Review on Vibration-Based Structural Health Monitoring Techniques and Technical Codes

Structural damages occur in modern structures during operations due to environmental and human factors. The damages accumulating with time may lead to a significant decrease in structure performance or even destruction; natural symmetry is broken, resulting in an unexpected life and economic loss. Therefore, it is necessary to monitor the structural response to detect the damage in an early stage, evaluate the health condition of structures, and ensure the operation safety of structures. In fact, the structure and the evaluation can be considered as a special symmetry. Among several SHM methods, vibration-based SHM techniques have been widely adopted recently. Hence, this paper reviews the vibration-based SHM methods in terms of the vibrational parameters used. In addition, the technical codes on vibration based SHM system have also been reviewed, since they are more important in engineering applications. Several related ISO standards and national codes have been developed and implemented, while more specific technical codes are still required to provide more detailed guidelines in practice to maintain structure safety and natural symmetry.

Optimal Trajectory Synthesis for Spacecraft Asteroid Rendezvous

Several researchers are considering the plausibility of being able to rapidly launch a mission to an asteroid, which would fly in close proximity of the asteroid to deliver an impulse in a particular direction so as to deflect the asteroid from its current orbit. Planetary motion, in general, and the motion of asteroids, in particular, are subject to planetary influences that are characterised by a kind of natural symmetry, which results in an asteroid orbiting in a stable and periodic or almost periodic orbit exhibiting a number of natural orbital symmetries. Tracking and following an asteroid, in close proximity, is the subject of this paper. In this paper, the problem of synthesizing an optimal trajectory to a NEO such as an asteroid is considered. A particular strategy involving the optimization of a co-planar trajectory segment that permits the satellite to approach and fly alongside the asteroid is chosen. Two different state space representations of the Hill–Clohessy–Wiltshire (HCW) linearized equations of relative motion are used to obtain optimal trajectories for a spacecraft approaching an asteroid. It is shown that by using a state space representation of HCW equations where the secular states are explicitly represented, the optimal trajectories are not only synthesized rapidly but also result in lower magnitudes of control inputs which must be applied continuously over extended periods of time. Thus, the solutions obtained are particularly suitable for low thrust control of the satellites orbit which can be realized by electric thrusters.

Perceptual spaces and their symmetries: The geometry of color space

Our sensory systems transform external signals into neural activity, thereby producing percepts. We are endowed with an intuitive notion of similarity between percepts, that need not reflect the proximity of the physical properties of the corresponding external stimuli. The quantitative characterization of the geometry of percepts is therefore an endeavour that must be accomplished behaviorally. Here we characterized the geometry of color space using discrimination and matching experiments. We proposed an individually tailored metric defined in terms of the minimal chromatic difference required for each observer to differentiate a stimulus from its surround. Next, we showed that this perceptual metric was particularly adequate to describe two additional experiments, since it revealed the natural symmetry of perceptual computations. In one of the experiments, observers were required to discriminate two stimuli surrounded by a chromaticity that differed from that of the tested stimuli. In the perceptual coordinates, the change in discrimination thresholds induced by the surround followed a simple law that only depended on the perceptual distance between the surround and each of the two compared stimuli. In the other experiment, subjects were asked to match the color of two stimuli surrounded by two different chromaticities. Again, in the perceptual coordinates the induction effect produced by surrounds followed a simple, symmetric law. We conclude that the individually-tailored notion of perceptual distance reveals the symmetry of the laws governing perceptual computations. Comment: 42 pages, 9 figures, 1 appendix. (v2) 47 pages, 10 figures, 1 appendix. (v3) Text modified after peer-review process. (v4) 34 pages, 1 appendix, 10 figures. Article accepted to be published at Mathematical Neuroscience and Applications

Natural symmetry

When a child is excited by something they identify in the natural world, there is a valuable opportunity to seize the moment and extend learning. Jenni Clarke explains how the adult can prompt and support without taking over.

One-Sided Sequent Systems for Nonassociative Bilinear Logic: Cut Elimination and Complexity

Bilinear Logic of Lambek [10] amounts to Noncommutative MALL of Abrusci [1]. Lambek [10] proves the cut–elimination theorem for a onesided (in fact, left-sided) sequent system for this logic. Here we prove an analogous result for the nonassociative version of this logic. Like Lambek [10], we consider a left-sided system, but the result also holds for its right-sided version, by a natural symmetry. The treatment of nonassociative sequent systems involves some subtleties, not appearing in associative logics. We also prove the PTIME complexity of the multiplicative fragment of NBL.

A functional equation of tail-balance for continuous signals in the Condorcet Jury Theorem

Consider an odd-sized jury, which determines a majority verdict between two equiprobable states of Nature. If each juror independently receives a binary signal identifying the correct state with identical probability p, then the probability of a correct verdict tends to one as the jury size tends to infinity (Marquis de Condorcet in Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix, Imprim. Royale, Paris, 1785). Recently, Alpern and Chen (Eur J Oper Res 258:1072–1081, 2017, Theory Decis 83:259–282, 2017) developed a model where jurors sequentially receive independent signals from an interval according to a distribution which depends on the state of Nature and on the juror’s “ability”, and vote sequentially. This paper shows that, to mimic Condorcet’s binary signal, such a distribution must satisfy a functional equation related to tail-balance, that is, to the ratio $$\alpha (t)$$ α ( t ) of the probability that a mean-zero random variable satisfies X$$>t$$ > t given that $$|X|>t$$ | X | > t . In particular, we show that under natural symmetry assumptions the tail-balances $$\alpha (t)$$ α ( t ) uniquely determine the signal distribution and so the distributions assumed in Alpern and Chen (Eur J Oper Res 258:1072–1081, 2017, Theory Decis 83:259–282, 2017) are uniquely determined for $$\alpha (t)$$ α ( t ) linear.

Why Black-Scholes Equations Are Effective Beyond Their Usual Assumptions: Symmetry-Based Explanation

Nobel-Prize-winning Black-Scholes equations are actively used to estimate the price of options and other financial instruments. In practice, they provide a good estimate for the price, but the problem is that their original derivation is based on many simplifying statistical assumptions which are, in general, not valid for financial time series. The fact that these equations are effective way beyond their usual assumptions leads to a natural conclusion that there must be an alternative derivation for these equations, a derivation that does not use the usual too-strong assumptions. In this paper, we provide such a derivation in which the only substantial assumption is a natural symmetry: namely, scale-invariance of the corresponding processes. Scale-invariance also allows us to describe possible generalizations of Black-Scholes equations, generalizations that we hope will lead to even more accurate estimates for the corresponding prices.

Voting Rules that are Unbiased but not Transitive-Symmetric

We explore the relation between two natural symmetry properties of voting rules. The first is transitive-symmetry – the property of invariance to a transitive permutation group – while the second is the "unbiased" property of every voter having the same influence for all i.i.d. probability measures. We show that these properties are distinct by two constructions – one probabilistic, one explicit – of rules that are unbiased but not transitive-symmetric.

De Finetti Theorems for Braided Parafermions

The classical de Finetti theorem in probability theory relates symmetry under the permutation group with the independence of random variables. This result has application in quantum information. Here we study states that are invariant with respect to a natural action of the braid group, and we emphasize the pictorial formulation and interpretation of our results. We prove a new type of de Finetti theorem for the four-string, double-braid group acting on the parafermion algebra to braid qudits, a natural symmetry in the quon language for quantum information. We prove that a braid-invariant state is extremal if and only if it is a product state. Furthermore, we provide an explicit characterization of braid-invariant states on the parafermion algebra, including finding a distinction that depends on whether the order of the parafermion algebra is square free. We characterize the extremal nature of product states (an inverse de Finetti theorem).

INFLUENCE OF CROSS SECTION HEIGHT AND NATURE OF REINFORCING GLUED WOODEN BEAMS ON THE DISTRIBUTION OF INTERNAL EFFORT

The main trends of modern construction is the production and use of light construction structures, which can significantly accelerate the construction of building objects. At the same time, the use of structural and finishing materials that meet modern environmental requirements is important. Structural elements of buildings have dominated for many centuries and have broad prospects for use in modern capital construction: they have high strength and rigidity; they are reliable and durable and have a low installation weight. In particular, in a number of Western countries, high-rise buildings are already being built using a frame made of glued wooden structures. Despite the natural symmetry of coniferous woods structure, its non-standard tracheids are the main reason for the variability of its mechanical properties. In addition, when calculating glued reinforced structures, it is necessary to take into account the so-called "scale effect" when calculating the bent glued wooden elements. The applied methods for the calculation of "low" reinforced beams sometimes give an error in the calculation of "high" beams. In this paper, the definition of a more rational method of calculating the "high" beams with symmetrical reinforcement and comparison of options for reinforcing such beams are performed