Values Of Control Variables Research Articles

Optimization control of wastewater treatment based on neural network and multi-objective optimization algorithm

In wastewater treatment, energy consumption and effluent quality are conflicting objectives. Improving effluent quality while reducing energy consumption has become a pressing issue. This paper proposes a dynamic optimal control method for the wastewater treatment process, utilizing neural networks and multi-objective dragonfly algorithm. A regression prediction model, based on a Self-Attention mechanism of a multi-scale convolutional neural network-bidirectional gated recurrent unit, is used to establish a soft measurement model for effluent quality and energy consumption, serving as the optimization objective function. The multi-objective dragonfly algorithm then optimizes this objective to determine the optimal set values for control variables. A Linear Active Disturbance Rejection Control, based on a scalable bandwidth linear extended state observer, is designed to track these optimal set values. The proposed method is tested using Benchmark Simulation Model No. 1 (BSM1). Results demonstrate that the method effectively obtains and tracks optimal set values of control variables, ensuring effluent quality meets standards and significantly reducing energy consumption compared to four other methods.

Surrogate gradient methods for data-driven foundry energy consumption optimization

In many industrial applications, data-driven models are more and more commonly employed as an alternative to classical analytical descriptions or simulations. In particular, such models are often used to predict the outcome of an industrial process with respect to specific quality characteristics from both observed process parameters and control variables. A major step in proceeding from purely predictive to prescriptive analytics, i.e., towards leveraging data-driven models for process optimization, consists of, for given process parameters, determining control variable values such that the output quality improves according to the process model. This task naturally leads to a constrained optimization problem for data-driven prediction algorithms. In many cases, however, the best available models suffer from a lack of regularity: methods such as gradient boosting or random forests are generally non-differentiable and might even exhibit discontinuities. The optimization of these models would therefore require the use of derivative-free techniques. Here, we discuss the use of alternative, independently trained differentiable machine learning models as a surrogate during the optimization procedure. While these alternatives are generally less accurate representations of the actual process, the possibility of employing derivative-based optimization methods provides major advantages in terms of computational performance. Using classical benchmarks as well as a real-world dataset obtained from an industrial environment, we demonstrate that these advantages can outweigh the additional model error, especially in real-time applications.

Prediction and decision of free-piston linear generator on starting process for multi-fuel adaptability

Free-piston linear generators, due to their variable compression ratio, are considered to possess excellent multi-fuel adaptability. Further, fuel-flexible is a weighty research topic for addressing energy source limitations, meeting powertrain generalization requirements, and achieving energy savings and emission reductions. The initial concern to solve is the rapid starting of various fuels within the same free-piston linear generator. This study aims to introduce a mechanical resonance starting performance prediction model based on an artificial neural network and provides a control decision method based on single-objective optimization with soft constraints to achieve flexible starting of a variety of fuels. This paper also assessed the starting performance using the free-piston linear generator prototype and conducted a comprehensive parameterized analysis to investigate the influence of parameters and control variables on starting performance. Using the starting decision method proposed, the control variable values for ethanol starting were derived on the prototype, resulting in driving current at 3.5A, intake air mass flow at 95 standard liters per minute, and intake air temperature at 335 K. This decision value effectively met the predefined requirements, successfully igniting and starting the prototype with ethanol. This outcome serves as a robust validation of the fuel-flexible capabilities within free-piston linear generator systems.

Study of Turing patterns in a SI reaction-diffusion propagation system based on network and non-network environments

The study of rumor propagation dynamics is of great significance to reduce false news and ensure the authenticity of news information. In this paper, a SI reaction-diffusion rumor propagation model with nonlinear saturation incidence is studied. First, through stability analysis, we obtain the conditions for the existence and local stability of the positive equilibrium point. By selecting suitable variable as the control parameter, the critical value of Turing bifurcation and the existence theorem of Turing bifurcation are obtained. Then, using the above theorem and multi-scale standard analysis, the expression of amplitude equation around Turing bifurcation point is obtained. By analyzing the amplitude equation, different types of Turing pattern are divided such as uniform steady-state mode, hexagonal mode, stripe mode and mixed structure mode. Further, in the numerical simulation part, by observing different patterns corresponding to different values of control variable, the correctness of the theory is verified. Finally, the effects of different network structures on patterns are investigated. The results show that there are significant differences in the distribution of users on different network structures.

Product form solutions of some queueing inventory problems in random environment

The public is often attracted by the offers given by the shopkeepers. These offers do make a crucial impact in the company's annual turnover. On a close watch it can be observed that these offers do change from time to time according to the seasonal variations. Here we investigate a single commodity Queueing-Inventory with 'offer' in random environment. The 'offer' can be anything given to the customers as incentives, who purchase the item. There are 'n' distinct environments. The offers in distinct environments are different. In some environments there may not be any offer. Here an environment dependent inventory control policy $ (s_i ,S) $ for $ 1\leq i \leq n $ is followed. Lead time, service and replenishment of the inventories are independent exponentially distributed random variables. It has been observed that when certain restrictions are imposed on the system, it admits asymptotic product form solution. Two such variants are discussed here. Long run behaviour of the system is analysed under the assumption of system stability. An optimization problem is constructed to compute the values of $ s_i $ and $ S $ that minimize the average system cost. The effect of environment in the optimum values of control variables, is also investigated.

Three-Phase Integrated-Optimized Power Electronic Transformer for Electric Vehicle Charging Infrastructure

This article proposes the high-frequency link three-phase integrated-optimized power electronic transformer (PET) for electric vehicle (EV) charging infrastructure in the distribution network. The structural elements and configuration of PET significantly affect its design and performance. However, the different topologies of PET available in the literature did not consider the influence of the circuit’s structural elements with their parasitic components. Consequently, it violates the value of control variables which fails to accomplish essential control characteristics required for EV charging infrastructure in the smart distribution network. Therefore, in this article, detailed modeling and analysis of the proposed PET are carried out at each stage by incorporating its structural effect to analyze the circuit behavior during different operating conditions. As a result, it provides the design and operating constraints for the proposed PET, employed in the design procedure and control algorithm. Furthermore, the dual-degree control (DDC) method is proposed to utilize the structural framework and dual control variables of the proposed PET to meet out significant aspects of EV charging infrastructure in the distribution network such as wide range of voltage regulation, active control over the power flow, and soft-switching operation. Finally, a 4-kW prototype of the proposed PET is built up, which has a bidirectional power flow feature and isolated dc dual-port output terminals. Hardware testing and experimental results verify the effectiveness of the proposed PET based on the DDC method.

Penerapan Seagulls Optimization Algorithm untuk Menyelesaikan Open Vehicle Routing Problem

This paper aims to solve the problem of Open Vehicle Routing Problem using Seagulls Optimization Algorithm. Open Vehicle Routing Problem (OVRP) is a variation of Vehicle Routing Problem (VRP) which will not return to the depot after visiting the last customer, is different from VRP which requires the vehicle to return to the depot because the company have insufficient number of vehicles for the distribution of products to customers so they must to rent vehicles and this OVRP aims to minimize the total cost of distributing products with the shortest optimal distance to meet the demands of each customer with private vehicles and rental vehicles. Seagulls Optimization Algorithm (SOA) is the algorithm inspired by the behaviour of seagulls in migrating and ways of attacking the pray of seagulls in nature. In general, the process begins with generating the initial position, evaluating the objective function, the migration process, the attacking process to get a new position, compare the objective function for the new position and the old position, update the position and save the best seagulls in each iteration until the maximum iteration is met. The program used to complete OVRP with Seagulls Optimization Algorithm is Borland C++ and implemented using 3 case examples, small data with 18 customers, medium data 50 customers and large data 100 customers. Based on the implementation results, it can be concluded that the higher number of seagulls, iterations and the smaller the control variable value tend to effect minimum cost gained.

Dynamic Programming Based Rapid Energy Management of Hybrid Electric Vehicles with Constraints on Smooth Driving, Battery State-of-Charge and Battery State-of-Health

Dynamic programming (DP) is currently the reference optimal energy management approach for hybrid electric vehicles (HEVs). However, several research concerns arise regarding the effective application of DP for optimal HEV control problems which involve a significant number of control variables, state variables and optimization constraints. This paper deals with an optimal control problem for a full parallel P2 HEV with constraints on battery state-of-charge (SOC), battery lifetime in terms of state-of-health (SOH), and smooth driving in terms of the frequencies of internal combustion engine (ICE) activations and gear shifts over time. The DP formulation for the considered HEV control problem is outlined, yet its practical application is demonstrated as unfeasible due to a lack of computational power and memory in current desktop computers. To overcome this drawback, a computationally efficient version of DP is proposed which is named Slope-weighted Rapid Dynamic Programming (SRDP). Computational advantage is achieved by SRDP in considering only the most efficient HEV powertrain operating points rather than the full set of control variable values at each time instant of the drive cycle. A benchmark study simulating various drive cycles demonstrates that the introduced SRDP can achieve compliance with imposed control constraints on battery SOC, battery SOH and smooth driving. At the same time, SRDP can achieve up to 78% computational time saving compared with a baseline DP approach considering the Worldwide Harmonized Light Vehicle Test Procedure (WLTP). On the other hand, the increase in the fuel consumption estimated by SRDP is limited within 3.3% compared with the baseline DP approach if the US06 Supplemental Federal Test Procedure is considered. SRDP could thus be exploited to efficiently explore the large design space associated to HEV powertrains.

Analysis of the Uncertainty Effect in Power System Losses: Uncertainties of Renewable Energy and Load

The energy loss minimization problem is increasingly gaining prominence as a result of widespread integration of renewable energy sources into the power systems. Thus, the optimal planning of power system is required to handle the technical issues due to the uncertainties in load demands and the intermittent characteristics in photovoltaic (PV) and wind turbine (WT) systems. In this paper, the impacts of various uncertainty scenarios have been considered while mitigating the total energy losses in the power network, where PV and WT systems are installed. Particle Swarm Optimization (PSO) algorithm has been implemented to determine the optimal values of control variables while taking into account the power system technical constraints. The influences of different uncertainty scenarios have been considered while alleviating total energy losses in the implementation of planning.

Minimizing Power Loss Using Modified Artificial Bee Colony Algorithm

Electrical energy losses are found in any part of the power system. In the power system, it is essential to minimize the real power loss in transmission lines. The voltage deviation at the load buses through controlling the reactive power flow is very important. This ensures the secured operation of power systems regarding voltage stability and the economics of the process due to loss minimization. In this paper, the Modified Artificial Bee Colony (MABC) algorithm is implemented to solve the power system's optimal reactive power flow problem. Generator bus voltages, transformer tap positions, and settings of switched shunt of compensators are used as decision variables to control the reactive power flow. These control variable values are adjusted for loss reduction. MABC algorithm is tested on the standard IEEE-30 bus test system. The results are compared with Firefly algorithm (FA) and Artificial Bee Colony (ABC) algorithm method to prove the effectiveness of the newest algorithm. The power loss results are quite productive, and the algorithm is the most efficient than the other methods such as ABC algorithm and FA algorithm. These results are produced by Matlab 2017b.

A Reproducing Kernel Hilbert Space Approach to Functional Calibration of Computer Models

This article develops a frequentist solution to the functional calibration problem, where the value of a calibration parameter in a computer model is allowed to vary with the value of control variables in the physical system. The need of functional calibration is motivated by engineering applications where using a constant calibration parameter results in a significant mismatch between outputs from the computer model and the physical experiment. Reproducing kernel Hilbert spaces (RKHS) are used to model the optimal calibration function, defined as the functional relationship between the calibration parameter and control variables that gives the best prediction. This optimal calibration function is estimated through penalized least squares with an RKHS-norm penalty and using physical data. An uncertainty quantification procedure is also developed for such estimates. Theoretical guarantees of the proposed method are provided in terms of prediction consistency and consitency of estimating the optimal calibration function. The proposed method is tested using both real and synthetic data and exhibits more robust performance in prediction and uncertainty quantification than the existing parametric functional calibration method and a state-of-art Bayesian method.

(DA-DOPF): A Day-Ahead Dynamic Optimal Power Flow With Renewable Energy Integration in Smart Grids

The performance of a power system can be measured and evaluated by its power flow analysis. Along with the penetration of renewable energies such as wind and solar, the power flow problem has become a complex optimization problem. In addition to this, constraint handling is another challenging task of this problem. The main critical problem of this dynamic power system having such variable energy sources is the intermittency of these VESs and complexity of constraint handling for a real-time optimal power flow (RT-OPF) problem. Therefore, optimal scheduling of generation sources with constraint satisfaction is the main goal of this study. Hence, a renewable energy forecasting–based, day-ahead dynamic optimal power flow (DA-DOPF) is presented in this paper with the forecasting of solar and wind patterns by using artificial neural networks. Moreover, contribution factors are calculated using triangular fuzzy membership function (T-FMF) in the sub-interval time slots. Furthermore, the superiority of feasible (SF) solution constraint handling approach is used to avoid the constraint violation of inequality constraints of optimal power flow. The IEEE 30-bus transmission network has been amended to integrate a solar photovoltaic and wind farm in different buses. In this approach, the computing program is based on MATPOWER which is a tool of MATLAB for load flow analysis which uses the Newton–Raphson technique because of its rapid convergence. Meteorological information has been gathered during the time frame January 1, 2015, to December 31, 2017, from Danyore Weather Station (DWS) at Hunza, Pakistan. A Levenberg–Marquardt calculation–based artificial neural network model is utilized to foresee the breeze speed and sunlight-based irradiance in light of its versatile nature. Finally, the results are discussed analytically to select the best generation schedule and control variable values.

WEDM of complex profile of IN718: multi-objective GA-based optimization of surface roughness, dimensional deviation, and cutting speed

Over the past decade, components featuring complex curved geometries have become a prerequisite for the high performance of aeroengines, thus necessitating stringent limits for excellent surface quality and high dimensional precision. As such, the manufacturing of complex features presents machining challenges. Wire electric discharge machining is a non-conventional process that has the potential to effectively mitigate these challenges, but further research is needed. Specifically, the coated wire electrodes that are incorporated in machining have been examined in terms of their impact on cutting speed, but their influence on the surface roughness and the dimensional accuracies is somewhat unexplored. In this experimental study, the influence of zinc-coated copper wire (BroncoCut-X) and corresponding process parameters (wire tension, pulse-on-time, pulse-off-time, servo voltage, and wire feed) were scrutinized to machine a complex profile in IN718 superalloy. The response characteristics associated with the complex profile, namely, surface roughness, dimensional deviation, and cutting speed, were thoroughly investigated. The machining results were analysed through main effect plots, analysis of variance, and scanning electron microscopy. The results revealed that BroncoCut-X was effective in machining the complex curved geometry profiles (convex, concave, straight, and inclined) and produced the best results for the concave geometrical feature. Considering the conflicting nature of response attributes, multi-objective genetic algorithm was employed to obtain the best combination of control parameters for the each geometry of the complex profile. The best optimal solution set the values of control variables at 2.6405 g wire tension, 2.9931 μs pulse-on-time, 22.4108 μs pulse-off-time, 54.620 V servo voltage, and 4.1730 mm/s wire feed. The exactness of multi-objective genetic algorithm was verified through confirmatory tests wherein the average percentage error was found less than 2%.

Trajectory optimization of an unmanned aerial–aquatic rotorcraft navigating between air and water

Unmanned aerial–aquatic vehicles are a new type of aircraft that can navigate in air and underwater. An unmanned aerial–aquatic rotorcraft (UAAR) is introduced to complete the task of navigating between air and underwater, and the trajectory optimization problem for this task is focused on in this study. The dynamics of a four-axle rotorcraft with eight rotors operating in air and underwater is described. On this basis, the trajectory optimization model is established, wherein the constraints on control variables and states in different media are included. The optimization index is denoted as the weighted sum of the terminal states. In view of the weakness of the teaching- and learning-based optimization (TLBO) algorithm, the formula for updating the individual grade in the teaching process is modified. Thus, this ensures that the algorithm avoids converging at the local optimum and improves the solution quality. Finally, an improved TLBO (ITLBO)-based trajectory optimization method for UAAR navigating between air and water is developed. The control variables are discretized with respect to height at a set of Chebyshev collocation points to reduce the terminal error of states, and the values of control variables at other heights are obtained via interpolation. In the simulation studies, the ITLBO-based method exhibits better performance in terms of optimizing the index when compared to the other two algorithms. Furthermore, the effects of the distribution and number of collocation points on the results are analyzed.

An optimal control model of COVID-19 pandemic: a comparative study of five countries

This paper formulates an optimal control model of COVID-19 pandemic spreading. We discuss the health sector performance of Argentina, Hungary, Egypt, Malaysia, and Iraq. A mathematical model describes an actual case number of COVID-19. We investigate three strategies depend on recovery rate, death rate, and together (optimal). These strategies represent the percent of the health sector development. The explicit solution of the model using the Pontryagin maximum principle is derived. The results showed the ranking of countries based on the new percent of the recovery and death cases. A new percent as a result to the control variable value (health sector development). Also, the development percent of the health sector of each country, was determined. For example, 0.005 led to a significant reduce the death rates in Malaysia. Meanwhile, a half of death rates could reduce by this percent in Egypt.

An Extended Control Strategy for Weakly Meshed Distribution Networks With Soft Open Points and Distributed Generation

As part of the smart grid concept, different strategies specialized for power flow control in distribution networks have been developed. One of the possible solutions to optimize the utilization of existing capacities and increase distributed generation penetration is the implementation of Soft Open Points. Soft Open Points are modular devices based on power electronic converters that enable closing loops in the network without negative consequences regarding fault current propagation. Introducing the concept of soft open points in the distribution network enables power flow control in a particular part of the network and voltage control in the soft open point connecting nodes. The control strategy proposed in this paper addresses the main obstacle for appropriate exploitation of soft open points, defining reference values for control variables in the case of large-scale distribution systems. Furthermore, the proposed strategy also deals with data unavailability problems, that is, soft open point control under communication interruption. The proposed control algorithm incorporates centralized optimal power flow calculations and an estimation algorithm based on a multivariate polynomial regression. The optimal power flow is used to calculate the control variables in normal operation modes. The procedure based on multivariate polynomial regression was used to estimate the reference values of the control variables when the optimal power flow results were unavailable. This feature makes the proposed algorithm applicable to communication interruptions when only limited data capture is available. The algorithm proposed in this study was implemented and tested on a test network considering different scenarios. Conclusions and simulation results make this algorithm applicable to an actual soft open point controller.

An Integrated Prediction and Optimization Model of a Thermal Energy Production System in a Factory Producing Furniture Components

Thermal energy is an important input of furniture components production. A thermal energy production system includes complex, non-linear, and changing combustion processes. The main focus of this article is the maximization of thermal energy production considering the inbuilt complexity of the thermal energy production system in a factory producing furniture components. To achieve this target, a data-driven prediction and optimization model to analyze and improve the performance of a thermal energy production system is implemented. The prediction models are constructed with daily data by using supervised machine learning algorithms. Importance analysis is also applied to select a subset of variables for the prediction models. The modeling accuracy of prediction algorithms is measured with statistical indicators. The most accurate prediction result was obtained using an artificial neural network model for thermal energy production. The integrated prediction and optimization model is designed with artificial neural network and particle swarm optimization models. Both controllable and uncontrollable variables were used as the inputs of the maximization model of thermal energy production. Thermal energy production is increased by 4.24% with respect to the optimal values of controllable variables determined by the integrated optimization model.

Choice of materials properties and of shell molds structure by investment models

The paper presents a mathematical model optimizing the choice of material and morphological structure of the shell mold (SM), which has the highest resistance to cracking when pouring liquid metal into it. To solve this problem, the theory of small elastoplastic deformations and the heat equation, as well as proven numerical methods, were used. The objective function min – max was constructed from control variables characterizing the properties of the molding material of the shell. The process of heating an axisymmetric shell mold was considered when pouring liquid metal into it. The resistance of the shell form was estimated by the stresses arising in it. An algorithm for solving this problem was compiled. Using numerical schemes and program complexes developed in previous studies, an algorithm for solving the optimization problem was constructed and the values of control variables were found in which the shell mold does not break even in the presence of a rigid process – pouring steel into a cold shell mold. Analysis of the influence of weight of each of the found parameters on the value of the constructed objective function is given. Using a mathematical experiment, the morphological structure of the shell mold was studied. The shell mold of five layers is considered. The corrected system of equations makes it possible to take into account the properties of the layers made of different materials. Calculations were performed when the layer of the shell mold from material found by optimization occupies different positions in its cross section. In this case, the remaining layers of the mold are made of traditional ceramics. The optimal location of this layer was found. It is shown that the presence of several layers with the found properties does not affect the increase in crack resistance of the shell mold.

Modeling and Optimizing the Property Choices of Materials and Structures of Shell Molds for Investment Casting

The paper presents a mathematical model for optimizing the choice of material and morphological structure of a shell mold (SM) that has the highest resistance to cracking when liquid metal is poured into it. In order to solve this problem, the theory of small elastoplastic deformations, the heat equation, and proven numerical methods are used. The min–max objective function of control variables characterizing the properties of the SM material is constructed. The process of heating an axisymmetric SM by pouring liquid metal into it is considered. The SM resistance is estimated by the stresses arising in it. An algorithm for solving this problem is constructed. Using numerical schemes and software tools developed in previous studies, an algorithm for solving the optimization problem is constructed, and the values of control variables are found, in which the SM cannot be destroyed even being exposed to a rigid process of pouring steel into the cold SM. The analysis of the weight’s influence of each parameter found on the value of the objective function constructed is performed. A mathematical experiment is used to study the morphological structure of the SM. A five-layer SM is considered. The corrected system of equations makes it possible to consider the properties of the layers made of different materials. Calculations are performed for the cases of different positions of one of the mold layers in the mold section. This layer is made of the material found by optimization, while other mold layers are made of traditional ceramics. The optimal location of this layer is found. It is shown that the presence of several layers with the found properties does not influence the increase in the crack resistance of the SM.

Averaged Optimization and Finite-Time Thermodynamics.

The paper considers typical extremum problems that contain mean values of control variables or some functions of these variables. Relationships between such problems and cyclic modes of dynamical systems are explained and optimality conditions for these modes are found. The paper shows how these problems are linked to the field of finite-time thermodynamics.