Rolling Element Bearing Diagnostics by Combination of Envelope Analysis and Wavelet Transform

Rolling element-bearing diagnostics has been studied over the last thirty years, and envelope analysis is widely recognized as being the best approach for detection and diagnosis of rolling element bearing incipient failure. But one of the on-going difficulties with envelope technique is to determine the best frequency band to envelop. Here, wavelet transform technique is introduced into envelope analysis to solve the problem by capturing bearing defects-sensory scales (i.e. frequency bands). A modulated Gaussian function is chosen to be the analytical wavelet because it coincides well with bearing defect-induced vibration signal patterns. Vibration signals measured from railway bearing tests were studied by the proposed method. Cases of bearings with single and multiple defects on inner and outer race under different testing conditions are presented. Experimental results showed that the proposed method allowed a more accurate local description and separation of transient signal part, which were caused by impacts between defects and the mating surfaces in the bearing. The combination method provides an effective signal detection technique for rolling element-bearing diagnostics.

IGIgram:An Improved Gini Index-Based Envelope Analysis for Rolling Bearing Fault Diagnosis

The transient impulse features caused by rolling bearing faults are often present in the resonance frequency band which is closely related to the dynamic characteristics of the machine structure.Informative frequency band identification is a crucial prerequisite for envelope analysis and thereby accurate fault diagnosis of rolling bearings.In this paper,based on the ratio of quasi-arithmetic means and Gini index,improved Gini indices(IGIs)are proposed to quantify the transient impulse features of a signal,and their effectiveness and advantages in sparse quantification are confirmed by simulation analysis and comparisons with traditional sparsity measures.Furthermore,an IGI-based envelope analysis method named IGIgram is developed for fault diagnosis of rolling bearings.In the new method,an IGI-based indicator is constructed to evaluate the impulsiveness and cyclostationarity of the narrow-band filtered signal simultaneously,and then a frequency band with abundant fault information is adaptively determined for extracting bearing fault features.The performance of the IGIgram method is verified on the simulation signal and railway bearing experimental signals and compared with typical sparsity measures-based envelope analysis methods and log-cycligram.The results demonstrate that the proposed IGIs are efficient in quantifying bearing fault-induced transient features and the IGIgram method with appropriate power exponent can effectively achieve the diagnostics of different axle-box bearing faults.

A Fault Diagnosis Approach for Broken Rotor Bars Based on EMD and Envelope Analysis

Empirical Mode Decomposition (EMD) used to deal with non-linear and non-stable signals,is a time-frequency analytical method that has been developed recently. In this paper the EMD method is used to filter the noise from the stator current signal that arises when rotor bars break. Then a Hilbert Transform is used to extract the envelope from the filtered signal. With the EMD method again,the frequency band containing the fault characteris-tic-frequency components,2sf,can be extracted from the signal's envelope. The last step is to use a Fast Fourier Trans-form (FFT) method to extract the fault characteristic frequency. This frequency can be detected in actual data from a faulty motor,as shown by example. Compared to the Extend Park Vector method this method is proved to be more sen-sitive under light motor load.

ASYMPTOTIC THEORY FOR THE CIRCUIT ENVELOPE ANALYSIS

Asymptotic theory for the circuit envelope analysis is developed in this paper.A typical feature of circuit envelope analysis is the existence of two significantly distinct timescales:one is the fast timescale of carrier wave,and the other is the slow timescale of modulation signal.We first perform pro forma asymptotic analysis for both the driven and autonomous systems.Then resorting to the Floquet theory of periodic operators,we make a rigorous justification for first-order asymptotic approximations.It turns out that these asymptotic results are valid at least on the slow timescale.To speed up the computation of asymptotic approximations,we propose a periodization technique,which renders the possibility of utilizing the NUFFT algorithm.Numerical experiments are presented,and the results validate the theoretical findings.

Evaluation of Energy Efficiency and Analysis of Influencing Factors of Company CW’s Manufacturing Workshops

In this work,the Slacks-Based Measure(SBM)model within Data Envelopment Analysis was employed to establish a set of indicators for evaluating the energy efficiency of manufacturing workshops.The energy efficiency of 12 Company CW’s manufacturing workshops from 2016 to 2022 was assessed.The findings indicated that aside from a few workshops operating at the production frontier,the rest exhibit significant fluctuations in energy efficiency and generally low energy efficiency.Subsequently,a combined GRA-Tobit analysis model was introduced to identify factors influencing the energy efficiency of Company CW’s manufacturing workshops.Regression analysis revealed that technological investments,employee quality,workshop production scale,investment in clean energy,and the level of pollution control all significantly impact the energy efficiency of Company CW’s manufacturing workshops.By evaluating the energy efficiency of Company CW’s manufacturing workshops and studying their influencing factors,this research aids company managers in understanding the energy efficiency of the manufacturing process.It optimizes the combination of various production elements,thereby offering effective guidance for improving the energy efficiency issues of the company’s manufacturing workshops,which can contribute to enhancing the corporation’s overall energy efficiency.

Implementation of Envelope Analysis on a Wireless Condition Monitoring System for Bearing Fault Diagnosis

Envelope analysis is an effective method for characterizing impulsive vibrations in wired condition monitoring(CM)systems. This paper depicts the implementation of envelope analysis on a wireless sensor node for obtaining a more convenient and reliable CM system. To maintain CM performances under the constraints of resources available in the cost effective Zigbee based wireless sensor network(WSN), a low cost cortex-M4 F microcontroller is employed as the core processor to implement the envelope analysis algorithm on the sensor node. The on-chip 12 bit analog-to-digital converter(ADC) working at 10 k Hz sampling rate is adopted to acquire vibration signals measured by a wide frequency band piezoelectric accelerometer. The data processing flow inside the processor is optimized to satisfy the large memory usage in implementing fast Fourier transform(FFT) and Hilbert transform(HT). Thus, the envelope spectrum can be computed from a data frame of 2048 points to achieve a frequency resolution acceptable for identifying the characteristic frequencies of different bearing faults. Experimental evaluation results show that the embedded envelope analysis algorithm can successfully diagnose the simulated bearing faults and the data transmission throughput can be reduced by at least 95% per frame compared with that of the raw data, allowing a large number of sensor nodes to be deployed in the network for real time monitoring.

Separation of closely spaced modes by combining complex envelope displacement analysis with method of generating intrinsic mode functions through filtering algorithm based on wavelet packet decomposition

One of the important issues in the system identification and the spectrum analysis is the frequency resolution, i.e., the capability of distinguishing between two or more closely spaced frequency components. In the modal identification by the empirical mode decomposition （EMD） method, because of the separating capability of the method, it is still a challenge to consistently and reliably identify the parameters of structures of which modes are not well separated. A new method is introduced to generate the intrin- sic mode functions （IMFs） through the filtering algorithm based on the wavelet packet decomposition （GIFWPD）. In this paper, it is demonstrated that the CIFWPD method alone has a good capability of separating close modes, even under the severe condition beyond the critical frequency ratio limit which makes it impossible to separate two closely spaced harmonics by the EMD method. However, the GIFWPD-only based method is impelled to use a very fine sampling frequency with consequent prohibitive computational costs. Therefore, in order to decrease the computational load by reducing the amount of samples and improve the effectiveness of separation by increasing the frequency ratio, the present paper uses a combination of the complex envelope displacement analysis （CEDA） and the GIFWPD method. For the validation, two examples from the previous works are taken to show the results obtained by the GIFWPD-only based method and by combining the CEDA with the GIFWPD method.

Data envelopment analysis for scale elasticity measurement in the stochastic case:with an application to Indian banking

In the nonparametric data envelopment analysis literature,scale elasticity is evaluated in two alternative ways:using either the technical efficiency model or the cost efficiency model.This evaluation becomes problematic in several situations,for example(a)when input proportions change in the long run,(b)when inputs are heterogeneous,and(c)when firms face ex-ante price uncertainty in making their production decisions.To address these situations,a scale elasticity evaluation was performed using a value-based cost efficiency model.However,this alternative value-based scale elasticity evaluation is sensitive to the uncertainty and variability underlying input and output data.Therefore,in this study,we introduce a stochastic cost-efficiency model based on chance-constrained programming to develop a value-based measure of the scale elasticity of firms facing data uncertainty.An illustrative empirical application to the Indian banking industry comprising 71 banks for eight years(1998–2005)was made to compare inferences about their efficiency and scale properties.The key findings are as follows:First,both the deterministic model and our proposed stochastic model yield distinctly different results concerning the efficiency and scale elasticity scores at various tolerance levels of chance constraints.However,both models yield the same results at a tolerance level of 0.5,implying that the deterministic model is a special case of the stochastic model in that it reveals the same efficiency and returns to scale characterizations of banks.Second,the stochastic model generates higher efficiency scores for inefficient banks than its deterministic counterpart.Third,public banks exhibit higher efficiency than private and foreign banks.Finally,public and old private banks mostly exhibit either decreasing or constant returns to scale,whereas foreign and new private banks experience either increasing or decreasing returns to scale.Although the application of our proposed stochastic model is illustrative,it can be potentially applied to all firms in the information and distribution-intensive industry with high fixed costs,which have ample potential for reaping scale and scope benefits.

Analysis of Economic Efficiency of Wildlife Law Enforcement in Serengeti Ecosystem Tanzania

Law enforcement remains to be the main strategy used to combat poaching and account for high budget share in protected area management. Studies on efficiency of wildlife law enforcement in the protected areas are limited. This study analyzed economic efficiency of wildlife law enforcement in terms of resource used and output generated using three different protected areas (PAs) of Serengeti ecosystem namely Serengeti National Park (SENAPA), Ikorongo/Grumeti Game Reserves (IGGR) and Ikona Wildlife Management Area (IWMA). Three years (2010-2012) monthly data on wildlife law enforcement inputs and outputs were collected from respective PAs authorities and supplemented with key informant interviews and secondary data. Questionnaire surveys were conducted to wildlife law enforcement staff. Shadow prices for non-marketed inputs were estimated, and market prices for marketed inputs. Data Envelopment Analysis (DEA) was used to estimate economic efficiency using Variable Return to Scale (VRS) and Constant Return to Scale (CCR) assumptions. Results revealed that wildlife law enforcement in all PAs was economically inefficient, with less inefficiency observed in IWMA. The less inefficiency in IWMA is likely attributed to existing sense of ownership and responsibility created through community-based conservation which resulted in to decrease in law enforcement costs. A slacks evaluation revealed a potential to reduce fuel consumption, number of patrol vehicles, ration and prosecution efforts at different magnitudes between studied protected areas. There is equal potential to recruit more rangers while maintaining the resting time. These finding forms the bases for monitoring and evaluation with respect to resource usage to enhance efficiency. It is further recommended to enhance community participation in conservation in SENAPA and IGGR to lower law enforcement costs. Collaboration between protected area, police and judiciary is fundamental to enhance enforcement efficiency. Despite old dataset, these findings are relevant since neither conservation policy nor institution framework has changed substantially in the last decade.

Sources of China's Economic Growth:An Analysis Based on Nonparametric Accounting Method

This paper improves the slacks-based method for estimating inefficiency,derives the criteria for the selection of the weights of output and input inefficiencies in the objective function,and creates a new nonparametric method for accounting economic growth.Based on this method,the paper estimates the sources of China s economic growth from 1978 to 2013.Our findings suggest that factor input and especially capital is a major source of economic growth for China as a whole and its major regions,and that economic growth in recent years is increasingly dependent on capital.For a rather long period of time before 2005,China s northeast,central and western regions lagged behind the eastern region in terms of economic growth,and TFP and factor input are major reasons behind such regional growth disparities.Although other regions have narrowed their disparities with and even overtaken the eastern region in terms of economic growth,the key driver is the rapid increase in the contribution of factor input.Advanced technologies of eastern region should be utilized to promote TFP progress in other regions,which is vital to economic growth in these regions and China as a whole.

Frame Work of Data Envelopment Analysis—A Model to Evaluate the Environmental Efficiency of China'S Industrial Sectors

Objective To evaluate the environmental and technical efficiencies of China＇s industrial sectors and provide appropriate advice for policy makers in the context of rapid economic growth and concurrent serious environmental damages caused by industrial pollutants. Methods A data of envelopment analysis （DEA） framework crediting both reduction of pollution outputs and expansion of good outputs was designed as a model to compute environmental efficiency of China＇s regional industrial systems. Results As shown by the geometric mean of environmental efficiency, if other inputs were made constant and good outputs were not to be improved, the air pollution outputs would have the potential to be decreased by about 60% in the whole China. Conclusion Both environmental and technical efficiencies have the potential to be greatly improved in China, which may provide some advice for policy-makers.

Fuzzy data envelopment analysis approach based on sample decision making units

The conventional data envelopment analysis （DEA） measures the relative efficiencies of a set of decision making units with exact values of inputs and outputs. In real-world prob- lems, however, inputs and outputs typically have some levels of fuzziness. To analyze a decision making unit （DMU） with fuzzy input/output data, previous studies provided the fuzzy DEA model and proposed an associated evaluating approach. Nonetheless, numerous deficiencies must still be improved, including the α- cut approaches, types of fuzzy numbers, and ranking techniques. Moreover, a fuzzy sample DMU still cannot be evaluated for the Fuzzy DEA model. Therefore, this paper proposes a fuzzy DEA model based on sample decision making unit （FSDEA）. Five eval- uation approaches and the related algorithm and ranking methods are provided to test the fuzzy sample DMU of the FSDEA model. A numerical experiment is used to demonstrate and compare the results with those obtained using alternative approaches.

Efficiency assessment of coal mine safety input by data envelopment analysis

In recent years improper allocation of safety input has prevailed in coal mines in China, which resulted in the frequent accidents in coal mining operation. A comprehensive assessment of the input efficiency of coal mine safety should lead to improved efficiency in the use of funds and management resources. This helps government and enterprise managers better understand how safety inputs are used and to optimize allocation of resources. Study on coal mine＇s efficiency assessment of safety input was con- ducted in this paper. A C^2R model with non-Archimedean infinitesimal vector based on output is established after consideration of the input characteristics and the model properties. An assessment of an operating mine was done using a specific set of input and output criteria. It is found that the safety input was efficient in 2002 and 2005 and was weakly efficient in 2003. However, the efficiency was relatively low in both 2001 and 2004. The safety input resources can be optimized and adjusted by means of projection theory. Such analysis shows that, on average in 2001 and 2004, 45% of the expended funds could have been saved. Likewise, 10% of the safety management and technical staff could have been eliminated and working hours devoted to safety could have been reduced by 12%. These conditions could have Riven the same results.

Analysis on Technical Efficiency of Rice Farms and Its Influencing Factors in South-western of Niger

The present study focused on analyzing the technical efficiency office farms in southwest of Niger. The data from January to March 2015 survey of 148 ms in three districts of south-western of Niger were analyzed by using DEA-Tobit two-step method. In the f＇ust step, data envelopment analysis （DEA） was applied to estimate technical, pure technical and scale efficiency. In the second step, Tobit regression was used to identify factors affecting technical efficiency. The results showed that rice producers in southwest of Niger could reduce their inputs by 52% and still produce the same level of rice output. The Tobit regression showed that factors, such as farm size, experience in rice farming, membership of cooperative, main occupation and land ownership had a direct impact on technical efficiency.

Bootstrapping Data Envelopment Analysis of Efficiency and Productivity of County Public Hospitals in Eastern, Central, and Western China after the Public Hospital Reform

China implemented the public hospital reform in 2012. This study utilized bootstrapping data envelopment analysis（DEA） to evaluate the technical efficiency（TE） and productivity of county public hospitals in Eastern, Central, and Western China after the 2012 public hospital reform. Data from 127 county public hospitals（39, 45, and 43 in Eastern, Central, and Western China, respectively） were collected during 2012–2015. Changes of TE and productivity over time were estimated by bootstrapping DEA and bootstrapping Malmquist. The disparities in TE and productivity among public hospitals in the three regions of China were compared by Kruskal–Wallis H test and Mann–Whitney U test. The average bias-corrected TE values for the four-year period were 0.6442, 0.5785, 0.6099, and 0.6094 in Eastern, Central, and Western China, and the entire country respectively, with average non-technical efficiency, low pure technical efficiency（PTE）, and high scale efficiency found. Productivity increased by 8.12%, 0.25%, 12.11%, and 11.58% in China and its three regions during 2012–2015, and such increase in productivity resulted from progressive technological changes by 16.42%, 6.32%, 21.08%, and 21.42%, respectively. The TE and PTE of the county hospitals significantly differed among the three regions of China. Eastern and Western China showed significantly higher TE and PTE than Central China. More than 60% of county public hospitals in China and its three areas operated at decreasing return scales. There was a considerable space for TE improvement in county hospitals in China and its three regions. During 2012–2015, the hospitals experienced progressive productivity; however, the PTE changed adversely. Moreover, Central China continuously achieved a significantly lower efficiency score than Eastern and Western China. Decision makers and administrators in China should identify the causes of the observed inefficiencies and take appropriate measures to increase the efficiency of county public hospitals in the three areas of China, especially in Central China.

Robust data envelopment analysis based MCDM with the consideration of uncertain data

The application of data envelopment analysis （DEA） as a multiple criteria decision making （MCDM） technique has been gaining more and more attention in recent research. In the practice of applying DEA approach, the appearance of uncertainties on input and output data of decision making unit （DMU） might make the nominal solution infeasible and lead to the efficiency scores meaningless from practical view. This paper analyzes the impact of data uncertainty on the evaluation results of DEA, and proposes several robust DEA models based on the adaptation of recently developed robust optimization approaches, which would be immune against input and output data uncertainties. The robust DEA models developed are based on input-oriented and outputoriented CCR model, respectively, when the uncertainties appear in output data and input data separately. Furthermore, the robust DEA models could deal with random symmetric uncertainty and unknown-but-bounded uncertainty, in both of which the distributions of the random data entries are permitted to be unknown. The robust DEA models are implemented in a numerical example and the efficiency scores and rankings of these models are compared. The results indicate that the robust DEA approach could be a more reliable method for efficiency evaluation and ranking in MCDM problems.

Empirical analysis on TFP change in Chinese logistics industry： A nonparametric Malmquist index approach

Through a nonparametric Malmquist index approach, this paper analyzes the total factor productivity change in China＇s logistics industry with panel data of logistics listed corporation from 1999 to 2006, which decomposed into technical efficiency and technical progress. The result shows： （1） The average growth rate of Chinese logistics corporations from 1999 to 2006 is 0.4%, which is mainly due to the improvement of technical efficiency; （2） Technical progress which took the negative effect of the decline could not be neglected; （3） The role of technical efficiency and technical progress are different with time varying.

Prediction Model of Data Envelopment Analysis with Undesirable Outputs

Data envelopment analysis (DEA) has become a standard non parametric approach to productivity analysis, especially to relative efficiency analysis of decision making units (DMUs). Extended to the prediction field, it can solve the prediction problem with multiple inputs and outputs which can not be solved easily by the regression analysis method.But the traditional DEA models can not solve the problem with undesirable outputs,so in this paper the inherent relationship between goal programming and the DEA method based on the relationship between multiple goal programming and goal programming is explored,and a mixed DEA model which can make all factors of inputs and undesirable outputs decrease in different proportions is built.And at the same time,all the factors of desirable outputs increase in different proportions.

Data envelopment analysis procedure with two non-homogeneous DMU groups

The classic data envelopment analysis（DEA） model is used to evaluate decision-making units＇（DMUs） efficiency under the assumption that all DMUs are evaluated with the same criteria setting. Recently, new researches begin to focus on the efficiency analysis of non-homogeneous DMU arose by real practices such as the evaluation of departments in a university, where departments argue for the adoption of different criteria based on their disciplinary characteristics. A DEA procedure is proposed in this paper to address the efficiency analysis of two non-homogeneous DMU groups. Firstly, an analytical framework is established to compromise diversified input and output（IO） criteria from two nonhomogenous groups. Then, a criteria fusion operation is designed to obtain different DEA analysis strategies. Meanwhile, Friedman test is introduced to analyze the consistency of all efficiency results produced by different strategies. Next, ordered weighted averaging（OWA） operators are applied to integrate different information to reach final conclusions. Finally, a numerical example is used to illustrate the proposed method. The result indicates that the proposed method relaxes the restriction of the classical DEA model,and can provide more analytical flexibility to address different decision analysis scenarios arose from practical applications.