Alternative Cost Function Research Articles

Adaptive Model Predictive Control for DAB Converter Switching Losses Reduction

The solid-state transformer is the enabling technology for the future of electric power systems. The increasing relevance of this equipment demands higher standards for efficiency and losses reduction. The dual active bridge (DAB) topology is the most usual DC-DC converter used in the solid-state transformer, and is responsible for part of its switching losses. The traditional phase-shift modulation used on DAB converters presents significant switching losses during the operation with reduced loads. The alternative Triangular and Trapezoidal Modulations have been proposed in recent literature; however, there are limitations on the maximum power these techniques can deal with. This paper presents an adaptive model predictive control to select among these three techniques, according to the converter model, the one that minimizes the switching losses and allows the current demanded by the load. Moreover, an alternative cost function is proposed, including the output voltage and current. Through real-time simulation, using a 1000 V/600 V 12 kW DAB converter, it is shown that the proposed control is able to reduce the losses on the converter. Furthermore, the proposed control presents fast and accurate response, and precise transition between the modulation techniques.

Spherical clustering in detection of groups of concomitant extremes

Summary There is growing empirical evidence that spherical $k$-means clustering performs well at identifying groups of concomitant extremes in high dimensions, thereby leading to sparse models. We provide one of the first theoretical results supporting this approach, but also demonstrate some pitfalls. Furthermore, we show that an alternative cost function may be more appropriate for identifying concomitant extremes, and it results in a novel spherical $k$-principal-components clustering algorithm. Our main result establishes a broadly satisfied sufficient condition guaranteeing the success of this method, albeit in a rather basic setting. Finally, we illustrate in simulations that $k$-principal components clustering outperforms $k$-means clustering in the difficult case of weak asymptotic dependence within the groups.

Inexact Generalized Gauss–Newton for Scaling the Canonical Polyadic Decomposition With Non-Least-Squares Cost Functions

The canonical polyadic decomposition (CPD) allows one to extract compact and interpretable representations of tensors. Several optimization-based methods exist to fit the CPD of a tensor for the standard least-squares (LS) cost function. Extensions have been proposed for more general cost functions such as β-divergences as well. For these non-LS cost functions, a generalized Gauss-Newton (GGN) method has been developed. This is a second-order method that uses an approximation of the Hessian of the cost function to determine the next iterate and with this algorithm, fast convergence can be achieved close to the solution. While it is possible to construct the full Hessian approximation for small tensors, the exact GGN approach becomes too expensive for tensors with larger dimensions, as found in typical applications. In this paper, we therefore propose to use an inexact GGN method and provide several strategies to make this method scalable to large tensors. First, the approximation of the Hessian is only used implicitly and its multilinear structure is exploited during Hessian-vector products, which greatly improves the scalability of the method. Next, we show that by using a compressed instance of the GGN Hessian approximation, the computation time of the inexact GGN method can be lowered even more, with only limited influence on the convergence speed. We also propose dedicated preconditioners for the problem. Further, the maximum likelihood estimator for Rician distributed data is examined in detail as an example of an alternative cost function. This cost function is useful for the analysis of the moduli of complex data, as in functional magnetic resonance imaging, for instance. We compare the proposed method to the existing CPD methods and demonstrate the method's speed and effectiveness on synthetic and simulated real-life data. Finally, we show that the method can scale by using randomized block sampling.

Exploring an Alternative Cost Function for Combinatorial Register-Pressure-Aware Instruction Scheduling

Multiple combinatorial algorithms have been proposed for doing pre-allocation instruction scheduling with the objective of minimizing register pressure or balancing register pressure and instruction-level parallelism. The cost function that is minimized in most of these algorithms is the peak register pressure (or the peak excess register pressure). In this work, we explore an alternative register-pressure cost function, which is the Sum of Live Interval Lengths (SLIL). Unlike the peak cost function, which captures register pressure only at the highest pressure point in the schedule, the proposed SLIL cost function captures register pressure at all points in the schedule. Minimizing register pressure at all points is desirable in larger scheduling regions with multiple high-pressure points. This article describes a Branch-and-Bound (B8B) algorithm for minimizing the SLIL cost function. The algorithm is based on two SLIL-specific dynamic lower bounds as well as the history utilization technique proposed in our previous work. The proposed algorithm is implemented into the LLVM Compiler and evaluated experimentally relative to our previously proposed B8B algorithm for minimizing the peak excess register pressure. The experimental results show that the proposed algorithm for minimizing the SLIL cost function produces substantially less spilling than the previous algorithm that minimizes the peak cost function. Execution-time results on various processors show that the proposed B8B algorithm significantly improves the performance of many CPU2006 benchmarks by up to 49% relative to LLVM's default scheduler. The geometric-mean improvement for FP2006 on Intel Core i7 is 4.22%.

Solving PhaseLift by Low-Rank Riemannian Optimization Methods for Complex Semidefinite Constraints

A framework, PhaseLift, was recently proposed to solve the phase retrieval problem. In this framework, the problem is solved by optimizing a cost function over the set of complex Hermitian positive semidefinite matrices. This approach to phase retrieval motivates a more general consideration of optimizing cost functions on semidefinite Hermitian matrices where the desired minimizers are known to have low rank. This paper considers an approach based on an alternative cost function defined on a union of appropriate manifolds. It is related to the original cost function in a manner that preserves the ability to find a global minimizer and is significantly more efficient computationally. A rank-based optimality condition for stationary points is given and optimization algorithms based on state-of-the-art Riemannian optimization and dynamically reducing rank are proposed. Empirical evaluations are performed using the PhaseLift problem. The new approach is shown to be an effective method of phase retrieval with...

Solving PhaseLift by Low-rank Riemannian Optimization Methods

A framework, PhaseLift, was recently proposed to solve the phase retrieval problem. In this framework, the problem is solved by optimizing a cost function over the set of complex Hermitian positive semidefinite matrices. This paper considers an approach based on an alternative cost function defined on a union of appropriate manifolds. It is related to the original cost function in a manner that preserves the ability to find a global minimizer and is significantly more efficient computationally. A rank-based optimality condition for stationary points is given and optimization algorithms based on state-of-the-art Riemannian optimization and dynamically reducing rank are proposed. Empirical evaluations are performed using the PhaseLift problem. The new approach is shown to be an effective method of phase retrieval with computational efficiency increased substantially compared to the algorithm used in original PhaseLift paper.

NETVOLC: An algorithm for automatic delimitation of volcano edifice boundaries using DEMs

Accurately delimiting boundaries is required for characterizing landforms through measurement of their geomorphometric parameters. Volcanism produces a wide range of landforms, from symmetric cones to very irregular massifs, that can gradually merge with the surroundings and contain other elements, thus complicating landform delimitation. Most morphometric studies of volcanoes delimit landforms manually, with the inconvenience of being time-consuming and subjective. Here we propose an algorithm, NETVOLC, for automatic volcano landform delimitation based on the premise that edifices are bounded by concave breaks in slope. NETVOLC applies minimum cost flow (MCF) networks for computing the best possible edifice outline using a DEM and its first- and second-order derivatives. The main cost function considers only profile convexity and aspect; three alternative functions (useful in complex cases) also consider slope, elevation and/or radial distance. NETVOLC performance is tested by processing the Mauna Kea pyroclastic cone field. Results using the main cost function compare favorably to manually delineated outlines in 2/3rds of cases, whereas for the remaining 1/3rd of cases an alternative cost function is needed, introducing some degree of subjectivity. Our algorithm provides a flexible, objective and time-saving tool for automatically delineating volcanic edifices. Furthermore, it could be used for delineating other landforms with concave breaks in slope boundaries. Finally, straightforward modifications can be implemented to extend the algorithm capabilities for delimiting landforms bounded by convex breaks in slope, such as summit craters and calderas.

Mixed Gaussian-lognormal four-dimensional data assimilation

In this paper, the current methods that are used for deriving the Gaussian cost function in four-dimensional variational (4D VAR) data assimilation, are extended to lognormal and mixed, lognormal and Gaussian, random variables (rv). It is also shown that transforming a lognormal rv into a Gaussian rv to use in a Gaussian based 4D VAR results in the analysis state being similar to a median in lognormal space. An alternative version of the functional approach is derived so that the minimum of this alternative cost function is the mode in lognormal space. However, the current approaches do not allow for a generalized probability density function (pdf) approach, to overcome this a general probability model is derived so that the mode is found for any pdf from Bayesian networks and conditional independence properties. It is shown that the current Gaussian cost function and the lognormal can be found by the probability model method. The paper is finished by comparing the median approach with the modal approach in the Lorenz 1963 model for both weak and strong constraint 4D VAR and show that the mode is a more reliable analysis statistic than the median under certain circumstances.

Mixed Gaussian-lognormal four-dimensional data assimilation

In this paper, the current methods that are used for deriving the Gaussian cost function in four-dimensional variational (4D VAR) data assimilation, are extended to lognormal and mixed, lognormal and Gaussian, random variables (rv). It is also shown that transforming a lognormal rv into a Gaussian rv to use in a Gaussian based 4D VAR results in the analysis state being similar to a median in lognormal space. An alternative version of the functional approach is derived so that the minimum of this alternative cost function is the mode in lognormal space. However, the current approaches do not allow for a generalized probability density function (pdf) approach, to overcome this a general probability model is derived so that the mode is found for any pdf from Bayesian networks and conditional independence properties. It is shown that the current Gaussian cost function and the lognormal can be found by the probability model method. The paper is finished by comparing the median approach with the modal approach in the Lorenz 1963 model for both weak and strong constraint 4D VAR and show that the mode is a more reliable analysis statistic than the median under certain circumstances.

Choosing among alternative cost function specifications: an application to Italian multi-utilities

The paper investigates the cost properties of a sample of Italian utilities providing in combination gas, water and electricity services. The estimates from a multi-product Composite cost function [Rev. Econ. Stat. 74 (1992) 221] are compared with the ones coming from other traditional functional forms such as the Standard Translog (ST), the Generalized Translog (GT), and the Separable Quadratic (SQ). The results show that the composite model provides a better description of data and highlight the presence of global scope and scale economies for the ‘median’ firm of the sample.

Generalized information potential criterion for adaptive system training

We have previously proposed the quadratic Renyi's error entropy as an alternative cost function for supervised adaptive system training. An entropy criterion instructs the minimization of the average information content of the error signal rather than merely trying to minimize its energy. In this paper, we propose a generalization of the error entropy criterion that enables the use of any order of Renyi's entropy and any suitable kernel function in density estimation. It is shown that the proposed entropy estimator preserves the global minimum of actual entropy. The equivalence between global optimization by convolution smoothing and the convolution by the kernel in Parzen windowing is also discussed. Simulation results are presented for time-series prediction and classification where experimental demonstration of all the theoretical concepts is presented.

Dynamic harmonic regression

This paper describes in detail a flexible approach to nonstationary time series analysis based on a Dynamic Harmonic Regression (DHR) model of the Unobserved Components (UC) type, formulated within a stochastic state space setting. The model is particularly useful for adaptive seasonal adjustment, signal extraction and interpolation over gaps, as well as forecasting or backcasting. The Kalman Filter and Fixed Interval Smoothing algorithms are exploited for estimating the various components, with the Noise Variance Ratio and other hyperparameters in the stochastic state space model estimated by a novel optimization method in the frequency domain. Unlike other approaches of this general type, which normally exploit Maximum Likelihood methods, this optimization procedure is based on a cost function defined in terms of the difference between the logarithmic pseudo-spectrum of the DHR model and the logarithmic autoregressive spectrum of the time series. The cost function not only seems to yield improved convergence characteristics when compared with the alternative ML cost function, but it also has much reduced numerical requirements. Copyright © 1999 John Wiley & Sons, Ltd.

Minimization of the maximum error signal in active control

This paper presents a new multichannel adaptive filtering algorithm for the active control of single frequency noise in acoustic systems. Most active control systems with multiple error sensors minimize the sum of the modulus squared output of these sensors. An adaptive algorithm is presented that minimizes an alternative cost function which, in the limit, is equal to the maximum of the modulus squared values of all the error sensors. The physical consequences of minimizing the maximum modulus squared output to achieve noise reduction are investigated. An analytical framework is developed that covers the steady state performance as well as the convergence properties. By means of simulations, the proposed algorithm has been applied to a linear model of a one-dimensional (1-D) acoustic system and compared with the classical least squares solutions. The proposed algorithm is also used in simulations of the control of the pressure measured at 32 microphone positions in a room using 16 loudspeakers, when the room is excited with an 88 Hz pure tone. The results of these simulations show that the observed convergence and steady-state properties agree well with the theoretical predictions. A comparison with the least squares solutions leads to the conclusion that the proposed algorithm leads to a more uniform acoustic field in the enclosure than the classical least squares algorithm.

An evaluation of a class of practical optimization techniques for structural dynamics applications

AbstractThis paper evaluates a class of practical optimization techniques for parameter identification of realistic structural dynamic systems. The techniques involve quasi‐Newton methods together with an efficient procedure for estimating complicated error functions. The optimization procedures are verified through their application to several representative examples, including finite‐element models of realistic structural systems. Extensive numerical and graphical results demonstrate the effects of various optimization algorithm parameters on the rate of convergence of the objective function, the parameter vector error norm and the gradient norm. Guidelines are presented as an aid for addressing several significant issues in the practical application of structural dynamics optimization procedures, such as sensitivity problems, uniqueness, initial value definition for the parameter vector, convergence rates, constraints, the effect of alternative cost function definitions, accuracy of alternative gradient evaluation procedures, alternative procedures for estimating the inverse of the Hessian matrix and the use of a quadratic approximation of the objective function.