Bilinear Components Research Articles

A nonlinear tunable piezoelectric resonant shunt using a bilinear component: theory and experiment

In this article, we propose a new concept for tuning a resonant piezoelectric shunt absorber thanks to the use of a nonsmooth electronic component. It consists in adding a voltage source in the resonant shunt circuit, which is a bilinear function of the voltage across the piezoelectric patch. The main advantage is the ability to change the electrical resonance frequency with the bilinear component gain, enabling a tuning as well as a possible reduction in the required inductance value. Furthermore, because of the intrinsic nonlinear nature of the bilinear component, a multi-harmonic response is at hand, leading to a nonlinear coupling between the mechanical and electrical modes. Two particular tunings between the electrical and the mechanical resonance frequencies are tested. The first one is one-to-one, for which the electrical resonance is tuned close to the mechanical one. It is proved to be similar to a classical linear resonant shunt, with the additional tuning ability. The second case consists in tuning the electrical circuit at half the mechanical resonance, leading to a two-to-one (2:1) internal resonance. The obtained response is also found to be similar to a classical resonant shunt near the main resonance. In either case, the shunt performances are analytically and numerically studied, leading to optimal values of the design parameters as well as an estimation of the amplitude reduction provided by the shunt. Finally, experimental validation is proposed, targeting the damping of the twisting mode of a hydrofoil structure, in which the bilinear component is realized with a diode.

Use of the reversible jump Markov chain Monte Carlo algorithm to select multiplicative terms in the AMMI-Bayesian model.

The model selection stage has become a central theme in applying the additive main effects and multiplicative interaction (AMMI) model to determine the optimal number of bilinear components to be retained to describe the genotype-by-environment interaction (GEI). In the Bayesian context, this problem has been addressed by using information criteria and the Bayes factor. However, these procedures are computationally intensive, making their application unfeasible when the model's parametric space is large. A Bayesian analysis of the AMMI model was conducted using the Reversible Jump algorithm (RJMCMC) to determine the number of multiplicative terms needed to explain the GEI pattern. Three a priori distributions were assigned for the singular value scale parameter under different justifications, namely: i) the insufficient reason principle (uniform); ii) the invariance principle (Jeffreys' prior) and iii) the maximum entropy principle. Simulated and real data were used to exemplify the method. An evaluation of the predictive ability of models for simulated data was conducted and indicated that the AMMI analysis, in general, was robust, and models adjusted by the Reversible Jump method were superior to those in which sampling was performed only by the Gibbs sampler. In addition, the RJMCMC showed greater feasibility since the selection and estimation of parameters are carried out concurrently in the same sampling algorithm, being more attractive in terms of computational time. The use of the maximum entropy principle makes the analysis more flexible, avoiding the use of procedures for correcting prior degrees of freedom and obtaining improper posterior marginal distributions.

Shrinkage in the Bayesian analysis of the GGE model: A case study with simulation.

The genotype main effects plus the genotype × environment interaction effects model has been widely used to analyze multi-environmental trials data, especially using a graphical biplot considering the first two principal components of the singular value decomposition of the interaction matrix. Many authors have noted the advantages of applying Bayesian inference in these classes of models to replace the frequentist approach. This results in parsimonious models, and eliminates parameters that would be present in a traditional analysis of bilinear components (frequentist form). This work aims to extend shrinkage methods to estimators of those parameters that composes the multiplicative part of the model, using the maximum entropy principle for prior justification. A Bayesian version (non-shrinkage prior, using conjugacy and large variance) was also used for comparison. The simulated data set had 20 genotypes evaluated across seven environments, in a complete randomized block design with three replications. Cross-validation procedures were conducted to assess the predictive ability of the model and information criteria were used for model selection. A better predictive capacity was found for the model with a shrinkage effect, especially for unorthogonal scenarios in which more genotypes were removed at random. In these cases, however, the best fitted models, as measured by information criteria, were the conjugate flat prior. In addition, the flexibility of the Bayesian method was found, in general, to attribute inference to the parameters of the models which related to the biplot representation. Maximum entropy prior was the more parsimonious, and estimates singular values with a greater contribution to the sum of squares of the genotype + genotype × environmental interaction. Hence, this method enabled the best discrimination of parameters responsible for the existing patterns and the best discarding of the noise than the model assuming non-informative priors for multiplicative parameters.

Library-aided bilinear unmixing of hyperspectral image using subspace clustering and multistep pruning

The bilinear mixing model is a more realistic, generalized model that can represent a wide range of real-world hyperspectral images with tolerable accuracy. The use of a spectral library makes the problem more tractable. However, the high mutual coherence of the spectral library creates computational as well as performance issues in library-aided bilinear unmixing. Besides, the high mutual coherence of the spectral library reduces the accuracy of these unmixing methods, and the high cardinality of the spectral library increases the computational complexity. We propose a computationally efficient, two-phase library pruning approach for unmixing hyperspectral image, which also withstands a highly coherent spectral library. In this work, we first segregate the data into pixels generated due to linear and bilinear interaction using the subspace clustering method and subsequent rank estimation strategy. We subsequently reduce the mutual coherence of the spectral library and prune the linear interactions. In the next stage, we create a library corresponding to the bilinear components assuming that only the secondary reflections of the pruned library elements may be prevalent in these pixels. We perform pruning using a novel, low-rank based, sequential approach. Finally, we compute the abundance of the matrix by exploiting sparseness of the abundance matrix and include its low-rankness, and spatial structural similarity as regularization. We validate the overall advantages of our proposed framework on several real and synthetic data experiments.

External Estimates for Reachable Sets of a Control System with Uncertainty and Combined Nonlinearity

The problem of estimating the trajectory tubes of a nonlinear control dynamic system with uncertainty in the initial data is studied. It is assumed that the dynamic system has a special structure in which the nonlinear terms are defined by quadratic forms in the state coordinates and the values of uncertain initial states and admissible controls are subject to ellipsoidal constraints. The matrix of the linear terms in the velocities of the system is not known exactly; it belongs to a given compact set in the corresponding space. Thus, the dynamics of the system is complicated by the presence of bilinear components in the righthand sides of the differential equations of the system. We consider a complicated case and generalize the author’s earlier results. More exactly, we assume the simultaneous presence in the dynamics of the system of bilinear functions and quadratic forms (without the assumption of their positive definiteness) and we also take into account the uncertainty in the initial data and the impact of the control actions, which may also be treated here as undefined additive disturbances. The presence of all these factors greatly complicates the study of the problem and requires an adequate analysis, which constitutes the main purpose of this study. The paper presents algorithms for estimating the reachable sets of a nonlinear control system of this type. The results are illustrated by examples.

SU‐F‐J‐138: An Extension of PCA‐Based Respiratory Deformation Modeling Via Multi‐Linear Decomposition

Purpose:To address and lift the limited degree of freedom (DoF) of globally bilinear motion components such as those based on principal components analysis (PCA), for encoding and modeling volumetric deformation motion.Methods:We provide a systematic approach to obtaining a multi‐linear decomposition (MLD) and associated motion model from deformation vector field (DVF) data. We had previously introduced MLD for capturing multi‐way relationships between DVF variables, without being restricted by the bilinear component format of PCA‐based models. PCA‐based modeling is commonly used for encoding patient‐specific deformation as per planning 4D‐CT images, and aiding on‐board motion estimation during radiotherapy. However, the bilinear space‐time decomposition inherently limits the DoF of such models by the small number of respiratory phases. While this limit is not reached in model studies using analytical or digital phantoms with low‐rank motion, it compromises modeling power in the presence of relative motion, asymmetries and hysteresis, etc, which are often observed in patient data. Specifically, a low‐DoF model will spuriously couple incoherent motion components, compromising its adaptability to on‐board deformation changes. By the multi‐linear format of extracted motion components, MLD‐based models can encode higher‐DoF deformation structure.Results:We conduct mathematical and experimental comparisons between PCA‐ and MLD‐based models. A set of temporally‐sampled analytical trajectories provides a synthetic, high‐rank DVF; trajectories correspond to respiratory and cardiac motion factors, including different relative frequencies and spatial variations. Additionally, a digital XCAT phantom is used to simulate a lung lesion deforming incoherently with respect to the body, which adheres to a simple respiratory trend. In both cases, coupling of incoherent motion components due to a low model DoF is clearly demonstrated.Conclusion:Multi‐linear decomposition can enable decoupling of distinct motion factors in high‐rank DVF measurements. This may improve motion model expressiveness and adaptability to on‐board deformation, aiding model‐based image reconstruction for target verification.NIH Grant No. R01‐184173

Bayesian Estimation of the Additive Main Effects and Multiplicative Interaction Model

ABSTRACTMuch research has been conducted using least squares estimates of the linear–bilinear model additive main effects and multiplicative interaction (AMMI). The main difficulty with the standard linear–bilinear models is that statistical inference on the bilinear effects of genotype × environment interaction cannot be incorporated easily into the biplot of the first two components. This research proposes a Bayesian approach for the inference on the parameters of the AMMI model using a Gibbs sampler that saves computing time and makes the algorithm stable. Data from one maize (Zea mays L.) multi‐environment trial (MET) was used for illustration. Vague but proper prior distributions were introduced. Results show that the various Markov chain Monte Carlo convergence criteria were met for all parameters. Bivariate highest posterior density (HPD) regions for the Bayesian–AMMI interactions are shown in the biplot of the first two bilinear components; these regions offer a statistical inference on the bilinear parameters and allow visualizing homogeneous groups of environments and genotypes.

Structure optimization of BiLinear Recurrent Neural Networks and its application to Ethernet network traffic prediction

The BiLinear Recurrent Neural Network (BLRNN) based on the bilinear polynomial has been successfully applied to several nonlinear time series prediction problems. In order to obtain faster convergence in training the BLRNN, two procedures are applied to the network: (i) a structure simplification procedure whereby the multiplications for bilinear components in the BLRNN are reduced and (ii) a pruning procedure entailing application of a genetic algorithm. A structurally optimized BLRNN is thereby obtained. The computational complexity of the optimized BLRNN is reduced by about half in terms of the number of weights while preserving its generalization ability. Experiments on application of the structurally optimized BLRNN to a network traffic prediction problem are conducted on a real-world Ethernet network traffic data set. Results show that the optimized BLRNN-based prediction scheme can reduce the training time by roughly half when compared with the original BLRNN while preserving the prediction accuracy of the latter in terms of Normalized Mean Square Error (NMSE).

Interlayer exchange coupling in iron/silicon nanostructures

A superexchange mechanism is considered for the interlayer exchange coupling in Fe/Si nanostructures. It is assumed that the most important role in this mechanism is played by iron-silicon interfaces, in whose immediate vicinity the contact-induced ferromagnetic phase of body-centered iron monosilicide forms and spin-polarized interface states arise. The magnetic coupling between iron layers is accomplished by means of the interaction of interface states through the normal-semiconductor spacer layer and involves both intraband and interband processes. The nonmonotonic character of the dependence of the interband exchange coupling on the spacer thickness and composition (the occurrence of a maximu, the change in shape, the possible sign reversal of the bilinear component) is caused by competition between the ferro-and antiferromagnetic super-exchange components and by the complex character of the spacer electronic spectrum (in particular, by the occurrence of several equivalent extrema in the semiconductor bands). This model qualitatively reproduces the main features of the mechanism of interlayer exchange coupling in real Fe/Si nanostructures.

A Perron Theorem for positive componentwise bilinear maps

It is proved that a Perron type theorem holds for positive maps with bilinear components whose defining matrices satisfy a maximality assumption with respect to certain entry ratios. The result is applied to a life history model which includes sexual reproduction.

Model-based shaping of vibroacoustic properties of gears

The work undertakes an issue of estimating and predicting the level and structure of the vibroacoustic signal generated by a pair of toothed wheels and propagated by the structure of the gear’s housing. Assuming that the basic role in transmission of such diagnostic information is played by the phenomena of amplitude and phase modulation of the vibroacoustic signal, it is pointed to the significance of the signal’s nonlinear components. For that reason in this work a model of a signal in the form of a Volterra series is assumed, which enables examination of the influence that disturb nonlinear components. On the basis of exemplary analysis of the contact conditions disturbances, the possibility of the generation of a bilinear component is presented. What serves this purpose is the model of nonlinear and instantaneous contact. Simultaneously problems of selection of signal analysis methods that enable realization of assumed aims are presented. Emphasizing the fact that defect development does not always lead to a significant growth of the vibroacoustic signal’s power, the importance of methods of higher-order spectral analysis like bispectrum and bicepstrum has been shown. June or ftp.aip.org.

POLYLIN: A FORTRAN IV program for the analysis of multiplicative (multilinear) trend components of interactions

The ci is the deviation of the Row i means from the grand mean; the same holds for Cj and the Column j mean. These are essentially the linear orthogonal polynomial coefficients for the row and column factors, respectively. The Cij provide the coefficients for the linear by linear component of the interaction. The sum of squares for the bilinear component is computed from: model results from testing the residual 55, that is, the difference between the total interaction 55 and the multilinear 55. If the model is successful, then the derived coefficients provide estimates of the psychological values along each factor. These values are generally on an interval scale, although ratio scale estimates can also be obtained depending on the experimental design (see Shanteau, 1974). The logic of this estimation procedure is based on the functional measurement approach (Anderson, 1974). The basis for the statistical test comes from developments of Mandel (l961) and Tukey (l949). Program Operation. POLYLIN is designed to extract the multilinear sum of squares from each interaction in up to a four-factor design. To extract each term, coefficients are calculated based on the marginal means: