Energy-based fault detection for an auto-thermal reformer

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auto-thermal reformer

Marais H.

12806218

Thesis

submitted in

fulfilment of the requirements for the degree

Philosophiae Doctor in

Computer and Electronic Engineering

at

the Potchefstroom Campus of the North-West University

Promoter:

Prof. G. van Schoor

Co-Promoter:

Prof. K.R. Uren

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I, Henri-Jean Marais hereby declare that the thesis entitled “Energy-based fault detection for an auto-thermal reformer” is my own original work and has not already been submitted to any

other university or institution for examination.

H. Marais

Student number: 12806218

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The effects of the so-called energy-crisis are being felt world-wide. Dwindling natural resources has seen an increase in research efforts to develop new energy efficient technologies, and to man-age existing facilities better. As the petroleum, more generally petrochemical, industry (PCI) is one of the main actors in a fuel-based energy environment the efficient operation of these plants is of foremost importance.

Innovative maintenance paradigms, such as risk- and condition-based maintenance (RBM or CBM), can provide a vast improvement in overall operational efficiency of petrochemical (PC) plants, but is rarely implemented. This lack of implementation can be attributed to several factors, chiefly the lack of proper plant models for the monitoring task. Existing techniques for implementing CBM requires either analytical models or makes use of data-driven model derivation techniques. The former is widely considered to be impractical for large PC plants, almost to the point of being im-possible. Data-driven methods, on the other hand, are often considered inaccurate, and the lack of formal validation methods hampers the trustworthiness of the derived models.

Monitoring of a PC plant is inherently a multi-domain problem as energy, in the form of natural resources, is converted into a form more suited to the requirements of modern systems. For this reason, energy-based monitoring of the PC plant would make sense, at least theoretically; In order to do this, an energy-based representation of the plant is required. Although there are well known energy-based modelling tools (such as Bond graphs), application of these techniques to PC plants pose a significant challenge, both from the modelling, and interpretation perspectives. Du Rand developed a technique for monitoring of a nuclear power plants Brayton cycle that made use of the enthalpy and entropy of various points in the cycle to perform fault detection.

In this work, the technique developed by Du Rand is applied to an auto-thermal reformer (ATR). The auto-thermal reformer is widely considered to be the most economically viable reforming technology and is also the first unit operation in a gas-to-liquids (GTL) process it is thus of critical importance. The primary contribution of this work shows that Du Rands method breaks down when applied to the ATR of a GTL process. Most notably it fails to identify changes in chemical composition of the product (synthesis gas).

With the concepts developed by Du Rand as input, exergy was investigated and considered to be more suitable for monitoring of the ATR. Exergy closely models the intuitive understanding of the physical world, in that it can be created, stored, transferred, and notably destroyed. Physical exergy, the component associated with physical properties (temperature, flow rates, pressure) is a mathematical combination of enthalpy and entropy and this closely follows Du Rands approach. However, chemical exergy also takes into account the amount of substance present, and, perhaps more importantly, the usefulness of said substance. Thus, chemical exergy allows for the detec-tion of composidetec-tional variadetec-tions, which for petrochemical applicadetec-tions of fault detecdetec-tion would be critical.

The identification of Exergy (both physical and chemical) as a usable modelling domain for petro-chemical process plants is considered to be a secondary contribution. It is expected that this will also have specific advantages in terms of hierarchical modelling and a reduction in the computa-tional complexity typically associated with fault detection.

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Firstly, I would like to thank my lovely wife for her unwavering support throughout this arduous journey. Your words of encouragement, and all the late night cups of coffee meant a lot to me. To my friends, Leenta and Andre, you were there in the good times and the bad. I cannot express

the value of your consistent input, words of encouragement, and support in words. Thank you! To my family, thank you for believing in me, and for your words of motivation. To my parents

specifically, thank you for showing me that hard work is always rewarded.

To each and everyone of the McTronX research group, thanks for all the hours spent discussing ideas over a cup of coffee. It is in these seemingly idle times, when the best ideas are born. To my promoters Professors George van Schoor and Kenny Uren, thank you for your guidance

throughout the last four years.

And finally, but certainly not least, to God all the grace. Without the talents and opportunities afforded me by Him, none of this would have been possible.

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List of Figures xi

List of Tables xv

List of Acronyms xvii

List of Symbols & Subscripts xviii

1 Introduction 1

1.1 Contextual background . . . 1

1.2 Motivation . . . 3

1.3 Detailed problem . . . 6

1.4 Possible contribution areas . . . 7

1.5 Research objectives . . . 7 1.5.1 Primary objective . . . 7 1.5.2 Secondary objective . . . 7 1.6 Methodology . . . 7 1.7 Identified contributions . . . 9 1.8 Thesis layout . . . 10 2 Fault detection 11 2.1 Condition monitoring . . . 11 2.1.1 Introduction . . . 11 2.1.2 Maintenance paradigms . . . 12

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2.1.4 Shortfalls . . . 15

2.2 Fault detection . . . 16

2.2.1 General remarks . . . 16

2.2.2 Common definitions . . . 16

2.2.3 Fault detection systems . . . 17

2.2.4 Comparison metrics . . . 18

2.2.5 Quantitative model-based methods . . . 20

2.2.6 Qualitative model-based methods . . . 22

2.2.7 Model-free methods . . . 25

2.2.8 Limitations of classical approaches . . . 26

2.2.9 Hybrid FDI schemes . . . 26

2.3 Energy-based modelling . . . 28 2.3.1 Multi-domain modelling . . . 29 2.3.2 Port-Hamiltonian methods . . . 30 2.3.3 Graph-based modelling . . . 31 2.4 Critical evaluation . . . 32 2.5 Concluding remarks . . . 33 3 Autothermal reforming 34 3.1 Fuel . . . 34 3.1.1 Synthetic fuels . . . 34 3.2 The GTL process . . . 35 3.2.1 Synthesis gas . . . 36 3.2.2 Synthesis . . . 37 3.2.3 Upgrading . . . 38 3.2.4 GTL process summary . . . 39 3.3 Reforming technologies . . . 39 3.3.1 Non-catalytic reforming . . . 39

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3.4 Autothermal reforming . . . 41 3.4.1 Reaction chemistry . . . 41 3.4.2 Reactor vessels . . . 44 3.4.3 Control parameters . . . 45 3.4.4 Commercial deployments . . . 46 3.5 Concluding remarks . . . 46

4 Modelling the ATR 48 4.1 Existing models from literature . . . 48

4.1.1 Rafiee’s model . . . 48

4.1.2 Hao’s model . . . 49

4.1.3 Bao’s model . . . 51

4.1.4 Panahi’s model . . . 52

4.1.5 Comparison of existing models . . . 53

4.1.6 Modelling software . . . 54

4.2 ATR model . . . 54

4.2.1 Simuation software . . . 54

4.2.2 Modelling assumptions . . . 55

4.2.3 Operating points . . . 56

4.2.4 Aspen Hysys®model . . . 56

4.2.5 Model validation . . . 58

4.3 Fault conditions . . . 58

4.3.1 Physical parameter variations . . . 59

4.3.2 Chemical variation . . . 60

4.3.3 Actuator faults . . . 61

4.3.4 Multiple faults . . . 62

4.3.5 Summary of faults . . . 62

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5.1 Theoretical underpinnings . . . 64

5.2 Methodology . . . 66

5.3 Results . . . 69

5.3.1 Limit function sensitivity . . . 69

5.3.2 Qualitative fault vectors . . . 69

5.4 Critical analysis . . . 71

5.4.1 Constant specific heat assumption . . . 71

5.4.2 Limitation of intrinsic properties . . . 73

5.4.3 Substance composition . . . 73

5.5 Benchmark metrics . . . 76

5.6 Concluding remarks . . . 77

6 Exergy based fault detection 78 6.1 Introduction . . . 78

6.2 Exergy-based fault detection . . . 79

6.3 Calculation of exergy . . . 80

6.3.1 Physical exergy . . . 80

6.3.2 Chemical exergy . . . 81

6.3.3 Standard reference environment . . . 81

6.4 Exergy in Aspen Hysys® . . . 82

6.4.1 Status Quo . . . 82

6.4.2 Existing attempts . . . 82

6.4.3 Proposed implementation . . . 83

6.5 Component results . . . 86

6.5.1 Limit function threshold . . . 86

6.5.2 Intrinsic exergy . . . 88

6.5.3 Extrinsic exergy . . . 88

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6.6 Hierarchical fault detection . . . 91 6.6.1 Motivation . . . 91 6.6.2 Methodology . . . 92 6.6.3 Identification of faults . . . 95 6.6.4 Results . . . 95 6.6.5 Illustrative Example . . . 96 6.7 Critical analysis . . . 97

6.7.1 Advantages of exergy-based FDI . . . 98

6.7.2 Hierarchical exergy-based FDI . . . 98

6.7.3 Shortfalls of exergy-based FDI . . . 100

6.8 Concluding remarks . . . 100 7 Conclusion 101 7.1 Brief summary . . . 101 7.2 Conclusions . . . 102 7.2.1 Energy-based FDI . . . 102 7.2.2 Exery-based FDI . . . 102 7.2.3 Hierarchical FDI . . . 103

7.2.4 Qualitative process modelling . . . 103

7.3 Original contributions . . . 104 7.3.1 Primary contribution . . . 104 7.3.2 Secondary contributions . . . 104 7.4 Future directions . . . 105 7.4.1 Recycle streams . . . 105 7.4.2 Scalability . . . 105 7.4.3 Structural methods . . . 105 7.4.4 Dynamic systems . . . 105 7.5 Closure . . . 105

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A Simulator output data 117

B User variables’ source code 131

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1.1 The SASOL GTL process (from [16]) . . . 4

1.2 A generic GTL process flow . . . 4

1.3 Graphical representation of research methodology . . . 8

1.4 Verification process used . . . 9

2.1 Jardine’s condition monitoring hierarchy [10] . . . 14

2.2 Schematic representation of difference between FDI and FDD . . . 17

2.3 A general diagnostic framework . . . 18

2.4 Venkatasubramanian’s diagnostic spaces [54] . . . 19

2.5 Classification of diagnostic systems (based on [54, 63]) . . . 20

2.6 Schematic representation of a mixing process . . . 23

2.7 Signed directed graph of the mixing process . . . 23

2.8 Typical knowledge silos present in FDI literature . . . 28

2.9 Generalised energy model of unit operation . . . 30

2.10 Bond graph of the hydraulic domain of a simple tank system [77] . . . 31

3.1 Generic anything-to-liquids (XTL) flowsheet [114] . . . 35

3.2 A simple natural gas GTL flowsheet . . . 36

3.3 Typical GTL capital investment . . . 36

3.4 Block diagram of a refinery process. From [119] . . . 38

3.5 Schematic representation of a high-temperature F-T refinery [119] . . . 38

3.6 Schematic representation of an ATR [122] . . . 44

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4.2 Hao’s proposed GTL flowsheet [133] . . . 50

4.3 Bao’s proposed GTL flowsheet [17] . . . 51

4.4 Panahi’s proposed GTL flowsheet [116] . . . 52

4.5 ATR model developed in Aspen Hysys® _{. . . 57}

4.6 ATR model with a post reformer leak modelled . . . 59

4.7 ATR model with fault in the reformer vessel . . . 60

4.8 ATR model with a faulty feed stream . . . 60

4.9 ATR model with a failed CO₂valve . . . 61

4.10 ATR model with a multiple fault . . . 62

5.1 Illustrative example of Du Rand’s Mollier diagrams . . . 67

5.2 Methodology for fault vector creation . . . 67

5.3 Threshold function . . . 68

5.4 Effect of sensitivity threshold value on energy-based diagnostic performance . . . . 70

5.5 Qualitative fault vectors - intrinsic(h, s)data pairs . . . 71

5.6 Graphical analysis result of qualitative(h, s)data pairs . . . 72

5.7 Graphical analysis of qualitative extrinsic(h, s)data pairs . . . 72

5.8 Syngas composition before and after a fault occurs . . . 75

6.1 Szargut’s reference elements [159] . . . 82

6.2 Flowchart of the user variable implementation in Aspen Hysys® . . . 85

6.3 Screen capture of the chemical exergies defined in the Aspen Hysys®_{simulation basis 86} 6.4 Effect of sensitivity threshold value on exergy-based diagnostic performance . . . . 87

6.5 Qualitative fault vectors - intrinsic exergy pairs . . . 88

6.6 Graphical analysis result of qualitative exergy data pairs . . . 89

6.7 Qualitative fault vectors - extrinsic exergy pairs . . . 89

6.8 Example of an energy-based productive structure . . . 91

6.9 Extended ATR model . . . 93

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6.12 Abstracted, exergy model of the ATR plant . . . 94

6.13 Abstracted, exergy model of the ATR process . . . 97

6.14 Abstracted, exergy model of the ATR plant . . . 97

6.15 Exergy-annotated component level diagnosis . . . 97

6.16 Sequential production process with feedback effects . . . 100

A.1 Enthalpy-Entropy approach - Raw data for F1 . . . 118

B.1 Enthalpy-Entropy approach - Raw data for F1 . . . 132

B.2 Enthalpy-Entropy approach - Raw data for F1 . . . 133

C.1 Hierarchical Exergy-based Fault Detection - Raw data for S1 . . . 135

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2.1 Comparison of TBM and CBM criteria [11] . . . 13

2.2 Chemical domain parameters . . . 29

2.3 Electrical domain parameters . . . 29

2.4 Hydraulic domain parameters . . . 29

2.5 Thermal domain parameters . . . 30

3.1 Syngas requirements for various processes (adapted from [5]) . . . 36

3.2 Comparison of various reforming technologies ( [5, 117]) . . . 39

3.3 Syngas H₂:CO ratio for various reforming processes . . . 41

3.4 Kinetic parameters for ATR reactions [124] . . . 43

3.5 Equilibrium constants for ATR reactions . . . 43

3.6 Adsorption constants for ATR POX reaction [127] . . . 43

3.7 Adsorption constants for ATR reactions [124] . . . 43

3.8 Typical ATR operating parameters . . . 46

4.1 Typical ATR operating parameters [132] . . . 49

4.2 Feed conditions and composition for Bao’s model . . . 51

4.3 ATR operating parameters [17] . . . 52

4.4 Panahi’s ATR operating parameters [116] . . . 53

4.5 GTL model comparison - Plant architecture . . . 53

4.6 ATR modelling comparison - Simulation parameters . . . 54

4.7 ATR model operating parameters . . . 57

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5.1 Entropy and Enthalpy relationships for common open systems . . . 65

5.2 Typical simulation output . . . 68

5.3 Normalised fault data . . . 68

5.4 Qualitative data after threshold application . . . 68

5.5 Correlation between extrinsic (h-s) data pairs and syngas metrics . . . 76

6.1 Validation data for physical exergy validation . . . 85

6.2 System level faults . . . 95

6.3 Results of hierarchical exergy-based FDI scheme: Plant level . . . 96

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FDI Fault detection and isolation

FDD Fault detection and diagnosis

GTL Gas to liquids FT Fischer-Tropsch LTFT Low-temperature Fischer-Tropsch HTFT High-temperature Fischer-Tropsch CM Condition monitoring IT Information technology TBM Time-based maintenance CBM Condition-based maintenance

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List of symbols

h Intrinsic enthalpy s Intrinsic entropy H Extrinsic enthalpy S Extrinsic entropy T Temperature R Gas constant p pressure m mass flow Q Heat flow b Intrinsic exergy B Extrinsic exergy

List of subscripts

0 Reference point or environment

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Introduction

In this chapter the raison d‘ˆetre for this study, as well as the detailed problem description, methodology and original contributions are provided. Additionally, a breakdown for the entire work is also provided on a chapter-by-chapter basis.

1.1 Contextual background

With the world’s population ballooning to over seven billion people, the demand for energy has never been higher. The higher energy demand forces higher consumption of fossil fuels. It is well known that the fossil fuel reserves (oil, natural gas, and coal) are finite and are being depleted at an alarming rate. Currently crude oil remains the principal source from which motor fuels and other organic synthesis products are manufactured [1].

Over the last few decades Brent crude prices have skyrocketed from $20-25 per barrel in 1999 [1] to between $80-120 per barrel over the last five years (2010 to 2015). The increasing cost of Brent crude is likely to continue well into the future. Considering that Brent crude reserves are expected

to only last for a further 50 years∗†_{[1], the increase in Brent crude prices is expected to persist. The}

outlook for coal reserves are less dire and it is estimated that 53000 billion barrels (oil equivalent)

are still‡available [1], and that proven natural gas reserves sit around the 30000 billion barrels (oil

equivalent) mark [1]. Even though there is much debate on the accuracy of the reserve estimates, it is obvious that coal presents a viable alternative to crude oil. The contribution of nuclear and renewable energy sources (wind, solar, and photovoltaic) to the total energy production capacity is estimated to be less than 10% [1], although this is expected to change over the coming decades as countries strive towards a more sustainable energy source. In the South African context coal is likely to dominate the energy landscape for at least another 20 years.

The process of transforming fossil fuels such as natural gas and coal into usable products is well established. Depending on the specific fossil fuel used as feedstock, the process is either referred

∗_{Rate of consumption: 40 billion barrels per year} †_{from the year 2000}

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to as gas-to-liquids (GTL) [1] or coal-to-liquids (CTL) [2]. At the core of both CTL and GTL tech-nology is a process referred to as Fisher-Tropsh (F-T) synthesis (FTS) [2]. During F-T synthesis, syngas (a mixture of carbon monoxide and hydrogen) is reacted with steam in the presence of a catalyst to form liquid products [1, 2]. The liquid products are then further processed to produce usable products ranging from waxes to transportation fuels.

Sasol is currently the world leader in commercial CTL technology [3, 4], and produces approxi-mately 30% [4] of the South African petrol and diesel requirements (by means of both CTL and GTL). The indirect liquifaction of coal (ICL) has an overall efficiency of about 50% [3] and taking into consideration that ICL is costly from a captital expenditure point of view [3], the overall prof-itability of any ICL operation boils down to plant efficiency. In the case of GTL technology, similar arguments can be made due to the similarities between the two processes. In the case of the GTL plant, the ICL process is replaced by a suitable reforming process [5]. Sasol’s GTL technology is currently (early 2000s) experiencing growth, especially in the international market, and is thus of more interest than the, largely, local CTL market.

When considering improving the efficiency of a plant, one might consider one of two aproaches i.e., process automation and operation optimisation. The aim of process automation, commonly referred to as advanced process control (APC), is to automatically control the process (typically by computerised means) such that an optimal working point is maintained [6]. This ensures that minimal energy wastage occurs due to the plant operating at suboptimal conditions. It has been shown that improvements in energy efficeincy of process plants due to APC can be as high as 5% [7] although this figure significantly reduces in plants already employing APC technology. Operation optimisation is accomplished by the deployment of operational research techniques to streamline plant operation and thus improve the overall efficiency, without necessarily affecting the technical efficiency of the process.

Maintenance planning forms a critical part of such a plant-wide optimisation effort. Maintenance is defined as the process of preserving a condition by the Oxford English dictionary and forms part of the key workflows present in any system life-cyle [8]. The study of maintenance and optimal

maintenance schedules has recieved much attention in recent years§ [9]. Historically,

mainte-nance was conducted reactively (run-to-failure or breakdown maintemainte-nance), with maintemainte-nance actions only being carried out if the device or component was no longer functional [10, 11]. Later on the maintenance philosophy evolved towards a more preventative paradigm. Preventative maintenance aims to replace components before complete failure occurs [10], and is primarily a time-based maintenance scheme [11]. Preventative maintenance is currently the dominant main-tenance paradigm in industry. In a review by Jardine [10] preventative mainmain-tenance is considered to be one of the main expenses of industrial operations. Although preventative maintenance aims to reduce unexpected failures, failure free operation is not guaranteed.

An improvement on preventative maintenance is predictive maintenance. In a predictive main-tenance paradigm the aim is to make use of prediction algorithms (specifically diagnostic and prognostic algorithms) to determine when to take maintenance actions [9–11]. In order to apply the aforementioned prediction algorithms, the condition of the equipment must be determined. The parameters to take into account when determining a machine, or component’s condition (state of health), is well documented for rotating machines (electric induction machines being the most common) [9, 10] and bearings. Some attention has also been given to the drive electronics and rotor-blades of wind turbines. Unfortunately, the parameters that could be used for condition

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monitoring of an entire petrochemical plant have not yet been determined. Furthermore, the highly coupled nature of such a plant would require special attention to the selection of monitor-ing parameters. One possibility is to make use of energy as the main, preferably sole, monitored parameter. In the work of Du Rand [12] entropy and enthalpy graphs were used to monitor the performance of the Brayton cycle of a nuclear power plant. Fundamentally, this boils down to using energy to model the behaviour, and thus also the condition, of the cycle.

The use of energy has received significant attention in two decades leading up to this work, es-pecially within the control systems domain [13]. One possible reason for this is that fundamen-tally all machines are simply energy conversion devices. In the case of an inverted pendulum, for instance, electrical energy is converted into potential energy and the controller simply aims to maximise the potential energy whilst minimising the electrical energy requirements. From a thermodynamic perspective, a petrochemical plant is simply an energy conversion process, with energy input, output, and energy losses and, although the energy can take on several forms it pro-vides a simple domain within which to model the system with only a single parameter, Energy. The use of energy as a modelling parameter has been illustrated by Chinneck et. al. [14, 15]. Al-though, it should be noted that in the work of [14] the graph-based approach followed is closely related to bond-graphs and didn’t have a condition monitoring focus. However, theoretically, the total energy-flow signature of the plant (or a component in the plant) can be determined, and this energy signature can then be further processed to determine the condition of the plant, thus using energy as the sole parameter when performing condition monitoring of a petrochemical plant. An additional benefit of using energy as a universal parameter is that the monitoring can take place from plant level right down to component level.

1.2 Motivation

A survey of scientific literature on condition monitoring resulted in a vast amount of information. This, however, is not surprising as condition monitoring has become more prevalent since late in the 20th century and has been applied mainly to rotating machines, specifically bearings [10, 11]. In order to understand the complexities of condition monitoring within a petrochemical plant, specifically a GTL process plant, a short introduction to the GTL process must be provided. A GTL process plant transforms natural gas into a liquid, and although the specific architecture and technology of each process plant is different, the process remains fundamentally the same. A pictographic representation of the Sasol GTL process [16] is shown in Figure 1.1.

The natural gas feedstock mostly consists of methane (CH₄) but also contains other hydrocarbons,

nitrogen, and sulphurous compounds [17]. Although not shown in Figure 1.1, the natural gas is processed to remove undesirable components before being fed to the reformer. In the reformer the natural gas is broken down to form a blend of carbon monoxide and hydrogen (referred to as syngas) [1]. It is common to find reformer models ranging from simple thermodynamic models, right through to CFD models including the complex chemical kinetics involved in the reactions. The Fischer-Tropsh reactor (Slurry Phase Reactor as in Figure 1.1) forms the core of the Sasol GTL process and is responsible for conversion of syngas, by the addition of water and heat, into liquids of varying degrees of viscosity. The output of the reactor can be adjusted to produce liquids ranging from waxes to naphta depending on the operating conditions of the reactor itself [1]. It is important to note that the products produced by the F-T reactor cannot be used directly as fuel,

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FIGURE 1.1: THESASOL GTLPROCESS(FROM[16])

and needs to be further refined (also known as upscaling) before it can be used as such. As is the case for the reformer, models of varying complexity exist for the F-T reactor.

Condition monitoring in its broadest sense has been applied for several decades to mainly rotating machines (typically induction motors) [9, 10, 18], and bearings [10, 18]. In recent years similar concepts have also been applied to wind-turbines [19], transformers [20, 21], and tool wear [22] in milling operations. Condition monitoring techniques were also applied to the Brayton cycle of a nuclear powerplant by Du Rand [12, 23–25], and also to machines within power plants [26]. However, the literature on the application of condition monitoring to large-scale industrial process plants, and petrochemical plants in particular, remains sparse.

One possible reason for the lack of condition monitoring of petrochemical plants is the nature of the plant itself. Most control systems can be classified as either being open-loop or closed-loop. When considering the GTL process (Figure 1.2) it can be considered as either a fed-batch or continuous fed-batch [6] process. Even though these processes are common in industry (paper manufacturing and aluminium refining [6] being typical examples), the GTL process in Figure 1.2 represents unique challenges.

FIGURE 1.2: AGENERICGTL PROCESS FLOW

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the feedstock composition. There will be a certain degree of composition variability in the natural gas feedstock, and subsequently plant operating parameters although the quality and quantity of production should remain relatively constant.

If one excludes statistical process control techniques as a condition monitoring method (which would be a crude method), no literature could be found on the application of condition monitoring to a petrochemical plant. It is generally the case that condition monitoring is only applied to a rotating machine, bearing, or pump [27] within the plant. In a case of condition monitoring of a pump [28], the main objective was to calculate the optimal maintenance point, given the economic factors involved and this is put forth as the main reason for the deployment of condition monitoring. The value that condition monitoring can provide is well entrenched in the risk-based maintenance (RBM) paradigm [29]. In a RBM environment the probability of failure is used to calculate the failure cost, and the failure cost is, in turn, used to perform optimal maintenance planning. It is argued that a reduction in maintenance downtime leads to a more profitable [27,28] and overall more efficient plant. It is also interesting to note that a hierarchical approach to RBM was only recently suggested in [29].

In a review article by Jardine [10] the components of a condition monitoring system is outlined, i.e., parameter monitoring, diagnostics, and prognostics. Parameter monitoring is the simplest layer of a CM system and simply involves the processing of the monitored signal, or parameter, by suitable means. In this case suitable might refer to either time or frequency-based techniques. Techniques employing wavelets allow the simultaneous analysis of both frequency and time do-main information at variable resolution scales [18]. Wavelet techniques have been employed for the condition monitoring of roller bearings [18] and, interestingly, the concept of signal energy was used to perform automated wavelet selection. Although the monitored parameter (vibration in the case of roller bearings [9] and rotating machines [10]) is typically only a single measurable value, derived parameters (by techniques such as sensor fusion [30]) can also be used.

In the work of Du Rand [12, 23–25] a novel approach was used for condition monitoring (Health monitoring according to Du Rand) of a Brayton cycle of a nuclear power plant. The approach entailed the use of the enthalpy ,h, and entropy ,s, graphs (h-s graphs) to determine the signatures of the process. Although this approach proved to be effective in terms of fault identification, it is unlikely that it could be applied as-is to a petrochemical process plant, specifically a GTL plant. The main reason for this is that the Brayton cycle considered by Du Rand is a thermodynamically closed system whereas a typical GTL process is closer to an open system even though there is a cyclic component to the operation of such a plant. Similar arguments can be made with regards to the shortfalls of condition monitoring techniques as applied to rotating machines and bearings. The concept put forth by Du Rand is essentially based on the thermodynamic characteristics, and thus, broadly speaking energy characteristics, of the Brayton cycle. If the h-s graph approach of Du Rand could be extended to the realm of petrochemical process plants, or indeed the petro-chemical industry as a whole, it would be highly beneficial. Specifically the robustness of the h-s graph technique to variations in operating conditions is of interest. Additionally, the energy-based approach used by Du Rand might also lend itself to the decoupling of sub-processes within the GTL-process. The latter would be particularly advantageous considering the vast scale of indus-trial process plants.

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1.3 Detailed problem

Inefficient maintenance procedures conducted at petrochemical process plants affect the entire plant’s efficiency and profitability. Condition monitoring is a mechanism by which the mainte-nance of machines can be optimised but existing methods fail when applied to industrial plants. Since the application of condition monitoring is based on the assumption that anomalous con-ditions can be detected, specifically the mechanisms and techniques used to detect and identify faulty conditions are of concern. In this work the detailed problem being considered is the break-down of existing fault detection and isolation (FDI) schemes in the petrochemical industries. Modern petrochemical process plants can be considered amongst some of the most complex en-gineering systems. Add to this the highly sensitive nature of actual process plants’ development and operations, and some simplifying assumptions will have to be made.

Representative complexity In order to explore the breakdown of existing FDI techniques within

the petrochemical process industries, a plant with representative complexity is required. At a minimum, thermal, fluid, and chemical domains must be included, although no specific requirements are made with regards to process controls. Considering that the production of synthesis gas is the most costly of the entire GTL process (synthesis gas preparation in Figure 1.2), this will be selected as a process of representative complexity. Since autothermal re-forming is most commonly deployed in the GTL industries, the rest of this work will focus on autothermal reforming as a means of producing the required synthesis gas.

Validity of simulation data Obviously, the verification aspects associated with FDI doesn’t lend

itself well to real-world process plants. For this reason, a validated process model in a rep-utable process simulator will be used as the plant. It is assumed that a process simulator

such as Aspen Hysys® will provide accurate results if the model being simulated can

rea-sonably be considered as being representative of real-world implementations. The latter is of specific importance, as physical plant design data cannot be obtained, and the design of a petrochemical plant falls outside the scope of this work.

Sensors For the purposes of evaluating the feasibility of the energy-based approach to FDI, it is

assumed that the energy flows can be measured at all points in the process. Although this is not realistic, the intent is not to determine the real-world applicability of the technique, but rather, if such an approach is theoretically feasible. For similar reasons, all measurements that would typically be provided by means of sensors are assumed to be perfectly accurate, noise-free, and time invariant.

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1.4 Possible contribution areas

Considering the vast scope of fault detection and isolation (FDI), it is not surprising that multiple areas of possible scientific contribution can be identified. Broadly speaking the following are areas where a scientific contribution can be made:

• Development of FDI scheme applicable to an ATR process plant;

• Investigating the suitability of Du Rand’s techniques to petrochemical process plants, and

the ATR specifically;

• Identification of a suitable parameter for modelling and monitoring of a petrochemical

pro-cess plant such as the ATR.

1.5 Research objectives

1.5.1 Primary objective

In this work the primary focus falls upon determining the suitability of the techniques developed by Du Rand to petrochemical processes. In order to accomplish this Du Rand’s techniques will be applied to a representative ATR process model.

1.5.2 Secondary objective

Should Du Rand’s techniques be unsuitable, the identification of a suitable modelling and moni-toring parameter for petrochemical processes is of concern.

1.6 Methodology

After the relevant literature is presented the engineering effort of this thesis commences in

Chap-ter 4. A representative model of an autothermal reformer is developed in Aspen Hysys® and

the developed model is validated against known operating points (presented in Chapter 3). A selection of single faults were identified that constitutes a representative sample of all possible faults. Additionally, a single multiple fault was included, as to ascertain the suitability of the FDI techniques to multiple fault scenarios. Du Rand’s techniques are specifically developed for thermodynamically closed systems. Since the ATR under consideration in this work is a ther-modynamically open system, suitable modifications were made that allow the application of Du Rand’s techniques to thermodynamically open systems. After the application of the modified ver-sion of Du Rand’s techniques, the technique was found to break down. Analysis of the underlying thermodynamic principles, resulted in the reasons for the failure as well as possible means of ad-dressing the identified shortfalls. Exergy is presented as a possible solution to the shortcomings

of Du Rand’s energy-based approach. Unfortunately, Aspen Hysys®does not support the

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the simulation environment. After these extensions were validated, the proposed technique was applied to the ATR process as before. Analysis revealed that the exergy-based scheme provided improved detection and isolation performance. Additionally, the additive nature of exergy al-lows hierarchical FDI. The ATR process model was extended, and a selection of faults identified that would allow verification of the hierarchical FDI scheme. By means of a selected example the suitability, and usability of the proposed exergy-based hierarchical FDI scheme is illustrated. The methodology outlined above is schematically presented in Figure 1.3.

Research question Development of autothermal reformer model Literature study Application of Du Rand's energy-based method Development of a exergy-based fault detection scheme Hierarchical application of the exergy-based FDI scheme Application and evaluation of exergy-based FDI scheme

AND

Validated process model

No Y Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 1 Conclusions and recommendations Chapter 7 Is Du Rand's energy-based technique feasible Provide reasons for the failure

Extend the simulation capabilities of

Aspen HysysR

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When developing an FDI scheme, or evaluating an existing scheme in a new environment, verifi-cation of the results is typically of concern. As mentioned, it is assumed that real-world verifica-tion of the techniques cannot be accomplished. For this reason a validated process model is used in lieu of access to a real-world installation.

This simplifies the verification of the FDI technique somewhat, as it allows specific faults to be introduced under controlled circumstances. Schematically, this is represented in Figure 1.4.

Validated process model Capture simulation data of faulty condition Induce fault condition Process simulation data with selected FDI technique Fault diagnosable Fault isolable N N Y Y Known fault (Verification process)

FIGURE 1.4: VERIFICATION PROCESS USED

1.7 Identified contributions

The primary contribution of this work is showing that the application of Du Rand’s techniques to petrochemical processes breaks down. In order to accomplish this, some implementation mod-ifications to Du Rand’s techniques were required. A critical analysis of theoretical underpinnings of Du Rand’s technique, provided the details for the identified failure.

A secondary contribution is the development of a novel, exergy-based, FDI scheme for a petro-chemical plant. Exergy-based analysis is common during design phases of process plants but is rarely used as an operational monitoring tool. An analysis of the suitability and limitations of the proposed exergy-based technique identified the potential advantages and limitations. It was shown that the exergy-based FDI scheme has improved performance as compared to the energy-based methods developed by Du Rand.

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An additional contribution is the novel application of exergy as a basis of hierarchical FDI for a petrochemical process plant. Although it can be seen as a form of thermoeconomic diagnosis, the focus is no longer on the economic effects of plant malfunctions but rather on the detection and isolation of faults. Exergy-based FDI lends itself particularly well to hierarchical implementation and this has pronounced advantages for industrial-scale process plants. The latter is especially true, when one considers that exergy allows the structural information (inherent in the plant) to be used during a qualitative modelling phase.

1.8 Thesis layout

A historic perspective on condition monitoring and fault detection and isolation, as well as how these two fields are related is covered in Chapter 2. Additionally a brief perspective on the merits of energy as a measurement parameter is also provided. Chapter 3 presents details of the overall gas to liquids process and some of the challenges associated with these processes. More detail, of specifically the auto-thermal reformer, as well as the process model developed is presented in

Chapter 4. Chapter 5 details the application of Du Rand’s method to the GTL process, elucidates

the shortfalls of said method, and proposes an alternative diagnostic method. The performance of the alternative method is investigated in Chapter 6 and concluding remarks are made in Chapter 7.

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Fault detection

A historic perspective on condition monitoring is provided. Fault detection and isolation techniques are dis-cussed and how this relates to condition monitoring. The chapter closes with a brief introduction to the merits of energy as a modelling parameter

2.1 Condition monitoring

2.1.1 Introduction

According to the Handbook of Condition Monitoring [31], condition monitoring (CM) can be defined as a holistic multidiscipline based on systems thinking. To this end, CM encompasses aspects of economics, instrumentation, IT, management, detection of faults and failures, prediction of failures, diagnostics and prognostics, maintenance procedures, and legal issues.

Modern industry is under increasing pressure to be more profitable, whilst at the same time being more efficient and environmentally friendly. According to Rao [31] there are three main aspects with which profitability can be increased:

• Increased availability of physical resources (feedstocks);

• Improved quality of human resources (higher skilled workers);

• Improved manufacturing methods and techniques (manufacturing and maintenance).

When one considers a petrochemical plant and the situation with regards to natural resources, increasing the availability of feedstocks is simply not realistic. Additionally, the highly automated nature of these plants and the skilled workforce employed by such, makes improving the qual-ity of the workforce also of little value. What remains then, is improvement in the process and associated operation thereof.

When one considers the cost of a failure the repair cost is foremost. However, this is not the only cost associated with a failure, and indeed, can even be the smallest cost incurred (see [32]).

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Additional (so called “hidden”) costs include loss of production, poor customer service, poor product quality, loss of machinery or other assets and (in extreme cases) loss of life [31, 32]. A perusal of the literature on condition monitoring reveals that the term itself is used somewhat ambiguously. In most cases condition monitoring implies that the maintenance process is in some way affected or informed by the condition of the machine in question. Technically this results in condition-based maintenance being performed. However, most of the condition monitoring literature refers to the actual determination of the condition of the part in question. For this reason, it is thus sensible to briefly consider the dominant maintenance paradigms.

2.1.2 Maintenance paradigms

During the rise of the industrial era, maintenance processes were primarily corrective, meaning that a piece of machinery was run to failure and then repaired [11]. For modern large-scale indus-trial processes this obviously has dire consequences. Currently maintenance processes involves regular shutdowns and replacement of critical components. Such maintenance processes are com-monly referred to as time-based maintenance (TBM) [33] or periodic maintenance [11]. Although TBM processes can lead to high-reliability systems but does so at an, often, excessive cost [33], it also assumes that component failure will occur at fixed intervals. Typically in TBM paradigms all key components will be replaced, regardless of the necessity thereof. The primary reason for this that that the risk (and associated cost) of a component failure simply exceeds the replacement cost. The regular transients caused in plant operations due to the implementation of TBM leads to in-efficiencies and thus also reduced profitability. Condition-based maintenance (CBM) is the most modern and popular technique to address the shortfalls of TBM [34], although it is not necessarily new concept; Initial work in this field was done in 1975 [11]. CBM attempts to inform the main-tenance process based on information gathered by a condition monitoring process [10]. The chief motivation for this is that 99% of components failures are preceded by some form of observable phenomenon [35]. Perusal of the CBM literature reveals that it is a very active research field span-ning from theoretical developments to practical implementations [10]. This poses the question as to why CBM has not yet replaced TBM as the dominant maintenance paradigm? With reference to Table 2.1, it is clear that there are three distinct activities in any maintenance paradigm. Data collection, albeit either failure-based data (typically supplied by OEMs [11]) or sensor data, some analysis of the data (modelling of sorts), and finally a process activity which affects the mainte-nance process itself.

2.1.3 Historic developments

In a review article by Jardine, the Process activity (see Table 2.1) is further expanded to include both diagnostic and prognostic elements. Since these are two distinctly different objectives, we present the historic developments according to the hierarchy developed by Jardine (depicted in Figure 2.1).

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TABLE 2.1:COMPARISON OFTBMANDCBMCRITERIA [11]

Time-based Condition-based

Principle

Collection Uses failure-time or user-based data Uses any parameter that indicates equipment conditions

Practical issues • Availability of failure data

• Very sensitive to recording errors • A set of adequate failure data is

difficult, time consuming, and expensive to gather

• High data collection costs [33] • Exposed to noise effects

Principle

Modelling Uses reliability theory Deterioration modelling Practical issues

• Unrealistic assumptions • Constant operating conditions

assumed

• Only effective for equipment in deteriorating state

• Requires large data sets • Data cleaning is required

Principle

Process Use of optimisation approach Use if failure prediction Practical issues

• Difficult to model and interpret • Decision model is not always stable • Time consuming model development • Limited practical value

• Insufficient time if current condition estimates are used

• Low reliability if future condition estimates are used

• Determination of failure limits may be biased

Data collection and processing

It can be argued that the data collection phase of any CM system is the most important, as this is which every decision will be based upon. It has been well documented that failures are preceded by some observable phenomenon [35]. Data collection can be classified as either on-line or off-line [10, 11]. In the case of on-off-line measurement data is collected continually, whereas off-off-line measurement is concerned with the periodic collection of data (after a certain number of hours, etc.). Regardless of the measurement mechanisms, it is not surprising to find several attempts at determining which parameters to measure.

Due to the sheer volume of condition monitoring literature available, a brief discussion of the salient efforts will be discussed here. The roots of condition monitoring lies in vibration moni-toring, and as such it is no surprise that this area still receives a lot of research attention. Review articles can be found on condition monitoring based on vibration analysis [36], condition monitor-ing in aircraft turbines [37], wind turbines [38,39], electrical motors [18,40–42], stationary electrical

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Data processing Diagnostics Prognostics

Data acquisition

FIGURE 2.1: JARDINE’S CONDITION MONITORING HIERARCHY[10]

machines [9, 20, 34, 43–45], and even switch-mode power converters [46] are common.

It is, however, notable that most of the literature on condition monitoring can broadly be classified into:

• Vibration monitoring;

• Sound or acoustic monitoring;

• Lubricant monitoring;

• Electrical monitoring.

Condition monitoring within process plants proves to be a significantly less active research field. Nuclear power plants have received the bulk of the attention (most likely due to safety issues) [12, 24, 25, 47, 48]. It should be noted that in the work of Du Rand [12, 24, 25] the Brayton power cycle of the plant was monitored, whilst other authors focused on improving manual processes by means of intelligent system techniques [47], or the monitoring of individual components [48]. According to Jardine collected data can be classified as [10]:

Value type: data that is singular. For example, pressure, temperature, and flowrate;

Waveform type: data is collected as a time series. For example, vibration data;

Multidimension type: multidimensional data such as x-ray images or thermographs.

For each of the data types, specific processing techniques dominate classical literature. In the case of waveform type data, time-domain techniques such as moving averages are common [10], al-though statistical techniques such as principal component analysis are gaining traction [49, 50]. In terms of frequency-domain analysis, the fast Fourier transform (FFT) or other spectral decompo-sition techniques are common [10]. Recently the wavelet transform has successfully been applied to the condition monitoring of induction machines [45], and it has also been applied with similar success (see [10]) to wind turbine rotor blades and other rotating devices.

Although the use of value type data appears to be more simplistic from an analysis point of view [10], this is however not the case. The main challenge associated with value-based data is the

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complex correlations and interactions between the various variables. This effect is exasperated when the number of variables increases, such as is typical in a petrochemical plant [49, 50]. In the broader context of a process plant, current literature seems to be more technique focused, and is thus more concerned with the detection of abnormal conditions than with the diagnosis, or even prognosis, of such abnormal conditions.

Diagnostics and prognostics

Once a suitable parameter (or set of parameters) has been identified, collected, and processed the next phase of a condition monitoring system is to perform diagnostic and prognostic functions [10, 31]. Although the classification of diagnostic techniques differ between authors ( [33] lists statistical, model-based and signal-based, whilst [10] mentions statistical, artificial intelligence, and residual generation), in general the diagnostic functions can be achieved. The situation is however, less rosy when considering the prognostic (estimation) functions with several authors [9, 10, 33] noting that there is still much work to be done in order to achieve reliable prognostics. Due to the sheer scale of industrial process plants, including petrochemical, it is not surprising that data-driven techniques [9] are increasingly receiving attention [49–51]. Jardine [10] notes that two of the main issues with artificial neural network (ANN) based diagnosis is the inability of the sys-tem to provide physical explanations, and the associated difficulty in training the ANN. Although expert systems could address the lack of physical explanations of ANNs, this too deteriorate when handling very large data sets (a phenomenon known as combinatorial explosion [10]).

2.1.4 Shortfalls

Although one could argue that petrochemical plants would suffer from similar negligence as other industrial systems (most notably poor maintenance processes) [31] this would be short-sighted, as most of the major energy accidents between 1907 and 2007 can be attributed to human factors (either operator or designer [32]). Due to the energy intensification exhibited by modern society, the frequency of energy disasters is likely to increase. According to [32] there are four factors that contribute to failure of large-scale industrial plants, complexity, tightness of coupling, speed of interaction, and human fallibility.

Other authors [49, 50, 52], have also noted the complexity and coupling problems, when attempt-ing to apply condition monitorattempt-ing to process plants, with some even arguattempt-ing that most imple-mentations pay little attention to these challenges [52]. A typical solution would be to deploy a dimensional reduction technique [53], although this is not proven to be successful due to the non-linearities of process plants.

Jardine [10], further notes that if data-driven analysis techniques were to be deployed, a decou-pling of the process elements could lead to improved execution performance. It would thus ap-pear that the seminal work done by Du Rand [12], could provide the required dimensional re-duction, as well as the decoupling of process elements, which have been identified as the chief implementation issues in condition monitoring.

Although much work remains to be done in terms of the diagnostic and, especially, prognostic functions, the acquisition and analysis of suitable data needs to be addressed first. Jardine notes

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that model-based machine diagnostics can be considered as an alternative method to the data-driven methods already discussed. As this falls into the realm of fault detection and isolation, this will be discussed next.

2.2 Fault detection

2.2.1 General remarks

Fault detection and diagnosis is the central component of abnormal event management [54]. Ab-normal event management (AEM) or abAb-normal situation management (AMS) [55], has received increasing attention from academia. Whilst a fault in a plant may not lead to a fatal disaster (in-terlock shutdown will occur once the fault condition is beyond certain designed levels) [55]) a loss of productivity or a reduction in product quality will occur. The need for ASM is even more pro-nounced if one considers that the economic losses associated with abnormal situations in petro-chemical industries in the US alone is estimated to be around the $20 billion a year mark [54, 55]. Historically, trained operators could be entrusted with the fault detection responsibilities, how-ever due to the increasingly complex structure of these plants (as noted by [32]) the task is becom-ing almost too complex for humans. This is also the case with highly skilled operators [55]. It is not surprising if one considers that modern petrochemical plants can have thousands of control loops that are monitored on time-bases ranging from every few seconds to once per minute [49], that the bulk of industrial accidents can be attributed to human failure [32]. Initial attempts at solutions to the detection of abnormal situations were based on simple limit checking [56, 57], but more advanced methods are required by modern plants.

2.2.2 Common definitions

A perusal on the literature would show that there are several acronyms used to refer to simi-lar aspects within the fault diagnostics sphere, with the more common being fault detection and isolation (FDI) [58] and fault detection and diagnosis (FDD) [59], sometimes also referred to as automatic fault detection and diagnosis (AFDD) [60]. Process fault detection (PFD) [55], is a more common term in older literature, and Ding [61] also mentions fault detection, isolation and analy-sis (FDIA). Regardless of the specific acronym used the following terms require a formal definition:

Fault According to [62] a fault is considered as any deviation of a process, or parameter, from

that which is considered to be normal. Thus a fault can be considered as an abnormality in the process under investigation. Additionally the time-behaviour of the fault can be considered as incipient, abrupt, or intermittent [56].

Failure Underlying cause of abnormalities [56] are referred to as failures, and are considered to

be root causes or basic events [54], which can also be referred to as faults or malfunctions.

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Fault isolation Concerned with determining the root-cause of the fault, or the faulty condition [58, 61].

Fault identification According to [58] and [61], fault identification is concerned with the

magni-tude of identified faults.

Fault diagnosis Fault diagnosis is defined by [58], as a combination of fault identification, and

fault isolation.

2.2.3 Fault detection systems

FDD is considered to be more complete than FDI since, any diagnostic system will require both isolation and identification functions [58, 63] (see Figure 2.2). However, it is common to find that diagnosis is used synonymously with isolation [11, 58]; owing to the fact that the additional cost of identification cannot be warranted.

Fault detection

Fault identification

Fault isolation

FDI

FDD

FIGURE 2.2: SCHEMATIC REPRESENTATION OF DIFFERENCE BETWEENFDIANDFDD

According to [54] an FDD system must be able to detect three distinct classes of faults:

• Gross parameter changes;

• Structural changes;

• Malfunctioning sensors and actuators.

Gross parameter changes refers to changes in parameters below the selected level of modelling [54], which in the fault classification of [58] would be considered a multiplicative fault class. Struc-tural changes, as the name suggests, fundamentally changes the structure of the underlying pro-cess. One could think of this fault class as describing hard failures such as leaking pipes, exploding reactors etc. Alternative literature classifies these failures as additive faults [58].

Although both [54] and [58] agree that sensor and actuator faults are to be considered, the way in which this is done differs. Fundamentally [54] considers this fault class to lead to gross changes, and would thus be considered by [58] to be multiplicative in nature. However, [58] argues that these types of faults are more additive, as the fundamental structure of the process is dependent thereon. This distinction is largely academic, and what is of value is that sensor and actuator faults are considered to be important enough, that an entire fault class is dedicated towards it.

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Furthermore, FDD systems consider the initial state to be normal or fault free [58], and that pro-cess and sensor noise falls outside of the scope of the FDD system [54, 58]. Unstructured uncer-tainties [54], or modelling errors [58] occur when the model cannot sufficiently account for plant behaviour. This may be due to changes in the operating point of the process [58] or simply to faults that were not modelled a priori [54]. Regardless of the cause of modelling error no FDD or FDI system can account for it.

In Figure 2.3 a general diagnostic framework is depicted (based on [54]), with the main sources of faults being indicated. Note that whilst the addition of the diagnostic system didn’t affect the existing feedback control scheme, the placement of sensors with the aim of FDD is receiving increasing attention [64, 65]. Plant controller Sensors Dynamic plant Actuators PROCESS DISTURBANCE STRUCTURAL FAILURE ACTUATOR FAILURE SENSOR FAILURE CONTROLLER FAILURE Diagnostic system Set point

FIGURE 2.3: AGENERAL DIAGNOSTIC FRAMEWORK

Based on Figure 2.3, it should be obvious that several distinctly different approaches can provide suitable FDI systems. Additionally, the specific objective of the FDI system (decision support, abnormal situation management, etc.) will also dictate specific architectural choices. For this reason comparison of various FDI implementations are critical.

2.2.4 Comparison metrics

In order to compare various FDD schemes, Venkatasubramanian [54] suggests a list of criteria, which is detailed below. It should be noted that the criteria suggested by [54], are to a large extent a combination of other works (as indicated where relevant).

Quick detection and diagnosis: An FDI system must be able to detect faults of relatively small

size, a reasonable time after their arrival [58], including small faults with incipient or abrupt behaviour [56].

Isolability: Refers to the ability of the FDI system to distinguish between different faults [58], or

different types of faults such as sensor, actuator, plant, or controller faults [56].

Robustness: Due to the inherent noise (process, sensor, or model) the capability of the FDI scheme

to function in such an environment is referred to as robustness [58].

Novel identifiability: The ability of the FDI system to determine if a specific condition is normal

or abnormal. In the case of the latter, the decision as to if the abnormal situation is known or unknown, is known as novel identifiability.

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Classification error estimate: An attempt at building the user’s confidence in the system by pro-viding a priori estimations on the classification error.

Adaptability: Ability of the FDI system to adjust over time, a typical example being adjustment

in operating points.

Explanation facility: Refers to the capacity of the diagnostic system to identify the abnormal

con-dition as well as the source thereof.

Modelling requirements: Although the exact modelling requirements vary significantly, one must

be cognicent of the fact that certain methods will require significantly more modelling effort (analytical process models) than others (statistical analysis techniques).

Storage and computation requirements: Recent advances in computing power notwithstanding,

any FDI system will place specific requirements on the required computing power and stor-age requirements. Usually, there is a trade-off between the computation power, storstor-age requirements, and performance of the system.

Multiple fault identifiability: Ability to diagnose multiple simultaneous faults, as enumeration

of all possible combinations of faults is computationally prohibitive (especially for large pro-cesses).

Regardless of the implementation specifics, FDI systems can be seen as classifier systems. In a typical classification system (and a diagnostic system specifically) there are typically four distinct spaces in which operations take place (shown schematically in Figure 2.4.

Measurement space Feature space Decision space Class space

FIGURE 2.4: VENKATASUBRAMANIAN’S DIAGNOSTIC SPACES [54]

The measurement space is a collection of measurements [x1, x2, ..., xn]with no specific knowledge

relating the measurement variables. These measurements are presented to the diagnostic system. Initially the diagnostic system is concerned with determining the key characteristics or features of the measurement space, such that the measurement space is transformed into a feature space

y= [y1, y2, ..., yi, ..., ym]

where yiis the ithfeature.

The transformation from the measurement space to the feature space usually makes use of a priori process knowledge, and aims to satisfy some objective function (such as a discriminant function, or simple threshold [54]). For various reasons, the feature space is usually dimensionally smaller than the measurements space.

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By suitable transformation the feature space is transformed into the decision space d= [d1, d2, ..., di, ..., dk]

such that direpresents a single decision. The decision space is then transformed into M (integer)

fault classes,

C= [C1, C2, ..., Ci, ..., CM]

thus mapping a specific subset of decisions into a specific class of fault. It should be noted that the class space also contains a normal class.

A basic assumption is that the feature space leads to better clustering (especially under fault con-ditions) than the raw measurement space. Mathematically then, this implies a simplification of the discriminant function. It is somewhat typical for the mapping from measurement space to feature space to be done by means of process knowledge, whilst the transformation between the feature and decision space is implemented as either a search or learning algorithm [54].

For an FDI system the a priori knowledge that is required is a set of failures, and the relationship between the failures and the process observations. If the knowledge is based on fundamental understanding, or first principles, it is known as deep, causal, or model-based knowledge [66]. On the other hand, shallow, compiled, or evidential knowledge, is based on historic process data. A further distinction can be made in model-based systems, namely quantitative or qualitative model-based knowledge.

In the quantitative model-based environment, knowledge is encoded in mathematical models based on the fundamental process physics. Qualitative model-based knowledge is centred around different units in the process. This distinction is schematically represented in Figure 2.5.

Quantitative model-based Observers Parity space Kalman filters Qualitative model-based Causal models Digraphs Fault trees Qualitative physics Abstraction hierarchy Structural Functional Process history based Qualitative Expert systems Qualitative trend analysis Quantitative Statistical Principal component analysis (PCA) Partial least squares (PLS) Statistical classifiers Artificial neural networks Diagnostic methods

FIGURE 2.5: CLASSIFICATION OF DIAGNOSTIC SYSTEMS(BASED ON[54, 63])

2.2.5 Quantitative model-based methods

The main requirement in quantitative model-based FDI is some explicit model of the plant under consideration. By comparing the response of the plant, with that of the model, inconsistencies

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(known as residuals) [54] can be determined. However, in order to check for inconsistencies some redundancy is required.

Hardware redundancy is the simplest form, and requires the use of multiple sensors to measure process parameters [58]. Whilst this is common in safety critical systems (such as aircraft) [54], it is not widely deployed due to the excessive costs. Analytical redundancy makes use of the func-tional relations between process variables, and is usually provided by a set of algebraic equations. In the case of chemical processes the analytical model of the plant is usually based on physical first principles such as mass, energy, and momentum balances and constitutive relationships. Analytic models are seldomly used in control and FDI of chemical processes due to the complexity involved in the development of such models [54,56,67], as well as the inherent non-linear nature of chemical processes. Recent advances in non-linear control, and improvements in computing technology have seen an improvement in the use of complex non-linear analytical models.

Observers

The main concern with observer-based FDI is the generation of residuals that are robust [56, 67] to process noise and modelling uncertainties. A set of observers is developed, such that each observer is sensitive to a specific subset of faults. Under normal conditions the residuals generated by the observers are close to zero. Under fault conditions only the observer that is sensitive to the fault generates a significant residual, thus resulting in simple isolation of the fault [54]. For a detailed discussion on observer design refer to [61, 68].

It should be noted that the observer-based approach addresses issues of:

• Isolability;

• Multiple fault detectability.

However, the issue of robustness remains [69] and this is especially true of complex systems. Due to the dependance of the observer on the model of the process, the greater the model dependence on process parameters; which in some systems, are uncertain. Non-linear observer development has also received consideration in the literature [69], and increasingly other computational intelli-gence techniques (such as artificial neural networks, and expert systems) have been deployed in the development of observers [69].

Parity equations

Parity equations are rearrangements and transformations of the state-space model [61] of the pro-cess under consideration [58]. Comparison of the consistency (parity) between plant inputs, and sensor outputs with the plant model leads to the generation of residuals [54]. Ideally, under steady-state conditions, the residuals (or parity equations) should be zero. However, due to pro-cess noise, modelling inaccuracies, gross sensor and actuator errors, and faults in the plant, real residuals are non-zero.

Parity equations are interesting alternatives to observers as the isolability of various faults can be determined a priori. Additionally, Gertler [58] and Isermann [56] showed that parity equations