Toda and Volterra lattice equations from discrete symmetries of KP hierarchies

The discrete models of the Toda and Volterra chains are being constructed out of the continuum two-boson KP hierarchies. The main tool is the discrete symmetry preserving the Hamiltonian structure of the continuum models. The two-boson currents of KP hierarchy are being associated with sites of the corresponding chain by successive actions of discrete symmetry.

Duracion de la vida: capitulos seleccionados del libro de Dublin, Lotka y Spiegelman Length of Life"

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Damage detection in nonlinear structures using discrete-time volterra series

Structural damage identification is basically a nonlinear phenomenon; however, nonlinear procedures are not used currently in practical applications due to the complexity and difficulty for implementation of such techniques. Therefore, the development of techniques that consider the nonlinear behavior of structures for damage detection is a research of major importance since nonlinear dynamical effects can be erroneously treated as damage in the structure by classical metrics. This paper proposes the discrete-time Volterra series for modeling the nonlinear convolution between the input and output signals in a benchmark nonlinear system. The prediction error of the model in an unknown structural condition is compared with the values of the reference structure in healthy condition for evaluating the method of damage detection. Since the Volterra series separate the response of the system in linear and nonlinear contributions, these indexes are used to show the importance of considering the nonlinear behavior of the structure. The paper concludes pointing out the main advantages and drawbacks of this damage detection methodology. © (2013) Trans Tech Publications.

Identification of nonlinear structures using discrete-time Volterra series

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Model updating of the non-linear vibrating structures through Volterra series and proper orthogonal decomposition

Classical procedures for model updating in non-linear mechanical systems based on vibration data can fail because the common linear metrics are not sensitive for non-linear behavior caused by gaps, backlash, bolts, joints, materials, etc. Several strategies were proposed in the literature in order to allow a correct representative model of non-linear structures. The present paper evaluates the performance of two approaches based on different objective functions. The first one is a time domain methodology based on the proper orthogonal decomposition constructed from the output time histories. The second approach uses objective functions with multiples convolutions described by the first and second order discrete-time Volterra kernels. In order to discuss the results, a benchmark of a clamped-clamped beam with an pre-applied static load is simulated and updated using proper orthogonal decomposition and Volterra Series. The comparisons and discussions of the results show the practical applicability and drawbacks of both approaches.

On volterra integral equations on time scales

The purpose of the present paper is to study some properties of solutions of Volterra integral equations on time scales. We generalize to a time scale some known properties concerning continuity and convergence of solutions from the continuous case.

Nonlinear features identified by Volterra series for damage detection in a buckled beam

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Non-parametric identification of a non-linear buckled beam using discrete-time Volterra Series

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Characterization of the nonlinear behavior of a F-16 aircraft using discrete-time Volterra series

The linearity assumption in the structural dynamics analysis is a severe practical limitation. Further, in the investigation of mechanisms presented in fighter aircrafts, as for instance aeroelastic nonlinearity, friction or gaps in wing-load-payload mounting interfaces, is mandatory to use a nonlinear analysis technique. Among different approaches that can be used to this matter, the Volterra theory is an interesting strategy, since it is a generalization of the linear convolution. It represents the response of a nonlinear system as a sum of linear and nonlinear components. Thus, this paper aims to use the discrete-time version of Volterra series expanded with Kautz filters to characterize the nonlinear dynamics of a F-16 aircraft. To illustrate the approach, it is identified and characterized a non-parametric model using the data obtained during a ground vibration test performed in a F-16 wing-to-payload mounting interfaces. Several amplitude inputs applied in two shakers are used to show softening nonlinearities presented in the acceleration data. The results obtained in the analysis have shown the capability of the Volterra series to give some insight about the nonlinear dynamics of the F-16 mounting interfaces. The biggest advantage of this approach is to separate the linear and nonlinear contributions through the multiple convolutions through the Volterra kernels.

Application of Volterra series in nonlinear mechanical system identification and in structural health monitoring problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Efficient Kernel Computation for Volterra Filter Structure Evaluation

Despite their generality, conventional Volterra filters are inadequate for some applications, due to the huge number of parameters that may be needed for accurate modelling. When a state-space model of the target system is known, this can be assessed by computing its kernels, which also provides valuable information for choosing an adequate alternate Volterra filter structure, if necessary, and is useful for validating parameter estimation procedures. In this letter, we derive expressions for the kernels by using the Carleman bilinearization method, for which an efficient algorithm is given. Simulation results are presented, which confirm the usefulness of the proposed approach.

Modellazione matematica delle non linearità di sistemi acustici mediante serie di Volterra modificate

In questa tesi si è studiato un metodo per modellare e virtualizzare tramite algoritmi in Matlab le distorsioni armoniche di un dispositivo audio non lineare, ovvero uno “strumento” che, sollecitato da un segnale audio, lo modifichi, introducendovi delle componenti non presenti in precedenza. Il dispositivo che si è scelto per questo studio il pedale BOSS SD-1 Super OverDrive per chitarra elettrica e lo “strumento matematico” che ne fornisce il modello è lo sviluppo in serie di Volterra. Lo sviluppo in serie di Volterra viene diffusamente usato nello studio di sistemi fisici non lineari, nel caso in cui si abbia interesse a modellare un sistema che si presenti come una “black box”. Il metodo della Nonlinear Convolution progettato dall'Ing. Angelo Farina ha applicato con successo tale sviluppo anche all'ambito dell'acustica musicale: servendosi di una tecnica di misurazione facilmente realizzabile e del modello fornito dalla serie di Volterra Diagonale, il metodo permette di caratterizzare un dispositivo audio non lineare mediante le risposte all'impulso non lineari che il dispositivo fornisce a fronte di un opportuno segnale di test (denominato Exponential Sine Sweep). Le risposte all'impulso del dispositivo vengono utilizzate per ricavare i kernel di Volterra della serie. L'utilizzo di tale metodo ha permesso all'Università di Bologna di ottenere un brevetto per un software che virtualizzasse in post-processing le non linearità di un sistema audio. In questa tesi si è ripreso il lavoro che ha portato al conseguimento del brevetto, apportandovi due innovazioni: si è modificata la scelta del segnale utilizzato per testare il dispositivo (si è fatto uso del Synchronized Sine Sweep, in luogo dell'Exponential Sine Sweep); si è messo in atto un primo tentativo di orientare la virtualizzazione verso l'elaborazione in real-time, implementando un procedimento (in post-processing) di creazione dei kernel in dipendenza dal volume dato in input al dispositivo non lineare.

Senator Vito Volterra [Illustration] : Professor der Mathematik

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Dissertazione accademica sopra un monumento etrusco ritrovato negli antichi suburbani di Volterra, 1746.

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