Abstract

Black Swan events are low probability, high impact events that cannot be predicted. These events are typically unprecedented so they are often not accounted for in traditional risk analysis. In civil engineering, these events are of particular importance because their unpredictability can lead to catastrophic consequences. Without the knowledge of the possibility of such events, there is no way to prepare for them or design against them.

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Many events have been referred to as Black Swans, such as 9/11 and the Tacoma Narrows bridge collapse, but the term can be used loosely and is sometimes used as an excuse to justify failures attributed to poor design. Therefore, a clearer framework is required for classifying events as Black Swans. True Black Swans are those events that could not possibly have been predicted beforehand, but this specification can be subjective depending on the observer. The nature of what is considered predictable is largely person dependent and will vary depending on the level of expertise. As a result, the classification of events as Black Swans is usually based on judgement and there is no formal method.

The methods of predicting and mitigating Black Swan events are severely limited. There is lots of uncertainty surrounding these events but their impact is severe and a greater understanding is required to try to reduce their occurrence. The literature review highlights the recommendation of using stress tests as a method to attempt to account for Black Swan events during risk analysis. Stress tests are often used in the finance industry as a method for measuring the resilience of a system under different failure mechanisms. Simulations are undertaken of all the different potential failure scenarios in order to calculate the probability of each scenario occurring and to recognise the weakest points of the system.

The effectiveness of stress testing was analysed through the use of the 2011 Fukushima Nuclear Disaster case study. The stress test was used to calculate the probability of this event happening and to inform the classification of this event as a Black Swan or not. The sequence of events that led to the nuclear reactor meltdown included flooding caused by the tsunami and numerous power failures. The probabilities of each of the possible failure scenarios were calculated using event tree analysis, to understand whether this event should have been anticipated. Sensitivity tests showed the importance of including historical data in analysis because it had a significant impact on the calculated probability of the event. The process of gathering the information required for the stress test, alongside the calculation of the 109 million year return period of the event, led to a strong case for the event being a Black Swan.

The use of a stress test proved to be an extremely useful tool in this risk analysis. It encourages the use of imagination to try to anticipate as many possible failure scenarios as possible, which is the only way to attempt to prevent a Black Swan event. Furthermore, the formation of a stress test requires understanding of the failure probabilities of each component in the system, which in turn emphasises the weakest parts of the system. This promotes more resilient design and building of systems that can cope better with potential Black Swan events. Lastly, the process allowed for sufficient knowledge of the event to be gathered in order to confidently make a judgement about the classification of an event as a Black Swan.

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Overall, this dissertation recommends the use of stress testing in risk analysis to attempt to minimise the chances of Black Swans. Although it cannot anticipate Black Swan events, it gives the best chance of preparing the system to be robust enough to cope with one should it occur. In order to produce the most reliable and informative stress test possible, more historical and modern data collection within the industry about failures and failure probabilities is encouraged.

List of Figures……………………………………………………….

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List of Tables………………………………………………………..

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1. Introduction…………………………………………………….

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2. Literature Review…………………………………………………

2.1. Black Swans………………………………………………….

2.2. Risk Analysis in Civil Engineering……………………………………

2.3. Acceptable Risk……………………………………………….

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2.4. The Fukushima Nuclear Disaster, Japan (2011)…………………………

2.5. Black Swan Mitigation Strategies……………………………………

2.6. Summary…………………………………………………….

3. Methodology……………………………………………………

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3.1. Outline and Aims……………………………………………..13

3.2. Data Collection and Assumptions………………………………….14

3.2.1. Modern Tidal Gauge Data……………………………………….14

3.2.2. 2011 Tsunami……………………………………………….15

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3.2.3. Historical Events……………………………………………..16

3.2.4. Power Failures………………………………………17

3.3. Return Periods of Tidal Data…………………………………….18

3.4. Probability Distributions for Tidal Data………………………………18

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3.5. Maximum Likelihood Estimation…………………………………..18

3.6. Goodness-of-fit………………………………………………19

3.6.1. Tide Height Frequency Curve…………………………………….19

3.6.1.1 Rayleigh Distribution…………………………………..20

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3.6.1.2 Gumbel Distribution…………………………………..21

3.6.1.3 Log-Normal Distribution………………………………..21

3.6.2. Gumbel Plotting Paper…………………………………………22

3.6.3. Chi-squared Test……………………………………………..22

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3.7. Inclusion of Historical Data………………………………………23

3.8. Return Period……………………………………………….25

3.9.  Risk Over Design Life………………………………………….26

3.10 Stress Test Design……………………………………………26

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4. Results and Discussion…………………………………………..29

4.1. Return Period of Tsunami Event…………………………………..29

4.1.1 Return Period Excluding Historical Data…………………………….29

4.1.2. Return Period Including Historical Data……………………………..29

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4.1.3. Conclusion…………………………………………………30

4.2. Risk Over Design Life………………………………………….30

4.3. Stress Testing……………………………………………….31

4.3.1. Stress Test Excluding Historical Data………………………………31

4.3.2. Stress Test Including Historical Data……………………………….32

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5. Conclusions…………………………………………………..33

5.1. The 2011 Fukushima Disaster……………………………………33

5.2. Stress Testing……………………………………………….34

5.3. Black Swans………………………………………………..35

5.4. Limitations………………………………………………….35

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5.5. Recommendations……………………………………………36

References………………………………………………………37

List of Figures

Figure 1: The corresponding action required for each level of risk (Health and Safety Executive, 1992)…….

Figure 2: The Farmer Curve for risk (Nuclear Energy Agency, 1992)…………………

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Figure 3: Sequence of events on 11th March 2011 in Fukushima……………………

Figure 4: The design of the Fukushima plant during the event (Acton, Hibbs, 2012)………

Figure 5: Example of an event tree used in a probabilistic safety assessment (Nuclear Energy Agency, 1992)…….

Figure 6: A summary of the methodology implemented in this dissertation……………..

Figure 7: The layout of the stress test, showing all the possible outcomes during the 2011 Fukushima Nuclear Disaster. The actual sequence of events is shown with red arrows……..

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Figure 8: Location of the tidal gauge at Soma in relation to the Fukushima nuclear power plant (Google Maps, 2017)…….

Figure 9: Annual Maximum Series of Tide Height at Soma, Japan (JOCD, 2016)………..

Figure 10: The tidal gauge data from 1974 – 2010 (JOCD, 2015) compared with the 2011 tide height…….

Figure 11: Plot showing the historical events, tidal gauge data and the 2011 event……….

Figure 12: Maximum likelihood estimation process……………………………..

Figure 13: Tide Height Frequency Curve using the Rayleigh Distribution………………

Figure 14: Tide Height Frequency Curve using the Gumbel distribution……………….

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Figure 15: Tide Height Frequency Curve using the Log-Normal Distribution……………

Figure 16: Comparison of the Gumbel and Log-Normal distributions on Gumbel Probability Paper…….

Figure 17: Frequency curve showing the Gumbel distribution fit to both the modern and historical data…….

Figure 18: Scenarios that form the stress test of the 2011 Fukushima Nuclear Disaster……

Figure 19: Stress test results without including the historical data……………………

Figure 20: Stress test results with the inclusion of historical data……………………

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List of Tables

Table 1: Examples of events referred to as Black Swans in literature…………………

Table 2: Coordinate locations of tidal gauge at Soma, Fukushima nuclear power plant and the epicentre of the 2011 earthquake…….

Table 3: Description of the historical tsunami events and the 2011 event (NGDC/WDS, 2015 and Smits, 2011)…….

Table 4: Probability of failure for each power source in the nuclear power plant…………

Table 5: Probability distributions suitable for tidal data…………………………..

Table 6: Values of parameters calculated through maximum likelihood estimation……….

Table 7: Standard deviation of T-year design event for the Gumbel and Log-Normal distribution…….

Table 8: The upper bin level for Chi-squared calculation………………………….

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Table 9: Calculated chi-Squared values for goodness-of-fit test…………………….

Table 10: Parameters for the Gumbel distribution, when historical events were included and a perception threshold of 690cm was used…….

Table 11: The variables in the 2011 Fukushima Nuclear Disaster……………………

Table 12: Probability of tide height exceeding the sea wall………………………..

Table 13: Calculation of the return period of the 2011 event based on the modern tidal gauge data only…….

Table 14: Calculation of the return period of the 2011 tsunami tide height based on the tidal gauge and historical data…….

Table 15: Calculation of the magnitude of the tide height for an exceedance risk of 10% over 50 years…….

Symbols

Abbreviations

1.    Introduction

The civil engineering industry is responsible for designing and maintaining significant networks of infrastructure. This infrastructure is built and designed to cope with the known risks it faces. However, there are also unknown risks that infrastructure cannot be protected from. These unknown risks are referred to as Black Swans and are described as rare events with an extreme impact that only become predictable after the fact (Taleb, 2007). The term originates from the finance industry to refer to unexpected and unprecedented events that lead to failure of financial systems. Conversely, in civil engineering, these types of scenarios can result in much more catastrophic effects and even loss of life. Therefore, it is important to gain a greater understanding of these events and to configure risk analysis methods to best cope with them. Currently, risk analysis is limited to covering events that have already occurred, and does not consider those that have not happened before. The uncertainty and randomness of such events means that eliminating Black Swans is unrealistic, but the knowledge gained from past events may enable the development of methods to reduce their possibility.

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Defining an event as a Black Swan is difficult because the criterion is extremely vague. Determining whether an event is rare or has an extreme impact is a matter of judgement and can be subjective. Therefore, a framework is required that can be implemented to all events to classify them as Black Swan events. The concern surrounding the subjectivity of the descriptors of a Black Swan is that the term can be used for events that were not truly unpredictable. This can lead to inadequate investigation of the incident because it is deemed too unpredictable to have been prevented.

Although the main characteristic of Black Swan events is their unpredictability, this dissertation aims to explore a method to reduce the frequency of them occurring. The financial industry has implemented stress testing as a tool to aid the discovery of Black Swan events before they happen. This procedure will be analysed to assess the suitability of its application in civil engineering. Performing a stress test involves a thorough scenario analysis, which will identify all the possible scenarios a system can face. This encourages the use of the imagination to identify events that have not happened before, rather than just basing the risk assessment on past, known events. The stress test calculates the probability of each scenario occurring and this informs the design of the system.

This method will be investigated using a case study, the 2011 Fukushima Nuclear disaster. It was an unexpected event that was not prepared for; thus it is a potential Black Swan. However, there have been criticisms of the risk analysis that informed the design of the power plant and there was suspicion that the events could have been predicted. The omission of historical events from the risk analysis and the insufficient height of the sea wall protecting the nuclear power plant are some of the flaws mentioned (Paté-Cornell, 2012). This incident provides a complex case study that will be used to assess the effectiveness of a stress test as a framework for classifying Black Swans and whether it could be a tool for preventing them.

The 2011 Fukushima Nuclear disaster was an intricate event made up of many elements. Some of the contributors include human error and political bias, which cannot be quantified or analysed simply. Therefore, the scenario analysis will be simplified to only consider the tsunami and the power failures that occurred. The stress test will be carried out to calculate the probability of the sequence of events that occurred. This will be found using event tree analysis and the probabilities of each of the components of the failure. Data and failure rates of each of the components were collected to model their failure probabilities. The probability of the event will be used to categorise the nuclear disaster as a Black Swan or not.

The objective is to conclude whether a stress test provides a suitable framework for classifying events as Black Swans and whether the process has any attributes that would be useful in minimising the possibility of Black Swans. This will allow for a recommendation of whether it is suitable for implementation in the civil engineering industry and its potential role in risk analysis.

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2.    Literature Review

2.1.            Black Swans

The term ‘Black Swan’ originates from when black swans were discovered in Australia in the 17^th century. Before this time, people believed that all swans were white and black swans were used as a metaphor to describe impossible events. Following their discovery, this belief was invalidated and the term is now used to represent unlikely and unpredictable events that do actually occur. The idea of Black Swan events has become popularised in the financial sector by Nassim Taleb. Taleb (2007, p xviii) describes Black Swan events as having three attributes, “rarity, extreme impact, and retrospective predictability”. These attributes can have severe consequences because they cannot be accounted for in traditional risk analysis. Risk assessments tend to be based on statistics that are informed by historical data and consequently, any potential unprecedented events will not be acknowledged (Paté-Cornell, 2012). Considering Black Swan events is particularly important within civil engineering because they could result in the failure of critical infrastructure and ultimately, a loss of life. These events will not have been encountered before and therefore, there would be no knowledge to prepare for or mitigate them.

A large number of events have been labelled as Black Swan events but they are supposed to be extremely rare, so questions arise as to whether the term is being used correctly.  Paté-Cornell (2012) suggests that some events are titled Black Swans in order to justify a lack of proactive risk management. Therefore, the concept of a Black Swan can be used as an excuse and simply labels an event as being too unpredictable to be accounted for. Similarly, other events are justified as Black Swans because they were seen as being unpreventable. However, this is not a quality recognised as an attribute of a Black Swan, and alone is not enough to classify an event as a Black Swan. Table 1 shows examples of events referred to as Black Swans in literature and the justification provided for why they fulfil the criteria of a Black Swan.

Table 1: Examples of events referred to as Black Swans in literature