Autoregressive Coefficients Research Articles

Maximum entropy spectral analysis: an application to gravitational waves data analysis

The maximum entropy spectral analysis (MESA) method, developed by Burg, offers a powerful tool for spectral estimation of a time-series. It relies on Jaynes’ maximum entropy principle, allowing the spectrum of a stochastic process to be inferred using the coefficients of an autoregressive process AR(p) of order p. A closed-form recursive solution provides estimates for both the autoregressive coefficients and the order p of the process. We provide a ready-to-use implementation of this algorithm in a Python package called memspectrum, characterized through power spectral density (PSD) analysis on synthetic data with known PSD and comparisons of different criteria for stopping the recursion. Additionally, we compare the performance of our implementation with the ubiquitous Welch algorithm, using synthetic data generated from the GW150914 strain spectrum released by the LIGO-Virgo-Kagra collaboration. Our findings indicate that Burg’s method provides PSD estimates with systematically lower variance and bias. This is particularly manifest in the case of a small (O(5000)) number of data points, making Burg’s method most suitable to work in this regime. Since this is close to the typical length of analysed gravitational waves data, improving the estimate of the PSD in this regime leads to more reliable posterior profiles for the system under study. We conclude our investigation by utilising MESA, and its particularly easy parametrisation where the only free parameter is the order p of the AR process, to marginalise over the interferometers noise PSD in conjunction with inferring the parameters of GW150914

A note on the asymptotic behavior of a mildly unstable integer-valued AR(1) model

This note examines the conditional least squares (CLS) estimators for integer-valued autoregressive (INAR) models, with a focus on the INAR(1) model. Our investigation reveals that the joint limiting distribution of the CLS estimators for the autoregressive coefficient and the mean of the model errors is degenerate in the case of mildly unstable INAR(1) models with moderate deviations from unity. This degeneracy may pose challenges for statistical inference. We provide commenting notes based on the asymptotic results to address this issue. Additionally, we conduct simulation studies and analyze a real-world dataset to validate the theoretical findings.

Movements classification system for transhumeral amputees using myoelectric signals

The extent of loss of functionality in people with transhumeral amputation or elbow disarticulation is considered highly compromised. The person with this impairment loses the primary muscle involved in the movement of the hand and fingers, and the elbow flexion/extension. In this sense, the development of myoelectric prostheses must include mechanisms that replicate these movements. Moreover, the control system for controlling a prosthesis must be robust and intuitive, where pattern recognition and artificial intelligence techniques represent an important and increasingly explored alternative. This study aims to develop a movement intention classification system based on myoelectric signals (MES) obtained from an elbow disarticulation amputee. Different features were extracted from the MES as the Mean absolute value (MAV), zero crossings (ZC), slope sign changes (SSC), waveform length (WL), and autoregressive (AR) coefficients. Machine learning classifiers (Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA), Support Vector Machines (SVM), K-Nearest Neighbors (KNN), Random Forests (RF), and Multilayer Perceptron (MLP)) were used to predict seven gestures: elbow flexion (EF), elbow extension (EE), forearm pronation (FP), forearm supination (FS), hand opening (HO), hand closing (HC), and rest (R). The results obtained with LDA, QDA, KNN, MLP, SVM, and RF were 60.84%, 71.05%, 77.10%, 78.06%, 78.57%, and 79.72% of accuracy, respectively. These results are promising and will allow the development of a myoelectric prosthesis control system for people with transhumeral amputation or elbow disarticulation.

Lag order selection for long-run variance estimation in econometrics

. Estimating the long-run variance (LRV) is crucial for several econometric issues. Constructing reliable heteroskedasticity autocorrelation consistent (HAC) variance-covariance matrices and implementing efficient generalized method of moments (GMM) estimation procedures require a consistent LRV estimate. A good VARHAC estimator (HAC matrix with the spectral density at frequency zero constructed using a VAR spectral estimation) requires accurately estimating the sum of autoregressive (AR) coefficients; however, a criterion that minimizes the innovation variance does not necessarily yield the best spectral estimate. This article implements an optimal VARHAC estimator using an alternative information criterion, considering the bias in the sum of the parameters for the AR estimator of the spectral density at frequency zero.

Empirical likelihood inference for time-varying coefficient autoregressive models

In this paper, we propose time-varying coefficient autoregressive models (TVARMs) of [Formula: see text]th order as a solution for capturing the nonlinear structure of multiple explanatory variables. The stationary [Formula: see text]-mixing sequence of autoregressive variables is considered. We apply empirical likelihood approach to investigate confidence regions of the autoregressive coefficients of the TVARMs, and establish the nonparametric version of Wilks’ theorem of the proposed empirical log-likelihood ratio. Further, the maximum empirical likelihood estimator of the autoregressive coefficients and its asymptotic distribution are also obtained. Besides, to determine the order of autoregression, penalized empirical likelihood approach is developed with the help of smoothly clipped absolute deviation penalty and the resultant penalized estimators have the oracle property. Simulation studies and an analysis of monthly Chinese price index dataset are used to demonstrate the effectiveness of our proposed methods.

HAND GRASPS RECOGNITION USING SINGLE-CHANNEL TRANSIENT-STATE SURFACE ELECTROMYOGRAPHY

The need to perform large hand-grasping strategies in daily life has promoted the development of robotic hands and prosthetic hands that mimic natural ones. This work presents a system for the detection of 10 basic hand grasps in healthy subjects based on single-channel transient-state Surface Electromyography (sEMG) signals. The studied grasps are large diameter, ring, knife index finger, writing tripod, power sphere, precision sphere, prismatic pinch, lateral, extension type, and parallel extension grasp. Signals were collected from 10 healthy volunteers using three sEMG electrodes connected to an Electromyography (EMG) shield using MATLAB as data acquisition software. The signals were classified using three different classifiers, i.e. [Formula: see text]-Nearest Neighbors ([Formula: see text]-NN), Diagonal Linear Discriminant Analysis (dl-DA), and Random Forest (RF). The used features were mean absolute value, integrated absolute value, variance, root mean square value, waveform length, Willison amplitude, slope sign change, zero crossing, autoregressive coefficients, and mean frequency. The results show that good classification accuracy is achieved when classifying a reduced number of grasps using a single-channel transient-state sEMG. The average accuracy for the different classifiers varied from 41.5% to 53.3% when classifying 10 grasps and from 78.4% to 91.9% when classifying five grasps using two features as a trainer. It is found that transient-state sEMG signals are efficient in the detection of different hand grasps, reducing the time to generate control signals and the number of channels.

ARX-Naïve Bayes based structural damage identification

ABSTRACT The nature of damage identification is close to a pattern recognition process that classifies different damage patterns. The naïve Bayes classifier (NBC) can effectively handle multiple-classification problems by choosing patterns with high probabilities. Therefore, by absorbing the autoregressive model with exogenous inputs (the ARX model), an ARX-Naïve Bayes damage identification strategy has been proposed in which the autoregressive coefficients of the ARX model are taken as the sensitive damage feature. The classification training and test sample datasets are then built on these coefficients corresponding to various damage scenarios. The model order of an AR model is first determined for the subsequent order selection of the ARX model, whose autoregressive coefficients are further used to construct the NBC. This procedure can enhance the pattern recognition robustness to uncertainties such as measurement noises. Different damage patterns are determined by calculating the sum of logarithmic likelihoods of testing samples. The effectiveness of the proposed method has been verified against a bridge benchmark model having different damage scenarios under the noise pollution. In addition, an experimental five-story shear frame structure was adopted for validation, showing that compared with the SVM algorithm suitable for handling binary classification problems, the proposed method excels in multi-classification of damage patterns.

Does “National Civilized City” policy mitigate air pollution in China? A spatial Durbin difference-in-differences analysis

“National Civilized City” (NCC) is regarded as China’s highest honorary title and most valuable city brand. To win and maintain the “golden city” title, municipal governments must pay close attention to various key appraisal indicators, mainly environmental ones. In this study we verify whether cities with the title are more likely to mitigate SO2 pollution. We adopt the spatial Durbin difference-in-differences (DID) model and use panel data of 283 Chinese cities from 2003 to 2018 to analyze the local (direct) and spillover effects (indirect) of the NCC policy on SO2 pollution. We find that SO2 pollution in Chinese cities is not randomly distributed in geography, suggesting the existence of spatial spillovers and possible biased estimates. Our study treats the NCC policy as a quasi-experiment and incorporates spatial spillovers of NCC policy into a classical DID model to verify this assumption. Our findings show: (1) The spatial distribution of SO2 pollution represents strong spatial spillovers, with the most highly polluted regions mainly situated in the North China Plain. (2) The Moran’s I test results confirms significant spatial autocorrelation. (3) Results of the spatial Durbin DID models reveal that the civilized cities have indeed significantly mitigated SO2 pollution, indicating that cities with the honorary title are acutely aware of the environment in their bid to maintain the golden city brand. As importantly, we notice that the spatial DID term is also significant and negative, implying that neighboring civilized cities have also mitigated their own SO2 pollution. Due to demonstration and competition effects, neighboring cities that won the title ostensibly motivates local officials to adopt stringent policies and measures for lowering SO2 pollution and protecting the environment in competition for the golden title. The spatial autoregressive coefficient was significant and positive, indicating that SO2 pollution of local cities has been deeply affected by neighbors. A series of robustness check tests also confirms our conclusions. Policy recommendations based on the findings for protecting the environment and promoting sustainable development are proposed.

An early force prediction control scheme using multimodal sensing of electromyography and digit force signals

Different grasping gestures result in the change of muscular activity of the forearm muscles. Similarly, the muscular activity changes with a change in grip force while grasping the object. This change in muscular activity, measured by a technique called Electromyography (EMG) is used in the upper limb bionic devices to select the grasping gesture. Previous research studies have shown gesture classification using pattern recognition control schemes. However, the use of EMG signals for force manipulation is less focused, especially during precision grasping.In this study, an early predictive control scheme is designed for the efficient determination of grip force using EMG signals from forearm muscles and digit force signals. The optimal pattern recognition (PR) control schemes are investigated using three different inputs of two signals: EMG signals, digit force signals and a combination of EMG and digit force signals. The features extracted from EMG signals included Slope Sign Change, Willison Amplitude, Auto Regressive Coefficient and Waveform Length. The classifiers used to predict force levels are Random Forest, Gradient Boosting, Linear Discriminant Analysis, Support Vector Machines, k-nearest Neighbors and Decision Tree. The two-fold objectives of early prediction and high classification accuracy of grip force level were obtained using EMG signals and digit force signals as inputs and Random Forest as a classifier. The earliest prediction was possible at 1000 ms from the onset of the gripping of the object with a mean classification accuracy of 90 % for different grasping gestures.Using this approach to study, an early prediction will result in the determination of force level before the object is lifted from the surface. This approach will also result in better biomimetic regulation of the grip force during precision grasp, especially for a population facing vision deficiency.

The local to unity dynamic Tobit model

This paper considers highly persistent time series that are subject to nonlinearities in the form of censoring or an occasionally binding constraint, such as are regularly encountered in macroeconomics. A tractable candidate model for such series is the dynamic Tobit with a root local to unity. We show that this model generates a process that converges weakly to a non-standard limiting process, that is constrained (regulated) to be positive. Surprisingly, despite the presence of censoring, the OLS estimators of the model parameters are consistent. We show that this allows OLS-based inferences to be drawn on the overall persistence of the process (as measured by the sum of the autoregressive coefficients), and for the null of a unit root to be tested in the presence of censoring. Our simulations illustrate that the conventional ADF test substantially over-rejects when the data is generated by a dynamic Tobit with a unit root, whereas our proposed test is correctly sized. We provide an application of our methods to testing for a unit root in the Swiss franc/euro exchange rate, during a period when this was subject to an occasionally binding lower bound.

중학생이 지각한 부모의 양육태도와 삶의 만족도 간의 관계

Objectives The purpose of this study is to examine the longitudinal mediating effect of teacher relationship perceptions on the relationship between middle school students' perceived parenting attitudes and life satisfaction, i.e., to determine how parenting attitudes affect adolescents' life satisfaction over time through teacher relationship perceptions. This study provides a basis for developing programs for adolescent mental health and highlights the importance of the role of teachers in guiding adolescents' lives.
 Methods The study utilized three years of data from 2019(middle 1) to 2021(middle 3) from the middle 1 panel of the Korea Child and Youth Panel Survey(KCYPS 2018). The total number of subjects was 2,325, and the data was analyzed using an autoregressive cross-lagged model. This model has the advantage of being able to consider temporal antecedence, which is difficult to reflect in conventional cross-sectional models, verify the size of the auto-regressive coefficient, and estimate the effect after controlling the prior state of the mediator and the dependent variable when estimating the mediating effect.
 Results Positive parenting attitudes at the earlier time point were found to have a positive effect on teacher relationship perceptions at the later time point, while negative parenting attitudes at the earlier time point had a negative effect on teacher relationship perceptions at the later time point. This suggests that adolescents' perceived parenting attitudes may closely influence the formation of relationships with teachers. In addition, we found that teacher relationship perceptions at the earlier time point influenced life satisfaction at the later time point. This means that the extent to which adolescents perceive their relationships with teachers to be positive affects their subsequent life satisfaction. In other words, teacher relationship perceptions have a longitudinal mediating effect on the relationship between parenting attitudes and life satisfaction.
 Conclusions These results suggest that the parents’ parenting attitudes at prior time points are influencing middle school students’ life satisfaction at later time points. We can also predict that adolescents' life satisfaction may vary depending on whether they perceive their teacher relationships as positive or negative in this pathway.

Condition monitoring of mooring systems for Floating Offshore Wind Turbines using Convolutional Neural Network framework coupled with Autoregressive coefficients

This research presents a novel approach proposed for the monitoring of mooring systems in Floating Offshore Wind Turbines (FOWTs), employing a combination of Convolutional Neural Networks (CNNs) and Auto-Regressive (AR) models. CNN finds broad application in monitoring intricate structures, as they adeptly handle noisy response data without necessitating profound domain expertise. The precision of CNNs relies on the extraction of meaningful features from input data, necessitating meticulous data curation and labeling for optimal computational efficiency and accurate estimation. Emphasis is placed on the preference for feature-rich small datasets over voluminous yet sparse datasets, aiming to enable CNNs to discern crucial patterns more effectively and mitigate issues such as overfitting and extensive preprocessing.The novelty of the proposed approach lies in the integration of AR models, which serve to compress data and enhance damage-sensitive characteristics in the input for CNNs. This integration involves deploying regression models fitted to historical responses, parameterized with AR coefficients sensitive to damage, and further classifying severity using CNNs. The sequential nature of this approach addresses challenges such as vanishing/exploding gradients, particularly for extended historical data, while also attenuating the impact of noise and irrelevant information through data compression.The study explores the effectiveness of the coupled AR-CNN method in monitoring FOWT mooring lines, with a specific focus on two levels of damage identification: detection with classification and damage severity across diverse damage and operational scenarios. The modified methodology exhibits superior outcomes by conducting a performance analysis against traditional CNNs and other machine-learning methods, highlighting the potential of the AR-CNN strategy to improve the precision of FOWT mooring line condition monitoring. These findings underscore the AR-CNN strategy’s potential to enhance the accuracy of FOWT mooring line condition monitoring.

Intraindividual time-varying dynamic network of affects: linear autoregressive mixed-effects models for ecological momentary assessment.

An interesting recent development in emotion research and clinical psychology is the discovery that affective states can be modeled as a network of temporally interacting moods or emotions. Additionally, external factors like stressors or treatments can influence the mood network by amplifying or dampening the activation of specific moods. Researchers have turned to multilevel autoregressive models to fit these affective networks using intensive longitudinal data gathered through ecological momentary assessment. Nonetheless, a more comprehensive examination of the performance of such models is warranted. In our study, we focus on simple directed intraindividual networks consisting of two interconnected mood nodes that mutually enhance or dampen each other. We also introduce a node representing external factors that affect both mood nodes unidirectionally. Importantly, we disregard the potential effects of a current mood/emotion on the perception of external factors. We then formalize the mathematical representation of such networks by exogenous linear autoregressive mixed-effects models. In this representation, the autoregressive coefficients signify the interactions between moods, while external factors are incorporated as exogenous covariates. We let the autoregressive and exogenous coefficients in the model have fixed and random components. Depending on the analysis, this leads to networks with variable structures over reasonable time units, such as days or weeks, which are captured by the variability of random effects. Furthermore, the fixed-effects parameters encapsulate a subject-specific network structure. Leveraging the well-established theoretical and computational foundation of linear mixed-effects models, we transform the autoregressive formulation to a classical one and utilize the existing methods and tools. To validate our approach, we perform simulations assuming our model as the true data-generating process. By manipulating a predefined set of parameters, we investigate the reliability and feasibility of our approach across varying numbers of observations, levels of noise intensity, compliance rates, and scalability to higher dimensions. Our findings underscore the challenges associated with estimating individualized parameters in the context of common longitudinal designs, where the required number of observations may often be unattainable. Moreover, our study highlights the sensitivity of autoregressive mixed-effect models to noise levels and the difficulty of scaling due to the substantial number of parameters.

Integrated Approach for ECG Signal Classification Using Fused Slantlet Transform and Autoregressive Features

Sudden cardiac death remains a significant concern, emphasizing the critical need for intelligent diagnostic techniques in cardiac disease detection. Cardiologic Vascular Diseases (CVD) pose a significant global health challenge, often associated with unhealthy lifestyle habits. Electrocardiogram (ECG) monitoring plays a crucial role in assessing heart function, but its interpretation can be challenging due to signal complexity. This study proposes a novel approach utilizing fused Slantlet-Spatial features alongside Auto Regression (AR) coefficients to classify electrocardiogram (ECG) signals. Leveraging the Slantlet Transform (SLT) for its superior time localization capabilities and the simplicity of AR coefficients, this methodology aims to enhance the accuracy of cardiac illness classification. Nineteen distinct features were extracted from 300 ECG signals, each comprising 512 samples, enriching the classification scheme's efficacy. The fused feature extraction technique demonstrated success in improving overall accuracy. Employing Binary Particle Swarm Optimization (BPSO), irrelevant features were pruned, resulting in a refined feature vector of only 14 relevant features. This reduction in feature dimensionality significantly influenced the classification accuracy. Subsequently, the refined feature vector was introduced to the classification stage, employing four distinct classifiers: Support Vector Machine (SVM) with various kernel functions, K-Nearest Neighbors (K-NN), Naïve Bayes (NB), and Decision Tree (DT). Simulation results revealed the feasibility of achieving an average classification accuracy of 99.67% across ECG signal categories. Notably, the polynomial kernel function-SVM classifier, with only 2-fold cross-validation, yielded optimal performance. This study emphasizes the potential of fused Slantlet-Spatial and AR features in enhancing the accuracy of cardiac disease classification. Moreover, the efficacy of BPSO in feature selection and the superior performance of the SVM classifier highlight promising avenues for further research in intelligent cardiac diagnosis systems. The proposed approach outperforms existing methods and contributes to the early detection of cardiovascular abnormalities, potentially improving patient outcomes.

Exposure of protected areas in Central America to extreme weather events.

Central America and the Caribbean are regularly battered by megadroughts, heavy rainfall, heat waves, and tropical cyclones. Although 21st-century climate change is expected to increase the frequency, intensity, and duration of these extreme weather events (EWEs), their incidence in regional protected areas (PAs) remains poorly explored. We examined historical and projected EWEs across the region based on 32 metrics that describe distinct dimensions (i.e., intensity, duration, and frequency) of heat waves, cyclones, droughts, and rainfall and compared trends in PAs with trends in unprotected lands. From the early 21st century onward, exposure to EWEs increased across the region, and PAs were predicted to be more exposed to climate extremes than unprotected areas (as shown by autoregressive model coefficients at p<0.05 significance level). This was particularly true for heat waves, which were projected to have a significantly higher average (tested by Wilcoxon tests at p<0.01) intensity and duration, and tropical cyclones, which affected PAs more severely in carbon-intensive scenarios. PAs were also predicted to be significantly less exposed to droughts and heavy rainfall than unprotected areas (tested by Wilcoxon tests at p<0.01). However, droughts that could threaten connectivity between PAs are increasingly common in this region. We estimated that approximately 65% of the study area will experience at least one drought episode that is more intense and longer lasting than previous droughts. Collectively, our results highlight that new conservation strategies adapted to threats associated with EWEs need to be tailored and implemented promptly. Unless urgent action is taken, significant damage may be inflicted on the unique biodiversity of the region.

Robust relation of streamwise velocity autocorrelation in atmospheric surface layers based on an autoregressive moving average model

We construct an autoregressive moving average (ARMA) model consisting of the history and random effects for the streamwise velocity fluctuation in boundary-layer turbulence. The distance to the wall and the boundary-layer thickness determine the time step and the order of the ARMA model, respectively. Based on the autocorrelation's analytical expression of the ARMA model, we obtain a global analytical expression for the second-order structure function, which asymptotically captures the inertial, dynamic and large-scale ranges. Specifically, the exponential autocorrelation of the ARMA model arises from the autoregressive coefficients and is modified to logarithmic behaviour by the moving-average coefficients. The asymptotic expressions enable us to determine model coefficients by existing parameters, such as the Kolmogorov and the Townsend–Perry constants. A consequent double-log expression for the characteristic length scale is derived and is justified by direct numerical simulation data with $Re_\tau \approx 5200$ and field-measured neutral atmospheric surface layer data with $Re_\tau \sim O(10^6)$ from the Qingtu Lake Observation Array site. This relation is robust because it applies to $Re_\tau$ from $O(10^4)$ to $O(10^6)$ , and even when the statistics of natural ASL deviate from those of canonical boundary-layer turbulence, e.g. in the case of imbalance in energy production and dissipation, and when the Townsend–Perry constant deviates from traditional values.

The effects of participation in Christian religious activities on the satisfaction with life of older adults: the mediating effects of depressive symptoms

ABSTRACT This study aimed to clarify the effects of Christian religious activities on depressive symptoms and life satisfaction among older adults by analysing longitudinal data. Causal relationships between the variables were assessed using autoregressive cross-lagged model analysis. First, autoregressive coefficients were examined for church participation, depressive symptoms, and life satisfaction. Second, the cross-lagged coefficients revealed that participation in church activities later had a significant effect on depressive symptoms. In addition, depressive symptoms had a significant effect on life satisfaction. Depressive symptoms had a significant effect on life satisfaction. Third, the results indicated that participation in church activities during the fifth period significantly affected life satisfaction during the seventh period through depressive symptoms during the sixth period. This pathway suggests that depressive symptoms mediates the relationship between older adults’ church participation and life satisfaction longitudinally (i.e., older adults’ church participation reduces their depressive symptoms, and reduced depressive symptoms increases their life satisfaction).

Enhancing Adaboost performance in the presence of class-label noise: A comparative study on EEG-based classification of schizophrenic patients and benchmark datasets

The performance of Adaboost is highly sensitive to noisy and outlier samples. This is therefore the weights of these samples are exponentially increased in successive rounds. In this paper, three novel schemes are proposed to hunt the corrupted samples and eliminate them through the training process. The methods are: I) a hybrid method based on K-means clustering and K-nearest neighbor, II) a two-layer Adaboost, and III) soft margin support vector machines. All of these solutions are compared to the standard Adaboost on thirteen Gunnar Raetsch’s datasets under three levels of class-label noise. To test the proposed method on a real application, electroencephalography (EEG) signals of 20 schizophrenic patients and 20 age-matched control subjects, are recorded via 20 channels in the idle state. Several features including autoregressive coefficients, band power and fractal dimension are extracted from EEG signals of all participants. Sequential feature subset selection technique is adopted to select the discriminative EEG features. Experimental results imply that exploiting the proposed hunting techniques enhance the Adaboost performance as well as alleviating its robustness against unconfident and noisy samples over Raetsch benchmark and EEG features of the two groups.

Autoregressive Coefficients Based Intelligent Protection of Transmission Lines Connected to Type-3 Wind Farms

Autoregressive Coefficients Based Intelligent Protection of Transmission Lines Connected to Type-3 Wind Farms

Structural damage identification under ambient temperature variations based on CNN and normalized modal flexibility-autoregressive coefficients hybrid index

This study proposes a novel method to identify structural damage considering ambient temperature variations. In this method, the normalized modal flexibility based index (nMFBI) and autoregressive (AR) coefficients are combined to form the nMFBI-AR hybrid index, and convolutional neural networks (CNN) are exploited to locate and quantify the damage. Moreover, the effects of ambient temperature variations and measurement noise are not considered in the training dataset, which is preferable in practical engineering. To verify the effectiveness of the proposed method, firstly, a numerical structure of a simply supported beam is investigated, and the performance of the nMFBI-AR index is evaluated by making a comparison with the nMFBI and AR indexes. Then, the proposed method is further verified by a test model of a three-story frame and a practical engineering example of a continuous rigid frame bridge. The results demonstrate that although the influence of ambient temperature variations and measurement noise are only considered in the test datasets, this approach has the best performance in locating and quantifying structural damage, and the errors are less than 16%, which is promising. In addition, this paper provides a guideline and a new idea for the study of damage index based on time-frequency hybrid information.