A tree-structured piecewise linear adaptive filter

Gelfand, S.B.; Ravishankar, C.

doi:10.1109/18.265499

Cited by 22 publications

(8 citation statements)

References 14 publications

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“…The condition for the growth of the binary tree is as follows: If RM SE t ε, then stop the partition of vertex t; if RM SE t > ε, then partition the subspace: calculate the center of gravity of corresponding outputs on the subspace [21] …”

Section: Fuzzy-tree Identification Methods IImentioning

confidence: 99%

Intelligent modeling and control for nonlinear systems with rate-dependent hysteresis

Mao

Ding²

2009

Sci. China Ser. F-Inf. Sci.

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A new modeling approach for nonlinear systems with rate-dependent hysteresis is proposed. The approach is used for the modeling of the giant magnetostrictive actuator, which has the rate-dependent nonlinear property. The models built are simpler than the existed approaches. Compared with the experiment result, the model built can well describe the hysteresis nonlinear of the actuator for input signals with complex frequency. An adaptive direct inverse control approach is proposed based on the fuzzy tree model and inverse learning and special learning that are used in neural network broadly. In this approach, the inverse model of the plant is identified to be the initial controller firstly. Then, the inverse model is connected with the plant in series and the linear parameters of the controller are adjusted using the least mean square algorithm by on-line manner. The direct inverse control approach based on the fuzzy tree model is applied on the tracing control of the actuator by simulation. The simulation results show the correctness of the approach.nonlinear systems with rate-dependent hysteresis, intelligent modeling and control, fuzzy tree model, T-S fuzzy model, adaptive inverse control Nonlinear systems with hysteresis generally exists in engineering, such as civil engineering, power engineering, control engineering, etc. For example, if there exists elastic-plastic components or dry friction, then relationship between the force and the displacement or the stress and the strain will be not inverse any longer. Thus the hysteresis curve is formed [1] . If the shape of the hysteresis curve varies with the frequency of the input signal, then the class of systems is called nonlinear systems with rate-dependent hysteresis. The active vibration control systems based on giant magnetostrictive actuators is a type of nonlinear systems with ratedependent hysteresis. The rate-dependent hysteresis of the magnetostrictive actuator is an essential nonlinear component, which cannot be eliminated, and it will affect the control accuracy and stability of the systems [2] .There are three classes of approaches for the modeling of hysteresis. One is the physical modeling theory, which is represented by Jiles-Atherton model. The other is the operator modeling theory,

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Section: Fuzzy-tree Identification Methods IImentioning

confidence: 99%

Intelligent modeling and control for nonlinear systems with rate-dependent hysteresis

Mao

Ding²

2009

Sci. China Ser. F-Inf. Sci.

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“…At the same time, a common feature of those techniques is that they were developed for the processing of a single signal, not of large signal sets as in this paper. In particular, piecewise linear filters in [19] have been obtained by arranging linear filters and thresholds in a tree structure. Piecewise linear filters discussed in [20] were developed using so-called threshold decomposition, which is a segmentation operator exploited to split a signal into a set of multilevel components.…”

Section: Other Relevant Filtersmentioning

confidence: 99%

“…Proof: The proof of Theorem 1 is given in Section 7. ✷ It is worthwhile to observe that, due to an arbitrary matrix M B j in (19), the filter F (p−1) is not unique. In particular, M B j can be chosen as the zero matrix O similarly to the generic optimal linear [5] (which is also not unique by the same reason).…”

Section: Determination Of Piecewise Linear Interpolation Filtermentioning

confidence: 99%

Filtering of stochastic signal sets: A new piecewise interpolation technique

Torokhti

2011

2011 IEEE Statistical Signal Processing Workshop (SSP)

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Suppose K Y and K X are large sets of observed and reference signals, respectively, each containing N signals. Is it possible to construct a filter F : K Y → K X that requires a priori information only on few signals, p ≪ N , from K X but performs better than the known filters based on a priori information on every reference signal from K X ? It is shown that the positive answer is achievable under quite unrestrictive assumptions. The device behind the proposed method is based on a special extension of the piecewise linear interpolation technique to the case of random signal sets. The proposed technique provides a single filter to process any signal from the arbitrarily large signal set. The filter is determined in terms of pseudo-inverse matrices so that it always exists.

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“…Therefore, they can be used for cases where the data record is small. One technique for building PWL lters is based on regression trees 10], and although continuity is not enforced, they have been successfully applied to problems in channel equalization and echo cancellation 10,11].…”

Section: Introductionmentioning

confidence: 99%

Piecewise linear system modeling based on a continuous threshold decomposition

Heredia

Arce

1996

IEEE Trans. Signal Process.

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The continuous threshold decomposition is a segmentation operator used to split a signal into a set of multilevel components. This decomposition method can be used to represent continuous multivariate piecewise linear (PWL) functions, and therefore can be employed to describe PWL systems de ned over a rectangular lattice. The resulting lters are canonical and have a multichannel structure that can be exploited for the development of rapidly convergent algorithms. The optimum design of the class of PWL lters introduced in the paper can be postulated as a least squares problem whose variables separate into a linear and a nonlinear part. Based on this feature, parameter estimation algorithms are developed. First, a block data processing algorithm that combines linear least-squares with grid localization through recursive partitioning is introduced. Second, a time-adaptive method based on the combination of an RLS algorithm for coe cient updating and a signed gradient descent module for threshold adaptation is proposed and analyzed. A system identi cation problem for wave propagation through a nonlinear multi-layer channel serves as a comparative example where the concepts introduced are tested against the Linear, Volterra and Neural Network alternatives.

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A tree-structured piecewise linear adaptive filter

Cited by 22 publications

References 14 publications

Intelligent modeling and control for nonlinear systems with rate-dependent hysteresis

Intelligent modeling and control for nonlinear systems with rate-dependent hysteresis

Filtering of stochastic signal sets: A new piecewise interpolation technique

Piecewise linear system modeling based on a continuous threshold decomposition

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