Nonlinear system modeling based on constrained Volterra series estimates

A simple nonlinear system modeling algorithm designed to work with limited \emph{a priori }knowledge and short data records, is examined. It creates an empirical Volterra series-based model of a system using an $l_{q}$-constrained least squares algorithm with $q\geq 1$. If the system $m\left( \cdot \right)$ is a continuous and bounded map with a finite memory no longer than some known $\tau$, then (for a $D$ parameter model and for a number of measurements $N$) the difference between the resulting model of the system and the best possible theoretical one is guaranteed to be of order $\sqrt{N^{-1}\ln D}$, even for $D\geq N$. The performance of models obtained for $q=1,1.5$ and $2$ is tested on the Wiener-Hammerstein benchmark system. The results suggest that the models obtained for $q>1$ are better suited to characterize the nature of the system, while the sparse solutions obtained for $q=1$ yield smaller error values in terms of input-output behavior

Can interhemispheric desynchronization of cerebral blood flow anticipate upcoming vasospasm in aneurysmal subarachnoid haemorrhage patients?

BACKGROUND: Asymmetry of cerebral autoregulation (CA) was demonstrated in patients after aneurysmal subarachnoid haemorrhage (aSAH). A classical method for CA assessment requires simultaneous measurement of both arterial blood pressure (ABP) and cerebral blood flow velocity (CBFV). In this study, we have proposed a cerebral blood flow asymmetry index based only on CBFV and analysed its association with the occurrence of vasospasm after aSAH. NEW METHOD: The phase shifts (PS) between slow oscillations in left and right CBFV (side-to-side PS) and between ABP and CBFV (CBFV-ABP PS) were estimated using multichannel matching pursuit (MMP) and cross-spectral analysis. RESULTS: We retrospectively analysed data collected from 45 aSAH patients (26 with vasospasm). Data were analysed up to 7th day after aSAH unless the vasospasm was detected earlier. A progressive asymmetry, manifested by a gradual increase in side-to-side PS on consecutive days after aSAH, was observed in patients who developed vasospasm (Radj2 = 0.14, p = 0.009). In these patients, early side-to-side PS was more positive than in patients without vasospasm (2.8° ± 5.6° vs -1.7° ± 5.7°, p = 0.011). No such a difference was found in CBFV-ABP PS. Patients with positive side-to-side PS were more likely to develop vasospasm than patients with negative side-to-side PS (21/7 vs 5/12, p = 0.0047). COMPARISON WITH EXISTING METHOD: MMP, in contrast to the spectral approach, accounts for non-stationarity of analysed signals. MMP applied to the PS estimation reflects the cerebral blood flow asymmetry in aSAH better than the spectral analysis. CONCLUSIONS: Changes in side-to-side PS might be helpful to identify patients who are at risk of vasospasm

A simple scheme for semi-recursive identification of Hammerstein system nonlinearity by Haar wavelets

A simple semi-recursive routine for nonlinearity recovery in Hammerstein systems is proposed. The identification scheme is based on the Haar wavelet kernel and possesses a simple and compact form. The convergence of the algorithm is established and the asymptotic rate of convergence (independent of the input density smoothness) is shown for piecewise-Lipschitz nonlinearities. The numerical stability of the algorithm is verified. Simulation experiments for a small and moderate number of input-output data are presented and discussed to illustrate the applicability of the routine

Learning low-dimensional separable decompositions of MIMO non-linear systems

We present a new internal structure exploration method developed for the multiple-input multiple-output (MIMO) dynamical systems with finite memory and almost arbitrary non-linear characteristic. The proposed Double Separation Algorithm applies distance correlation screening for pre-selection of those system inputs that contribute to the consecutive outputs and, based on the first-stage inference outcomes, estimates projection coefficients sensitive to the existence of additive system sub-characteristics. In effect, the proposed approach allows for effective exploration of the internal system structure. A numerical experiment on an MIMO nonlinear finite impulse response (NFIR) system illustrates the ability of the proposed approach to indicate which of the system inputs contribute to which of the system outputs. The experiment also illustrates the ability of the approach to detect which of the nonlinear sub-characteristics, recovered in the first stage of the approach, can be separated into a sum of lower-dimensional sub-characteristics.</p

Empirical recovery of input nonlinearity in distributed element models

International audienceTwo algorithms recovering an input nonlinearity in a nonlinear distributed element modeled as a Hammerstein system are proposed. The first is based on the empirical distribution function while the other on the empirical Haar orthogonal series. Both algorithms self-adjust their accuracy to a local density of the input measurements