Marginal Distribution Of Data Research Articles

Distance-guided domain adaptation for bearing fault diagnosis under variable operating conditions

Abstract Transfer learning (TL) has demonstrated effective application in diagnosing bearing faults under varying operating conditions. The current TL methods achieve domain alignment by minimizing the variation in the marginal distribution of data between the source and target domains in the feature space. However, this approach yields incomplete similarity, leading to domain shift and a decrease in diagnostic performance. To overcome this problem, this paper proposes a new distance-guided domain adaptation (DGDA) method that consists of two modules: Deep domain adaptive correlation alignment (Deep CORAL) combined with Joint Maximum Mean Discrepancy (JMMD) for guided domain adaptation. Deep CORAL employs nonlinear transformations to synchronize second-order statistical correlations across source and target domains, thus ensuring feature-level alignment between these domains. JMMD is utilized to align the joint distribution of input features and output labels within the activation layer in the deep network, thereby bolstering domain alignment. Building on this, we propose a network structure that merges ResNet and BiLSTM, powered by wavelet kernels, serving as a feature extractor. This structure is designed to learn domain-invariant features and incorporates attention mechanisms to amplify important information while diminishing the impact of redundant data. An analysis of bearing experiments is used to demonstrate the effectiveness of this method, and the proposed method significantly outperforms several popular methods in diagnostic performance.

A new deep transfer learning network based on convolutional auto-encoder for mechanical fault diagnosis

Deep learning has gained a great achievement in the intelligent fault diagnosis of rotating machineries. However, the labeled data is scarce in actual engineering and the marginal distribution of data is discrepant under different conditions. Transfer learning provides a feasible way to overcome these difficulties. Considering the effect of noise on the transfer fault diagnosis, this work puts forward a new deep transfer learning network based on convolutional auto-encoder(CAE-DTLN) to implement the mechanical fault diagnosis in target domain without labeled data. In the proposed framework, CAE is used as the feature extractor as it has the ability of noise removal. Moreover, both CORrelation ALignment (CORAL) loss and domain classification loss are integrated to enhance the effect of domain confusion. The proposed model is applied to the fault transfer diagnosis of planetary gearboxes under different working loads and noise levels, and it is compared with other typical fault transfer diagnosis models. The experimental results show that CAE-DTLN has higher diagnosis accuracy and stronger generalization ability. The average diagnostic accuracy of CAE-DTLN is over 99%. Moreover, the proposed transfer learning model has better anti-noise performance.

The PIT-trap-A "model-free" bootstrap procedure for inference about regression models with discrete, multivariate responses.

Bootstrap methods are widely used in statistics, and bootstrapping of residuals can be especially useful in the regression context. However, difficulties are encountered extending residual resampling to regression settings where residuals are not identically distributed (thus not amenable to bootstrapping)—common examples including logistic or Poisson regression and generalizations to handle clustered or multivariate data, such as generalised estimating equations. We propose a bootstrap method based on probability integral transform (PIT-) residuals, which we call the PIT-trap, which assumes data come from some marginal distribution F of known parametric form. This method can be understood as a type of “model-free bootstrap”, adapted to the problem of discrete and highly multivariate data. PIT-residuals have the key property that they are (asymptotically) pivotal. The PIT-trap thus inherits the key property, not afforded by any other residual resampling approach, that the marginal distribution of data can be preserved under PIT-trapping. This in turn enables the derivation of some standard bootstrap properties, including second-order correctness of pivotal PIT-trap test statistics. In multivariate data, bootstrapping rows of PIT-residuals affords the property that it preserves correlation in data without the need for it to be modelled, a key point of difference as compared to a parametric bootstrap. The proposed method is illustrated on an example involving multivariate abundance data in ecology, and demonstrated via simulation to have improved properties as compared to competing resampling methods.

A distribution-free method for forecasting non-gaussian time series

The non-linear instantaneous transformation is a method to model and forecast non-Gaussian time series. A restriction of this method is that the marginal distribution of data must be known, or a general distribution form has to be determined. A difficulty of this method is that in practice the distribution of observed data is usually unknown, and it needs to be determined by fitting the data. In this study, a distribution-free plotting position formula is applied to the non-linear instantaneous transformation method. Synthetic time series and observed data are used to illustrate the proposed method, which does not require fitting the marginal distribution of the data to be forecasted.

Nonparametric Analysis of Temporal Trend When Fitting Parametric Models to Extreme­Value Data

A topic of major current interest in extreme­value analysis is the investigation of temporal trends. For example, the potential influence of “greenhouse” effects may result in severe storms becoming gradually more frequent, or in maximum temperatures gradually increasing, with time. One approach to evaluating these possibilities is to fit, to data, a parametric model for temporal parameter variation, as well as a model describing the marginal distribution of data at any given point in time. However, structural trend models can be difficult to formulate in many circumstances, owing to the complex way in which different factors combine to influence data in the form of extremes. Moreover, it is not advisable to fit trend models without empirical evidence of their suitability. In this paper, motivated by datasets on windstorm severity and maximum temperature, we suggest a nonparametric approach to estimating temporal trends when fitting parametric models to extreme values from a weakly dependent time series. We illustrate the method through applications to time series where the marginal distributions are approximately-Pareto, generalized­Pareto, extreme­value or Gaussian. We introduce time­varying probability plots to assess goodness of fit, we discuss local­likelihood approaches to fitting the marginal model within a window and we propose temporal cross­validation for selecting window width. In cases where both location and scale are estimated together, the Gaussian distribution is shown to have special features that permit it to playa universal role as a “nominal” model for the marginal distribution.