Adaptive hinging hyperplanes and its applications in dynamic system identification

Optimizing scheduling of refinery operations based on piecewise linear models

“…It appears that for both modeling methods, a small number of grids are sufficient to model the processes. The modeling accuracy, in terms of relative sum of squared errors (RSSE) (Xu et al, 2009), is compared in Table 2. It is not surprising that in all cases, the multi-CPWL models are less accurate than multiple CPWL models developed separately, because multi-CPWL has an additional constraint that all response functions have the same partition (i.e.…”

“…In the community of systems engineering, a range of PWL representations have been reported, such as canonical representation of section-wise piecewise linear functions (Chua & Kang, 1977), hinging hyperplanes (Breiman, 1993), generalized piecewise linear functions (Lin et al, 1994), high level canonical piecewise linear functions (Juliá n et al, 1999), generalized hinging hyperplanes (Wang & Sun, 2005), and adaptive hinging hyperplanes (Xu et al, 2009). Nevertheless, these compact PWL representations often result in a large number of subregions (Huang et al, 2012), and thus the model structure becomes too complex to be useful in practice.…”

Three-Stage Decomposition Modeling for Quality of Gas-Phase Polyethylene Process Based on Adaptive Hinging Hyperplanes and Impulse Response Template

“…29 The most important advantage is that the identification algorithm of AHH model is designed inspired by multivariate adaptive regression splines (MARS) as a recursive regression method, which is simpler and can be executed more efficiently than that of the GHH model. 29 By a slight modification on the basis function of MARS, the basis function of AHH keeps the basic form of hinging functions and can be written as From the above discussion, the AHH model is nonlinear region-wide, but linear in each subregion, and the operator used is only "min" or "max"; therefore, it has more stability than high-order splines and the error would not be magnified when used in prediction. 29 Conversely, high-order splines are unstable and more likely to magnify the prediction errors under misleading structures, especially in the case of noise and small sample size.…”

Optimization on distillation via piecewise linear approximation

“…Ref. [9] proposes a new CPWL representation called adative hinging hyperplanes (AHH) and corresponding identification algorithm is given in [10]. It combines the properties of GHH and multivariate adaptive regression splines (MARS) method and has approximation capability to any continuous function with required precision.…”