Orthonormal basis selection for LPV system identification, the Fuzzy-Kolmogorov c-Max approach

A fuzzy clustering approach is developed to select pole locations for orthonormal basis functions (OBFs), used for identification of linear parameter varying (LPV) systems. The identification approach is based on interpolation of locally identified linear time invariant (LTI) models, using globally fixed OBFs. Selection of the optimal OBF structure, that guarantees the least worst-case local modelling error in an asymptotic sense, is accomplished through the fusion of the Kolmogorov n-width (KnW) theory and fuzzy c-means (FcM) clustering of observed sample system pole

A prediction-error identification framework for linear parameter-varying systems

Identification of Linear Parameter-Varying (LPV) models is often addressed in an Input-Output (IO) setting using particular extensions of classical Linear Time-Invariant (LTI) prediction-error methods. However, due to the lack of appropriate system-theoretic results, most of these methods are applied without the understanding of their statistical properties and the behavior of the considered noise models. Using a recently developed series expansion representation of LPV systems, the classical concepts of the prediction-error framework are extended to the LPV case and the statistical properties of estimation are analyzed in the LPV context. In the introduced framework it can be shown that under minor assumptions, the classical results on consistency, convergence, bias and asymptotic variance can be extended for LPV predictionerror models and the concept of noise models can be clearly understood. Preliminary results on persistency of excitation and identifiability can also established

Model structures for identification of linear parameter-varying (LPV) models

Describing nonlinear dynamic systems by linear parameter-varying models has become an attractive tool for control of complex systems with regimedependent (linear) behavior. For the identification of LPV models from experimental data a number of methods has been presented in the literature but a full picture of the underlying identification problem is still missing. In this contribution a solid system theoretic basis for the description of model structures for LPV models is presented, together with a general approach to the LPV identification problem. Use is made of a series expansion approach to LPV modeling, employing orthogonal basis function expansions

LPV system identification with globally fixed orthonormal basis functions

A global and a local identification approach are developed for approximation of linear parameter-varying (LPV) systems. The utilized model structure is a linear combination of globally fixed (scheduling-independent) orthonormal basis functions (OBFs) with scheduling-parameter dependent weights. Whether the weighting is applied on the input or on the output side of the OBFs, the resulting models have different modeling capabilities. The local identification approach of these structures is based on the interpolation of locally identified LTI models on the scheduling domain where the local models are composed from a fixed set of OBFs. The global approach utilizes a priori chosen functional dependence of the parameter-varying weighting of a fixed set of OBFs to deliver global model estimation from measured I/O data. Selection of the OBFs that guarantee the least worst-case modeling error for the local behaviors in an asymptotic sense, is accomplished through the fuzzy Kolmogorov c-max approach. The proposed methods are analyzed in terms of applicability and consistency of the estimates

Discretization of linear fractional representations of LPV systems

Commonly, controllers for Linear Parameter- Varying (LPV) systems are designed in continuous-time using a Linear Fractional Representation (LFR) of the plant. However, the resulting controllers are implemented on digital hardware. Furthermore, discrete-time LPV synthesis approaches require a discrete-time model of the plant which is often derived from continuous-time first-principle models. Existing discretization approaches for LFRs suffer from disadvantages like alternation of dynamics, complexity, etc. To overcome the disadvantages, novel discretization methods are derived. These approaches are compared to existing techniques and analyzed in terms of approximation error, considering ideal zero-order hold actuation and sampling

LPV system identification with globally fixed orthonormal basis functions

A global and a local identification approach are developed for approximation of linear parameter-varying (LPV) systems. The utilized model structure is a linear combination of globally fixed (scheduling-independent) orthonormal basis functions (OBFs) with scheduling-parameter dependent weights. Whether the weighting is applied on the input or on the output side of the OBFs, the resulting models have different modeling capabilities. The local identification approach of these structures is based on the interpolation of locally identified LTI models on the scheduling domain where the local models are composed from a fixed set of OBFs. The global approach utilizes a priori chosen functional dependence of the parameter-varying weighting of a fixed set of OBFs to deliver global model estimation from measured I/O data. Selection of the OBFs that guarantee the least worst-case modeling error for the local behaviors in an asymptotic sense, is accomplished through the fuzzy Kolmogorov c-max approach. The proposed methods are analyzed in terms of applicability and consistency of the estimates

Tur\'an Graphs, Stability Number, and Fibonacci Index

The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight upper bounds for the Fibonacci index in terms of the stability number and the order of general graphs and connected graphs. Tur\'an graphs frequently appear in extremal graph theory. We show that Tur\'an graphs and a connected variant of them are also extremal for these particular problems.Comment: 11 pages, 3 figure

Metabolomic and Functional Genomic Analyses Reveal Varietal Differences in Bioactive Compounds of Cooked Rice

Emerging evidence supports that cooked rice (Oryza sativa L.) contains metabolites with biomedical activities, yet little is known about the genetic diversity that is responsible for metabolite variation and differences in health traits. Metabolites from ten diverse varieties of cooked rice were detected using ultra performance liquid chromatography coupled to mass spectrometry. A total of 3,097 compounds were detected, of which 25% differed among the ten varieties. Multivariate analyses of the metabolite profiles showed that the chemical diversity among the varieties cluster according to their defined subspecies classifications: indica, japonica, and aus. Metabolite-specific genetic diversity in rice was investigated by analyzing a collection of single nucleotide polymorphisms (SNPs) in genes from biochemical pathways of nutritional importance. Two classes of bioactive compounds, phenolics and vitamin E, contained nonsynonymous SNPs and SNPs in the 5′ and 3′ untranslated regions for genes in their biosynthesis pathways. Total phenolics and tocopherol concentrations were determined to examine the effect of the genetic diversity among the ten varieties. Per gram of cooked rice, total phenolics ranged from 113.7 to 392.6 µg (gallic acid equivalents), and total tocopherols ranged between 7.2 and 20.9 µg. The variation in the cooked rice metabolome and quantities of bioactive components supports that the SNP-based genetic diversity influenced nutritional components in rice, and that this approach may guide rice improvement strategies for plant and human health

Investigation of the Effect of a Diamine-Based Friction Modifier on Micropitting and the Properties of Tribofilms in Rolling-Sliding Contacts

The effect of N-Tallow-1,3-DiaminoPropane (TDP) on friction, rolling wear and micropitting has been investigated with the ultimate objective of developing lubricants with no or minimal environmental impact. A Mini Traction Machine (MTM-SLIM) has been utilised in order to generate tribofilms and observe the effect of TDP on anti-wear tribofilm formation and friction. Micropitting was induced on the surface of specimens using a MicroPitting Rig (MPR). The X-ray Photoelectron Spectroscopy (XPS) surface analytical technique has been employed to investigate the effect of TDP on the chemical composition of the tribofilm while Atomic Force Microscopy (AFM) was used to generate high resolution topographical images of the tribofilms formed on the MTM discs. Experimental and analytical results showed that TDP delays the Zinc DialkylDithioPhosphate (ZDDP) anti-wear tribofilm formation. TDP in combination with ZDDP induces a thinner and smoother anti-wear tribofilm with a modified chemical structure composed of mixed Fe/Zn (poly)phosphates. The sulphide contribution to the tribofilm and oxygen-to-phosphorous atomic concentration ratio are greater in the bulk of the tribofilm derived from a combination of TDP and ZDDP compared to a tribofilm derived from ZDDP alone. Surface analysis showed that utilising TDP effectively mitigates micropitting wear in the test conditions used in this study. Reduction of micropitting, relevant to rolling bearing applications, can be attributed to the improved running-in procedure, reduced friction, formation of a smoother tribofilm and modification of the tribofilm composition induced by TDP