State space models for condition monitoring: a case study

A Condition Monitoring system can increase safety, quality and availability in industrial plants. Safety requirements are especially important in critical machineries, like a turbine driving a centrifugal compressor located at a petrochemical plant in the case study presented in this paper. A Condition Monitoring system is set up for vibration data coming from the turbine. Four years of monthly data observed at two different locations of the equipment are analysed. The core of the system is a model to forecast the state of the machine using data provided by the Condition Monitoring system at each moment in time. The model is based on the State Space framework whose associated recursive algorithms (Kalman Filter and Fixed Interval Smoothing) provide the basis for a number of different operations, from which the most important in the present context is the extrapolation of the distribution of forecasts on which the probability of failure is estimated. The cost model on which the decision of making a preventive replacement is taken is based on the ‘expected cost per unit time’ for a pre-determined critical value of the vibration measure. The system is thoroughly tested on the data.     

Vibration — A tool for machine diagnostics and condition monitoring

Vibration is an effective tool in detecting and diagnosing some of the incipient failures of machines and equipment. The present paper deals with the basic principles, which may help in identifying its diagnostic ability, the scope of its diagnostic capabilities, the instrumentation in vogue for its monitoring and the state-of-the-art of the monitoring techniques and programs. A few case studies are also given to illustrate how machine troubles/failures are diagnosed with the help of vibration signatures.     

RCM predictive maintenance of railway systems based on unobserved components models

Turnouts are probably the most important infrastructure elements of the railway system because of its effect on the system safety, reliability and quality of the service. In this paper, a predictive maintenance system in point mechanism, called RCM², has been implemented for increasing the quality service. RCM² is based on the integration of the two other types of maintenance techniques, namely Reliability Centred Maintenance (RCM₁) and Remote Condition Monitoring (RCM₂). The core of the system consists of an Unobserved Components model set-up in a State Space framework, in which the unknown elements of the system are estimated by Maximum Likelihood. The detection of faults in the system is based on the correlation estimate between a curve free from faults (that is, continuously updated as new curves are incorporated in the data base) with the current curve data. If the correlation falls far from one, a fault is at hand. The detection system is tested on a set of 476 experiments carried out by the Universities of Sheffield and Castilla-La Mancha.     

A multi-criteria decision model to determine inspection intervals of condition monitoring based on delay time analysis

In periodic monitoring, the main problem is determining the inspection interval of condition monitoring. For this problem, the decision variable is represented by the time of next inspection of condition monitoring. There are several studies that deal with prescribing inspection intervals. But only a few of these allow the decision maker to observe simultaneously more than one aspect. This does not accord with the natural tendency of the decision maker who desires to see the decision problem from a broader perspective, by having different viewpoints or dimensions of choices. Therefore, the main objective of this paper is to propose a decision model, which can simultaneously determine inspection intervals for condition monitoring regarding the failure behavior of equipment to be inspected, features of maintainability and decision maker preferences about cost and downtime.     

Multivariate Model Identification and Stochastic Control of a Chemical Reactor

Multivariate time series and process identification methods are used to develop a dynamicstochastic model for a packed bed tubular reactor carrying out highly exothermic hydrogenolysis reactions. A canonical analysis procedure is used on the data collected from the reactor to first reduce the dimensionality of the identification and control problems. The identified transfer function-ARIMA model is transformed into a state space model form and used to develop a multivariable optimal stochastic controller for the reactor. The controlled variables are inferred production rates reconstructed from temperature and flow measurements. The parameters of the inferential equation are updated recursively using measurements of actual concentrations available periodically. The controller is implemented using a process minicomputer, and is shown to perform very well.     

Principal component analysis applied to filtered signals for maintenance management

This paper presents an approach for detecting and identifying faults in railway infrastructure components. The method is based on pattern recognition and data analysis algorithms. Principal component analysis (PCA) is employed to reduce the complexity of the data to two and three dimensions. PCA involves a mathematical procedure that transforms a number of variables, which may be correlated, into a smaller set of uncorrelated variables called ‘principal components’. In order to improve the results obtained, the signal was filtered. The filtering was carried out employing a state–space system model, estimated by maximum likelihood with the help of the well‐known recursive algorithms such as Kalman filter and fixed interval smoothing. The models explored in this paper to analyse system data lie within the so‐called unobserved components class of models. Copyright © 2009 John Wiley & Sons, Ltd.     

A reliability centered approach to remote condition monitoring. A railway points case study

Railway turnouts, consisting of switches and a crossing, are complex electro-mechanical devices which are exposed to severe environmental influences and which are essential for the operation of any railway bar horizontal lifts. Their safe and reliable operation must be assured if the rail mode of transport is to flourish. Conventionally, the continuous availability of turnout mechanisms has been assured by high levels of routine maintenance, to some extent tailored to the criticality of a particular point location. However, traffic increases and shortened maintenance windows require better approaches to turnout maintenance. The authors of the present paper undertook the development of algorithms to detect gradual failure in railway turnout which should allow a move to an RCM² approach to the management of switch and crossing maintenance. They demonstrate the approach using data from tests on a commonly found point mechanism and include a discussion of the benefits of adopting a Kalman Filter for pre-processing the data collected during tests.     

Perturbation analysis for continuous and discrete flow models: a study of the delivery time impact on the optimal buffer level

In this paper, a manufacturing system composed of a single-product machine, a buffer and a stochastic demand is considered. Two models are presented: continuous and discrete flow models including constant delivery times, machine failures and random demands. The objective is to determine the value of the optimal buffer level, for a hedging point policy which minimises the total average cost function. The cost function is the sum of inventory, transportation and lost sales costs. Infinitesimal perturbation analysis is used for optimisation of the failure-prone manufacturing system. The trajectories of buffer level are studied for the continuous and discrete cases and the infinitesimal perturbation analysis estimators are evaluated. These estimators are shown to be unbiased and then they are implemented in an optimisation algorithm which determines the optimal buffer level in the presence of constant delivery time. Numerical results are presented for continuous and discrete flow models and then compared in order to evaluate the application of the infinitesimal perturbation analysis on the discrete flow model.     

On statistical inference in time series analysis of the evolution of road safety

Data collected for building a road safety observatory usually include observations made sequentially through time. Examples of such data, called time series data, include annual (or monthly) number of road traffic accidents, traffic fatalities or vehicle kilometers driven in a country, as well as the corresponding values of safety performance indicators (e.g., data on speeding, seat belt use, alcohol use, etc.). Some commonly used statistical techniques imply assumptions that are often violated by the special properties of time series data, namely serial dependency among disturbances associated with the observations. The first objective of this paper is to demonstrate the impact of such violations to the applicability of standard methods of statistical inference, which leads to an under or overestimation of the standard error and consequently may produce erroneous inferences. Moreover, having established the adverse consequences of ignoring serial dependency issues, the paper aims to describe rigorous statistical techniques used to overcome them. In particular, appropriate time series analysis techniques of varying complexity are employed to describe the development over time, relating the accident-occurrences to explanatory factors such as exposure measures or safety performance indicators, and forecasting the development into the near future. Traditional regression models (whether they are linear, generalized linear or nonlinear) are shown not to naturally capture the inherent dependencies in time series data. Dedicated time series analysis techniques, such as the ARMA-type and DRAG approaches are discussed next, followed by structural time series models, which are a subclass of state space methods. The paper concludes with general recommendations and practice guidelines for the use of time series models in road safety research.     

基于卡尔曼滤波的机械振动WSNs时间抖动累积误差抑制方法

针对机械振动无线传感器网络连续高频采样的时间抖动累积误差大的问题,提出一种基于卡尔曼滤波的时间抖动累积误差抑制方法.首先设计基于IEEE 802.11标准的机械振动采集节点,并分析其时间抖动累积误差产生的原因;然后通过父子链路轮询时钟同步,采用卡尔曼滤波估计节点间时钟的频率偏移;最后各节点根据实际采样频率与时钟频率的关...     

Markovian models for deadlock analysis in automated manufacturing systems

Deadlocks constitute a major issue in the desing and operation of discrete event systems. In automated manufacturing systems, deadlocks assume even greater importance in view of the automated operation. In this paper, we show that Markov chains with absorbing states provide a natural model of manufacturing systems with deadlocks. With illustrative examples, we show that performance indices such as mean time to deadlock and mean number of finished parts before deadlock can be efficiently computed in the modelling framework of Markov chains with absorbing states. We also show that the distribution of time to deadlock can be computed by conducting a transient analysis of the Markov chain model.     

Condition-based fault tree analysis (CBFTA): A new method for improved fault tree analysis (FTA), reliability and safety calculations

Condition-based maintenance methods have changed systems reliability in general and individual systems in particular. Yet, this change does not affect system reliability analysis. System fault tree analysis (FTA) is performed during the design phase. It uses components failure rates derived from available sources as handbooks, etc. Condition-based fault tree analysis (CBFTA) starts with the known FTA. Condition monitoring (CM) methods applied to systems (e.g. vibration analysis, oil analysis, electric current analysis, bearing CM, electric motor CM, and so forth) are used to determine updated failure rate values of sensitive components. The CBFTA method accepts updated failure rates and applies them to the FTA. The CBFTA recalculates periodically the top event (TE) failure rate (λ_TE) thus determining the probability of system failure and the probability of successful system operation—i.e. the system's reliability.FTA is a tool for enhancing system reliability during the design stages. But, it has disadvantages, mainly it does not relate to a specific system undergoing maintenance.CBFTA is tool for updating reliability values of a specific system and for calculating the residual life according to the system's monitored conditions. Using CBFTA, the original FTA is ameliorated to a practical tool for use during the system's field life phase, not just during system design phase.This paper describes the CBFTA method and its advantages are demonstrated by an example.     

A farewell to R: time-series models for tracking and forecasting epidemics

The time-dependent reproduction number, R_t, is a key metric used by epidemiologists to assess the current state of an outbreak of an infectious disease. This quantity is usually estimated using time-series observations on new infections combined with assumptions about the distribution of the serial interval of transmissions. Bayesian methods are often used with the new cases data smoothed using a simple, but to some extent arbitrary, moving average. This paper describes a new class of time-series models, estimated by classical statistical methods, for tracking and forecasting the growth rate of new cases and deaths. Very few assumptions are needed and those that are made can be tested. Estimates of R_t, together with their standard deviations, are obtained as a by-product.     

The hierarchical Tobit model: A case study in Bayesian computing

In this paper we discuss the potentials of a new Bayesian inference tool, called the Gibbs sampler, for the analysis of the censored regression or Tobit model. Tobit models have a wide range of applications in empirical sciences, like econometrics and biometrics. The estimation results of the simple Tobit model will be compared to a hierarchical Tobit model, and the Gibbs sampling approach to the related classical algorithm of expectation-maximisation (EM). The underlying botanical example of this paper is concerned with the censoring mechanism in plant reproduction and proposes the Bayesian Tobit model for the growth relationship between the reproductive part and the rest of the plant.     

Combining task analysis and fault tree analysis for accident and incident analysis: A case study from Bulgaria

Understanding the reasons for incident and accident occurrence is important for an organization's safety. Different methods have been developed to achieve this goal. To better understand the human behaviour in incident occurrence we propose an analysis concept that combines Fault Tree Analysis (FTA) and Task Analysis (TA). The former method identifies the root causes of an accident/incident, while the latter analyses the way people perform the tasks in their work environment and how they interact with machines or colleagues. These methods were complemented with the use of the Human Error Identification in System Tools (HEIST) methodology and the concept of Performance Shaping Factors (PSF) to deepen the insight into the error modes of an operator's behaviour. HEIST shows the external error modes that caused the human error and the factors that prompted the human to err. To show the validity of the approach, a case study at a Bulgarian Hydro power plant was carried out. An incident – the flooding of the plant's basement – was analysed by combining the afore-mentioned methods. The case study shows that Task Analysis in combination with other methods can be applied successfully to human error analysis, revealing details about erroneous actions in a realistic situation.     

Vibration analysis of a functionally graded beam under a moving mass by using different beam theories

Vibration of a functionally graded (FG) simply-supported beam due to a moving mass has been investigated by using Euler–Bernoulli, Timoshenko and the third order shear deformation beam theories. The material properties of the beam vary continuously in the thickness direction according to the power-law form. The system of equations of motion is derived by using Lagrange’s equations. Trial functions denoting the transverse, the axial deflections and the rotation of the cross-sections of the beam are expressed in polynomial forms. The constraint conditions of supports are taken into account by using Lagrange multipliers. In this study, the effects of the shear deformation, various material distributions, velocity of the moving mass, the inertia, Coriolis and the centripetal effects of the moving mass on the dynamic displacements and the stresses of the beam are discussed in detail. To validate the present results, the dynamic deflections of the beam under a moving mass are compared with those of the existing literature and a comparison study for free vibration of an FG beam is performed. Good agreement is observed. The results show that the above-mentioned effects play a very important role on the dynamic responses of the beam and it is believed that new results are presented for dynamics of FG beams under moving loads which are of interest to the scientific and engineering community in the area of FGM structures.     

A statistical monitoring approach for automotive on‐board diagnostic systems

The current generation of vehicle models are increasingly being equipped with on‐board diagnostic (OBD) systems aimed at assessing the ‘state of health’ of important anti‐pollution subsystems and components. In order to promptly diagnose and fix quality and reliability problems that may potentially affect such complex diagnostic systems, even during advanced development prior to mass production, some vehicle prototypes undergo a testing phase under realistic conditions of use (a mileage accumulation campaign). The aim of this work is to set up a statistical tool for improving the reliability of the OBD system by monitoring its operation during the mileage accumulation campaign of a new vehicle model. A dedicated software program was developed by the authors to filter the large experimental database recorded during the mileage accumulation campaign and to extract the time series of the diagnostic indices to be analysed. A model‐based monitoring approach, using continuous time autoregressive (CAR) models for the time‐series structure and traditional control charts for the estimated residuals, is adopted. A Kalman recursion procedure for the estimation of the unknown CAR model parameters is described. An application of the proposed approach is presented for a diagnostic index related to the state of health of the oxygen sensor. Copyright © 2006 John Wiley & Sons, Ltd.     

Non-stationary functional series modeling and analysis of hardware reliability series: a comparative study using rail vehicle interfailure times

A novel reliability modeling and analysis framework based upon the distinct class of non-stationary Functional Series (FS) models is introduced. This framework allows for non-stationary reliability modeling, evolution assessment, analysis (including non-stationarity assessment, dependency assessment, as well as cycle detection), and prediction. The Functional Series framework is used for the modeling and analysis of two rail vehicle reliability series (Times Between Failures, TBFs), while comparisons with alternative (ARIMA, adaptive RARMA–RML, and Bayesian) modeling approaches are also made. The results indicate the advantages and usefulness of the Functional Series framework, as the TBF modeling accuracy is improved, its non-stationarity and serial dependency are established, the presence of cyclic patterns is revealed, and reliability evolution is assessed. It is conjectured that the cycles revealed in the TBF series may be related to maintenance policies. Finally, reliability prediction is shown to be feasible, although the “larger” excursions in the TBF series are difficult to accurately predict.