State space models for condition monitoring: a case study
Introduction
Maintenance is one of the departmental areas that most has changed in modern companies during the last decades. These changes are due mainly to a relevant increase in the quantity and variety of physical activities (process, machines and buildings) that must be maintained in the actual idea of globalisation of activities [36]; more complex designs; more technological maintenance and organization policies; and the acceleration of technical changes in maintenance. Besides, maintenance is responding to varying expectations, like the influence that the anomalies and failures have over the machineries about safety, quality, availability and cost in the enterprise [34].
Condition Monitoring is one of the maintenance policies that require an intense use of modern technologies. It is based on the periodical acquisition of data about a variable in order to verify the condition of the critical machinery, diagnosis of the faults and evaluation of the remaining life time of the machine [33].
Many examples can be found in the literature showing the advantages of the application of a Condition Monitoring Program (see e.g. [6], [12], [22], [25], [28], [42], [49]). These advantages have been also shown for different types of industry, like the paper mill industry [44]; manufacturing industry [30]; or nuclear power plants [14].
The main advantages reported are: the need to control only those machines that show the beginning of a malfunction; an increase in the availability of the industrial plants; the capacity to carry out quality checks of both internal and subcontracted maintenance interventions; an increase in the security of the factory; a best programming of maintenance actions; effective programming of supplies and staff; costs are brought down in relation to spare parts and labour and certification is easier.
There are a wide variety of Condition Monitoring techniques, like vibration analysis, lubricant analysis, thermography, ultrasound, etc. However, one of the techniques most applied in this moment to plants with continuous processes is the vibration analysis [8]. This is mainly due to its suitability to the rotative and reciprocating machines, the high number of anomalies and failures that can be diagnosed, its null influence over the availability of the machine for the acquisition of predictive data, etc. [6].
Within the context of Condition Monitoring, numerous developments that make use of alert and alarm levels can be found in the literature. Establishing conditions in order to find optimal alarm values were searched by [26] and [27] and applied to linear discrete time-series models by [45]. Application of Principal Component analysis to the problem of finding alarm conditions and predicting the failure time is described in [25]. Bayesian forecasting approaches in which certain variations in the model parameters and an on-line prediction scheme is set up can be seen in [1].
The cost analysis in Condition Monitoring has been analysed by [10], in which a predictive maintenance program is developed by considering the lowest cost to replace the system. An application to a continuously deteriorating system is shown in [13]. Such a system is inspected at random times sequentially and a probabilistic method based on the semi-regenerative property of the evolution process is applied in order to calculate the long-time expected cost per unit of time. In this study the critical threshold and the parameters of the maintenance scheduling function are considered to reach the minimal cost. The model developed by [9] uses a cost function to coordinate the inspection and replacement of two components and minimise the long-run maintenance cost of the system. In [2], a model based on Monte Carlo simulations is applied and finds out the optimal degradation thresholds of maintenance intervention to minimise the expected total system cost over a given mission time. In [17], an analytical model is developed for a condition-based inspection/replacement policy for a stochastically and continuously deteriorating single-unit system. The replacement threshold and the inspection schedule are considered as decision variables and are proposed to implement the maintenance policy using a multi-level control-limit rule in order to minimize the long run expected maintenance cost per unit time. A mathematical model for the maintained system cost is derived.
Other contributions on the prediction of failures or the remaining operating time in Condition Monitoring are listed next. In [41], a model to provide the remaining operating time of a component using experts' judgement is developed, given an indication of incipient failure. Markov models are used in [42] based on relevant condition predictor for reliability prediction in systems under Condition Monitoring. In [48], a support systems using probabilistic safety assessment techniques and information is developed. The system uses artificial neural networks for safety status/transient condition monitoring and rule-based systems for diagnosis and emergency procedure generation has been applied for the development of a prototype operator adviser system for a reactor in a nuclear plant. In [46], the Dempster–Shafer theory is applied to compare two types of a monitoring system: automatic or human. The condition of the system is determined by means of H–M cooperative systems incorporating human judgements. In [31], a predictive model is developed using Monte Carlo simulations to describe the evolution of the degrading system and genetic algorithm for determining the optimal degradation level beyond which preventive maintenance has to be performed in a continuously monitored multi-component system. In [19], the relationship between the type of deterioration and condition-based optimum inspection intervals, optimum repair level, minimum average maintenance costs and mean time to repair is shown by means of a decision system described as a discrete Markov decision problem.
However, the use of advanced tools for forecasting the remaining operating time in real applications is not fully exploited yet in modern companies.
The Kalman filter has been used in different type of applications, like the on-line failure detection in nuclear power plants [47]; in DC motor to predict failures placing an exponential attenuator at the output end of the motor model to simulate aging failures, resulting in small prediction errors [50], [51] or in the detection of faults in turnouts in the infrastructure elements of railway systems [16], [37].
The usual analysis techniques exploited are some sort of trend analysis, a technique that is not regarded often as a refined mathematical model in other areas within the Operations Research. In this paper, a complex prediction model is developed for vibration data within the State Space class applied to real data in the petrochemical industry. This represents a novel point of view regarding the usual diagnostic techniques exploited in Condition Monitoring Programs. Thus, this article is contributing to the application of useful complex models in the maintenance area, where ‘little attention is paid to data collection and to consideration of the usefulness of models for solving real problems through model fitting and validation’ [43].
The layout of the paper is as follows. In Section 2 some important notions on vibration analysis relevant for the equipment analysed are introduced, as well as the data obtained from the industrial equipment. Section 3 presents the formal statistical set up used, namely the State Space framework, by which the vibration data is analysed, with an especial discussion about the particular model used in this paper. Section 4 introduces the cost model used in order to foresee when a preventive replacement should be carried out based on the point forecasts and their distributions (i.e. the output of the model). Section 5 exposes the main empirical findings. In Section 6, some concluding remarks are given.
Section snippets
Condition monitoring based on vibration analysis
The specific equipment analysed is a turbine driving a centrifugal compressor located at a petrochemical plant. This machine is critical to the production process, because it adjusts the pressure in the head of the housing state machine. This feature justifies the exploitation of a Condition Monitoring system on this machine.
The acquisition of data used in the analysis is rather complicated due to the specificity of this kind of data in the industrial plant, the high cost of acquisition and the
The forecasting model
The model used for forecasting the state of the machine is one often found in the engineering literature, namely a model that filters out the noise from a bivariate signal composed of the two time series in Fig. 1, i.e. the global vibration data from the bearings at two locations of the turbine. Formally, the model iswhere zk are the bivariate output series; vk is a bivariate random Gaussian perturbation; and k is the time sub-index.
The main differences among versions of the model
The cost model
The cost model for the Condition Monitoring of our equipment is an extension to the bivariate case of [11]. The key decision at each moment in time is whether a preventive replacement of the key part of the equipment should be made, and if not, the best time estimate when it should be replaced. The measure upon which the decision is taken is the expected cost per unit time based on a pre-determined critical value of the vibration measure. Such measure is defined as
Case study
Table 1, Table 2 and Fig. 2 present some typical results of application of model (1a), (1b) to the time series shown in Fig. 1, up to the middle of the sample. The reader must bear in mind that in a real situation the model is re-estimated as new data points become available, and the point estimates of parameters and their uncertainty change accordingly.
Several points emerge from Table 1:
- •
It must be taken into account that some transformations of these parameters were estimated, instead of the
Conclusion
The important changes occurring along the last decades in the maintenance departmental areas are demanding more refined and accurate methods in order to optimise the performance of such departments. In that regard, Condition Monitoring is one of the most modern maintenance policies. It is based on the periodical acquisition of data about a variable in order to verify the condition of the critical machinery, and diagnosis of the faults and evaluation of the remaining lifespan of the machine need
Acknowledgements
The authors are grateful to the editor and two anonymous referees for their comments on a previous draft of this paper.
References (52)
- et al.
Simulation modelling of repairable multi-component deteriorating systems for on condition maintenance optimisation
Reliab Eng Syst Safety
(2002) - et al.
Control of Wear applied to compressor: trends in lubricant analysis
Int J Sci Technol Friction Lubricat Wear. Elsevier
(1999) - et al.
A condition-based maintenance policy with non-periodic inspections for a two-unit series system
Reliab Eng Syst Safety
(2005) - et al.
Predictive maintenance: the one-unit replacement model
Int J Production Economics
(1998) - et al.
A state space condition monitoring model for furnace erosion prediction and replacement
Eur J Oper Res
(1997) - et al.
Sequential condition-based maintenance scheduling for a deteriorating system
Eur J Oper Res
(2003) - et al.
A condition-based maintenance policy for stochastically deteriorating systems
Reliab Eng Syst Safety
(2002) - et al.
Optimum condition-based maintenance policies for deteriorating systems with partial information
Reliab Eng Syst Safety
(1996) - et al.
Efficient tests for normality, homoskedasticity and serial independence of regression residuals
Econ Lett
(1980) Predictive maintenance using PCA
Control Eng Pract
(1995)
Indirect predictive monitoring in flexible manufacturing systems
Robot Comput Integr Manufact
Condition based maintenance optimization by means of genetic algorithms and Monte Carlo simulation
Reliab Eng Syst Safety
Schmid Felix RCM2 predictive maintenance of railway systems based on unobserved components models
Reliab Eng Syst Safety
Stopping time optimisation in Condition Monitoring
Reliab Eng Syst Safety
Reliability prediction for condition-based maintained systems
Reliab Eng Syst Safety
On the application of mathematical models in maintenance
Eur J Oper Res
Design condition for incorporating human judgement into monitoring systems
Reliab Eng Syst Safety
An operator support system for research reactor operations and fault diagnosis through a connectionist framework and PSA based knowledge based systems
Reliab Eng Syst Safety
An experiment of state estimation for predictive maintenance using Kalman filter on a DC motor
Reliab Eng Syst Safety
State estimation for predictive maintenance using Kalman filter
Reliab Eng Syst Safety
A Bayesian approach to event prediction
J Time Series Anal
The control of the setting up of a predictive maintenance programme using a system of indicators
Omega
Cited by (51)
Data-driven prognostics and health management (PHM) for predictive maintenance of industrial components and systems
2023, Risk-informed Methods and Applications in Nuclear and Energy Engineering: Modeling, Experimentation, and ValidationForecasting: theory and practice
2022, International Journal of ForecastingCitation Excerpt :Here, well-known forecasting models as VARIMAX/GARCH (see also Section 2.3) are successfully used (Baptista et al., 2018; Cheng, Yu, & Chen, 2012; García, Pedregal, & Roberts, 2010; Gomez Munoz, De la Hermosa Gonzalez-Carrato, Trapero Arenas, & Garcia Marquez, 2014). State Space models based on the Kalman Filter are also employed (Pedregal & Carmen Carnero, 2006; Pedregal, García, & Roberts, 2009 and Section 2.3.6). Recently, given the irruption of the Industry 4.0, physical and digital systems are getting more integrated and Machine Learning/Artificial Intelligence are drawing the attention of practitioners and academics alike (Carvalho et al., 2019).
A state-space-based prognostics model for lithium-ion battery degradation
2017, Reliability Engineering and System SafetyExperimental designs for autoregressive models applied to industrial maintenance
2015, Reliability Engineering and System SafetyCitation Excerpt :Obtaining such amount of information is usually cheap either in financial terms or time terms. However, there are cases where the cost of obtaining the information is expensive [7,9,10] or the time consumption is large [11]. For such cases, the issue of selecting optimally the times at which observations should be taken is of paramount importance.
PREDICTIVE MAINTENANCE USING RNN AND LSTM MODELS
2023, Journal of Theoretical and Applied Information Technology