DISTRIBUTED MONITORING SYSTEM RELIABILITY ESTIMATION WITH CONSIDERATION OF STATISTICAL UNCERTAINTY

Taking into account the whole system structure and the component reliability estimation uncertainty, a system reliability estimation method based on probability and statistical theory for distributed monitoring systems is presented. The variance and confidence intervals of the system reliability estimation are obtained by expressing system reliability as a linear sum of products of higher order moments of component reliability estimates when the number of component or system survivals obeys binomial distribution. The eigenfunction of binomial distribution is used to determine the moments of component reliability estimates, and a symbolic matrix which can facilitate the search of explicit system reliability estimates is proposed. Furthermore, a case of application is used to illustrate the procedure, and with the help of this example, various issues such as the applicability of this estimation model, and measures to improve system reliability of monitoring systems are discussed.

Discussion on Statistical Monitoring and Evaluation of High-Quality Development of County Economy

The county economy serves as the fundamental unit in China’s economic development and construction.There exists a significant correlation between the quality and level of county economic development and the overall economic construction level of the country.In recent years,China’s economy has experienced rapid growth,contributing to an improved living environment and substantial economic income for its citizens.However,this progress has also brought to light certain issues,such as an unbalanced industrial structure and inefficient resource utilization,leading to problems such as low efficiency and severe environmental pollution.Therefore,it becomes imperative to enhance the statistical monitoring and evaluation of high-quality county economic development.This approach aims to gather insights into the development status of the county economy and provide essential data support for decision-making in county economic development.Consequently,this paper proposes development suggestions for the statistical monitoring and evaluation of high-quality county economic development,serving as a crucial starting point for future initiatives.

Multivariate Statistical Process Monitoring and Control: Recent Developments and Applications to Chemical Industry

Multivariate statistical process monitoring and control (MSPM&C) methods for chemical process monitoring with statistical projection techniques such as principal component analysis (PCA) and partial least squares (PLS) are surveyed in this paper. The four-step procedure of performing MSPM&C for chemical process, modeling of processes, detecting abnormal events or faults, identifying the variable(s) responsible for the faults and diagnosing the source cause for the abnormal behavior, is analyzed. Several main research directions of MSPM&C reported in the literature are discussed, such as multi-way principal component analysis (MPCA) for batch process, statistical monitoring and control for nonlinear process, dynamic PCA and dynamic PLS, and on-line quality control by inferential models. Industrial applications of MSPM&C to several typical chemical processes, such as chemical reactor, distillation column, polymerization process, petroleum refinery units, are summarized. Finally, some concluding remarks and future considerations are made.

Multivariate Statistical Process Monitoring of an Industrial Polypropylene Catalyzer Reactor with Component Analysis and Kernel Density Estimation

Abstract Data-driven tools, such as principal component analysis （PCA） and independent component analysis （ICA） have been applied to different benchmarks as process monitoring methods. The difference between the two methods is that the components of PCA are still dependent while ICA has no orthogonality constraint and its latentvariables are independent. Process monitoring with PCA often supposes that process data or principal components is Gaussian distribution. However, this kind of constraint cannot be satisfied by several practical processes. To ex-tend the use of PCA, a nonparametric method is added to PCA to overcome the difficulty, and kernel density estimation （KDE） is rather a good choice. Though ICA is based on non-Gaussian distribution intormation, .KDE can help in the close monitoring of the data. Methods, such as PCA, ICA, PCA.with .KDE（KPCA）, and ICA with KDE,（KICA）, are demonstrated and. compared by applying them to a practical industnal Spheripol craft polypropylene catalyzer reactor instead of a laboratory emulator.

Statistical Monitoring of Chemical Processes Based on Sensitive Kernel Principal Components

The kernel principal component analysis （KPCA） method employs the first several kernel principal components （KPCs）, which indicate the most variance information of normal observations for process monitoring, but may not reflect the fault information. In this study, sensitive kernel principal component analysis （SKPCA） is proposed to improve process monitoring performance, i.e., to deal with the discordance of T2 statistic and squared prediction error SVE statistic and reduce missed detection rates. T2 statistic can be used to measure the variation di rectly along each KPC and analyze the detection performance as well as capture the most useful information in a process. With the calculation of the change rate of T2 statistic along each KPC, SKPCA selects the sensitive kernel principal components for process monitoring. A simulated simple system and Tennessee Eastman process are employed to demonstrate the efficiency of SKPCA on online monitoring. The results indicate that the monitoring performance is improved significantly.

A Robust Statistical Batch Process Monitoring Framework and Its Application

In order to reduce the variations of the product quality in batch processes, multivariate statistical process control methods according to multi-way principal component analysis (MPCA) or multi-way projection to latent structure (MPLS) were proposed for on-line batch process monitoring. However, they are based on the decomposition of relative covariance matrix and strongly affected by outlying observations. In this paper, in view of an efficient projection pursuit algorithm, a robust statistical batch process monitoring (RSBPM) framework,which is resistant to outliers, is proposed to reduce the high demand for modeling data. The construction of robust normal operating condition model and robust control limits are discussed in detail. It is evaluated on monitoring an industrial streptomycin fermentation process and compared with the conventional MPCA. The results show that the RSBPM framework is resistant to possible outliers and the robustness is confirmed.

New Method for Multivariate Statistical Process Monitoring

A new method using discriminant analysis and control charts is proposed for monitoring multivariate process operations more reliably.Fisher discriminant analysis （FDA） is used to derive a feature discriminant direction （FDD） between each normal and fault operations,and each FDD thus decided constructs the feature space of each fault operation.Individuals control charts （XmR charts） are used to monitor multivariate processes using the process data projected onto feature spaces.Upper control limit （UCL） and lower control limit （LCL） on each feature space from normal process operation are calculated for XmR charts,and are used to distinguish fault from normal.A variation trend on an XmR chart reveals the type of relevant fault operation.Applications to Tennessee Eastman simulation processes show that this proposed method can result in better monitoring performance than principal component analysis （PCA）-based methods and can better identify step type faults on XmR charts.

Quality Based Prioritized Sensor Fault Monitoring Methodology

To improve the detection and identification performance of the Statistical Quality Monitoring （SQM） system, a novel quality based Prioritized Sensor-Fault Detection （PSFD） methodology is proposed. Weighted by the Vp （variable importance in projection） index, which indicates the importance of the sensor variables to the quality variables, the new monitoring statistic, Qv, is developed toensure that the most vital sensor faults be detected successfully. Subsequently, the ratio between the Detectable Minimum Faulty Magnitude （DMFM） of the most important sensor and of the least important sensor is only gpmin/gpmax 〈〈 1. The Structured Residuals are designed according to the Vp index to identify and then isolate them. The theoretical findings are fully supported by simulation studies performed on the Tennessee Eastman process.

Site Characterization Index for Continuous Power Quality Monitoring Based on Higher-order Statistics

The high penetration of distributed generation(DG)has set up a challenge for energy management and consequently for the monitoring and assessment of power quality(PQ).Besides,there are new types of disturbances owing to the uncontrolled connections of non-linear loads.The stochastic behaviour triggers the need for new holistic indicators which also deal with big data of PQ in terms of compression and scalability so as to extract the useful information regarding different network states and the prevailing PQ disturbances for future risk assessment and energy management systems.Permanent and continuous monitoring would guarantee the report to claim for damages and to assess the risk of PQ distortions.In this context,we propose a measurement method that postulates the use of two-dimensional(2D)diagrams based on higher-order statistics(HOSs)and a previous voltage quality index that assesses the voltage supply waveform in a continous monitoring campaign.Being suitable for both PQ and reliability applications,the results conclude that the inclusion of HOS measurements in the industrial metrological reports helps characterize the deviations of the voltage supply waveform,extracting the individual customers’pattern fingerprint,and compressing the data from both time and spatial aspects.The method allows a continuous and robust performance needed in the SG framework.Consequently,the method can be used by an average consumer as a probabilistic method to assess the risk of PQ deviations in site characterization.

Quality-related monitoring of papermaking wastewater treatment processes using dynamic multiblock partial least squares

Environmental problems have attracted much attention in recent years,especially for papermak-ing wastewater discharge.To reduce the loss of effluence discharge violation,quality-related multivariate statistical methods have been successfully applied to achieve a robust wastewater treatment system.In this work,a new dynamic multiblock partial least squares(DMBPLS)is pro-posed to extract the time-varying information in a large-scale papermaking wastewater treatment process.By introducing augmented matrices to input and output data,the proposed method not only handles the dynamic characteristic of data and reduces the time delay of fault detection,but enhances the interpretability of model.In addition,the DMBPLS provides a capability of fault location,which has certain guiding significance for fault recovery.In comparison with other mod-els,the DMBPLS has a superior fault detection result.Specifically,the maximum fault detection rate of the DMBPLS is improved by 35.93%and 12.5%for bias and drifting faults,respectively,in comparison with partial least squares(PLS).