## 1 Introduction  
A rolling bearing is largely applied to rotating machinery and is essential to any manufacturing or processing enterprises in modern industry. A rolling bearing is sensitive to the operating condition of the mechanical equipment and a lot of different problems will lead to failure [1; 2]. The bearing invalidation takes a great proportion of the mechanical equipment failure and accidents, and costs much maintenance capital expenditure. Therefore, it is greatly important and necessary to monitor the bearing operating condition to avoid equipment shutdown and even industrial accidents [3]. With the development of signal processing and analysis in recent decades, a large number of different techniques and methods are widely used for fault diagnosis and condition monitoring of the rolling bearing [4]. Essential Empirical Mode Decomposition (EEMD) is a self-adaptive time-frequency analysis method and has a good ability to process non-linear and non-stationary time series [5]. EEMD is developed from the empirical mode decomposition (EMD) algorithm by added a Gaussian white noise. However, the problem of mode mixing and boundary effect analysis severely limits the application of EEMD [6]. Wavelet Packet (WP) analysis is the further improvement of the wavelet analysis and shows excellent performance in fault diagnosis and feature extraction [7]. However,the WP method also has the problem of energy leakage, border distortion, a large calculation amount, and so on [8]. On the other hand, the WP is not suitable for the non-stationary signal analysis. [PERSON] firstly introduced the concept of entropy into the information theory in 1948, which formally realized the measure of the useful information in an event. Entropy can effectively reflect the irregularity and uncertainty of signal. Approximate Entropy (ApEn) is proposed by [PERSON] to measure the probability of generating a new pattern in the time series [9]. The larger the probability of generating a new pattern, the larger the ApEn. Based on ApEn, the Sample Entropy (SamEn) is introduced to assess the complexity of time series [10]. SamEn is designed to reduce the error of ApEn and shows great precision. The computation complexity of SamEn is \(O(N^{2})\). Because SamEn merely measures the degree of signal complexity in one dimension, [PERSON] presented the Multiscale Entropy (MSE) to evaluate the irregularity of the signal at different time scales [11]. MSE is commonly used in many applications, such as biomedical signa [12]. [PERSON] proposed the Permutation Entropy (PerEn) method from the perspective of permutation patterns [13]. As PerEn only measures the order relation of the amplitude value in the time series, the computation complexity of PerEn is just \(O(N)\)[14]. However, PerEn does not make use of additional information about amplitude except the order, which quite limits its application. Combined with the merit of SamEn and PerEn, [PERSON] put forward the Dispersion Entropy (DisEn) which is suitable for short signals and shows excellent performance in measuring the signal complexity [15]. As mentioned above, to further accurately assess the degree of richness of signal information, the paper develops the MDE_rms_ as a characteristic index of signal, which could improve the cumulative distribution function of the time series and measures the signal irregularity and uncertainty at different time scales. In this paper, a new feature extraction method combining sparse reconstruction and MDE_rms_ is proposed for the fault diagnosis of a rolling bearing. Firstly, the vibration signal is intercepted into an array of sliding short signal segments. The obtained truncation segments are called Sliding matrix sequences (SMS), and the local fault signature is separately hidden in the SMS. To improve the stability and accuracy of entropy, each short sliding segment of the SMS is reconstructed into sparse sequence by Hankel-matrix.