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The fault frequencies are as they are and cannot be improved. One can only improve its estimation quality. This paper proposes a fault diagnosis method by combining local mean decomposition (LMD) and the ratio correction method to process the short-time signals. Firstly, the vibration signal of rolling bearing is decomposed into a series of product functions (PFs) by LMD. The PF, which contains the richest fault information, is selected to perform envelope spectrum analysis by the Hilbert transform (HT). Secondly, the Hilbert envelope spectrum of the selected PF is corrected with the ratio correction method. Finally, higher precision fault frequencies are extracted from the corrected Hilbert envelope spectrum, and then the fault location is accurately determined. The proposed method of this paper can be used in online real-time monitoring technology of rolling bearing failure.

For transition economies, the virtues of financial development for economic growth are obvious; however, bank competition has dubious effects due to various firm characteristics. This study uses Chinese banking and firm data from 1998 to 2011 to examine how bank competition affects firm innovation and how firm size and ownership influence the effects of bank competition. The results show that bank competition promotes firm-level innovation and that this positive effect is stronger for small firms and non-stateowned enterprises (non-SOEs). In addition, bank competition has a more beneficial influence on innovation for transparent firms and domestic firms. These conclusions thus shed light on the real effects of bank competition and the determinants of firm innovation in developing countries.

Purpose Bank financing is an important external financing source for firm research and development (R&D) investment. This study aims to use an exponential quadratic specification to investigate the effect of bank competition on firm R&D investment and its underlying mechanisms. Moreover, this study checks bank competition’s heterogeneous effects on firm R&D investment. Design/methodology/approach Based on data of Chinese manufacturing firms and bank branches, this study uses the Tobit estimator, instrumental variable method and Heckman two-step approach to test the relationship between bank competition and firm R&D investment. Findings The results show robustness evidence of an inverted-U relationship between bank competition and firm R&D investment. Specifically, increases in bank competition promote firm R&D investment until bank competition reaches the turning point and reduce firm R&D investment after crossing the turning point. Financing costs and financial constraints can explain the inverted-U relationship between bank competition and firm R&D investment. Heterogeneity examinations reveal that R&D investment is more sensitive to bank competition in non-state-owned enterprises, small firms and high-tech firms. Originality/value This study contributes to the literature on the relationship between bank competition and firm innovation. The authors investigate the heterogeneity of R&D investment influenced by bank competition and depict the economic effects brought by bank competition. This study sheds light on the real effects of bank competition and the determinants of firm R&D investment in transition economies. The conclusions provide empirical evidence for reducing credit discrimination and improving capital allocation efficiency in developing countries.

Based on the geographic coordinates of bank branches and firms, this study analyzes the impact of firm‐level bank competition on corporate green innovation and its underlying mechanisms. The findings of this study are mainly as follows. First, bank competition promotes corporate green innovation by reducing transaction costs, increasing the possibility and quantity of firms applying for green patents. Second, bank competition increases the share of green innovation while reducing the share of nongreen innovation. Third, environmental regulation strengthens the promotion effect of bank competition on corporate green innovation, and the strengthening effect is greatest when environmental regulation is between its 50th and 75th quantile. The proportion of state‐owned banks weakens the promotion effect of bank competition on corporate green innovation. This paper is helpful to understand the impact of the banking system on sustainable economic development.