Mechanical Engineering in Uncertainties From Classical Approaches to Some Recent Developments. Группа авторов
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СКАЧАТЬ to the challenges and the usefulness of this distinction. This debate arises from the controversy between Niels Bohr and Albert Einstein concerning the nature of randomness observed at the quantum scale. For the former, it was a fundamental randomness, while for the latter, it was linked to an incomplete knowledge of phenomena at these scales. To illustrate his point of view, Einstein stated that “God does not play dice”. Subsequent theoretical and experimental work by physicists seems to have proved Niels Bohr right: randomness observed at these scales is intrinsic to quantum nature. Now that the debate at the microscopic scale has been closed, one may raise the same question at the macroscopic level of mechanics, which is the subject of this book. Are there uncertainties at the macroscopic level of an intrinsically aleatory nature that can affect mechanical systems? Or are all uncertainties at the macroscopic level related only to a lack of knowledge?

      An example from the mechanical field is now provided to illustrate the uncertainty associated with free will. Anyone who has seen a construction excavator at work has quickly realized that it is an illusion to try to predict the load that its articulated arms will be subjected to during its lifetime, as the conditions under which the machine is used can be extremely unexpected. The ingenuity (if we look on the positive side) of the operators of the machine means that they will always find new uses for the machine, which the engineer designing the machine would never have thought of. For example, using the bucket to push a truck that the excavator has just loaded and that skids up the slope to get out of the hole, and also using it for different kinds of demolitions. Consequently, it is not possible to consider the uncertainty about the loads being applied on the arms of the machine as an uncertainty of a purely epistemic nature, solely linked to lack of knowledge and therefore reducible by improving knowledge. As a matter of fact, this would mean that an improvement in knowledge would ultimately be able to predict the ways in which operators will decide to use the machine, which is obviously contrary to free will.

      Another uncertainty of an intrinsically aleatory nature at the macroscopic level is that related to chaotic systems. Chaos theory has shown that such systems cannot be predicted beyond a more or less long-term horizon. A classic example of a chaotic system is the atmospheric system, which is reflected by the fact that the state of the system (namely what is commonly known as weather) cannot be predicted beyond a certain period of time; this is the famous butterfly effect. Note that it is the system itself that is chaotic and not just our modeling of the system. An improvement of our models will therefore not change anything in the system itself, which will remain chaotic. Because of their chaotic nature, and therefore unpredictability in the more or less long term, chaotic systems are a source of aleatory uncertainty, which cannot be reduced by improvement in knowledge.

      In order to illustrate this with a mechanical case, let us again consider the case of the gusts that an aircraft will experience. When designing a new model of aircraft, it is useful for the engineer to know the amplitude of the gusts that the aircraft will experience during its lifetime in order to be able to size the aircraft structure as efficiently as possible. The amplitude of these gusts can then be considered as aleatory, irreducible uncertainty. Indeed, due to the chaotic system that is the atmosphere, it is not possible to predict air movements on a scale of a few meters over a time scale of several decades (that is, the lifetime of the aircraft). Moreover, it should be noted that the chaotic nature of the atmospheric system is further amplified by interaction with human free will. Uncertainty about human response to climate change makes it difficult to predict the state of the atmospheric system on the time and space scales under consideration. The engineer therefore has no means of reducing this uncertainty about the amplitude of gusts by improving knowledge.

      After having seen two sources of uncertainty that are inherently aleatory in nature at the macroscopic scale, one may ask whether other uncertainties can be classified as aleatory. While the previous two sources are intrinsically aleatory, the classification of other sources of uncertainty may depend on the situation. It should not be forgotten that the classification between epistemic and aleatory uncertainty introduced in the previous section is specific to the problem under consideration. When we considered the favorable outcome of the “coin toss” as aleatory uncertainty, the rules of the game are fixed (in particular, considering that the toss cannot be biased). If it is considered that biasing the toss is part of the rules of the game, then the uncertainty about the outcome is obviously reducible.

      In mechanical problems, the engineer is responsible for articulating the problem, and, in particular, for setting “the rules of the game”, namely what can and cannot be changed. The classification is then specific to the problem under consideration and an uncertainty on the same physical quantity can then be classified as being epistemic for certain problems and aleatory for others.

      In light of this ambivalence, the interest of classifying uncertainties into epistemic and aleatory for a given problem can be questioned. From the author’s perspective, the usefulness of this classification is most apparent from an engineering point of view in terms of distinguishing between reducible and irreducible uncertainties. This distinction is important because the solutions to be provided by the engineer to these two types of uncertainties are very different. For the former, the solutions essentially consist of seeking to reduce uncertainties, while for the latter, the solutions essentially consist of designing the systems in their presence (for example, by integrating partial safety factors, redundancies or by explicitly calculating the reliability of the system).

      The interest of alternative approaches to modeling epistemic uncertainties is also questionable compared to the probabilistic approach typically used for aleatory uncertainties. Clearly, since the distinction between epistemic and aleatory uncertainty is based on the engineer’s decisions regarding the problem to be considered, this, in itself, cannot justify СКАЧАТЬ