Existing Cost Function Research Articles

Spatial and Temporal Sampling Properties of a Large GNSS-R Satellite Constellation

Using large constellations of smallsats, mission designers can improve sampling density and coverage. We develop performance metrics that characterize key sampling properties for applications in numerical weather prediction and optimize orbit design parameters of the constellation with respect to those metrics. Orbits are defined by a set of Keplerian elements, and the relationship between those elements and the spatial and temporal coverage metrics are examined in order to maximize global and zonal (latitude-dependent) coverage. Additional optimization is performed by dividing a constellation into multiple orbit planes. An iterative method can be applied to this design process to compare the performance of current and previous designs. The main objective of this work is the design of optimized configurations of satellites in low Earth orbiting constellations to maximize the spatial and temporal sampling and coverage provided by its sensors. The key innovations developed are a new cost function which measures the temporal sampling properties of a satellite constellation, and the use of it together with existing cost functions for spatial sampling to design satellite constellations that optimize performance with respect to both performance metrics.

Cost Reassignment for Improving Security of Adaptive Steganography Using an Artificial Immune System

The cost function is crucial to the security of adaptive image steganography, However, some existing cost functions are heuristically designed and hard to be optimal in the undetectability against the evolving steganalyzer. In this letter, we propose a cost reassignment algorithm for adaptive steganography based on artificial immune system. Under the scenario of minimizing additive distortion, this method reassigns the cost by adjusting the modification probability distribution obtained by the cost function, and dynamically optimizes the adjustment mode through the immunity-based information hiding model, so that the modified pixels are more concentrated in the regions that are difficult to be detected. The experimental results show that the proposed method is suitable for a variety of the state-of-the-art cost functions and can achieve better performance on resisting the steganalysis.

Cost function research for SPSA algorithm: An application of the cross-correlation function in periodic disturbance energy estimation

Active vibration control of stable rotating machinery with a time-variant structure is a research priority in the field. Simultaneous perturbation stochastic approximation (SPSA), a model-free active control strategy, has attracted a lot of attention from researchers. This paper studies the cost function of the SPSA algorithm to improve its performance in controlling periodic vibration. After the weight vector being perturbed by a perturbation vector, the existing cost functions of the SPSA algorithm can reveal the overall energy variation but hardly detail the variation of each harmonic wave. Therefore, the adaptive notch filter with the SPSA algorithm using these cost functions shows a low convergence speed and a bad control effect in active periodic disturbance controlling. In order to detail the energy variation of each harmonic, this paper proposes a cost function using the weighted cross correlation function. When the algorithm calculates the energy of each harmonic wave, the disturbances from other harmonics and background noise are reduced. The interference noises in the estimated gradient of the cost function are reduced indirectly. The algorithm convergence performance improves. To illustrate that, the simulations of controlling harmonic waves and the experiments of eliminating the vibration of the pump inlet pipeline are conducted. The results indicate that the adaptive notch filter with the proposed cost function has reached the fastest convergence speed and the best control effect so far among the use of other cost functions mentioned in this paper.

Tacho-less sparse CNN to detect defects in rotor-bearing systems at varying speed

Automatic identification of bearing and rotor defects, when operated at varying speed is challenging. To make this challenging task possible, a tacho-less deep learning model is developed which can effectively learn, even from small data set. For accurate learning from small data set, existing CNN is made sparse. Sparsity is incorporated in the CNN by adding newly developed sparsity cost in the existing cost function of CNN to enhance the learning capability of CNN. The method works in the following steps. First, vibration signals are processed with Fourier synchro squeezed transform (FSST) to obtain tachometer information. The extracted tachometer information is used to change the time domain signal to angular domain signal. Second, wavelet transform of angular domain signals is carried out to produce time–frequency images. Third, time–frequency images of angular domain signals are applied to the improved version of CNN. After learning, time–frequency images obtained from angular domain signals of defective bearings and rotor are applied to detect defects. The defect identification accuracy attained by the proposed method is 96.6 %. This accuracy is higher as compared to the accuracy achieved by the methods used in existing works. This has been made possible due to sparsity cost functions assimilated in the cost function of CNN that evade avoidable activation of neurons in the feature extraction layers of CNN, which makes the learning of modified CNN becomes deeper in comparison to existing CNN.

Sparse transfer learning for identifying rotor and gear defects in the mechanical machinery

It is incredibly difficult to build a data-driven machine learning model for the automatic detection of defects in rotating machinery. The existing techniques, based on machine learning models, work satisfactory for one machinery but unsatisfactorily for others. The problem of identifying defects becomes sever when the enough training data is not available. Here, a sparse deep learning model is put forward that can efficiently learn from the limited training data. The existing cost function of CNN has been improved by adding sparsity cost for the purpose of improving the performance of deep learning. To assimilate the sparsity, unnecessary activation of neurons is averted in the feature extraction layer of CNN. A trigonometric sparsity cross entropy (TSCE) function is built to obtain the sparsity cost. The updated CNN is trained with enough samples from the source domain. Thereafter, fine-tuning of the model is carried out from small data samples of the target domain for detecting defects. The testing of proposed deep learning model is carried out on two types of data set, one is gear and another is rotor. The concluding results obtained from the proposed work has been compared with current state-of-the-artwork. The comparison analysis shows the usefulness of the proposed methodology over the existing methods.

An improved hybrid genetic algorithm to construct balanced Boolean function with optimal cryptographic properties

Boolean functions are used as nonlinear filter functions and combiner functions in several stream ciphers. The security of these stream ciphers largely depends upon cryptographic properties of Boolean functions. Finding a balanced Boolean function with optimal cryptographic properties is an open research problem in the cryptographic community. Since the number of n-variable Boolean functions is $$2^{2^n}$$ , it is not computationally feasible to search the entire space of such functions for cryptographically significant functions when $$n \ge 6$$ . In general, the construction of Boolean functions with optimal or near optimal cryptographically significant properties is formulated as combinatorial optimization problems. In this paper, we apply the Genetic algorithm with the integration of a local search procedure called hybrid GA (HGA) searching for the Boolean functions with high nonlinearity and low autocorrelation. The performance of the Genetic algorithm depends upon the tuning parameters such as crossover mechanism, mutation probability, selection criteria, and the choice of fitness/cost function. To achieve an optimal trade-off among two cryptographic properties, the choice of the cost function plays an important role for finding an optimal solution. So our main focus is to construct balanced Boolean functions using HGA with a new cost function and compare it with existing cost functions. Our experimental results shows that the HGA is more efficient than GA and the new cost function is more efficient than existing cost functions for reaching the optimal solutions.

Novel Convolutional Neural Network (NCNN) for the Diagnosis of Bearing Defects in Rotary Machinery

This work presents the development of novel convolutional neural network (NCNN) for effective identification of bearing defects from small samples. For effective feature learning from small training data, cost function of convolution neural network (CNN) is modified by adding additional sparsity cost in the existing cost function. A novel trigonometric cross-entropy function is developed to compute the sparsity cost. The proposed cost function introduces sparsity by avoiding unnecessary activation of neurons in the hidden layers of CNN. For identification of bearing defects from small training samples, NCNN-based transfer learning is applied in the following manner. First, the raw vibration signals as well as envelope signals from source domain machine are obtained. Thereafter, these envelope signals are applied to NCNN for the learning of features from the big training data acquitted from the source domain. After feature learning, knowledge gained from NCNN is transferred to do fine-tuning of NCNN from small training samples of target domain. Thereafter, defect identification is carried out by applying the test data of target domain to fine-tuned NCNN. The experimental result validates that the proposed cross-entropy function introduces sparsity in CNN and, hence, creates an effective deep learning which can even work under a situation when training data are not available in abundant.

Optimal uncertainty-guided neural network training

The neural network (NN)-based direct uncertainty quantification (UQ) methods have achieved the state of the art performance since the first inauguration, known as the lower–upper-bound estimation (LUBE) method. However, currently-available cost functions for uncertainty guided NN training are not always converging, and all converged NNs do not generate optimized prediction intervals (PIs). In recent years researchers have proposed different quality criteria for PIs that raise a question about their relative effectiveness. Most of the existing cost functions of uncertainty guided NN training are not customizable, and the convergence of the NN training is uncertain. Therefore, in this paper, we propose a highly customizable smooth cost function for developing NNs to construct optimal PIs. The method computes the optimized average width of PIs, PI-failure distances, and the PI coverage probability (PICP) for the test dataset. We examine the performance of the proposed method for wind power generation, electricity demand, and temperature forecast datasets. Results show that the proposed method reduces variation in the quality of PIs, accelerates the training, and improves convergence probability from 99.2% to 99.8%.

Improved CNN for the diagnosis of engine defects of 2-wheeler vehicle using wavelet synchro-squeezed transform (WSST)

In this work, deep learning based diagnostic procedure is developed for the identification of engine defects of 2-wheeler vehicle. The process starts with acquisition of vibration data. Second, time domain signals are converted into angular domain. Third, random distribution of angular domain signals is done to have training and test data. Further, processing of training and test data is carried out using wavelet synchro-squeezed transform (WSST) to form time–frequency images. Then, cost function of convolution neural network (CNN) is modified by introducing a new entropy-based regularization function in the existing cost function which can meaningfully reduce the activation in the hidden layer of CNN so as to make the learning really deep. Thereafter, training of improved CNN is carried out using WSST images of training samples. In the next step, WSST images of test data are applied to tuned CNN for the identification of defects. A comparison of proposed method has been carried by existing deep learning solutions and the method proposed in the state-of-artwork. The comparison shows that the proposed method is at least 3.8 % more superior in terms of accuracy than the existing defect diagnosis methods while diagnosing defects of internal combustion (IC) engine of 2-wheeler vehicle.

Unified Subspace Fitting Framework and Its Performance Analysis for Direct Position Determination in the Presence of Multipath Propagation

The cost functions and their performances of direct position determination (DPD) methods in the presence of multipath propagation are investigated. We first establish a general DPD (GDPD) model in the presence of multi-path propagation and point out that the existing cost functions cannot get the emitter positions correctly because of the singularity of the manifold matrix in a multipath propagation scenario. Eight cost functions are developed for the GDPD model and formulated in a unified subspace fitting (USF)-based framework, which provides insight into their algebraic and asymptotic relations. Moreover, we derive the closed-form expressions of the asymptotic distributions of the estimation errors, which are optimized by those cost functions. Besides, the optimal cost function for achieving an optimal asymptotic performance is derived based on the optimization theory. Finally, the numerical simulations and Cramer–Rao lower bound are provided to verify the analytical results and show that: 1) the cost functions which work well in the single-path DPD model cannot find the emitters correctly in a multipath scenario; 2) the signal subspace fitting cost functions and noise subspace fitting cost functions, which are proposed in this paper, find the emitters accurately in the multipath propagation scenarios; 3) the optimal-weighted-subspace-fitting cost function holds the best asymptotic performance under the USF framework; and 4) the asymptotic performance of a multiple dimension cost function is better than a 1D cost function.

Real-time Battery Energy Management for Residential Solar Power System

Abstract An energy storage system is a key element of renewable-based power generation. Its flexible operational capabilities reduce not only the impact of intermittent power generation but also operational costs. In this paper, a dynamic penalty function is proposed to the charging term of the cost function to efficiently manage the battery energy and thereby reducing operational costs. The charging/discharging periods of the battery are effectively controlled based on the solar power generation and residential real-time electricity prices (RRTP). The optimisation problem formulated for the application of real-time energy management is solved with the help of particle swarm optimisation (PSO). It is shown that the proposed cost function can reduce operational costs over a time horizon of 96 hours by 4.2 per cent as compared to the cost function reported in the literature. Simulation studies are carried out to demonstrate the effectiveness of the proposed cost function over the existing cost function.

Single server retrial queues with speed scaling: Analysis and performance evaluation

Recently, queues with speed scaling have received considerable attention due to their applicability to data centers, enabling a better balance between performance and energy consumption. This paper proposes a new model where blocked customers must leave the service area and retry after a random time, with retrial rate either varying proportionally to the number of retrying customers (linear retrial rate) or non-varying (constant retrial rate). For both, we first study a basic case and then subsequently incorporate the concepts of a setup time and a deactivation time in extended versions of the model. In all cases, we obtain a full characterization of the stationary queue length distribution. This allows us to evaluate the performance in terms of the mentioned balance between performance and energy, using an existing cost function as well as a newly proposed variant thereof. This paper presents the derivation of the stationary distribution as well as several numerical examples of the cost-based performance evaluation.

The Pluto+ Algorithm

Affine transformations have proven to be powerful for loop restructuring due to their ability to model a very wide range of transformations. A single multidimensional affine function can represent a long and complex sequence of simpler transformations. Existing affine transformation frameworks such as the Pluto algorithm, which include a cost function for modern multicore architectures for which coarse-grained parallelism and locality are crucial, consider only a subspace of transformations to avoid a combinatorial explosion in finding transformations. The ensuing practical trade-offs lead to the exclusion of certain useful transformations: in particular, transformation compositions involving loop reversals and loop skewing by negative factors. In addition, there is currently no proof that the algorithm successfully finds a tree of permutable loop bands for all affine loop nests. In this article, we propose an approach to address these two issues (1) by modeling a much larger space of practically useful affine transformations in conjunction with the existing cost function of Pluto, and (2) by extending the Pluto algorithm in a way that allows a proof for its soundness and completeness for all affine loop nests. We perform an experimental evaluation of both, the effect on compilation time, and performance of generated codes. The evaluation shows that our new framework, Pluto+, provides no degradation in performance for any benchmark from Polybench. For the Lattice Boltzmann Method (LBM) simulations with periodic boundary conditions, it provides a mean speedup of 1.33 × over Pluto. We also show that Pluto+ does not increase compilation time significantly. Experimental results on Polybench show that Pluto+ increases overall polyhedral source-to-source optimization time by only 15%. In cases in which it improves execution time significantly, it increased polyhedral optimization time by only 2.04 × .

Exploring Algorithmic Limits of Matrix Rank Minimization Under Affine Constraints

Many applications require recovering a matrix of minimal rank within an affine constraint set, with matrix completion a notable special case. Because the problem is NP-hard in general, it is common to replace the matrix rank with the nuclear norm, which acts as a convenient convex surrogate. While elegant theoretical conditions elucidate when this replacement is likely to be successful, they are highly restrictive and convex algorithms fail when the ambient rank is too high or when the constraint set is poorly structured. Nonconvex alternatives fare somewhat better when carefully tuned; however, convergence to locally optimal solutions remains a continuing source of failure. Against this backdrop, we derive a deceptively simple and parameter-free probabilistic PCA-like algorithm that is capable, over a wide battery of empirical tests, of successful recovery even at the theoretical limit where the number of measurements equals the degrees of freedom in the unknown low-rank matrix. Somewhat surprisingly, this is possible even when the affine constraint set is highly ill-conditioned. While proving general recovery guarantees remains evasive for nonconvex algorithms, Bayesian-inspired or otherwise, we nonetheless show conditions whereby the underlying cost function has a unique stationary point located at the global optimum; no existing cost function we are aware of satisfies this property. The algorithm has also been successfully deployed on a computer vision application involving image rectification and a standard collaborative filtering benchmark.

Simulated evolution and simulated annealing algorithms for solving multi-objective open shortest path first weight setting problem

Optimal utilization of resources in present-day communication networks is a challenging task. Routing plays an important role in achieving optimal resource utilization. The open shortest path first (OSPF) routing protocol is widely used for routing packets from a source node to a destination node. This protocol assigns weights (or costs) to the links of a network. These weights are used to determine the shortest path between all sources to all destination nodes. Assignment of these weights to the links is classified as an NP-hard problem. This paper formulates the OSPF weight setting problem as a multi-objective optimization problem, with maximum utilization, number of congested links, and number of unused links as the optimization objectives. Since the objectives are conflicting in nature, an efficient approach is needed to balance the trade-off between these objectives. Fuzzy logic has been shown to efficiently solve multi-objective optimization problems. A fuzzy cost function for the OSPF weight setting problem is developed in this paper based on the Unified And-OR (UAO) operator. Two iterative heuristics, namely, simulated annealing (SA) and simulated evolution (SimE) have been implemented to solve the multi-objective OSPF weight setting problem using a fuzzy cost function. Results are compared with that found using other cost functions proposed in the literature (Sqalli et al. in Network Operations and Management Symposium, NOMS, 2006). Results suggest that, overall, the fuzzy cost function performs better than existing cost functions, with respect to both SA and SimE. Furthermore, SimE shows superior performance compared to SA. In addition, a comparison of SimE with NSGA-II shows that, overall, SimE demonstrates slightly better performance in terms of quality of solutions.

On optimal network selection in a dynamic multi-RAT environment

A significant challenge to enable multimedia service delivery in a dynamic multiple radio access technologies (multi-RAT) environment is the coordination of vertical handovers between different RATs. Cost function approach has been widely adopted to make vertical handover decision by ranking candidate networks. Although this mechanism can reflect accurately the change of network states and user requirements, it results in frequent, and often, unnecessary handovers which have detrimental impact on QoS, signaling load and system capacity. In this letter, we introduce a novel measurement-based network selection technique that provides a pragmatic way to acquire QoS information. In addition, it augments the handover decision of existing cost function approach, through handover initiation, to provide an optimal network selection outcome. OPNET simulations verify that the proposed technique can reduce unnecessary handovers considerably, improve overall QoS and system capacity.