Architecture for hybrid modelling and its application to diagnosis and prognosis with missing data

Highlights

• An architecture for hybrid modelling is proposed oriented to diagnosis and prognosis.

• Physics-based and data-driven modelling are combined to deal with missing data.

• Context-driven services are identified as the key to increase the results’ accuracy.

• A test case is presented for rotating machinery, determining the state of a bearing.

• A multi-body model and a semi-supervised learning algorithm are used in this work.

Abstract

The advances in technology involving internet of things, cloud computing and big data mean a new perspective in the calculation of reliability, maintainability, availability and safety by combining physics-based modelling with data-driven modelling. This paper proposes an architecture to implement hybrid modelling based on the fusion of real data and synthetic data obtained in simulations using a physics-based model. This architecture has two levels of analysis: an online process carried out locally and virtual commissioning performed in the cloud. The former results in failure detection analysis to avoid upcoming failures whereas the latter leads to both diagnosis and prognosis. The proposed hybrid modelling architecture is validated in the field of rotating machinery using time-domain and frequency-domain analysis. A multi-body model and a semi-supervised learning algorithm are used to perform the hybrid modelling. The state of a rolling element bearing is analysed and accurate results for fault detection, localisation and quantification are obtained. The contextual information increases the accuracy of the results; the results obtained by the model can help improve maintenance decision making and production scheduling. Future work includes a prescriptive analysis approach.

Introduction

Information and communication technologies (ICTs) have made considerable progress in sensing, data storage, data mining, simulation capabilities and online computing. When these ICTs are integrated with physical assets, the result is a cyber-physical system. The internet of things and big data have transformed the connectivity between the elements of an enterprise, leading to the fourth stage of industrialisation, known as Industry 4.0 [1], characterised by smart assets that dynamically interact with each other and with all levels of the business model.

The self-awareness and self-capabilities of cyber-physical systems have an impact on maintenance. Since its first application in the middle of the 20th century to the automotive, military and aerospace industries, condition based maintenance (CBM) has proved to be an efficient maintenance policy from economic and safety points of view. It has many advantages over the two traditional approaches, corrective and scheduled maintenance, including the ability to anticipate fatal failure thanks to updated information on the state of assets. This results in better maintenance planning; tasks are performed only when it is completely necessary, the risk if reaching a faulty state is reduced, and the use of the asset is maximised. Thus, despite the need for an initial investment when first applying this maintenance approach, it reduces the cost of maintenance [2].

CBM, combined with proper decision support systems, leads to a maximisation of resources and increased productivity and, therefore, to business efficiency. Taking this to the next level of analysis and opening the door to 21st century realities, Lee et al. [3] propose a five-level structure (named 5C architecture) for the development of cyber-physical systems within a manufacturing environment. These five levels, shown in Fig. 1, have the following functions: acquiring and storing data using a sensor network; transforming the acquired data into valuable information; connecting the assets to get more knowledge about the individuals using the network information; developing proper human-machine interfaces; and allowing the assets themselves to make decisions about their operation. With this intelligent equipment, the maintenance processes can be automated in such a way as to optimise resources. These tasks require a distributed system framework, as centralising the information decreases the performance [4].

The application of CBM has a number of challenges: defining the problem for which the maintenance policy is to be applied, identifying the application level, measuring performance, selecting the method to apply diagnosis and prognosis, defining the sensing strategy, defining the monitoring strategy, allocating time and resources to conduct experiments, selecting the solution, and, finally, analysing the costs and benefits [5]. This paper focuses on the first step: the methods for carrying out diagnosis and prognosis. The objective of the diagnosis process is to examine symptoms and syndromes to determine the nature of faults or failures (kind, situation, extent), whereas prognosis deals with the analysis of the symptoms of faults to predict future condition and residual life within design parameters [6].

A new trend in modelling combines traditional methods, i.e. physics-based modelling with data-driven modelling [7]. Physics-based modelling is based on the first principles for constructing a set of ordinary or partial differential equations representing the dynamics of the system in certain conditions, even those difficult to achieve by testing. Simulations of different component faults can be done without any cost associated with damage seeding [8]. In contrast, data-driven modelling is based on the construction of a set of equations without any knowledge of the system, simply by relating the inputs to a set of outputs by means of a learning process using a large amount of data obtained from the monitored asset. The combination of these modelling approaches, known as hybrid modelling, uses the advantages of each approach. Its ability to fuse data from different sources could be extremely helpful to maintenance decision making and production scheduling [9].

The new technologies mentioned at the beginning can be used to good effect in hybrid modelling. For one thing, the connectivity of cyber-physical assets allows them to share data and receive information about the required tasks. As a result, they become self-aware and can self-actuate. For another, the computational cost related to the use of physics-based modelling for virtual commissioning is reduced by the use of supercomputers in a cloud computing framework [10]. Moreover, big data capabilities lead to the proper management of the high volume of data stored over the life of the machines of an industry and to improved data mining. In short, hybrid modelling can be used to create smart assets, thereby facilitating and improving CBM.

Despite its obvious promise, at this point, little work discusses hybrid modelling. The diagnosis process is tackled by Matei et al. [11]. They propose a hybrid framework for a railway switch, obtaining accurate results in detection but succeeding only partially in fault identification. Medjaher and Zerhouni [12] present a two-phase methodology for hybrid prognosis. The first phase develops a physics-based model in both healthy and damaged conditions; the second phase computes the residuals when comparing the measurements with the simulation results. These residuals are indicative of the state of the monitored asset; its remaining useful life (RUL) can be computed by comparing the residuals with a predefined performance. A framework called hybrid mathematical informational modelling (HMIM) in which a neural network is used to analyse the differences between the measurements and the mathematical model’s response is proposed by Ghaboussi et al. [13]. They apply the HMIM framework to a beam-to-column connection and conclude that the hybrid approach is capable of representing the issues the mathematical model cannot capture by itself. In contrast, Didona and Romano [14] propose a data fusion framework for measurements and synthetic data generated by a physics-based model and study its implementation in computer systems. Other authors present a data fusion strategy for the prognosis of rolling element bearings (REBs) in flight operating conditions [15] and the degradation of a battery [16]. Data fusion can also relate continuous data with categorical data; the latter type are very common in the real world. Working in this area, Otey et al. [4] suggest a model for outliers and anomaly detection. Although some authors propose frameworks for hybrid modelling [11], [12], [13], there are no clear architectures for this purpose in the research literature.

There are two important things to consider when implementing a CBM strategy for an asset: how to deal with missing data on its reliability evolution and the role of contextual information in its operation.

Maintenance data are formed by pieces of information very different in nature. Data can be acquired from sensors placed at different points of the asset while the operators produce information, either handwritten or digitalised, including work orders, maintenance reports, information about stocks and maintenance planning, among others. These latter records often have poor quality because of inappropriate reporting equipment, missing or lost information during data migration from paper documents to digital sources, unrecorded events, etc. [17].

Another common scenario is a lack of data when assets cannot be operated to their maintenance limit. This situation occurs in many industries, such as the transport, energy or chemistry sectors, in which safety is more important than other factors of efficiency and reliability. Only those elements of low criticality are operated until failure; all components and subsystems affecting the safety of the systems are replaced in early stages of degradation, even far from the maintenance limit, because of strong regulatory conditions. A lack of data also occurs with early replacements of components as a result of opportunistic maintenance [9]. Overprotection and excessive maintenance tasks lead to a situation in which maintainers have little historical information about the behaviour of the assets – a handicap when trying to estimate their future response.

Other reasons for getting missing data or incomplete data are sensor failure, communication failure and storage size restrictions. Thus, there is an interest to prepare the models in advance to overcome these limitations. There are some approaches based on data-driven modelling in the literature, in which some authors use artificial neural networks to improve diagnosis in systems such as wind turbines or cutting machines [18], [19].

It should be highlighted that the aforementioned assets are considered to be systems of systems, characterised by nonlinear structures, with a large scale spatial scope, dynamic and responsive behaviour, and going beyond a single scientific discipline [20]. This implies complexity when implementing a maintenance approach as the interaction between components and subsystems means it is difficult to obtain a complete fault catalogue corresponding to all the individual systems and to the different combinations when they work together and produce new faults.

To summarise, there is a lack of data on the operation of these assets. The amount of data available for maintenance planning is schematically represented in Fig. 2. As the figure shows, few components can be operated until failure (i.e., minimum criticality) or have no degradation. Thus, in the majority of cases, data are obtained until intermediate points are reached between the operating start points and the maintenance threshold. These data points are called suspensions.

Given the lack of data, the use of synthetic data generated by physics-based models describing the operation of the assets is a must. Those scenarios involving common operating conditions can be simulated, as well as those difficult to reproduce in real operation, such as extreme operating conditions or damage situations that cannot be seeded to the system to learn about its behaviour because of safety, economic or environmental reasons. The fusion of synthetic data and acquired data from sensors placed in the assets combining physics-based modelling techniques with purely data-driven methods results in a hybrid modelling approach.

When combining the modelling strategies and fusing data to improve maintenance performance, the concept of context is a key to efficient diagnosis and prognosis [21]. Context is defined as “any information that can be used to characterise the situation of entities (i.e., whether a person, place, or object) that are considered relevant to the interaction between a user and an application, including the user and the application themselves” [22]. This definition, applied to the field of maintenance, means having the appropriate information on the conditions of the operation of an asset. The context includes information such as working temperature, humidity, applied loads, operating speed and information about any other system with which the asset interacts, among others. The context has a great influence on the behaviour of physical assets and should not be omitted. Sensors must be added to obtain this information and provide context-driven services, as shown in Fig. 3.

As mentioned, this paper proposes a framework for hybrid modelling combining the physics-based and data-driven modelling approaches and using both data fusion and context awareness. It suggests a two level architecture. One level is responsible for analysing the condition monitoring (CM) data acquired from an asset for early failure detection. The second level carries out the virtual emulation of the behaviour of the asset and performs deeper analysis using data fusion. The architecture is validated by being applied to a rotating machine; more specifically, the response of a gearbox’s REBs is monitored.

The paper has the following structure. The architecture for hybrid modelling for CBM is proposed in Sections 2 Proposed architecture for hybrid modelling, 3 Validation of the architecture validates the architecture by applying it to a rotating machine; finally, Section 4 offers concluding remarks.