Cost Function Research Articles

Cooperative Decision-Making Approach for Multiobjective Finite Control Set Model Predictive Control Without Weighting Parameters

Finite control set model predictive control (FCS-MPC) has gained increasing popularity as an emerging control strategy for electrical drive systems. However, it is still a challenging task to optimize weighting parameters, as multiple objectives are involved in the customized cost function. A cooperative decision-making approach for FCS-MPC is proposed in this article, to solve the optimization problems with manifold control objectives. By splitting the cost function, the optimization problem underlying multi-objective FCS-MPC is separated into a series of decomposed optimization problems. By doing so, the dimension of the decomposed problem is reduced to one. To collect the information for decision-making, an efficient sorting algorithm is applied for each control objective. The theory behind the cooperative decision-making approach is comprehensively analyzed, to validate both the effectiveness and efficiency of the proposed scheme. More specifically, the highlight is the adaptive mechanism on the number of desired candidates, to obtain a decent performance for torque and flux. The candidate which minimizes the switching frequency is selected as the optimal. The proposed scheme is experimentally verified and compared with the existing FCS-MPC without weighting parameters.

Handling noise and overfitting in surrogate models based on non-uniform rational basis spline entities

This paper proposes a general and systematic approach to generate a surrogate model based on non-uniform rational basis spline (NURBS) hyper-surfaces as a solution of a constrained non-linear programming problem, which is solved through a gradient-based algorithm by considering two formulations. The first formulation, which is the general one, is prone to the curse of dimensionality. The second one separates dimensions in the NURBS domain and allows saving computational time and resources. The optimisation process consists of three steps, which are solved sequentially. Each step is characterised by different design variables and solving strategies. The gradient of the cost function, for both formulations and for each optimisation step, is derived analytically by exploiting the properties of NURBS entities, hence enhancing computational efficiency and accuracy. One of the main features of the presented methodology lies the incorporation of a smoothing term in the problem formulation. This term plays a crucial role in controlling overfitting phenomenon and attenuating local oscillations within the dataset. These oscillations may be due to various sources, such as inherent noise, model instabilities, measurement uncertainties, or numerical precision limitations. The effectiveness of the proposed approach is tested on both analytical benchmark problems and real-world engineering problems taken from the literature.

T-EER: Parameter-Free Tandem Evaluation of Countermeasures and Biometric Comparators.

Presentation attack (spoofing) detection (PAD) typically operates alongside biometric verification to improve reliablity in the face of spoofing attacks. Even though the two sub-systems operate in tandem to solve the single task of reliable biometric verification, they address different detection tasks and are hence typically evaluated separately. Evidence shows that this approach is suboptimal. We introduce a new metric for the joint evaluation of PAD solutions operating in situ with biometric verification. In contrast to the tandem detection cost function proposed recently, the new tandem equal error rate (t-EER) is parameter free. The combination of two classifiers nonetheless leads to a set of operating points at which false alarm and miss rates are equal and also dependent upon the prevalence of attacks. We therefore introduce the concurrent t-EER, a unique operating point which is invariable to the prevalence of attacks. Using both modality (and even application) agnostic simulated scores, as well as real scores for a voice biometrics application, we demonstrate application of the t-EER to a wide range of biometric system evaluations under attack. The proposed approach is a strong candidate metric for the tandem evaluation of PAD systems and biometric comparators.

The 4DEnVar-based weakly coupled land data assimilation system for E3SM version 2

Abstract. A new weakly coupled land data assimilation (WCLDA) system based on the four-dimensional ensemble variational (4DEnVar) method is developed and applied to the fully coupled Energy Exascale Earth System Model version 2 (E3SMv2). The dimension-reduced projection four-dimensional variational (DRP-4DVar) method is employed to implement 4DVar using the ensemble technique instead of the adjoint technique. With an interest in providing initial conditions for decadal climate predictions, monthly mean anomalies of soil moisture and temperature from the Global Land Data Assimilation System (GLDAS) reanalysis from 1980 to 2016 are assimilated into the land component of E3SMv2 within the coupled modeling framework with a 1-month assimilation window. The coupled assimilation experiment is evaluated using multiple metrics, including the cost function, assimilation efficiency index, correlation, root-mean-square error (RMSE), and bias, and compared with a control simulation without land data assimilation. The WCLDA system yields improved simulation of soil moisture and temperature compared with the control simulation, with improvements found throughout the soil layers and in many regions of the global land. In terms of both soil moisture and temperature, the assimilation experiment outperforms the control simulation with reduced RMSE and higher temporal correlation in many regions, especially in South America, central Africa, Australia, and large parts of Eurasia. Furthermore, significant improvements are also found in reproducing the time evolution of the 2012 US Midwest drought, highlighting the crucial role of land surface in drought lifecycle. The WCLDA system is intended to be a foundational resource for research to investigate land-derived climate predictability.

Dynamic departure pushback control at airports: Part A—Linear penalty‐based algorithms and policies

AbstractAirport surface congestion can lead to significantly long taxi‐out times, thus resulting in increased fuel‐burn costs as well as excessive emissions of greenhouse gases. To curtail this undesirable syndrome, in this article, we propose a new penalty‐based dynamic departure pushback control (PDPC) strategy, which employs a linear penalty function dependent not only on the taxiway queue limit but also on the current queue length to ration the pushback frequency at airports, and trades taxiway queueing times with gate‐hold delays to minimize the total operational cost (fuel‐burn and gate‐hold costs). Using data from Beijing Capital International (PEK) airport, four different departure pushback control policies, namely: (i) no‐control (baseline case); (ii) traditional ‐control; (iii) PDPC with a constant taxiway limit; and (iv) PDPC with varying taxiway limits; are compared. Detailed Monte Carlo simulations, which showcase the sensitivity of the total cost function to various problem parameters are presented, and our results indicate that deploying the PDPC policy results in a 42% reduction in total operational costs and a 68% reduction in fuel‐burn (kg) as compared to the baseline case. To analytically reinforce these simulation results, an iterative Markov chain‐based optimization algorithm is also developed to estimate the optimal values of the pushback rate and taxiway queue limit that minimize the total cost function. Such an analytical framework is very useful in the absence of reliable airport data as it only requires estimates of the historical pushback request rates and service times at the taxiway, while yet retaining the capability to closely mirror the simulation results. Our Monte Carlo simulations as well as the Markov chain optimization model validate the strength and impact of the proposed PDPC policy, and demonstrate its practical efficacy in reducing airport surface congestion when applied using data from PEK airport.

Eco-Driving on Hilly Roads in a Mixed Traffic Environment: A Model Predictive Control Approach

Human driving behavior significantly affects vehicle fuel economy and emissions on hilly roads. This paper presents an ecological (eco) driving scheme (EDS) on hilly roads using nonlinear model predictive control (NMPC) in a mixed traffic environment. A nonlinear optimization problem with a relevant prediction horizon and a cost function is formulated using variables impacting the fuel economy of vehicles. The EDS minimizes vehicle fuel usage and emissions by generating the optimum velocity trajectory considering the longitudinal motion dynamics, the preceding vehicle’s state, and slope information from the digital road map. Furthermore, the immediate vehicle velocity and angle of the road slope are used to tune the cost function’s weight utilizing fuzzy inference methods for smooth maneuvering on slopes. Microscopic traffic simulations are used to show the effectiveness of the proposed EDS for different penetration rates on a real hilly road in Fukuoka City, Japan, in a mixed traffic environment with the conventional (human-based) driving scheme (CDS). The results show that the fuel consumption and emissions of vehicles are significantly reduced by the proposed NMPC-based EDS compared to the CDS for varying penetration rates. Additionally, the proposed EDS significantly increases the average speed of vehicles on the hilly road. The proposed scheme can be deployed as an advanced driver assistance system (ADAS).

Mean-variance portfolio selection with non-linear wealth dynamics and random coefficients

This paper studies the continuous time mean-variance portfolio selection problem with one kind of non-linear wealth dynamics. To deal the expectation constraint,  an auxiliary stochastic control problem is firstly solved by two new generalized stochastic Riccati equations from which a candidate portfolio in feedback form is constructed, and the corresponding wealth process will never cross the vertex of the parabola. In order to verify the optimality of the candidate portfolio, the convex duality  (requires the monotonicity of the cost function) is established to give another more direct expression of the terminal wealth level.  The variance-optimal martingale measure and the link between the non-linear financial market and the classical linear market are also provided. Finally, we obtain the efficient frontier  in closed form. From our results, people are more likely to invest their money in riskless asset compared with the classical linear market.

Bearing Fault Diagnosis via Stepwise Sparse Regularization with an Adaptive Sparse Dictionary

Vibration monitoring is one of the most effective approaches for bearing fault diagnosis. Within this category of techniques, sparsity constraint-based regularization has received considerable attention for its capability to accurately extract repetitive transients from noisy vibration signals. The optimal solution of a sparse regularization problem is determined by the regularization term and the data fitting term in the cost function according to their weights, so a tradeoff between sparsity and data fidelity has to be made inevitably, which restricts conventional regularization methods from maintaining strong sparsity-promoting capability and high fitting accuracy at the same time. To address the limitation, a stepwise sparse regularization (SSR) method with an adaptive sparse dictionary is proposed. In this method, the bearing fault diagnosis is modeled as a multi-parameter optimization problem, including time indexes of the sparse dictionary and sparse coefficients. Firstly, sparsity-enhanced optimization is conducted by amplifying the regularization parameter, making the time indexes and the number of atoms adaptively converge to the moments when impulses occur and the number of impulses, respectively. Then, fidelity-enhanced optimization is carried out by removing the regularization term, thereby obtaining the high-precision reconstruction amplitudes. Simulations and experiments verify that the reconstruction accuracy of the SSR method outperforms other sparse regularization methods under most noise conditions, and thus the proposed method can provide more accurate results for bearing fault diagnosis.

Congestion-aware Spatio-Temporal Graph Convolutional Network Based A* Search Algorithm for Fastest Route Search

The fastest route search, which is to find a path with the shortest travel time when the user initiates a query, has become one of the most important services in many map applications. To enhance the user experience of travel, it is necessary to achieve accurate and real-time route search. However, traffic conditions are changing dynamically, especially the frequent occurrence of traffic congestion may greatly increase travel time. Thus, it is challenging to achieve the above goal. To deal with it, we present a congestion-aware spatio-temporal graph convolutional network based A* search algorithm for the task of fastest route search. We first identify a sequence of consecutive congested traffic conditions as a traffic congestion event. Then, we propose a spatio-temporal graph convolutional network that jointly models the congestion events and changing travel time to capture their complex spatio-temporal correlations, which can predict the future travel time information of each road segment as the basis of route planning. Further, we design a path-aided neural network to achieve effective origin-destination (OD) shortest travel time estimation by encoding the complex relationships between OD pairs and their corresponding fastest paths. Finally, the cost function in the A* algorithm is set by fusing the output results of the two components, which is used to guide the route search. Our experimental results on the two real-world datasets show the superior performance of the proposed method.

Vibration suppression of smart composite beam using model predictive controller

Abstract This work presents an adaptive model predictive control (MPC) strategy to suppress the vibration in a laminated composite beam. The control method incorporates a system identification algorithm to estimate the system parameters online, which provides a precise simulation of system dynamics. A fixed-free cantilever composite beam equipped with piezoelectric actuators was used to evaluate the efficacy of the control method. The sensors and actuators are securely bonded to the upper and lower surfaces at arbitrary locations along the beam’s length. A unified mechanical displacement field is applied to all layers, while displacements are considered independently for each layer. The beam is composed of eight layers of material, each with a thickness of 0.2 mm and orientations specified as (90°/0°/90°/0°). To achieve the best performance, the parameters of the MPC were adjusted numerically. The numerical analysis revealed that placing the actuator near the clamped end at the fixed end resulted in superior control outcomes, with a settling time of approximately 1.8 s. Conversely, the longest settling time occurred when the actuator was positioned at the free end, taking around 4 s. This model could potentially be expanded to address vibration in more intricate beams exhibiting nonlinear characteristics. The deflection readings measured at the end of the beam have been utilized as feedback control signals for predicting future behavior over a predetermined control horizon. The subsequent cost function is minimized through a quadratic equation to determine the sequence of optimal yet constrained control inputs. The suggested active vibration control system is then implemented and assessed numerically to examine the effectiveness of the control method.

Unified approach to the inverse median location problem under the sum and the max objectives applying ordered median function

ABSTRACT In this paper, we propose a unified approach to solving the inverse 1-median problem on trees under both the sum and max objectives by using the ordered median function. For the problem under the k-centrum cost function, we investigate the structure of an optimal solution and transform the problem into a univariate optimization problem where the parameter equals the k largest cost. We take advantage of the convexity of the objective function to efficiently find the optimal solution in O ( nlog ⁡ n ) time, where n is the number of vertices in the tree. For the problem under the centdian cost function, we parameterize it based on the maximum cost item and prove that the induced cost function is convex. We leverage this insight to develop a combinatorial algorithm that solves the corresponding problem in O ( nlog ⁡ n ) time.

Near-Optimal Tracking Control of Partially Unknown Discrete-Time Nonlinear Systems Based on Radial Basis Function Neural Network

This paper proposes an optimal tracking control scheme through adaptive dynamic programming (ADP) for a class of partially unknown discrete-time (DT) nonlinear systems based on a radial basis function neural network (RBF-NN). In order to acquire the unknown system dynamics, we use two RBF-NNs; the first one is used to construct the identifier, and the other one is used to directly approximate the steady-state control input, where a novel adaptive law is proposed to update neural network weights. The optimal feedback control and the cost function are derived via feedforward neural network approximation, and a means of regulating the tracking error is proposed. The critic network and the actor network were trained online to obtain the solution of the associated Hamilton–Jacobi–Bellman (HJB) equation within the ADP framework. Simulations were carried out to verify the effectiveness of the optimal tracking control technique using the neural networks.

Pro-active component image placement in Edge computing environments

Edge computing has attracted a lot of attention both from industry and academia in recent years and is considered as a key enabler for addressing the increasingly strict requirements of Next Generation applications. Contrary to Cloud computing, in Edge computing the computation are placed closer to the end-users into the so-called Edge, to facilitate low-latency and high-bandwidth applications and services that would not be feasible using cloud and far remote processing alone. However, the distributed, dynamic and heterogeneous environment in the Edge computing along with the diverse applications’ requirements make service placement in such infrastructure a challenging issue. One important aspect of Edge computing is the management of the placement of the applications in the network system so as to minimize each application’s runtime, given the resources of system’s devices and the capabilities of the system’s network. To this end, we propose an empirical experimental analysis, by comparing the results of different placements strategies and various edge communication networks. In particular, we model the problem of proactive placement of application images as a Minimum Vertex Cover problem. Our results demonstrate that the Greedy implementation seems to offer the best tradeoff in terms of performance, cost function and execution time.

An Imperfect Production Inventory Model for Instantaneous Deteriorating Items with Preservation Investment Under Inflation on Time Value of Money

Effective inventory management is crucial for businesses dealing with deteriorating items, where demand is influenced not only by traditional factors but also dependent on the selling price. This research paper proposes a comprehensive inventory model that considers the dynamic nature of demand for deteriorating items and incorporates the impact of inflation on the time value of money, all within the context of an imperfect production and screening process. To reduce the waste of products, the proposed model uses a rework process to convert imperfect items into perfect ones. Additionally, this study incorporates preservation technology investment to alleviate the rate of deterioration under partially backlogged shortages. The incorporation of an imperfect production process further enhances the model’s practical applicability by addressing real-world scenarios where production may not always be flawless. The study employs mathematical modeling and optimization techniques to derive optimal ordering policies that balance the conflicting objectives of minimizing costs. To validate the model, numerical analysis has been performed, and the convexity of the total cost function has been shown graphically and analytically using MATHEMATICA software. Sensitivity analyses are conducted to assess the robustness of the proposed model under varying parameters, providing valuable insights for decision-makers.

Saddle-Point Equilibrium Strategy for Linear Quadratic Uncertain Stochastic Hybrid Differential Games Based on Subadditive Measures

This paper describes a kind of linear quadratic uncertain stochastic hybrid differential game system grounded in the framework of subadditive measures, in which the system dynamics are described by a hybrid differential equation with Wiener–Liu noise and the performance index function is quadratic. Firstly, we introduce the concept of hybrid differential games and establish the Max–Min Lemma for the two-player zero-sum game scenario. Next, we discuss the analysis of saddle-point equilibrium strategies for linear quadratic hybrid differential games, addressing both finite and infinite time horizons. Through the incorporation of a generalized Riccati differential equation (GRDE) and guided by the principles of the Itô–Liu formula, we prove that that solving the GRDE is crucial and serves as both a sufficient and necessary precondition for identifying equilibrium strategies within a finite horizon. In addition, we also acquire the explicit formulations of equilibrium strategies in closed forms, alongside determining the optimal values of the cost function. Through the adoption of a generalized Riccati equation (GRE) and applying a similar approach to that used for the finite horizon case, we establish that the ability to solve the GRE constitutes a sufficient criterion for the emergence of equilibrium strategies in scenarios extending over an infinite horizon. Moreover, we explore the dynamics of a resource extraction problem within a finite horizon and separately delve into an H∞ control problem applicable to an infinite horizon. Finally, we present the conclusions.

Evaluation of low-dose computed tomography reconstruction using spatial-radon domain total generalized variation regularization.

The x-ray radiation dose in computed tomography (CT) examination has been a major concern for patients. Lowing the tube current and exposure time in data acquisition is a straightforward and cost-effective strategy to reduce the x-ray radiation dose. However, this will inevitably increase the noise fluctuations in measured projection data, and the corresponding CT image quality will be severely degraded if noise suppression is not performed during image reconstruction. To reconstruct high-quality low-dose CT image, we present a spatial-radon domain total generalized variation (SRDTGV) regularization for statistical iterative reconstruction (SIR) based on penalized weighted least-squares (PWLS) principle, which is called PWLS-SRDTGV for simplicity. The presented PWLS-SRDTGV model can simultaneously reconstruct high-quality CT image in space domain and its corresponding projection in radon domain. An efficient split Bregman algorithm was applied to minimize the cost function of the proposed reconstruction model. Qualitative and quantitative studies were performed to evaluate the effectiveness of the PWLS-SRDTGV image reconstruction algorithm using a digital 3D XCAT phantom and an anthropomorphic torso phantom. The experimental results demonstrate that PWLS-SRDTGV algorithm achieves notable gains in noise reduction, streak artifact suppression, and edge preservation compared with competing reconstruction approaches.

A Reduced Complexity Acoustic-Based 3D DoA Estimation with Zero Cyclic Sum.

Accurate direction of arrival (DoA) estimation is paramount in various fields, from surveillance and security to spatial audio processing. This work introduces an innovative approach that refines the DoA estimation process and demonstrates its applicability in diverse and critical domains. We propose a two-stage method that capitalizes on the often-overlooked secondary peaks of the cross-correlation function by introducing a reduced complexity DoA estimation method. In the first stage, a low complexity cost function based on the zero cyclic sum (ZCS) condition is used to allow for an exhaustive search of all combinations of time delays between pairs of microphones, including primary peak and secondary peaks of each cross-correlation. For the second stage, only a subset of the time delay combinations with the lowest ZCS cost function need to be tested using a least-squares (LS) solution, which requires more computational effort. To showcase the versatility and effectiveness of our method, we apply it to the challenging acoustic-based drone DoA estimation scenario using an array of four microphones. Through rigorous experimentation with simulated and actual data, our research underscores the potential of our proposed DoA estimation method as an alternative for handling complex acoustic scenarios. The ZCS method demonstrates an accuracy of 89.4%±2.7%, whereas the ZCS with the LS method exhibits a notably higher accuracy of 94.0%±3.1%, showcasing the superior performance of the latter.

A game theoretic approach to wireless body area networks interference control

AbstractIn this paper we consider a scenario where there are two wireless body area networks (WBANs) interfere with each other from a game theoretic perspective. In particular, we envision two WBANs playing a potential game to enhance their performance by decreasing interference to each other. Decreasing interference extends the sensors' batteries life time and reduces the number of re‐transmissions. We derive the required conditions for the game to be a potential game and its associated the Nash equilibrium (NE). Specifically, we formulate a game where each WBAN has three strategies. Depending on the payoff of each strategy, the game can be designed to achieve a desired NE. Furthermore, we employ a learning algorithm to achieve that NE. In particular, we employ the Fictitious play (FP) learning algorithm as a distributed algorithm that WBANs can use to approach the NE. The simulation results show that the NE is mainly a function of the power cost parameter and a reliability factor that we set depending on each WBAN setting (patient). However, the power cost factor is more dominant than the reliability factor according to the linear cost function formulation that we use throughout this work.

Hybrid hyperplane gradient learning algorithm for RBF neural network

Gradient-based algorithms are still popularly used for training radial basis function neural network (RBFNN). However, these algorithms may lead to the vanishing gradient (saddle point or local minimum) problem, which is one of the common problems that limit learning performance. To cope with this, a hybrid hyperplane gradient learning algorithm (HHGLA) is proposed to improve the learning performance of the RBFNN in this paper. First, a hyperplane gradient (HPG), based on a hyperspace constructed by a solution population (SP), is introduced. Thus, the search process can cross the surface of the cost function to avoid the appearance of vanishing gradient. Second, an adaptive learning rate is designed to restrict the search process into this hyperspace. Then, during the learning process, the hyperspace is constantly contracted to approximate the global optimal solution. Third, the convergence property of HHGLA-based RBFNN is thoroughly analyzed to ensure its application success. Finally, empirical comparisons of the proposed HHGLA-RBFNN are given to illustrate its superiority. The simulation results show the feasibility of HHGLA-RBFNN of accuracy.

A Data-Driven Approach for Generalizing the Laminar Kinetic Energy Model for Separation and Bypass Transition in Low- and High-Pressure Turbines

Abstract No common laminar kinetic energy (LKE) transition model has to date been able to predict both separation-induced and bypass transition, both phenomena commonly found in low-pressure turbines and high-pressure turbines. Here, a data-driven approach is adopted to develop a more general LKE transition model suitable for both transition modes. To achieve this, two strategies are adopted. The first is to extend the computational fluid dynamics (CFD)-driven model training framework for simultaneously training models on multiple turbine cases, subject to multiple objectives. By increasing the training data set, different transition modes can be considered. The second strategy employed is the use of a newly derived set of local non-dimensionalized variables as training inputs to reduce the search space. Because one of the training turbine cases is characterized by strong unsteady effects, for the first time an unsteady solver is utilized during the CFD-driven training, and the time-averaged results are used to calculate the cost function as part of the model development process. The results show that the data-driven models do perform better, in terms of their predictions of pressure coefficient, wall shear stress, and wake losses, than the baseline model. The models were then tested on two previously unseen testing cases, one at a higher Reynolds number and one with a different geometry. For both testing cases, stable solutions were obtained with results improved over the predictions using the baseline models.