Cost Function Research Articles

An Operator Splitting Scheme for Distributed Optimal Load-Side Frequency Control With Nonsmooth Cost Functions

An Operator Splitting Scheme for Distributed Optimal Load-Side Frequency Control With Nonsmooth Cost Functions

Enhanced Model-Free Predictive Speed Control Without Weighting Factors for PMSM Based on Newly Designed Cost Function

Enhanced Model-Free Predictive Speed Control Without Weighting Factors for PMSM Based on Newly Designed Cost Function

Dynamic Event-Triggered Safe Control for Nonlinear Game Systems With Asymmetric Input Saturation.

This article focuses on the Pareto optimal issues of nonlinear game systems with asymmetric input saturation under dynamic event-triggered mechanism (DETM). First, the safe control is guaranteed by transforming the system with safety constraints into the one without state constraints utilizing barrier function. The united cost function integrating nonquadratic utility function is constructed to provide the foundation to achieve the Pareto optimal solutions. Then, the adaptive dynamic programming method with concurrent learning is proposed to approximate the Pareto optimal strategies wherein both current and historical data are utilized. To further lessen the consumptions of computation/communication resources, the DETM is integrated into the adaptive algorithm framework which can avoid Zeno phenomena. All the signals of the closed-loop system are proved to be uniformly ultimately bounded. Finally, the simulation results are given to validate the effectiveness of the proposed method from several aspects.

Estimating the Cowper–Symonds Parameters for High-Strength Steel Using DIC Combined with Integral Measures of Deviation

Cowper–Symonds parameters were estimated for the complex-phase high-strength steel with a commercial name of SZBS800. The parameter estimation was based on a series of conventional tensile tests and unconventional high-strain rate experiments. The parameters were estimated using a reverse engineering approach. LS-Dyna was used for numerical simulations, and the material’s response was modelled using a piece-wise linear plasticity model with a visco-plastic formulation of the Cowper–Symonds material model. A multi-criteria cost function was defined and applied to obtain a response function for the parameters p and C. The cost function was modelled with a response surface, and the optimal parameters were estimated using a real-valued genetic algorithm. The main novelty and innovation of this article is the definition of a cost function that measures a deviation between the deformed geometry of the flat plate-like specimens and the results of the numerical simulations. The results are compared to the relevant literature. A critical evaluation of our results and references is another novelty of this article.

Machine-learning aided calibration and analysis of porous media CFD models used for rotating packed beds

The proposed research is an attempt to advance the state-of-the-art of the numerical modelling of RPB by combining Computational Fluid Dynamics and Machine Learning approaches. The latter creates an accurate framework that should help quantify the potential of Rotating Packed Beds (RPB) technology to intensify conventional CO2 capture processes. To this end, a direct sensitivity analysis is detailed to supplement a machine-learning (ML) algorithm built for calibrating resistance coefficients needed for porous media modelling. The algorithm is used to improve CFD predictions of dry pressure drop in rotating packed beds (RPBs) for a wide range of operating conditions. The sensitivity derivatives with respect to the packing resistance coefficients are demonstrated for the first time in RPBs, which is not available in the current CFD open source and commercial codes. In this regard, sensitivity differential equations are derived from three-dimensional Navier-Stokes equations for porous media in a rotating reference frame. These sensitivity equations are discretized using a finite volume scheme and solved to obtain the sensitivity pressure drop differences at the packing edges. The results are validated against the predictions of the analytical sensitivity analysis and the finite difference approximation. After, the Newton – Gauss method that employs the sensitivity pressure drop derivatives, is used to minimize the error (cost function) between the pressure drop obtained from CFD simulations and the available experimental data. This is achieved by tuning the packing resistance coefficients to the RBPs' operating conditions (gas flowrate and rotating speed) and correlate them using an artificial neural network (ANN). The results of the proposed approach show a significant improvement in porous media-based CFD predictions of RPBs' pressure drop across a wide range of operating conditions and this over conventional porous media-based CFD models. This is necessary for CFD models to be reliably used as a tool that can efficiently improve existing RPBs' designs and/or participate in RPBs' design innovation.

Extension of a low-tech Model Predictive Control (MPC) algorithm for grid-supportive heat pump operation

This paper presents the further development of a low-tech Model Predictive Control (MPC) for the grid-friendly operation of heat pumps. The developed algorithm is already available in the literature [1] and successfully implemented in multiple buildings. The overall goal is, to predictively optimize comfort parameters taking into account weather forecast data for 48 h. A simple mathematical building model and an optimization function are used to calculate the heating (or cooling) requirement and determine the optimum heating (cooling) output curve over time.Based on the initial results, the algorithm is extended to include an energy price forecast. This modification enables the simultaneous optimization of comfort and heat supply costs. This forecast-based cost & comfort function is designed for the use of heat pumps in buildings with thermally activated components (TAB). The extension enables the MPC to process day-ahead electricity prices or other price signals in addition to weather forecast data. This means that the operation of heat pumps can be shifted to periods that are beneficial to the grid.The algorithm is analysed and validated in a Matlab/Simulink building simulation for a heating period of one sample month. A case study with different price scenarios is the main part of this paper. Depending on the assumed price fluctuation, the simulation leads to cost savings between 6.65 % and 12.5 % for the observation period of one month. The simulation results thus show that heat generation can be shifted to times with lower electricity prices, which leads to a significant reduction in heating costs without any significant loss of comfort. In conclusion, the developed low-tech MPC enables grid-supportive operation of heat pumps.

A reliable deterministic method for multi-area economic dispatch considering power losses

This paper offers a reliable deterministic method for solving multi-area economic dispatch (MAED). The proposed method can handle nonlinear power losses in electrical networks and discrete and nonlinear characteristics in power plants, such as fuel change facilities and nonconvex cost functions. To this end, the presented method reformulates the products of two variables in the power loss terms as one-dimensional expressions. Then, it converts all nonlinear terms in the MAED into linear segments. Moreover, it handles discrete decisions in fuel selection through binary variables. We assess the performance of the proposed method by some MAED test systems. The results show that the method can reliably obtain accurate solutions in the adopted test systems. It converges to costs of 10604.7, 654.7, 121592.7, 124628.4, and 169528.9 respectively in 2-area 4-unit, 3-area 10-unit, 4-area 40-unit, 2-area 40-unit, and 10-area 130-unit. These findings reproduce or outperform results found in earlier optimization algorithms. Moreover, the computational time evaluations indicate that the method can solve the adopted MAED problems in less than one minute, showing its efficiency. Overall, the obtained results confirm the efficacy of the method’s efficacy in handling the MAED with discrete and nonlinear terms.

An effective channel allocation designed using hybrid memory dragonfly with imperialist competitive algorithm in distributed mobile adhoc network

SummaryThe channel availability problem reaches a higher degree in mobile ad hoc networks (MANETs) and garners a lot of attention in communication networks. Because increased mobile usage might result in a lack of channel allocation, an improved channel allocation technique is presented to tackle the availability problem. The distributed dynamic channel allocation (DDCA) model is built in this paper using the hybrid memory dragonfly with imperialist competitive (HMDIC) method. Based on optimization logic, this strategy assigns the channel to mobile hosts. The MANET provides a dispersed network within the coverage region in the absence of base station infrastructure. The HMDIC optimizer approach in this circumstance randomly begins every respective node to update and store their pbest value utilizing RAM dragonfly employing satellite images. The constraint values are then used to construct the cost function, which results in a strong kind of global optimum solution. The channels are therefore distributed in an effective manner. The HMDIC algorithm is used in this research to build a novel channel allocation system. It makes advantage of the exploration capabilities to successfully explore the individual node using MDA (Modified Dragonfly Algorithm) and locate the global best solution using imperialist competitive algorithm (ICA). Both of these combined tactics are more effective in accelerating the convergence of the allocation model. To validate the performance, the HMDIC‐based DDCA system provides promising results in terms of assigning available channels, thereby enhancing channel reuse efficiency and fractional interference.

Mathematical derivation of a unified equations for adjoint lattice Boltzmann method in airfoil and wing aerodynamic shape optimization

Unified equations of the adjoint lattice Boltzmann method (ALBM) are derived for five applicable objective functions in 2D/3D aerodynamic shape optimization problems. The derived equations include the adjoint equation, boundary condition, terminal condition and gradient of the cost function. In this research, firstly, these relations are extracted for each objective in details and then the general form of ALBM equations are presented for all defined practical aerodynamic objective function. Five applicable cost functions which are the most important objectives in optimization of aerodynamic geometries include desired pressure and viscous shear stress (VSS) inverse design, drag and moment at fixed lift and finally lift to drag ratio at fixed angle of attack. The new extracted relations are based on the circular and spherical function scheme, and are valid for viscous/inviscid, compressible/incompressible and 2D/3D flows in all continuous flow regimes. Proof of new extracted general relations have been performed by authors.

Quantifying and enabling the resiliency of a microgrid considering electric vehicles using a Bayesian network risk assessment

With the increase in the number of natural disasters, caused by climate change, the role of emission and resilience has become more outstanding. In this paper, a novel model for quantifying and enabling the resiliency of a microgrid, using a Bayesian network risk assessment approach is presented. The three objective functions of cost, pollution, and resilience are optimized simultaneously using an improved lexicographic augmented ɛ-constraint method. It should be mentioned that these items are included in the proposed model due to the irreplaceable role of electric vehicles (EVs) and renewable energy sources (RESs) in distribution systems. Moreover, with the Bayesian network, the interaction between random variables is considered and a graphic view of casual relationships between stochastic and probabilistic variables is investigated in this study. The Monte Carlo scenario-based technique has handled the uncertainties of EVs and RESs. The proposed mixed integer linear programming (MILP) is implemented in the GAMS software environment under the CPLEX solver and finally, the results are discussed.

Residual growth control for general maps and an approximate inverse function result

The need to control the residual of a potentially nonlinear function F\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {F}$$\\end{document} arises in several situations in mathematics. For example, computing the zeros of a given map, or the reduction of some cost function during an optimization process are such situations. In this note, we discuss the existence of a curve t↦x(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t\\mapsto x(t)$$\\end{document} in the domain of the nonlinear map F\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {F}$$\\end{document} leading from some initial value x0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$x_0$$\\end{document} to a value u such that we are able to control the residual F(x(t))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {F}(x(t))$$\\end{document} based on the value F(x0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {F}(x_0)$$\\end{document}. More precisely, we slightly extend an existing result from J.W. Neuberger by proving the existence of such a curve, assuming that the directional derivative of F\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {F}$$\\end{document} can be represented by x↦A(x)F(x0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$x \\mapsto \\mathcal {A}(x)\\mathcal {F}(x_0)$$\\end{document}, where A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {A}$$\\end{document} is a suitable defined operator. The presented approach covers, in case of A(x)=-Id\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {A}(x) = -\ extsf{Id}$$\\end{document}, some well known results from the theory of so-called continuous Newton methods. Moreover, based on the presented results, we discover an approximate inverse function result.

Robust algorithms for spherical angle-of-arrival source localization

The performance of traditional algorithms for spherical angle-of-arrival (AOA) source localization will be significantly degraded when there are outliers in the angle measurements. By using the symmetric α-stable (SαS) distribution to describe the measurement noise containing outliers and constructing the cost function using the lp-norm, we propose a robust algorithm for spherical AOA source localization: the spherical iteratively reweighted pseudolinear estimator (SIRPLE). The SIRPLE is similar to the iteratively reweighted least squares (IRLS), with the difference that a homogeneous least squares (HLS) problem is solved in each iteration. The SIRPLE suffers from bias problems owing to the nature of the pseudolinear estimators. To overcome this problem, the instrumental variable (IV) method is introduced and the spherical iteratively reweighted instrumental variable estimator (SIRIVE) is proposed. Theoretical analysis shows that the SIRIVE is asymptotically unbiased and it can achieve the theoretical error covariance of the constrained least lp-norm estimation. Extensive simulation analyses demonstrate the better performance of the SIRIVE compared to the conventional spherical AOA source localization methods and the SIRPLE under SαS noise environment. The performance of the SIRIVE is similar to that of the Nelder–Mead algorithm (NM), but the SIRIVE are computationally more efficient. In addition, the SIRIVE is nearly unbiased and the root mean square error (RMSE) performance is close to the Cramér–Rao lower bound (CRLB).

Low-correlation multilinear dimensionality reduction applied to volcano-seismic classification

In the present work, a technique for reducing the dimensionality of tensor data, called Low-Correlation Multilinear Dimensionality Reduction (LC-MDR), is proposed. The method optimizes a cost function that takes into account the data correlation, generating variables with low correlation. The LC-MDR fits the input data correlation into a new tensor decomposition denoted by Even-Order Nested PARAFAC Decomposition (EONPD), a proposed extension of the Nested PARAFAC Decomposition (NPD) for higher-order tensors. In addition, a generalization of the EONPD, denoted by Higher-Order Nested PARAFAC Decomposition (HONPD), is also presented. Contrarily to existing approaches that use orthogonal transformation matrices, the LC-MDR does not impose this constraint on the transformation matrices in order to minimize the output correlation. The proposed technique was evaluated in a classification system of volcano-seismic events using data obtained from the Ubinas volcano in 2009 using a full tensorial classification framework. The results showed significant gains for the LC-MDR when compared with concurrent techniques in terms of accuracy, data correlation and processing time.

A switching norm based least mean Square/Fourth adaptive technique for sparse channel estimation and echo cancellation

To realize rapid data transmission, the broadband transmission technique is being extensively explored and applied in existing wireless communication systems. The multi-path channel in broadband wireless communication systems is sparse and this sparsity can be used as prior knowledge to estimate the channel. To make use of sparsity, this paper recommends a switching norm-based least mean square/fourth (SN-LMS/F) adaptive approach for sparse channel estimation and echo cancellation. The suggested SN-LMS/F is implemented by adding a soft parameter adjustment function (SPF) into the conventional LMS/F adaptive method's cost function and utilizes both the l0 and l1 norm to exploit system sparsity with reduced complexity. The simulated output indicates that the suggested SN-LMS/F adaptive technique provides a more desirable performance for sparse channel estimation and echo cancellation with reduced execution time.

Integrating 3DVAR and ANN for inversion optimization of physical models of fuel-assembly bowing

This study introduces a novel inversion optimization method for the core physical model of fuel-assembly bowing, integrating measurement data based on three-dimensional variational (3DVAR) data assimilation and artificial neural network (ANN) techniques. Recognizing the deviation between theoretical physical models and actual core conditions due to factors like uneven coolant distribution and fuel-assembly bowing, this work aims to enhance model reliability and simulation accuracy. By generating a dataset through random perturbation and employing ANN for training, the method establishes a relationship between the core physical model and model-simulated values corresponding to measurement data. The construction of the cost function, essential for optimizing the inversion process, is executed using 3DVAR. To verify its validity, the method is implemented, and an inversion optimization process is developed using our self-developed Bamboo-C code system. The optimization process, validated through application in a commercial pressurized water reactor (PWR) in a nuclear power plant (NPP) in China, demonstrates a significant reduction in the relative errors of power distribution, thus affirming the method’s efficacy in achieving a more realistic model of fuel-assembly bowing. The integration of measurement data into the optimization process addresses the critical need for accurate core physical models in nuclear engineering, offering a promising avenue for enhancing the safety and efficiency of nuclear reactor operations.

Adaptive dynamic programming-based multi-fault tolerant control of reconfigurable manipulator with input constraint

In this paper, a multi-fault tolerant controller considering actuator saturation is proposed. Based on the adaptive dynamic programming(ADP) algorithm, the fault tolerant control of the reconfigurable manipulator with sensor and actuator faults are carried out. Firstly, combined with the state space expression, the nonlinear transformation of sensor fault is performed by adopting the differential homeomorphism principle. An improved cost function is constructed based on the fault estimation function obtained by the fault observer, and combined with hyperbolic tangent function to deal with input constraint problem. Then, an evaluation neural network (NN) is established and the Hamilton–Jacobi–Bellman (HJB) equation is solved by online strategy iterative algorithm. Furthermore, based on Lyapunov theorem, the stability of reconfigurable manipulator systems with multi-fault are proved. Lastly, the simulation studies are used to certify the effectiveness of the presented fault tolerant control (FTC) scheme.

Permeability prediction using logging data from tight reservoirs based on deep neural networks

Permeability is a critical parameter for evaluating reservoir properties, and accurate prediction is an important basis for identifying high-quality reservoirs and geological modeling. However, the strong heterogeneity, complex lithology and diagenesis in the reservoirs of this region pose a major challenge for the accurate assessment of reservoir permeability. In recent years, the use of machine learning (ML) to solve problems in geophysical well logging and related fields has gained much attention thanks to advances in data science and artificial intelligence. ML is any predictive algorithm or combination of algorithms that learns from data and makes predictions without being explicitly coded with a deterministic model. The most immediate example is deep neural networks (DNN) that are trained with data to minimize a cost function and make predictions. The tight reservoirs in the Chang 7 Member of the Ordos Basin host significant oil and gas resources and have recently emerged as the main focus of unconventional oil and gas exploration and development. In this work, we performed DNN-based permeability prediction for the tight reservoirs in the Ordos Basin area. From 19 well logs, we selected effective data points from 17 wells for DNN training after preprocessing and used the remaining two wells for testing. First, we trained the DNN with all collected parameters as inputs, resulting in permeability prediction R2 values of 0.64 and 0.72 for the two wells, indicating a good fit. We then optimized the input parameters by performing a crossplot analysis between these parameters and the permeability. Using the same network structure (with all hyperparameters set the same), we trained the DNN again to obtain a new DNN-based model. The prediction results showed that removing input parameters with poor correlation to permeability improved the prediction accuracy with R2 values of 0.70 and 0.87 for the two wells.

Cost-effectiveness of lures in attracting mammals: a large scale camera-trapping field test on European species

The cost-effectiveness of different attractants during camera trapping surveys has been seldom evaluated. To contribute in filling this knowledge gap we (1) compare the effectiveness of a suite of attractants in detecting widely distributed mammals in Europe and (2) evaluate the cost-effectiveness of these attractants, by calculating the costs associated to reach a specific monitoring objective. We conducted a large-scale field experiment across four study areas in central and northern Italy, encompassing a variety of environments, from lowland forest to alpine beech forest. We focused on comparing the following low cost and readily available attractants: sardines, peanut butter, a commercial lure and we used a camera with no attractant as control, collecting data on a suite of small to large mammals. We found that for seven of our 13 target species detectability varied with the type of attractant used. Specifically, sardines proved to be the most effective attractant for canids and the porcupine, peanut butter was most effective for mustelids but was avoided by the roe deer, whereas the commercial lure was the most effective with red deer. Through a power analysis combined with a cost function analysis we were able to show striking differences in the cost-effectiveness of the different methods, sometimes in the order of magnitude of tens of thousands of euros, which strongly emphasizes the critical importance played by the choice of whether to use an attractant or not and the type of attractant to be used.

On concentration of the empirical measure for radial transport costs

Let μ be a probability measure on Rd and μN its empirical measure with sample size N. We prove a concentration inequality for the optimal transport cost between μ and μN for radial cost functions with polynomial local growth, that can have superpolynomial global growth. This result generalizes and improves upon estimates of Fournier and Guillin. The proof combines ideas from empirical process theory with known concentration rates for compactly supported μ. By partitioning Rd into annuli, we infer a global estimate from local estimates on the annuli and conclude that the global estimate can be expressed as a sum of the local estimate and a mean-deviation probability for which efficient bounds are known.

Model-free aperiodic tracking for discrete-time systems using hierarchical reinforcement learning

In the operation of practical systems, it is often a challenging task to deal with limited knowledge of the system dynamics, therefore, it is needed to obtain a framework for the simultaneous learning and control of dynamic systems, able to cope with uncertain dynamics. This paper proposes a model-free aperiodic tracking control method based on MAXQ hierarchical reinforcement learning for unknown dynamics in discrete-time systems. Firstly, a MAXQ hierarchical framework is developed for aperiodic tracking control that decomposes the task into pre-control and accurate control subtasks. The former achieves sub-optimal tracking which prompts the implementation of accurate control. The latter implements aperiodic tracking based on the pre-control result to reduce resource occupation. The structure of the MAXQ framework simplifies the complexity of the tracking task, and the incorporation of pre-control accelerates the learning process in the formal control stage. Secondly, considering the disparities between the control inputs and the control update instants, pre-control is decomposed to learn the triggering strategy and control policy, respectively. Meanwhile, the control policy learns optimal control inputs by minimizing the cost function. Similarly, the triggering strategy and control policy are also separately learned in accurate control. In contrast to traditional aperiodic triggering mechanisms, in accurate control stage, the triggering strategy is developed based on the cumulative error of the pre-control result, thus avoiding the influence of accidental factors and the cumulative effects of errors, enhancing system robustness. Thirdly, the proposed tracking control is derived by using only the input, output, and reference signal data from the system, without relying on system dynamics. It is applicable to both linear and nonlinear systems, demonstrating strong generalizability. Finally, simulation examples are provided to validate the effectiveness and superiority of the proposed method.