Set Of Product Functions Research Articles

Fault feature extraction of rolling bearings using local mean decomposition-based enhanced sparse coding shrinkage

Rolling bearing are one of the most important rotating components in the rotating machine and they are prone to failure due to complex harsh working conditions. However, it’s a difficult issue to extract the fault feature from heavy noisy signal. In this paper, a new multilayer hybrid denoising method called local mean decomposition (LMD)-based enhanced sparse coding shrinkage (SCS) (named LMD-EnSCS) is proposed for impulse component extraction from bearing vibration signals. First, LMD is used to decompose the signal into a set of product functions (PFs) to enable impulse component as prominent as possible. Moreover, the multiple criteria is proposed to select the effective PF components. The rest filtering layer is used to enhance and extract the impulsive feature through minimum entropy deconvolution (MED) and sparse coding shrinkage (SCS) respectively. MED is able to enhance the impulsive component of noisy signal, which improve the impulsive extraction ability of SCS effectively. The simulation signal and bearing signal are used to verify the effectiveness and superiority of LMD-EnSCS, and the results show that LMD-EnSCS can extract the fault feature and perform well for bearing fault diagnosis.

Weak Fault Feature Extraction of Rolling Bearings Using Local Mean Decomposition-Based Multilayer Hybrid Denoising

Extraction of the weak fault features under strong background noise is crucial to early fault diagnosis in bearings. A new method called local mean decomposition (LMD)-based multilayer hybrid denoising (LMD-MHD) is proposed for signal denoising in this paper. LMD is a novel self-adaptive time-frequency analysis method. It can decompose the signal into a set of product functions (PFs), and is thus particularly suitable for processing of multicomponent amplitude-modulated and frequency-modulated signals. The first filtering layer of LMD-MHD is to use a multiple criteria decision to select the effective PF components. The second filtering layer is to use the wavelet threshold denoising (WTD) as the prefilter of singular value decomposition (SVD) implementation, which enables the preserved singular values to consist of the most important information of the PFs. The final denoising layer of LMD-MHD is to use SVD to extract the most important principal features from Hankel matrix of the PFs. The order of effective ranks of the Hankel matrix is determined by the number of main frequencies in the fast Fourier transformation (FFT) result of the signal. The filtering is finished based on the reconstructed signal from the decomposition result of SVD. The results of experimental analysis on the simulation signals and vibration signal collected from rolling bearings indicate that LMD-MHD is effective for extracting the weak fault features and performs well for bearing fault diagnosis.

Time–frequency analysis based on ensemble local mean decomposition and fast kurtogram for rotating machinery fault diagnosis

Abstract A time–frequency analysis method based on ensemble local mean decomposition (ELMD) and fast kurtogram (FK) is proposed for rotating machinery fault diagnosis. Local mean decomposition (LMD), as an adaptive non-stationary and nonlinear signal processing method, provides the capability to decompose multicomponent modulation signal into a series of demodulated mono-components. However, the occurring mode mixing is a serious drawback. To alleviate this, ELMD based on noise-assisted method was developed. Still, the existing environmental noise in the raw signal remains in corresponding PF with the component of interest. FK has good performance in impulse detection while strong environmental noise exists. But it is susceptible to non-Gaussian noise. The proposed method combines the merits of ELMD and FK to detect the fault for rotating machinery. Primarily, by applying ELMD the raw signal is decomposed into a set of product functions (PFs). Then, the PF which mostly characterizes fault information is selected according to kurtosis index. Finally, the selected PF signal is further filtered by an optimal band-pass filter based on FK to extract impulse signal. Fault identification can be deduced by the appearance of fault characteristic frequencies in the squared envelope spectrum of the filtered signal. The advantages of ELMD over LMD and EEMD are illustrated in the simulation analyses. Furthermore, the efficiency of the proposed method in fault diagnosis for rotating machinery is demonstrated on gearbox case and rolling bearing case analyses.

Gearbox fault diagnosis based on local mean decomposition, permutation entropy and extreme learning machine

This paper presents a fault diagnosis method for gearbox based on local mean decomposition (LMD), permutation entropy (PE) and extreme learning machine (ELM). LMD, a new self-adaptive time-frequency analysis method, is applied to decompose the vibration signal into a set of product functions (PFs). Then, PE values of the first five PFs (PF-PE) are calculated to characterize the complexity of the vibration signal. Finally, for the purpose of less time-consuming and higher accuracy, ELM is used to identify and classify of gearbox in different fault types. The experimental results demonstrate that the proposed method is effective in diagnosing and classifying different states of gearbox in short time.

Improved LMD, Permutation Entropy and Optimized K-Means to Fault Diagnosis for Roller Bearings

A novel bearing vibration signal fault feature extraction and recognition method based on the improved local mean decomposition (LMD), permutation entropy (PE) and the optimized K-means clustering algorithm is put forward in this paper. The improved LMD is proposed based on the self-similarity of roller bearing vibration signal extending the right and left side of the original signal to suppress its edge effect. After decomposing the extended signal into a set of product functions (PFs), the PE is utilized to display the complexity of the PF component and extract the fault feature meanwhile. Then, the optimized K-means algorithm is used to cluster analysis as a new pattern recognition approach, which uses the probability density distribution (PDD) to identify the initial centroid selection and has the priority of recognition accuracy compared with the classic one. Finally, the experiment results show the proposed method is effectively to fault extraction and recognition for roller bearing.

A new rolling bearing fault diagnosis method based on multiscale permutation entropy and improved support vector machine based binary tree

A new bearing vibration feature extraction method based on multiscale permutation entropy (MPE) and improved support vector machine based binary tree (ISVM-BT) is put forward in this paper. Local mean decomposition (LMD), a new self-adaptive time–frequency analysis method, is utilized to decompose the roller bearing vibration signal into a set of product functions (PFs) and then MPE method is used to characterize the complexity of the principal PF component in different scales. After the feature extraction, a new pattern recognition approach called ISVM-BT is introduced to accomplish the fault identification automatically, which has the priority of high recognition accuracy compared with other classifiers. Besides, the Laplacian score (LS) is introduced to refine the fault feature by sorting the scale factors. Finally, the rolling bearing fault diagnosis method based on LMD, MPE, LS and ISVM-BT is proposed and the experimental results indicate the proposed method is effective in identifying the different categories of rolling bearings.

An ensemble local means decomposition method and its application to local rub-impact fault diagnosis of the rotor systems

Targeting the shock characteristics of the vibration signal of a rotor system with local rub-impact fault, a local rub-impact fault diagnosis method of rotor system based on ELMD (ensemble local means decomposition) is proposed in this paper. The local mean decomposition (LMD) is a newly self-adaptive time–frequency analysis method, by which any complicated multi-component signal could be decomposed into a set of product functions (PFs) whose instantaneous frequencies in theory have physical significance. Unfortunately, mode mixing phenomenon which makes the decomposition results devoid of physical meaning is common when LMD is performed in practice. Targeting this shortcoming, the filter bank structure of white noise by LMD is obtained by numerical experiments, and then an improved method based upon noise-assisted analysis, ensemble local mean decomposition, is put forward. In ELMD, firstly, different white noise is added to the targeted signal; secondly, LMD is used to decompose the noise-added signal into product functions (PFs); finally, the ensemble means of corresponding PF components derived from LMD is regarded as the final decomposition result. The analytical results from simulation signal and experimental rotor local rub-impact signal demonstrate that the ELMD approach can be used to overcome the mode mixing of the original LMD method effectively.

Training for Old Age

This paper attempts to develop production functions (PF) between aerobic exercise inputs and long-run health outputs. Future studies could use such PF for estimating the benefits and costs (broadly defined) of different exercise programs to help develop optimal (utility maximizing) ones. To develop the PF, the paper reviewed the biomedical literature for the major dose-response relations between health, physical fitness, and exercise. Where relevant, the paper converted the dose-response relationships from relative risks to absolute probabilities and standardized terminology and units of measures. The paper develops a clear set of biological PF that illustrate, quantitatively, how increases in peak cardiorespiratory (CR) fitness as measured by a short stress test reduce the probability of all-cause mortality; how increasing intensities of short (approximately 30 min, three to five times a week) exercise sessions increase peak CR fitness or retard its age-related decline; and how consistent exercise reduces the risk of myocardial infarctions (MI). The exercise-long-run health PF developed in this paper should provide a useful framework for other studies to estimate the broadly defined costs and benefits of different exercise programs and to help develop optimal ones.

Differential savings, factor shares, and endogenous growth cycles

Abstract The paper analyzes the dynamic properties of the neoclassical one-sector growth model with differential savings in the sense of Kaldor–Pasinetti. The economy exhibits unstable steady states and fluctuations if the income distribution varies sufficiently and if shareholders save more than workers. The paper analyzes in detail the dynamics for the case with a fixed proportions technology as well as with a smooth approximation. If the savings propensities differ by an arbitrarily small amount, the system exhibits topological chaos in the sense of Li and Yorke for an open set of production functions. The analytical results are supplemented by numerical experiments.

Design of fast self-testing checkers for m-out-of-2m and m-out-of-(2m ± 1) codes

A new design method for high-speed self-testing checkers for m/2m and m/(2m± I) codes. The new design has a three- or four-level structure and is based on partitioning the input lines into k ≥ 3 blocks of approximately the same size p i . For each block, all p i , threshold functions in the two-level form are generated. These are combined through common AND gates into the so-called product functions. Finally, two output OR gates partition the set of product functions into two classes. The resulting circuit preserves self-testing and code-disjoint properties through properly partitioning the set of product functions by using an enclosed procedure. The new checkers are built using less hardware than existing fast designs.

An economic model for selecting Douglas-fir reforestation projects

This study presents an economic model for designing and selecting an optimal reforestation program. Given an initial set of resource and policy constraints, the model permits the user to select simultaneously the best set of reforestation projects to execute, the method of reforestation to employ, and the best initial stocking in new plantations. The model was developed for use by managers of large-scale, public land reforestation programs in the Douglas-fir Region of the Western United States. Results of the study include a package of linked computer programs which provides a completely automated procedure for designing and selecting a reforestation program. The programs have the following functions: The first program, FOREST, simulates a regime of harvests in plantations consistent with the goal of maximizing present net worth subject to specified constraints. It also generates a set of production functions which describe in terms of present net worth per acre the relationship between number of trees at age ten years and the cost of obtaining that number of trees. The second program, REGEN II, first calculates the present net worth per acre of alternative reforestation techniques (hand planting, aerial seeding, and natural regeneration) which can be applied to a particular tract of land. Then the same program uses a linear programming model to select the set of tracts, techniques, and initial stocking density which maximizes the present net worth of the whole reforestation program within a set of multiple constraints imposed by available projects, budget, seeds, and seedlings. A third program, FINAL, lists all projects recommended for reforestation in the current year, method of treatment, seeding density or initial spacing in plantations scheduled for hand planting, and resource requirements.

Estimation of a Set of Homothetic Production Functions: A Time Series Analysis of American Postwar Manufacturing

This study investigates several key parameters of the production process for the manufacturing sector of the United States. Attention is focused on the behavior as well as the magnitude of the elasticity of substitution, neutral and nonneutral technical progress (in a Hicksian sense), and the returns to scale. Several papers have been concerned with one or a combination of several of these parameters at the two-digit level of aggregation [7; 14; 16; 25]. However, this paper attempts a more comprehensive approach to production function estimation. By hypothesizing five relations in which the marginal rate of technical substitution is functionally dependent on the capital-labor ratio and nonneutral technical progress (i.e., the cost minimizing relation), a set of production functions is derived that includes the Cobb-Douglas and CES as well as four VES production functions. Estimating all five relations yields not only results on the elasticity of substitution and nonneutral technical progress, but it also enables us to determine the descriptive ability of each of the competing specifications. By incorporating the property of homotheticity, a set of transformations is introduced that allows for returns to scale to be constant or vary with the level of output. Homotheticity has been used in this context [3; 25]. However, estimation of an explicit homothetic transformation that allows us to determine the behavior of the returns to scale is an advancement. Estimation is based on time series data, * The author is an assistant professor of economics at Tulane University. I acknowledge the advice and criticism received from John R. Moroney, David B. Humphrey and an unknown referee. In addition, I thank Mark Schupack for making the data available. 1949-65, for the U. S. manufacturing sector aggregated according to the two-digit classification. Because the time series ends in a strong expansionary period, the problems associated with slack terminal years (and the resultant disequilibria) are avoided. In addition, the homothetic transformations are estimated twice; once with data adjusted for capacity utilization rates and again for unadjusted data.l A potentially significant source of measurement error is measurement of capital in existence (as is usual) when capital in use is required. By using both series, an estimate of the bias in estimating the homothetic transformation due to the capital data misspecification is obtainable. The plan of the paper is as follows. The theoretical relations are presented in Section I. Section II contains the econometric specifications as well as a discussion of the estimation procedure. Section III comprises results and analysis, and some concluding remarks appear in Section IV.

Ethnic Relations in the Social Structure of an Industrial Work Force

The personnel of an industrial enterprise form a group functionally associated for the production of material goods. Each member of the group performs a specific businesslike function of work within its complex and preplanned system of divided and coordinated labor. A unity of practical functions comprises the basic structural stratum of a work force at a place of production. The set of production functions performed in an industrial enterprise has two interrelated aspects. On the one hand, all the work functions performed in the work force of an industrial enterprise resulting in the production of a specific tangible product have a purely technological character. The technological aspect of the work functions performed in an industrial enterprise is, in a certain sense, independent of the level of development of society. It reflects not the social development of society, but achievements in science and industrial engineering. On the other hand, however, this technological process is carried out by human beings, and they establish well-defined social connections with each other in the process of production. It is the unity of the social ties among people, conditioned by the technology of production, that constitutes the fundamental structural stratum of a work force.