Ki H. Chon

Linear and nonlinear ARMA model parameter estimation using an artificial neural network

Addresses parametric system identification of linear and nonlinear dynamic systems by analysis of the input and output signals. Specifically, the authors investigate the relationship between estimation of the system using a feedforward neural network model and estimation of the system by use of linear and nonlinear autoregressive moving-average (ARMA) models. By utilizing a neural network model incorporating a polynomial activation function, the authors show the equivalence of the artificial neural network to the linear and nonlinear ARMA models. They compare the parameterization of the estimated system using the neural network and ARMA approaches by utilizing data generated by means of computer simulations. Specifically, the authors show that the parameters of a simulated ARMA system can be obtained from the neural network analysis of the simulated data or by conventional least squares ARMA analysis. The feasibility of applying neural networks with polynomial activation functions to the analysis of experimental data is explored by application to measurements of heart rate (HR) and instantaneous lung volume (ILV) fluctuations.

A dual-input nonlinear system analysis of autonomic modulation of heart rate

Linear analyses of fluctuations in heart rate and other hemodynamic variables have been used to elucidate cardiovascular regulatory mechanisms. The role of nonlinear contributions to fluctuations in hemodynamic variables has not been fully explored. This paper presents a nonlinear system analysis of the effect of fluctuations in instantaneous lung volume (ILV) and arterial blood pressure (ABP) on heart rate (HR) fluctuations. To successfully employ a nonlinear analysis based on the Laguerre expansion technique (LET), we introduce an efficient procedure for broadening the spectral content of the ILV and ABP inputs to the model by adding white noise. Results from computer simulations demonstrate the effectiveness of broadening the spectral band of input signals to obtain consistent and stable kernel estimates with the use of the LET. Without broadening the band of the ILV and ABP inputs, the LET did not provide stable kernel estimates. Moreover, we extend the LET to the case of multiple inputs in order to accommodate the analysis of the combined effect of ILV and ABP effect on heart rate. Analyses of data based on the second-order Volterra-Wiener model reveal an important contribution of the second-order kernels to the description of the effect of lung volume and arterial blood pressure on heart rate. Furthermore, physiological effects of the autonomic blocking agents propranolol and atropine on changes in the first- and second-order kernels are also discussed.

Nonlinear system analysis of renal autoregulation in normotensive and hypertensive rats

The authors compared the dynamic characteristics in renal autoregulation of blood flow of normotensive Sprague-Dawley rats (SDR) and spontaneously hypertensive rats (SHR), using both linear and nonlinear systems analysis. Linear analysis yielded only limited information about the differences in dynamics between SDR and SHR. The predictive ability, as determined by normalized mean-square errors (NMSE), of a third-order Volterra model is better than for a linear model. This decrease in NMSE with a third-order model from that of a linear model is especially evident at frequencies below 0.2 Hz. Furthermore, NMSE are significantly higher in SHR than SDR, suggesting a more complex nonlinear system in SHR. The contribution of the third-order kernel in describing the dynamics of renal autoregulation in arterial blood pressure and blood flow was found to be important. Moreover, the authors have identified the presence of nonlinear interactions between the oscillatory components of the myogenic mechanism and tubuloglomerular feedback (TGF) at the level of whole kidney blood flow in SDR. An interaction between these two mechanisms had previously been revealed for SDR only at the single nephron level. However, nonlinear interactions between the myogenic and TGF mechanisms are not detected for SHR.

Application of fast orthogonal search to linear and nonlinear stochastic systems

Standard deterministic autoregressive moving average (ARMA) models consider prediction errors to be unexplain able noise sources. The accuracy of the estimated ARMA model parameters depends on producing minimum prediction errors. In this study, an accurate algorithm is developed for estimating linear and nonlinear stochastic ARMA model parameters by using a method known as fast orthogonal search, with an extended model containing prediction errors as part of the model estimation process. The extended algorithm uses fast orthogonal search in a two-step procedure in which deterministic terms in the non-linear difference equation model are first identified and then reestimated, this time in a model containing the prediction errors. Since the extended algorithm uses an orthogonal procedure, together with automatic model order selection criteria, the significant model terms are estimated efficiently and accurately. The model order selection criteria developed for the extended algorithm are also crucial in obtaining accurate parameter estimates. Several simulated examples are presented to demonstrate the efficacy of the algorithm.

Nonlinear analysis of renal autoregulation in rats using principal dynamic modes

AbstractThis article presents results of the use of a novel methodology employing principal dynamic modes (PDM) for modeling the nonlinear dynamics of renal autoregulation in rats. The analyzed experimental data are broadband (0–0.5 Hz) blood pressure-flow data generated by pseudorandom forcing and collected in normotensive and hypertensive rats for two levels of pressure forcing (as measured by the standard deviation of the pressure fluctuation). The PDMs are computed from first-order and second-order kernel estimates obtained from the data via the Laguerre expansion technique. The results demonstrate that two PDMs suffice for obtaining a satisfactory nonlinear dynamic model of renal autoregulation under these conditions, for both normotensive and hypertensive rats. Furthermore, the two PDMs appear to correspond to the two main autoregulatory mechanisms: the first to the myogenic and the second to the tubuloglomerular feedback (TGF) mechanism. This allows the study of the separate contributions of the two mechanisms to the autoregulatory response dynamics, as well as the effects of the level of pressure forcing and hypertension on the two distinct autoregulatory mechanisms. It is shown that the myogenic mechanism has a larger contribution and is affected only slightly, while the TGF mechanism is affected considerably by increasing pressure forcing or hypertension (the emergence of a second resonant peak and the decreased relative contribution to the response flow signal).

Comparative nonlinear modeling of renal autoregulation in rats: Volterra approach versus artificial neural networks

Volterra models have been increasingly popular in modeling studies of nonlinear physiological systems. In this paper, feedforward artificial neural networks with two types of activation functions (sigmoidal and polynomial) are utilized for modeling the nonlinear dynamic relation between renal blood pressure and flow data, and their performance is compared to Volterra models obtained by use of the leading kernel estimation method based on Laguerre expansions. The results for the two types of artificial neural networks (sigmoidal and polynomial) and the Volterra models are comparable in terms of normalized mean-square error (NMSE) of the respective output prediction for independent testing data. However, the Volterra models obtained via the Laguerre expansion technique achieve this prediction NMSE with approximately half the number of free parameters relative to either neural-network model. Nonetheless, both approaches are deemed effective in modeling nonlinear dynamic systems and their cooperative use is recommended in general, since they may exhibit different strengths and weaknesses depending on the specific characteristics of each application.

Compact and accurate linear and nonlinear autoregressive moving average model parameter estimation using Laguerre functions

A linear and nonlinear autoregressive moving average (ARMA) identification algorithm is developed for modeling time series data. The algorithm uses Laguerre expansion of kernals (LEK) to estimate Volterra-Wiener kernals. However, instead of estimating linear and nonlinear system dynamics via moving average models, as is the case for the Volterra-Wiener analysis, we propose an ARMA model-based approach. The proposed algorithm is essentially the same as LEK, but this algorithm is extended to include past values of the ouput as well. Thus, all of the advantages associated with using the Laguerre function remain with our algorithm; but, by extending the algorithm to the linear and nonlinear ARMA model, a significant reduction in the number of Laguerre functions can be made, compared with the Volterra-Wiener approach. This translates into a more compact system representation and makes the physiological interpretation of higher order kernels easier. Furthermore, simulation results show better performance of the proposed approach in estimating the system dynamics than LEK in certain cases, and it remains effective in the presence of significant additive measurement noise.

Nonlinear system identification of heart rate variability via an artificial neural network model

An artificial neural network (ANN) with a back propagation algorithm employing a polynomial output function at the hidden unit was utilized for the analysis of the dynamic relationship between instantaneous lung volume (ILV), arterial blood pressure (ABP) and heart rate (HR). Due to a relationship between Volterra models and ANNs, impulse response functions describing the effects of ILV on HR and ABP on HR were obtained using a 3rd-order polynomial function neural network. Consequently, the dynamics of HR responses were well captured even for frequencies less than 0.3 Hz. Furthermore, the normalized residual mean square error (NRMSE) with this method was considerably less than that of previous linear analysis techniques. Thus, the results indicated the presence of a nonlinear dynamic relationship between ILV, ABP and HR.