Piecewise integrable neural network: An interpretable chaos identification framework.

Artificial neural networks (ANNs) are an effective data-driven approach to model chaotic dynamics. Although ANNs are universal approximators that easily incorporate mathematical structure, physical information, and constraints, they are scarcely interpretable. Here, we develop a neural network framework in which the chaotic dynamics is reframed into piecewise models. The discontinuous formulation defines switching laws representative of the bifurcations mechanisms, recovering the system of differential equations and its primitive (or integral), which describe the chaotic regime.

Constructed complex motions and chaos.

Constructed motions and dynamic topology are new trends in solving nonlinear systems or system interactions. In nonlinear engineering, it is significant to achieve specific complex motions to satisfy expected dynamical behaviors (e.g., nonlinear motions, singularities, bifurcations, chaos, etc.), and complex motion application and control. To achieve such expected motions and global dynamical behaviors, mapping dynamics, constructed networks, random/discontinuous dynamic theorems, etc., are applied to quantitatively determine the complex motions. These theories adopt the symbolic dynamic abstracts and topological structures with nonlinear dynamics to investigate constructed complex motions to satisfy expected dynamical behaviors.

A Genetic Algorithm Procedure for the Automatic Updating of FEM Based on Ambient Vibration Tests.

The dynamic identification of the modal parameters of a structure, in order to gain control of its functionality under operating conditions, is currently under discussion from a scientific and technical point of views. The experimental observations obtained through structural health monitoring (SHM) are a useful calibration reference of numerical models (NMs). In this paper, the procedures for the identification of modal parameters in historical bell towers using a stochastic subspace identification (SSI) algorithm are presented. Then, NMs are manually calibrated on the identification's results. Finally, the applicability of a genetic algorithm for the automatic calibration of the elastic parameters is considered with the aim of searching for the properties of the autochthonous material, in order to reduce modelling error following the model assurance criterion (MAC). In this regard, several material values on the same model are examined to see how to approach the evolution and the distribution of these features, comparing the characterization proposed by the genetic algorithm with the results considered by the manual iterative procedure.

Chaotic vibrations of the duffing system with fractional damping.

We examined the Duffing system with a fractional damping term. Calculating the basins of attraction, we demonstrate a broad spectrum of non-linear behaviour connected with sensitivity to the initial conditions and chaos. To quantify dynamical response of the system, we propose the statistical 0-1 test as well as the maximal Lyapunov exponent; the application of the latter encounter a few difficulties because of the memory effect due to the fractional derivative. The results are confirmed by bifurcation diagrams, phase portraits, and Poincaré sections.

Theoretical prediction of experimental jump and pull-in dynamics in a MEMS sensor.

The present research study deals with an electrically actuated MEMS device. An experimental investigation is performed, via frequency sweeps in a neighbourhood of the first natural frequency. Resonant behavior is explored, with special attention devoted to jump and pull-in dynamics. A theoretical single degree-of-freedom spring-mass model is derived. Classical numerical simulations are observed to properly predict the main nonlinear features. Nevertheless, some discrepancies arise, which are particularly visible in the resonant branch. They mainly concern the practical range of existence of each attractor and the final outcome after its disappearance. These differences are likely due to disturbances, which are unavoidable in practice, but have not been included in the model. To take disturbances into account, in addition to the classical local investigations, we consider the global dynamics and explore the robustness of the obtained results by performing a dynamical integrity analysis. Our aim is that of developing an applicable confident estimate of the system response. Integrity profiles and integrity charts are built to detect the parameter range where reliability is practically strong and where it becomes weak. Integrity curves exactly follow the experimental data. They inform about the practical range of actuality. We discuss the combined use of integrity charts in the engineering design. Although we refer to a particular case-study, the approach is very general.

Controlling practical stability and safety of mechanical systems by exploiting chaos properties.

In this paper, a method for controlling the global nonlinear dynamics of mechanical systems is applied to two models: the model of Augusti and an inverted guyed pendulum. These simplified models represent a large class of structures liable to buckling exhibiting interacting buckling phenomena. These structures may fail at load levels well below the theoretical buckling load due to complex nonlinear phenomena that decrease the safety and the dynamic integrity of the structure; this often occur as a consequence of imperfections and of the erosion of the basins of attraction of the safe pre-buckling solutions. So, it is of paramount practical importance to increase the safety of these structures in a dynamic environment. This can be achieved by increasing the integrity of the basins of attraction of the safe solutions, a goal that is attained by a control method which consists of the (optimal) elimination of homoclinic (or heteroclinic) intersection by properly adding superharmonic terms to a given harmonic excitation. By means of the solution of an appropriate optimization problem, it is possible to select the amplitudes and the phases of the added superharmonics in such a way that the manifolds distance is as large as possible. The results show that this methodology increases the integrity of the basins of attraction of the system and, consequently, the practical safety of the structure.

A Preliminary Validation of a New Surgical Procedure for the Treatment of Primary Bladder Neck Obstruction Using a Computational Modeling Approach.

A new surgical procedure for the treatment of primary bladder neck obstruction with maintenance of anterograde ejaculation is proposed. In place of monolateral or bilateral bladder neck incision, associated with a loss of ejaculation rate of up to 30%, the new surgical procedure consists of laser drilling the bladder neck with a number of holes and without muscle fiber disruption. The effect of this novel procedure has been studied numerically, with a simplified two-dimensional numerical model of the internal urethral sphincter, varying the position and the number of holes in the fibrotic region of the urethral tissue. Results show an improvement of the urethral sphincter opening by increasing the number of holes, ranging from about 6% to 16% of recovery. Moreover, a non-aligned position of holes positively influences the opening recovery. The concentrations of maximum principal strain and stress have been registered in the proximity of the interface between the physiologic and diseased sphincter, and in those regions where the radial thickness is significantly thinner. The effects on the first five patients have been included in the study, showing improvement in micturition, lower urinary tract symptoms, sustained ejaculatory function, and quality of life.

Axial-transversal coupling in the free nonlinear vibrations of Timoshenko beams with arbitrary slenderness and axial boundary conditions.

The nonlinear free oscillations of a straight planar Timoshenko beam are investigated analytically by means of the asymptotic development method. Attention is focused for the first time, to the best of our knowledge, on the nonlinear coupling between the axial and the transversal oscillations of the beam, which are decoupled in the linear regime. The existence of coupled and uncoupled motion is discussed. Furthermore, the softening versus hardening nature of the backbone curves is investigated in depth. The results are summarized by means of behaviour charts that illustrate the different possible classes of motion in the parameter space. New, and partially unexpected, phenomena, such as the changing of the nonlinear behaviour from softening to hardening by adding/removing the axial vibrations, are highlighted.

The dynamical integrity concept for interpreting/ predicting experimental behaviour: from macro- to nano-mechanics.

The dynamical integrity, a new concept proposed by J.M.T. Thompson, and developed by the authors, is used to interpret experimental results. After reviewing the main issues involved in this analysis, including the proposal of a new integrity measure able to capture in an easy way the safe part of basins, attention is dedicated to two experiments, a rotating pendulum and a micro-electro-mechanical system, where the theoretical predictions are not fulfilled. These mechanical systems, the former at the macro-scale and the latter at the micro-scale, permit a comparative analysis of different mechanical and dynamical behaviours. The fact that in both cases the dynamical integrity permits one to justify the difference between experimental and theoretical results, which is the main achievement of this paper, shows the effectiveness of this new approach and suggests its use in practical situations. The men of experiment are like the ant, they only collect and use; the reasoners resemble spiders, who make cobwebs out of their own substance. But the bee takes the middle course: it gathers its material from the flowers of the garden and field, but transforms and digests it by a power of its own. Not unlike this is the true business of philosophy (science); for it neither relies solely or chiefly on the powers of the mind, nor does it take the matter which it gathers from natural history and mechanical experiments and lay up in the memory whole, as it finds it, but lays it up in the understanding altered and digested. Therefore, from a closer and purer league between these two faculties, the experimental and the rational (such as has never been made), much may be hoped. (Francis Bacon 1561-1626) But are we sure of our observational facts? Scientific men are rather fond of saying pontifically that one ought to be quite sure of one's observational facts before embarking on theory. Fortunately those who give this advice do not practice what they preach. Observation and theory get on best when they are mixed together, both helping one another in the pursuit of truth. It is a good rule not to put overmuch confidence in a theory until it has been confirmed by observation. I hope I shall not shock the experimental physicists too much if I add that it is also a good rule not to put overmuch confidence in the observational results that are put forward until they have been confirmed by theory. (Arthur Stanley Eddington 1882-1944).

Optimal control and anti-control of the nonlinear dynamics of a rigid block.

This paper deals with control and anti-control of overturning of a rigid block subjected to a generic periodic excitation. Attention is focused on two relevant thresholds, corresponding to heteroclinic bifurcation and immediate overturning, and representing lower and upper bounds of the region where toppling can occur. The two opposite problems of increasing (control) or decreasing (anti-control) of these two curves by properly modifying the shape of the excitation are investigated in depth and the optimal excitations permitting their maximum variations are determined. The notions of 'global' and 'one-side' control (anti-control) are utilized and their different importance for the various cases is discussed. The effects of control (anti-control) of one curve on the uncontrolled (non-anti-controlled) curve are also investigated, both analytically and with numerical overturning charts. A good agreement is seen to occur.