Dear Colleagues,

Complex industrial systems are unique, even when they are of the same design, often because of unique operating conditions and histories. As failures of complex industrial systems are rare events, it is generally impossible to develop an effective calibrating database to cover all failure scenarios via empiricism. Thus, empirical models are generally expensive, because of the need for large, labor-intensive calibrating databases that cover the impact of all conceivable independent variables. Empirical models also fail to capture the mechanism of failure and they, generally, fail to yield the accuracy of prediction to make them useful for maintenance and life extension analyses of complex industrial systems (e.g., nuclear power reactors or oil and gas pipelines). Of great importance is that empirical models have limited prediction factors, PF (time of prediction/calibrating data record). Commonly, for an empirical model, 1 < PF < 10, whereas for deterministic models, 1 < PF < 1000 or more. Indeed, this feature of determinism is being exploited in modeling the fate of metallic canisters for the disposal of high-level nuclear waste (HLNW) where a PF of > 100,000 is required to ensure that the waste can be isolated from the biosphere for sufficient time for the fission product nuclides to decay to harmless levels.

In a more mundane scenario, we might ask: “Why is accurate prediction important?” Corrosion damage is responsible for huge economic losses in industrialized societies (3–4.5% of GDP per year or about USD 0.630 to USD 0.945 trillion in the US in 2020 based on a GDP of USD 21 trillion). The worldwide cost is three to four times greater, making corrosion one of the costliest of all-natural phenomena. For comparison, the cost of hurricanes and earthquakes is estimated to be < USD 100 billion annually. Approximately 30% of that cost could be avoided by better application of existing corrosion control technology, if only we knew in advance where and when corrosion damage might occur. Thus, if we knew when and where failures might occur, systems might be serviced during scheduled outages (SOs), thereby avoiding costly, unscheduled down time, because the cost of an SO is already built into the price of the product. The most insidious forms of corrosion are localized corrosion, such as pitting, stress corrosion cracking, corrosion fatigue, hydrogen embrittlement, and crevice corrosion, because they often produce failures with little outward sign of accumulated damage. To date, prediction has been made largely upon the basis of empirical models, e.g., extreme value statistics, which generally have failed to produce the required accuracy of prediction to be truly useful in an engineering sense.

Much has been written about the philosophical basis of science, extending all the way back 2870 years when Aristotle (384–322 BC) published his treatise, Physics [1] in 350 BC. Although Aristotle is often credited with defining the concept of causality, upon which modern scientific philosophy is based, in the opinion of the author, this attribution is perhaps a little overstated. Although he did discuss at some length the nature of “cause” and the resulting “effect”, but not always in those specific terms, he did not do so in terms of quantifiable concepts, such as “force” or “displacement”, respectively. Nevertheless, Aristotle, for his time, displayed great insight into the philosophical basis of the natural world as is displayed by his statement: “It is plain then that nature is a cause, a cause that operates for a purpose.” Indeed, in his writings, it is possible to detect the foundation of Newton’s Laws of Motion, which are generally regarded as being the foundation of modern physics but which were formulated about 2200 years later. Undoubtedly, Newton was conversant with the writings of Aristotle, as were many prominent natural philosophers of Newton’s time. A comprehensive discussion of the philosophical basis of science is well beyond the scope of this Special Issue and the reader will find many, outstanding treatise on the subject identified on the Web. Names such as Plato, Al Ghazali, Al-Khwarizmi, Bacon, Kant, Newton, Galilei, Descartes, Leibniz, Mach, Poincaré, Einstein, Russell, Whitehead, Popper, Kuhn, and Torretti, to name but a few of the more prominent philosophers spanning the period from Aristotle to the present day. Below, the views on “science” are strictly those of the author and no pretense is made that the views represent those of mainstream scientists or previous or current scientific philosophers.

Extensive enquiry by the author on the nature of science and the role of determinism in the scientific process has led him to conclude that “science” is a process wherein there occurs a transition from empiricism (what we observe) to determinism (the condensation of scientific knowledge in the form of the natural laws). A particularly important feature of the natural laws is that they are time and space invariant. Accordingly, the laws are as valid on Planet Mars as they are on Planet Earth and they will remain valid for all time. It is true that, occasionally, natural laws are revised to reflect a more complete understanding of the bases of the laws. A good example is the reformulation of the laws of energy conservation and mass conservation into the law of mass–energy conservation on the basis of Einstein’s famous formula, E = mc², where m is the rest mass, and c is the velocity of light in a vacuum.

The transition from empiricism to determinism involves the development of theories and models, with the “scientific method” being used to nudge the models toward reality. In this regard, we can never achieve “reality”, because we view our surroundings through imperfect senses and we interpret the results through imperfect intellects. Indeed, the purpose in developing more precise instruments (e.g., electron microscopes) is to extend our senses to higher resolution. Likewise, the development of high-speed computers has extended our intellect into the analysis of more complex systems. In any event, theories represent an understanding of how a system operates and interacts with its surroundings. Importantly, not all theories predict or calculate. For example, Darwin’s Theory of Evolution explains the evolution of biological systems through the process of natural selection but it cannot tell us how the human race will evolve over the next million years. On the other hand, the predictive arm of a theory, if it exists, must have a theoretical basis (the theory itself) and, if it is deterministic, its predictions are constrained by the relevant natural laws. Thus, for an electrochemical/corrosion model, the prediction is constrained by the laws of mass–energy and charge conservation and by mass–charge equivalency (Faraday’s law). It is this characteristic that imbues the model with the quality of “determinism”.

Finally, it is vital in deterministic prediction to recognize the concept of the system evolutionary path (SEP), which is defined as the path taken by the system in terms of those independent variables that have a significant impact on the damage accumulation rate. For example, in the case of the intergranular stress corrosion cracking (IGSCC) of sensitized stainless steel in the coolant (water at 288 ^oC) circuit of a Boiling Water (Nuclear) Reactor (BWR), the relevant independent variables are identified as temperature, corrosion potential (ECP), stress intensity factor, coolant flow velocity, coolant conductivity, degree of sensitization of the steel, including sensitization induced by neutron irradiation of in-core components, hardness and yield strength (if annealing occurs during operation), and possibly many others. Variables, such as steel composition, that remain invariant during the operation of the system are not included unless they affect some other independent variable that does change over the operating history of the system. For example, stainless steel contains a certain amount of carbon (typically 0.02–0.1%) that is instrumental in the phenomenon of sensitization, whereby the carbon reacts with chromium to precipitate chromium carbide (Cr₂₃C₆) on the grain boundaries and depleting the neighboring regions adjacent to the boundaries of passivity-inducing Cr. These grain boundaries become the preferred paths for the propagation of cracks in the phenomenon of IGSCC. As sensitization may occur at the operating temperature of a BWR (288 ^oC), albeit slowly, and noting that the formation of grain boundary chromium carbides may be accelerated by neutron irradiation, the chromium content becomes an important independent variable that should be included in defining the SEP. As we cannot predict the idiosyncrasies of future plant operation, specification of the SEP is usually carried out upon the bases of the past operating histories of similar plants or on idealized paths that are specified by the designers and/or the operators. Regardless, the accurate prediction of the accumulation of damage requires accurate specification of the SEP, and that is frequently one of the more difficult tasks in the overall problem.

1. 350 BC PHYSICS by Aristotle, translated by R. P. Hardie and R. K. Gaye

Prof. Dr. Digby Macdonald
Guest Editor

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