Zhimin Xi

A copula-based sampling method for data-driven prognostics

This paper develops a Copula-based sampling method for data-driven prognostics and health management (PHM). The principal idea is to first build statistical relationship between failure time and the time realizations at specified degradation levels on the basis of off-line training data sets, then identify possible failure times for on-line testing units based on the constructed statistical model and available on-line testing data. Specifically, three technical components are proposed to implement the methodology. First of all, a generic health index system is proposed to represent the health degradation of engineering systems. Next, a Copula-based modeling is proposed to build statistical relationship between failure time and the time realizations at specified degradation levels. Finally, a sampling approach is proposed to estimate the failure time and remaining useful life (RUL) of on-line testing units. Two case studies, including a bearing system in electric cooling fans and a 2008 IEEE PHM challenge problem, are employed to demonstrate the effectiveness of the proposed methodology.

Random Field Characterization Considering Statistical Dependence for Probability Analysis and Design

The proper orthogonal decomposition method has been employed to extract the important field signatures of random field observed in an engineering product or process. Our preliminary study found that the coefficients of the signatures are statistically uncorrelated but may be dependent. To this point, the statistical dependence of the coefficients has been ignored in the random field characterization for probability analysis and design. This paper thus proposes an effective random field characterization method that can account for the statistical dependence among the coefficients for probability analysis and design. The proposed approach has two technical contributions. The first contribution is the development of a natural approximation scheme of random field while preserving prescribed approximation accuracy. The coefficients of the signatures can be modeled as random field variables, and their statistical properties are identified using the chi-square goodness-of-fit test. Then, as the paper’s second technical contribution, the Rosenblatt transformation is employed to transform the statistically dependent random field variables into statistically independent random field variables. The number of the transformation sequences exponentially increases as the number of random field variables becomes large. It was found that improper selection of a transformation sequence among many may introduce high nonlinearity into system responses, which may result in inaccuracy in probability analysis and design. Hence, this paper proposes a novel procedure of determining an optimal sequence of the Rosenblatt transformation that introduces the least degree of nonlinearity into the system response. The proposed random field characterization can be integrated with any advanced probability analysis method, such as the eigenvector dimension reduction method or polynomial chaos expansion method. Three structural examples, including a microelectromechanical system bistable mechanism, are used to demonstrate the effectiveness of the proposed approach. The results show that the statistical dependence in the random field characterization cannot be neglected during probability analysis and design. Moreover, it is shown that the proposed random field approach is very accurate and efficient.

A Copula-based sampling method for data-driven prognostics and health management

This paper develops a Copula-based sampling method for data-driven prognostics and health management (PHM). The principal idea is to first build statistical relationship between failure time and the time realizations at specified degradation levels on the basis of off-line training data sets, then identify possible failure times for on-line testing units based on the constructed statistical model and available on-line testing data. Specifically, three technical components are proposed to implement the methodology. First of all, a generic health index system is proposed to represent the health degradation of engineering systems. Next, a Copula-based modeling is proposed to build statistical relationship between failure time and the time realizations at specified degradation levels. Finally, a sampling approach is proposed to estimate the failure time and remaining useful life (RUL) of on-line testing units. Two case studies, including a bearing system in electric cooling fans and a 2008 IEEE PHM challenge problem, are employed to demonstrate the effectiveness of the proposed methodology.

A Unified Framework for Evaluating Supply Chain Reliability and Resilience

As the complexity of supply chain structures and the frequency of their disruptions rise, businesses are increasingly recognizing the value of supply chain reliability and resilience (SCRR). A number of efforts have been devoted to define SCRR or to develop risk mitigation strategies for their improvement. However, a key question remaining to be answered is how SCRR should be quantified. Existing methods are insufficient in addressing this question on two important fronts: First, they do not adequately represent the interdependencies between different supply chain nodes; second, they do not allow for the modeling of actionable decisions and thus cannot be used to guide improvement strategies. This paper aims to fill this gap by proposing a unified framework for evaluating SCRR that internalizes design inputs and is flexible to varying degrees of data availability. The proposed framework captures risks involved in the supply, the demand, the firm itself, and the external environment. It also contributes to the literature by relating SCRR to the supply chains risk-mitigating capabilities prior to or postdisruptions. A novel method using the supply chains inherent buyer–supplier relationships is designed to model node interdependencies. Two example applications are discussed to demonstrate how this framework can be utilized to assist in reliable and resilient supply chain design.

Data Driven Prognostics With Lack of Training Data Sets

Data-driven prognostics typically requires sufficient offline training data sets for accurate remaining useful life (RUL) prediction of engineering products. This paper investigates performances of typical data-driven methodologies when the amount of training data sets is insufficient. The purpose is to better understand these methodologies especially when offline training datasets are insufficient. The neural network, similarity-based approach, and copula-based sampling approach were investigated when only three run-to-failure training units were available. The example of lithium-ion (Li-ion) battery capacity degradation was employed for the demonstration.Copyright

State of Charge Estimation of Lithium-Ion Batteries Considering Model Bias and Parameter Uncertainties

Up to date, model and parameter uncertainties are generally overlooked by majority of researchers in the field of battery study. As a consequence, accuracy of the SOC estimation is dominated by the model fidelity and may vary from cell-to-cell. This paper proposes a systematic framework with associated methodologies to quantify the battery model and parameter uncertainties for more effective battery SOC estimation. Such a framework is also generally applicable for estimating other battery performances of interest (e.g. capacity and power capability). There are two major benefits using the proposed framework: i) consideration of the cell-to-cell variability, and ii) accuracy improvement of the low fidelity model comparable to the high fidelity without scarifying computational efficiency. One case study is used to demonstrate the effectiveness of the proposed framework.© 2014 ASME

Engineering Recoverability: A New Indicator of Design for Engineering Resilience

Design of engineering resilient systems is an emerging research field. The contribution of this paper is to i) define engineering resilience on the basis of various resilience concepts in different fields; ii) propose the engineering recoverability as a new component in the framework of designing engineering resilient systems; and iii) introduce a general mathematical formulation to quantify the engineering resilience. One case study of a CNC machining system is used to demonstrate the value of designing engineering resilient systems.Copyright

Validation Metric for Dynamic System Responses under Uncertainty

To date, model validation metric is prominently designed for non-dynamic model responses. Though metrics for dynamic responses are also available, they are specifically designed for the vehicle impact application and uncertainties are not considered in the metric. This paper proposes the validation metric for general dynamic system responses under uncertainty. The metric makes use of the popular U-pooling approach and extends it for dynamic responses. Furthermore, shape deviation metric was proposed to be included in the validation metric with the capability of considering multiple dynamic test data. One vehicle impact model is presented to demonstrate the proposed validation metric.

Model Validation Metric and Model Bias Characterization for Dynamic System Responses Under Uncertainty

Quantification of the accuracy of analytical models (math or computer simulation models) and characterization of the model bias are two essential processes in model validation. Available model validation metrics, whether qualitative or quantitative, do not consider the influence of the number of experimental data for model accuracy check. In addition, quantitative measure from the validation metric does not directly reflect the level of model accuracy, i.e. from 0% to 100%, especially when there is a lack of experimental data. If the original model prediction does not satisfy accuracy criteria compared to the experimental data, instead of revising the model conceptually, characterization of the model bias may be a more practical approach to improve the model accuracy because there is probably no ideal model which can predict the actual physical system with no error. So far, there is a lack of effective approaches that can accurately characterize the model bias for multiple dynamic system responses. To overcome these limitations, the first objective of this study is to develop a model validation metric for model accuracy check considering different number of experimental data. Specifically, a validation metric using the Bhattacharya distance (B-distance) is proposed with three notable benefits. First of all, the metric directly compares the distributions of two set of uncertain system responses from model prediction and experiment rather than the distribution parameters (e.g. mean and variance). Second, the B-distance quantitatively measures the degree of accuracy from 0% to 100% between the distributions of the uncertain system responses. Third, reference accuracy metric with respect to different number of experimental data can be effectively obtained so that hypothesis test can be performed to identify whether the two distributions are identical or not in a probability manner. The second objective of this study is to propose an effective approach to accurately characterize the model bias for dynamic system responses. Specially, the model bias is represented by a generic random process, where realizations of the model bias at each time step could follow arbitrary distributions. Instead of using the traditional Bayesian or Maximum Likelihood Estimation (MLE) approach, we propose a novel and efficient approach to identify the model bias using a generic random process modeling technique. A vehicle safety system with 11 dynamic system responses is used to demonstrate the effectiveness of the proposed approach.Copyright

Diagnostics and Prognostics of Lithium-Ion Batteries

This paper investigates recent research on battery diagnostics and prognostics especially for Lithium-ion (Li-ion) batteries. Battery diagnostics focuses on battery models and diagnosis algorithms for battery state of charge (SOC) and state of health (SOH) estimation. Battery prognostics elaborates data-driven prognosis algorithms for predicting the remaining useful life (RUL) of battery SOC and SOH. Readers will learn not only basics but also very recent research developments on battery diagnostics and prognostics.Copyright