen protein interaction networks between the human and B. pseudomallei, a critical biothreat agent. We have identified novel virulence factors and their interacting partners in the human proteome. These PPIs can be further validated by high-throughput experiments and may give new insights on how B. pseudomallei interacts with its host, which will help medical researchers in developing better prevention measures.

Reachable domain for satellite relative motion along elliptic orbit with uncertainty and process noise

For satellite close-range relative motion under uncertainty and process noise, the relative reachable domain is the confidence region, upon providing a user-defined probability level, of the occurrence of a flying trajectory. The relative reachable domain is a risk-assessing tool used to prevent inadvertent collisions. This study conducted a follow-up relative reachable domain investigation with two improvements: (1) the reference orbit of the close-range relative motion is generalized to an arbitrary elliptic orbit and (2) the process noise during the relative motion is incorporated. The equation of the relative reachable domain envelope, the boundary of the relative reachable domain, is derived. An algorithm is proposed to solve for the relative reachable domain envelope. By comparing the solved relative reachable domain envelopes with the results of a direct Monte Carlo simulation, the accuracy of the proposed algorithm is verified. Moreover, a relative reachable domain-based collision detection method is presented to screen out encounters that have a low chance of collision. The proposed collision detection method exhibits efficiency and reliability in deciding whether a passive flyby mission is safe or not.

A boundary integral approach to linear and nonlinear transient wave scattering

In this work, we introduce a method for solving linear and nonlinear scattering problems for wave equations using a new hybrid approach. This new approach consists of a reformulation of the governing equations into a form that can be solved by a combination of a domain-based method and a boundary-integral method. Our reformulation is aimed at a situation in which we have a collection of compact scattering objects located in an otherwise homogeneous unbounded space.The domain-based method is used to propagate the equations governing the wave field inside the scattering objects forward in time. The boundary integral method is used to supply the domain-based method with the required boundary values for the wave field.In this way, the best features of both methods come into play. The response inside the scattering objects, which can be caused by both material inhomogeneity and nonlinearities, is easily considered using the domain-based method, and the boundary conditions supplied by the boundary integral method makes it possible to confine the domain-method to the inside of each scattering object.

Prediction of Protein-Protein Interactions Based on Domain.

Protein-protein interactions (PPIs) play a crucial role in various biological processes. To better comprehend the pathogenesis and treatments of various diseases, it is necessary to learn the detail of these interactions. However, the current experimental method still has many false-positive and false-negative problems. Computational prediction of protein-protein interaction has become a more important prediction method which can overcome the obstacles of the experimental method. In this work, we proposed a novel computational domain-based method for PPI prediction, and an SVM model for the prediction was built based on the physicochemical property of the domain. The outcomes of SVM and the domain-domain score were used to construct the prediction model for protein-protein interaction. The predicted results demonstrated the domain-based research can enhance the ability to predict protein interactions.

A 3D nonlinear Maxwell’s equations solver based on a hybrid numerical method

In this paper, we explore the possibility of solving 3D Maxwell’s equations in the presence of a nonlinear and/or inhomogeneous material response. We propose using a hybrid approach, which combines a boundary integral representation with a domain-based method. This hybrid approach has previously been successfully applied to 1D linear and nonlinear transient wave scattering problems. The basic idea of the approach is to propagate Maxwell’s equations inside the scattering objects forward in time using a domain-based method, while a boundary integral representation of the electromagnetic field is used to supply the domain-based method with the Required surface values. Thus, no grids outside the scattering objects are needed, and this greatly reduces the computational cost and complexity.

Exact wave propagation analysis of moderately thick Levy-type plate with piezoelectric layers using spectral element method

Spectral element method (SEM) is an accurate and efficient frequency domain-based method which has been frequently used in different analyses of various structures. In the present research, for the first time, this method is employed to deal with the wave propagation analysis of moderately thick rectangular plates with two piezoelectric layers attached on the top and bottom surfaces. The equations of motion are derived by taking into account the Mindlin plate theory assumptions and using the Hamilton's principle. The Maxwell's equation is employed to obtain the governing equation of electric potential in the piezoelectric layers. The differential equations are transformed into the frequency domain by employing the discrete Fourier transform and then a closed-form solution for the Levy type plate attached to piezoelectric layers is introduced. The dynamic stiffness matrix for the smart plate is obtained by applying the exact dynamic shape functions. Accurate and efficient numerical algorithms are introduced to extract the natural frequencies and the dynamic response of the structure under impact loading. The validation of the presented method is accomplished by comparing the obtained natural frequencies and dynamic response with the existing results in the literature and also the results obtained by the Abaqus software. Also, the effects of boundary condition and thickness of the plate and piezoelectric layers on the results are investigated. Independence to the mesh structure and less computational time are the most important advantages of the SEM compared with similar numerical methods like the finite element method.

Propagation coefficient spectrum based locating method for cable insulation degradation

To solve the complexity of the conventional time-domain reflectometry method for locating minor cable ageing degradation, a frequency domain-based method for locating cable ageing degradation based on propagation coefficient spectrum is proposed in this study. First, the change pattern of cable input impedance spectrum in frequency-domain reflectometry is analysed to reveal the relationship between input impedance spectrum and propagation coefficient, and thus finds out the working mechanism of ageing degradation on propagation coefficient spectrum. Then, in the experiment, a vector network analyser is used to measure propagation coefficient spectrum and the inverse discrete Fourier transform is applied to locate cable ageing degradation. Finally, kurtosis analysis is performed on locating curves of different bandwidth and the upper limit of frequency of the testing signal is decided. Within a certain limit, the method proposed in this study can locate degradation with higher accuracy and resolution than several time/frequency-domain based methods currently adopted.

Research on Fault Feature Extraction Method Based on NOFRFs and Its Application in Rotor Faults

Rub‐impact between the rotating and static parts is a more common fault. The occurrence of faults is often accompanied by the generation of nonlinear phenomena. However, it is difficult to find out because the nonlinear characteristics are not obvious at the beginning of the fault. As a new frequency domain‐based method, nonlinear output frequency response functions (NOFRFs) use the vibration response to extract the nonlinear characteristics of the system. This method has a better recognition rate for fault detection. Also, it has been applied in structural damages detection, but the high‐order NOFRFs have the characteristics that the signals are weak and the features are difficult to extract. On this basis, the concept of the weighted contribution rate of the NOFRFs is proposed in this paper. The variable weighted coefficients with orders are used to amplify the influence of high‐order NOFRFs on the nonlinearity of the system so as to extract its fault characteristics. The new index RI is proposed based on Clenshaw–Curtis quadrature formula to eliminate the effect of artificially selected weighted coefficients on sensitivity. Especially in the early stage of the fault, the new index varies greatly with the deepening of the fault. Both simulation and experimental results verify the validity and practicability of the new index. The new index has certain guiding significance in the detection of mechanical system faults.