Multivariate Multiscale Sample Entropy Research Articles

Unbiased Multivariate Multiscale Sample Entropy

The development of multi-channel data acquisition techniques has provided richer prior information for studying the nonlinear dynamic characteristics of complex systems. However, conventional nonlinear feature extraction algorithms prove unsuitable in the context of multi-channel data. Previously, the Multivariate Multiscale Sample Entropy (MMSE) algorithm was introduced for multi-channel data analysis. Although the MMSE algorithm generalized the multiscale sample entropy algorithm, presenting a novel method for multidimensional data analysis, it remains deficient in theoretical underpinning and suffers from shortcomings, such as missing cross-channel correlation information and having biased estimation results. In this paper, unbiased multivariate multiscale sample entropy algorithm (UMMSE) is proposed. UMMSE increases the embedding dimension from <i>M</i> to <i>M</i> + <i>p</i>. This increasing strategy facilitates the reconstruction of a deterministic phase space. By virtue of theoretical scrutiny grounded in probability theory and subsequent experimental validation, this paper illustrates the algorithm's effectiveness in extracting inter-channel correlation information through the integration of cross-channel conditional probabilities. The computation of similarities between sample points across different channels is recognized as a potential source of bias and instability in algorithms.Through simulation experiments, this study delineates the parameter selection range for the UMMSE algorithm. Subsequently, diverse simulation signals are employed to showcase the UMMSE algorithm's efficacy in extracting both within-channel and cross-channel correlation information. Ultimately, this paper demonstrates that the new algorithm has the lowest computational cost compared with traditional MMSE algorithms.

Internal Short-Circuit Fault Diagnosis for Batteries of Energy Storage Stations Based on Multivariate Multiscale Sample Entropy

Internal Short-Circuit Fault Diagnosis for Batteries of Energy Storage Stations Based on Multivariate Multiscale Sample Entropy

Optimized multivariate multiscale slope entropy for nonlinear dynamic analysis of mechanical signals

Slope entropy (SloEn) is an effective nonlinear dynamic method to represent the complexity of time series, which has been extensively applied to various mechanical signal processing. However, it is only applicable to the analysis of single-channel time series at a single scale. Additionally, thresholds γandδ of SloEn can affect the division of symbols. To address these limitations, this paper firstly develops multivariate SloEn (mvSloEn) and extends it to multiscale mvSloEn (mvMSloEn), which not only accounts for the correlation of time series complexity within and across channels, but also mirrors the complexity of multi-channel time series over multiple scales. Furthermore, the sea-horse optimization-mvMSloEn (SHO-mvMSloEn) is proposed through utilizing the sea-horse optimizer (SHO) to fine-tune the thresholds for improved performance. Finally, the proposed SHO-mvMSloEn is applied to three real-world datasets and the highest classification accuracies are all over 98 %, superior to the existing multivariate multiscale dispersion entropy (mvMDE), multivariate multiscale fuzzy entropy (mvMFE), and multivariate multiscale sample entropy (mvMSE), which demonstrates that the proposed SHO-mvMSloEn always exhibits the best feature extraction capability.

Improved multivariate multiscale sample entropy and its application in multi-channel data.

Entropy, as a nonlinear feature in information science, has drawn much attention for time series analysis. Entropy features have been used to measure the complexity behavior of time series. However, traditional entropy methods mainly focus on one-dimensional time series originating from single-channel transducers and are incapable of handling the multidimensional time series from multi-channel transducers. Previously, the multivariate multiscale sample entropy (MMSE) algorithm was introduced for multi-channel data analysis. Although MMSE generalizes multiscale sample entropy and provides a new method for multidimensional data analysis, it lacks necessary theoretical support and has shortcomings, such as missing cross-channel correlation information and having biased estimation results. This paper proposes an improved multivariate multiscale sample entropy (IMMSE) algorithm to overcome these shortcomings. This paper highlights the existing shortcomings in MMSE under the generalized algorithm. The rationality of IMMSE is theoretically proven using probability theory. Simulations and real-world data analysis have shown that IMMSE is capable of effectively extracting cross-channel correlation information and demonstrating robustness in practical applications. Moreover, it provides theoretical support for generalizing single-channel entropy methods to multi-channel situations.

Which Multivariate Multi-Scale Entropy Algorithm Is More Suitable for Analyzing the EEG Characteristics of Mild Cognitive Impairment?

So far, most articles using the multivariate multi-scale entropy algorithm mainly use algorithms to analyze the multivariable signal complexity without clearly describing what characteristics of signals these algorithms measure and what factors affect these algorithms. This paper analyzes six commonly used multivariate multi-scale entropy algorithms from a new perspective. It clarifies for the first time what characteristics of signals these algorithms measure and which factors affect them. It also studies which algorithm is more suitable for analyzing mild cognitive impairment (MCI) electroencephalograph (EEG) signals. The simulation results show that the multivariate multi-scale sample entropy (mvMSE), multivariate multi-scale fuzzy entropy (mvMFE), and refined composite multivariate multi-scale fuzzy entropy (RCmvMFE) algorithms can measure intra- and inter-channel correlation and multivariable signal complexity. In the joint analysis of coupling and complexity, they all decrease with the decrease in signal complexity and coupling strength, highlighting their advantages in processing related multi-channel signals, which is a discovery in the simulation. Among them, the RCmvMFE algorithm can better distinguish different complexity signals and correlations between channels. It also performs well in anti-noise and length analysis of multi-channel data simultaneously. Therefore, we use the RCmvMFE algorithm to analyze EEG signals from twenty subjects (eight control subjects and twelve MCI subjects). The results show that the MCI group had lower entropy than the control group on the short scale and the opposite on the long scale. Moreover, frontal entropy correlates significantly positively with the Montreal Cognitive Assessment score and Auditory Verbal Learning Test delayed recall score on the short scale.

Multivariate Multiscale Cosine Similarity Entropy and Its Application to Examine Circularity Properties in Division Algebras

The extension of sample entropy methodologies to multivariate signals has received considerable attention, with traditional univariate entropy methods, such as sample entropy (SampEn) and fuzzy entropy (FuzzyEn), introduced to measure the complexity of chaotic systems in terms of irregularity and randomness. The corresponding multivariate methods, multivariate multiscale sample entropy (MMSE) and multivariate multiscale fuzzy entropy (MMFE), were developed to explore the structural richness within signals at high scales. However, the requirement of high scale limits the selection of embedding dimension and thus, the performance is unavoidably restricted by the trade-off between the data size and the required high scale. More importantly, the scale of interest in different situations is varying, yet little is known about the optimal setting of the scale range in MMSE and MMFE. To this end, we extend the univariate cosine similarity entropy (CSE) method to the multivariate case, and show that the resulting multivariate multiscale cosine similarity entropy (MMCSE) is capable of quantifying structural complexity through the degree of self-correlation within signals. The proposed approach relaxes the prohibitive constraints between the embedding dimension and data length, and aims to quantify the structural complexity based on the degree of self-correlation at low scales. The proposed MMCSE is applied to the examination of the complex and quaternion circularity properties of signals with varying correlation behaviors, and simulations show the MMCSE outperforming the standard methods, MMSE and MMFE.

Combine Harvester Bearing Fault-Diagnosis Method Based on SDAE-RCmvMSE.

In the fault monitoring of rolling bearings, there is always loud noise, leading to poor signal stationariness. How to accurately and efficiently identify the fault type of rolling bearings is a challenge. Based on multivariate multiscale sample entropy (mvMSE), this paper introduces the refined composite mvMSE (RCmvMSE) into the fault extraction of the rolling bearing. A rolling bearing fault-diagnosis method based on stacked auto encoder and RCmvMSE (SDAE-RCmvMSE) is proposed. In the actual environment, the fault-diagnosis method use the multichannel vibration signals of the bearing as the input of stacked denoising autoencoders (SDAEs) to filter the noise of the vibration signals. The features of denoise signals are extracted by RCmvMSE and the rolling bearing operation-state diagnosis is completed with a support-vector machine (SVM) model. The results show that in the original test data, the accuracy rates of SDAE-RCmvMSE, RCmvMSE, and commonplace features of vibration signals combined with SVM (CFVS-SVM) methods are 99.5%, 100%, and 96% respectively. In the data with noise, the accuracy rates of RCmvMSE and CFVS-SVM are 97.75% and 93.08%, respectively, but the accuracy of SDAE-RCmvMSE is still 100%.

Intelligent Roller Bearing Fault Diagnosis in Industrial Internet of Things

Advanced research studies on industrial Internet of things require effective feature extraction and accurate machinery health state evaluation. For roller bearing, a well-known mechanical component most extensively used in the industry, its running status directly affects the operation of the entire machinery and equipment. For intelligent fault diagnosis of roller bearing, the selection of the intrinsic mode function (IMF) modes in approaches of ensemble empirical mode decomposition (EEMD)/variational mode decomposition (VMD) becomes a tricky problem. To solve this problem, this study proposed an efficient scheme on roller bearing fault diagnosis that combines the refined composite multivariate multiscale sample entropy (RCMMSE) with different classifiers. Firstly, the synthetic noise signals are introduced to compare the effectiveness of the multiscale sample entropy (MSE) and the RCMMSE models. Secondly, the random noise signals are used to compare the performance of EEMD and VMD methods, where the envelope spectrum characteristics of fault signals are well described. Moreover, EEMD/VMD methods are utilized to decompose the roller bearing vibration signals into various modes to get the entropy values. Finally, the obtained RCMMSE is adopted as a feature vector and subsequently employed as an input of support vector machine, random forest, and probabilistic neural network models to conduct roller bearing fault identification. The extensive experimental results prove that this proposed scheme performs well and the classification accuracy of VMD-RCMMSE is higher than EEMD-RCMMSE.

Variational Embedding Multiscale Diversity Entropy for Fault Diagnosis of Large-Scale Machinery

The large-scale machinery generally requires multiple accelerometers for condition monitoring. The multichannel vibration signals carry a wealth of fault information. Synchronous fault feature extraction using multichannel signals will significantly improve the diagnostic performance. The multivariate entropy method is able to synchronously extract the fault features from multiple sensors, but how to recognize the single fault occurring on different channels remains unexplored. In this article, we propose a novel feature extraction method called variational embedding multiscale diversity entropy, which constructs the phase space with different structures. The proposed variational phase space construction strategy will generate a different probability distribution for each channel, which results in a better separability for multichannel feature extraction. Combined with the random forest classifier, a novel fault diagnosis scheme is developed for condition monitoring of the large-scale machinery. One simulated signal and two experimental data are designed to validate the effectiveness of the proposed strategy. The results demonstrate that the proposed method has the best multichannel feature extraction ability compared with three existing methods: multivariate multiscale sample entropy, multivariate multiscale fuzzy entropy, and multivariate multiscale permutation entropy.

Variational Embedding Multiscale Sample Entropy: A Tool for Complexity Analysis of Multichannel Systems.

Entropy-based methods have received considerable attention in the quantification of structural complexity of real-world systems. Among numerous empirical entropy algorithms, conditional entropy-based methods such as sample entropy, which are associated with amplitude distance calculation, are quite intuitive to interpret but require excessive data lengths for meaningful evaluation at large scales. To address this issue, we propose the variational embedding multiscale sample entropy (veMSE) method and conclusively demonstrate its ability to operate robustly, even with several times shorter data than the existing conditional entropy-based methods. The analysis reveals that veMSE also exhibits other desirable properties, such as the robustness to the variation in embedding dimension and noise resilience. For rigor, unlike the existing multivariate methods, the proposed veMSE assigns a different embedding dimension to every data channel, which makes its operation independent of channel permutation. The veMSE is tested on both stimulated and real world signals, and its performance is evaluated against the existing multivariate multiscale sample entropy methods. The proposed veMSE is also shown to exhibit computational advantages over the existing amplitude distance-based entropy methods.

Complexity Analysis of Three-Dimensional Fractional-Order Chaotic System Based on Entropy Theory

Complexity analysis of fractional-order chaotic system is an interesting topic in recent years. How to measure the complexity of fractional-order chaotic system correctly and effectively is the basis of its theoretical analysis and engineering application. In this paper, complexity analysis of three-dimensional fractional-order chaotic system based on multivariate multiscale fuzzy entropy (mvMFE), multivariate multiscale sample entropy (mvMSE) and multivariate multiscale dispersion entropy (mvMDE) respectively is proposed. In the case of single parameter change, different entropy such as mvMFE, mvMSE and mvMDE are used to analyze how complexity varies with parameter. In the case of two parameters change, the change of complexity is analyzed by the chromatomap which takes two parameters as independent variable, and mvMFE, mvMSE, and mvMDE as the dependent variable when the two parameters change simultaneously. Aiming at the performance problem when the complexity of three-dimensional fractional-order chaotic system is analyzed by mvMFE, mvMSE, and mvMDE, the maximum complexity under single parameter and the detection area under two parameters are used as indicators. The result shows that the performance of mvMDE is the best, and the nonlinear term in the mathematical model of fractional-order chaotic system is positively correlated with the complexity of the system. This will provide a new method for measuring the complexity of fractional-order chaotic system, and lay the basis of theoretical analysis and practical application of fractional chaotic system in the fields of image encryption, sound encryption, image compression-encryption technique, and secure communication.

Spatiotemporal complexity patterns of resting-state bioelectrical activity explain fluid intelligence: Sex matters.

Neural complexity is thought to be associated with efficient information processing but the exact nature of this relation remains unclear. Here, the relationship of fluid intelligence (gf) with the resting‐state EEG (rsEEG) complexity over different timescales and different electrodes was investigated. A 6‐min rsEEG blocks of eyes open were analyzed. The results of 119 subjects (57 men, mean age = 22.85 ± 2.84 years) were examined using multivariate multiscale sample entropy (mMSE) that quantifies changes in information richness of rsEEG in multiple data channels at fine and coarse timescales. gf factor was extracted from six intelligence tests. Partial least square regression analysis revealed that mainly predictors of the rsEEG complexity at coarse timescales in the frontoparietal network (FPN) and the temporo‐parietal complexities at fine timescales were relevant to higher gf. Sex differently affected the relationship between fluid intelligence and EEG complexity at rest. In men, gf was mainly positively related to the complexity at coarse timescales in the FPN. Furthermore, at fine and coarse timescales positive relations in the parietal region were revealed. In women, positive relations with gf were mostly observed for the overall and the coarse complexity in the FPN, whereas negative associations with gf were found for the complexity at fine timescales in the parietal and centro‐temporal region. These outcomes indicate that two separate time pathways (corresponding to fine and coarse timescales) used to characterize rsEEG complexity (expressed by mMSE features) are beneficial for effective information processing.

A unified multi-level spectral–temporal feature learning framework for patient-specific seizure onset detection in EEG signals

Epileptic seizure onset detection in electroencephalography (EEG) signals is a challenging task due to the severe variation of seizures. Recently, automatic seizure onset detection frameworks fail to fully consider both nonstationary and stochastic characteristics of EEGs in nature, which may lead to information default and further produce suboptimal recognition performance consequently. In this work, we propose a patient-specific seizure onset detection method based on fully exploration of auxiliary supplementary spectral–temporal information in EEG signals. Specifically, prior to feature extraction procedure, EEG signals are firstly decomposed into 5 groups of coefficients at different levels based on the clinical interest. Representative feature in temporal-domain, which is a translation of the nonlinear property of EEG signals, is then extracted by a combination of principal component analysis and common spatial pattern (PCA-CSP) and multivariate multiscale sample entropy (MMSE) in parallel and dimensionally reduced by a tree-based feature selection algorithm. Supplementary information in spectral-domain is further explored by the proposed unified maximum mean discrepancy autoencoder (uMMD-AE). Finally, an optimal combination of features above is identified and fed into a series of support vector machine classifiers with a decision fusion module for the intelligent recognition of epileptic EEGs. The proposed method achieves an average sensitivity, latency and false detection rate of 97.2%, 1.10s and 0.64/h respectively on Children Hospital Boston-Massachusetts Institute of Technology (CHB-MIT) Scalp EEG Database. Competitive experimental results demonstrate the efficacy of the proposed unified multi-level spectral–temporal feature learning framework in epileptic EEG recognition, validating its effectiveness in the automatic patient-specific seizure onset detection.

Generalized multivariate multiscale sample entropy for detecting the complexity in complex systems

Using the first moment in coarse-graining the original time series in different time scales will lose some important information of the complexity. In this paper, we propose the generalized multivariate multiscale sample entropy (GMMSE) to analyze the complexity for multivariate time series. Before empirical analysis, numerical simulation is conducted by applying GMMSE1 (mean), GMMSE2 (variance), GMMSE3 (skewness) to the autoregressive fractionally integrated moving average (ARFIMA) processes. The simulated results illustrate that GMMSE2 is more appropriate to analyze the complexity of ARFIMA time series. Then we apply GMMSE method to traffic multivariate time series and discuss their complexities over different time scales. Comparing the GMMSE1, GMMSE2 and GMMSE3 results for different detectors, GMMSE2 and GMMSE3 can clearly differentiate the detectors with different complexity and reflect the characteristics and similarities of the complexity of traffic data between different locations. Besides, both the effect of traffic accident and the effect of the weekday and weekend patterns containing in traffic signals on the complexity can be detected by GMMSE2 and GMMSE3 methods. GMMSE2 and GMMSE3 are capable of providing more important information and knowledge concerning the complexity of traffic time series and will bring enhanced understanding of the properties of traffic system.

An integrated method based on refined composite multivariate hierarchical permutation entropy and random forest and its application in rotating machinery

Fault feature extraction of rotating machinery is crucial and challenging due to its nonlinear and nonstationary characteristics. In order to resolve this difficulty, a quality nonlinear fault feature extraction method is required. Hierarchical permutation entropy has been proven to be a promising nonlinear feature extraction method for fault diagnosis of rotating machinery. Compared with multiscale permutation entropy, hierarchical permutation entropy considers the fault information hidden in both high frequency and low frequency components. However, hierarchical permutation entropy still has some shortcomings, such as poor statistical stability for short time series and inability of analyzing multichannel signals. To address such disadvantages, this paper proposes a new entropy method, called refined composite multivariate hierarchical permutation entropy. Refined composite multivariate hierarchical permutation entropy can extract rich fault information hidden in multichannel signals synchronously. Based on refined composite multivariate hierarchical permutation entropy and random forest, a novel fault diagnosis framework is proposed in this paper. The effectiveness of the proposed method is validated using experimental and simulated signals. The results demonstrate that the proposed method outperforms multivariate multiscale fuzzy entropy, refined composite multivariate multiscale fuzzy entropy, multivariate multiscale sample entropy, multivariate multiscale permutation entropy, multivariate hierarchical permutation entropy, and composite multivariate hierarchical permutation entropy in recognizing the different faults of rotating machinery.

Sex-Specific Dependence of Linear and Nonlinear Postural Control Metrics on Anthropometrics During Clinical Balance Tests in Healthy Young Adults.

Previous work suggests that balance behavior is a sex-dependent, complex process that can be characterized by linear and nonlinear metrics. Although a certain degree of center of pressure variability may be expected based on sexual dimorphism, there is evidence to suggest that these effects are obscured by potential interactions between sex and anthropometric factors. To date, no study has accounted for such interactive effects using both linear and nonlinear measures. This investigation sought to analyze interactive models featuring sex, height, and weight as predictors of linear and nonlinear aspects of postural control. Cross-sectional study. Controlled laboratory. A total of 26 males (23.80 [3.44]y, 177.87 [6.44]cm, 81.70 [10.80]kg) and 28 females (21.14 [2.03]y, 169.57 [8.80]cm, 64.48 [8.86]kg) were sampled from a healthy university population. Linear (range [RNG], velocity [VEL], and SD) and nonlinear (detrended fluctuation analysis scaling exponent, multivariate multiscale sample entropy [MMSECI]) summary metrics of center of pressure time series. Participants stood on a force plate for 20 seconds in 3 conditions: double (D), single (S), and tandem (T) stance. Data for each stance condition were analyzed using regression models with interaction terms for sex × height and sex × weight. In D, weight had a positive, significant main effect on VELy, MMSECId, and MMSECIv. In men, height was observed to have a positive effect on SDy (S), RNGy (S), and RNGx (T) and a negative effect on MMSECIv (T). In women, weight was observed to have a positive effect on SDy and VELx (both T). Our findings suggest that men and women differ with respect to certain linear and nonlinear aspects of balance behavior, and that these differences may reflect sex-specific behavioral patterns in addition to effects related to sexual dimorphism.

Multivariate Multiscale Dispersion Entropy of Biomedical Times Series

Due to the non-linearity of numerous physiological recordings, non-linear analysis of multi-channel signals has been extensively used in biomedical engineering and neuroscience. Multivariate multiscale sample entropy (MSE–mvMSE) is a popular non-linear metric to quantify the irregularity of multi-channel time series. However, mvMSE has two main drawbacks: (1) the entropy values obtained by the original algorithm of mvMSE are either undefined or unreliable for short signals (300 sample points); and (2) the computation of mvMSE for signals with a large number of channels requires the storage of a huge number of elements. To deal with these problems and improve the stability of mvMSE, we introduce multivariate multiscale dispersion entropy (MDE–mvMDE), as an extension of our recently developed MDE, to quantify the complexity of multivariate time series. We assess mvMDE, in comparison with the state-of-the-art and most widespread multivariate approaches, namely, mvMSE and multivariate multiscale fuzzy entropy (mvMFE), on multi-channel noise signals, bivariate autoregressive processes, and three biomedical datasets. The results show that mvMDE takes into account dependencies in patterns across both the time and spatial domains. The mvMDE, mvMSE, and mvMFE methods are consistent in that they lead to similar conclusions about the underlying physiological conditions. However, the proposed mvMDE discriminates various physiological states of the biomedical recordings better than mvMSE and mvMFE. In addition, for both the short and long time series, the mvMDE-based results are noticeably more stable than the mvMSE- and mvMFE-based ones. For short multivariate time series, mvMDE, unlike mvMSE, does not result in undefined values. Furthermore, mvMDE is faster than mvMFE and mvMSE and also needs to store a considerably smaller number of elements. Due to its ability to detect different kinds of dynamics of multivariate signals, mvMDE has great potential to analyse various signals.

Detecting the Flow Pattern Transition in the Gas-Liquid Two-Phase Flow Using Multivariate Multi-Scale Entropy Analysis

Abstract Due to the complex flow structure and non-uniform phase distribution in the vertical upward gas-liquid two-phase flow, an eight-electrode rotating electric field conductance sensor is used to obtain multi-channel conductance signals. The flow patterns of the vertical upward gas-liquid two-phase flow are classified according to the images obtained from a high-speed camera. Then, we employ the multivariate weighted multi-scale permutation entropy (MWMPE) to detect the instability of flow pattern transition in the gas-liquid two-phase flow. Afterwards, we compare the results of the MWMPE with those of the single-channel weighted multi-scale permutation entropy (SCWMPE) and multivariate multi-scale sample entropy (MMSE). The comparison results indicate that, compared with the SCWMPE and MMSE, the MWMPE has superior performance in terms of the high-resolution presentation of flow instability in the gas-liquid two-phase flow. Finally, we extract the mean value of the MWMPE in whole scales and the entropy rate of the MWMPE in the small scales. The results indicate that the normalized mean value and normalized entropy rate of MWMPE are very sensitive to the transitions of flow patterns, thus allowing the detection of the instability of flow pattern transition.

Refined Composite Multivariate Multiscale Dispersion Entropy and Its Application to Fault Diagnosis of Rolling Bearing

Many nonlinear dynamic and statistic methods, including multiscale sample entropy (MSE) and multiscale fuzzy entropy (MFE), have been widely studied and employed to fault diagnosis of the rolling bearing. Multiscale dispersion entropy (MDE) is a powerful tool for complexity measure of time series, and compared with MSE and MFE, it gets much better performance and costs less time for computation. Since single-channel time series analysis will cause information missing, inspired by multivariate multiscale sample entropy (MMSE) and multivariate multiscale fuzzy entropy (MMFE), refined composite multivariate multiscale dispersion entropy (RCMMDE) was proposed in this paper. After that, RCMMDE was compared with MDE, MMSE, and MMFE by analyzing synthetic signals and the results show that the RCMMDE has certain advantages in terms of robustness. A hybrid fault diagnostics approach is proposed for rolling bearing with a combination of RCMMDE, multi-cluster feature selection, and support vector machine. Also, the proposed method is compared with MDE, MMSE, and MMFE, as well as multivariate multiscale dispersion entropy-based fault diagnosis methods by analyzing the experimental data of rolling bearing, and the result shows that the proposed method gets a higher identification rate than the existing other fault diagnosis methods.

Robust Fault Diagnosis of Rolling Bearings Using Multivariate Intrinsic Multiscale Entropy Analysis and Neural Network Under Varying Operating Conditions

olling bearings are crucial components in mechanical, civil and aerospace engineering. The practical working conditions of rolling bearings are complex and tough, hence fault diagnosis of rolling bearings under varying operating conditions is very challenging. This paper proposes a robust fault diagnosis approach of rolling bearings using multivariate intrinsic multiscale entropy analysis and neural network under varying operating conditions. The proposed approach deals with multivariate signal collected from multi-sensor acquisition system to capture much dynamical characteristic information. Multivariate intrinsic multiscale entropy analysis consists of adaptive projection intrinsically transformed multivariate empirical mode decomposition with adaptive noise (APIT-MEMD-AN) and improved multivariate multiscale sample entropy (IMMSE) with smoothed coarse graining process. Intrinsic mode functions (IMFs) obtained by APIT-MEMD-AN depict dynamical properties of multivariate signals. IMMSE of certain orders IMFs are adopted as input values of back propagation (BP) neural network to achieve fault classification of rolling bearings. APIT-MEMD-AN and IMMSE endow the proposed approach with the underlying adaptivity and robustness, making the proposed approach a fully data driven and robust method. Theoretical derivations, numerical simulations and experimental results verify the effectiveness and superiority of the proposed approach. The research work demonstrates the proposed approach is promising in fault diagnosis of rotary machinery under varying operating conditions.