Finite impulse response model

B.M. Wise, N.L. Ricker, Identification of finite impulse response models with continuum... 

For more details about the relationship between multivariate finite impulse response models and (parsimonious) VARMAX models in chemical process analysis, see e.g. Seppala et al. (2002). 

Dayal, B. S. J. F. MacGregor (1996), Identification of finite impulse response models methods and robustness issues , Ind. Eng. Chem. Res. 35, 4078-4090. 

Integer N is selected so that N t > tg, the settling time of the process (see Chapter 5). Note that an equivalent version of Eq. 7-43 can be written with y(k) instead of y k + 1) on the left-hand side (as in Section 7.4) by shifting the index backward one sampling period. A related discrete-time model can be derived from Eq. 7-43 and is called the finite step response model, or just the step response model. To illustrate this relationship, we consider a simple (finite) impulse response model where N = 3. Expanding the summation in Eq. 7-43 gives... 

The step-response model is also referred to as a finite impulse response (FIR) model or a discrete convolution model. 

There are several other chemometric approaches to calibration transfer that will only be mentioned in passing here. An approach based on finite impulse response (FIR) filters, which does not require the analysis of standardization samples on any of the analyzers, has been shown to provide good results in several different applications.81 Furthermore, the effectiveness of three-way chemometric modeling methods for calibration transfer has been recently discussed.82 Three-way methods refer to those methods that apply to A -data that must be expressed as a third-order data array, rather than a matrix. Such data include excitation/emission fluorescence data (where the three orders are excitation wavelength, emission wavelength, and fluorescence intensity) and GC/MS data (where the three orders are retention time, mass/charge ratio, and mass spectrum intensity). It is important to note, however, that a series of spectral data that are continuously obtained on a process can be constructed as a third-order array, where the three orders are wavelength, intensity, and time. 

It is clear that the foregoing problem formulation necessitates the prediction of future outputs y[k + i k]. This, in turn, makes necessary the use of a model for the process and external disturbances. To start the discussion on process models, assume that the following finite-impulse-response (FIR) model describes the dynamics of the controlled process ... 

Since this work deals with the aggregated simulation and planning of chemical production processes, the focus is laid upon methods to determine estimations of the process models. For process control this task is the crucial one as the estimations accuracy determines the accuracy of the whole control process. The task to find an accurate process model is often called process identification. To describe the input-output behaviour of (continuously operated) chemical production plants finite impulse response (FIR) models are widely used. These models can be seen as regression models where the historical records of input/control measures determine the output measure. The term "finite" indicates that a finite number of historical records is used to predict the process outputs. Often, chemical processes show a significant time-dynamic behaviour which is typically reflected in auto-correlated and cross-correlated process measures. However, classic regression models do not incorporate auto-correlation explicitly which in turn leads to a loss in estimation efficiency or, even worse, biased estimates. Therefore, time series methods can be applied to incorporate auto-correlation effects. According to the classification shown in Table 2.1 four basic types of FIR models can be distinguished. 

Alternatively, the noise type can be ignored applying so-called non-parsimoniovs finite impulse-response (FIR) models by increasing N, the number of lagged observations of the control variable(s). This method has some serious drawbacks e.g. biased and instable estimates/forecasts in case of finite samples. See e.g. Dayal and MacGregor (1996) and references therein. 

We begin with the single input, single output (SISO) case and assume that the process to be identified is stable, linear, time invariant and can be represented by the following discrete-time, finite impulse response (FIR) transfer function model ... 

Non-linear Finite Impulse Response (NFIR) models, which use Ut-k as regressors, k= 1,. ..N... 

Another type of discrete-time model, the finite impulse response (FIR) or convolution model, has become important in computer control. This model can be written as... 

This work focused on non linear time invariant processes. An approach to deal with time varying model was proposed by Genceli and Nikolau [16] using a finite impulse response (FIR) model that was updated in real time. Recently, Alexandridis and Sarimveis [17] proposed an adaptive model predictive control using a non linear... 

The FRF, G(tw), can be obtained by various methods such as finite element method (FEM), Timoshenko beam theory (Cao and Altintas 2004), impulse response method (Ewins 2001), or widely used frequency response analysis (Ewins 2001). Hybrid methods such as the receptance coupling substructure analysis (RCSA) (Schmitz and Duncan 2005) have also been utilized in practice. For example, excitation force generated in milling process can be estimated by an analytical model of the milling process (Altintas 2000). 

Impulse Response for the Krogh Cylinder Model with Plug Flow in the Capillary (Phase 1), Finite Diffusional Resistance Perpendicular to Flow Direction in the Tissue (Phase 2) and No Resistance at the Capillary Wall (Phase Boundary). Equivalent to Case 2. 

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