Optimal Scheme Research Articles

Peak-shaving cost of power system in the key scenarios of renewable energy development in China: Ningxia case study

Renewable energy has developed rapidly in Ningxia, and it has become the first provincial power system in China whose renewable energy power generation output exceeds the power load of the whole region. The access of a high proportion of renewable energy puts forward higher requirements for the peak-shaving capacity of the Ningxia power system. In order to solve the problem of calculating the peak-shaving cost in the key scenarios of renewable energy development in Ningxia, a quantitative model of the peak-shaving cost of the power system considering time-of-use price is proposed. We take Ningxia power system as an example to study. First, the key scenarios of the Ningxia power system peak-shaving are obtained, and the technical cost characteristic boundaries of various peak-shaving resources are determined. Second, according to the characteristics of typical daily renewable energy and load in Ningxia, the quantification model of the power system peak-shaving cost is established. The model takes the minimum total cost of the power system as the objective function and considers the constraints such as technical output of thermal power units, charge-discharge characteristics of energy storage and time-of-use price mechanism. Finally, the model is solved and the peak-shaving cost and unit output under the optimal scheme are obtained. This example shows that the model can effectively evaluate the peak-shaving cost and unit output of the Ningxia power system under the key scenarios of peak-shaving.

Anti-derivatives approximator for enhancing physics-informed neural networks

This study presents a novel strategy for constructing an approximator for arbitrary univariate functions. The proposed approximation utilizes the anti-derivatives of a Fourier series expansion for the presumed piecewise function, resulting in a remarkable feature that enables the simultaneous approximation of an arbitrary function and its anti-derivatives. These anti-derivatives can be employed to discover solution curves for systems of ordinary differential equations based on an optimization scheme, even in the presence of chaotic dynamics. Additionally, the anti-derivatives approximator is extended as an adaptive activation function for physics-informed neural networks, leveraging the high-order differentiability of the anti-derivatives. Systematic experiments have demonstrated the outstanding merits of the proposed anti-derivatives-based approximator, including its ability to construct regression models for volatile data and their anti-derivatives, solve differential equations, and enhance the capabilities of physics-informed neural networks.

A Multi-period Optimal Distribution Model of Emergency Resources for Responding to COVID-19 Under Uncertain Conditions

Ideally, optimal emergency resource allocation would have been vital for effective relief work during the COVID-19 outbreak. However, the suddenness of the epidemic and uncertainty of its spread added some difficulties to distributing emergency resources. First, this study introduces triangular fuzzy numbers to describe the uncertainty of supply and demand of emergency resources, and interval numbers to describe the time required for resource transportation under disaster conditions. To minimize the total delivery time and difference in the total satisfaction rate, this study constructs an optimal model for emergency resource distribution under uncertain conditions that considers both efficiency and equity. Subsequently, an improved genetic algorithm (IMGA) is proposed to obtain the optimal decision scheme. Finally, a case study on emergency resource distribution during the COVID-19 pandemic is conducted for model verification. The results demonstrate that the proposed model can improve the efficiency and effect of emergency resource distribution. The model allocates some emergency resources to each demand site during each emergency period, which can help avoid large losses caused by extreme shortages of resources at a certain demand point. The emergency resource allocation scheme considers the transportation time and degree of impact, which is beneficial for enhancing the flexibility of decision-making and practical applicability of distribution operations. A comparative analysis of the algorithms shows that the proposed IMGA is an effective method for managing emergency resource distribution optimization problems because it has higher solving efficiency, better convergence, and stronger stability. These findings can provide decision support for the optimal distribution of large-scale, multiperiod emergency resources during the COVID-19 pandemic.

Constructal design for H-shaped compound heat transfer path in a rectangular heat generation body

An H-shaped compound heat transfer path (HSCHTP) model in a rectangular heat generation body (RHGB) is built in present article. With specified total volumes of HSCHTP and RHGB, constructal design for HSCHTP model is conducted by varying path length ratios and radius. The minimum complex functions composed of thermal and flow performances are acquired, and the multi-objective optimizations are performed furtherly. Three decision-making approaches are introduced to obtain the optimal design scheme (ODS) from Pareto-optimal frontiers. It indicates that complex function after triple-optimization is reduced by 14.7 % compared with that of initial design. Compared with performance of RHGB with no heat conduction path, complex function after optimization is reduced by 77.5 %. Thus, performance of the HSCHTP is apparently superior to that with no heat conduction path in this case. The complex function minimization is a special case of the multi-objective optimization (MOO). The fifth order path radius, adjacent order and internal order length ratios acquired by MOO are distributed within the ranges of 1.50mm-1.60 mm, 1.39–1.47 and 0.066–0.90, respectively. By chasing for the smallest deviation-index, optimal structure of HSCHTP acquired by LINMAP decision-making method is taken for the ODS when multiple requirements are considered in the heat dissipation designs.

Prediction and control of profile for silicon steel strip in the whole tandem cold rolling based on PSO-BP algorithm

In the rolling process of silicon steel strip of the five-stand UCMW tandem cold rolling line, the quality of finished profile is the result of cooperative control of five stands, the exit profiles of the first four stands jointly decide the exit profile of the fifth stand, so it is necessary to accurately control the strip profile in the rolling process. However, the shapemeter is only typically equipped at the exit of fifth stand, making it impossible to obtain the strip profile of the first four stands. A profile prediction model for the whole tandem cold rolling based on PSO-BP algorithm is established, compared with the finite element method, this model can satisfy the demand for fast prediction of strip profile and quickly analyzing the profile change characteristics for five stands according to the adjustment of profile control parameters in the industrial field. Firstly, a 3D elastic-plastic finite element model of rolls and strip for five stands is built, and a large number of profile calculation data are as the training sample sets to build the PSO-BP model. Through the transfer calculation of strip profile between adjacent stands, the PSO-BP model of five stands is established, and the validity is verified by comparing with the actual measured data. Secondly, to improve the quality of product profile, focusing on the unreasonable setting of production parameters, many improvement schemes of WRB and WRS for five stands are designed, and the PSO-BP model is used to quickly calculate the strip profile, then comparing the result of each scheme, the optimum improvement scheme is selected, which is furtherly carried out rolling experiments in the industrial field, and the quality of strip profile is well improved. At present, the new scheme has been successfully applied to industrial production.

Aircraft routing using dynamic programming and reinforcement learning: A customer-centric approach

Over the past few decades, the airline industry has evolved into a sophisticated business, with conventional objectives such as operational efficiency, effective fleet assignment, flight punctuality, and equitable crew scheduling being the primary focus. Nevertheless, given the growing accessibility to customer feedback (either through public forums or private data), it is crucial to make business decisions that cater to the customers’ requirements in addition to conventional goals. Within aircraft operations, there is a series of decisions to be made, such as flight scheduling, fleet assignment, aircraft routing, and crew scheduling. After designating a fleet type to each flight leg, airlines ascertain the sequence of flight legs, or strings, to be operated by individual aircrafts, while complying with obligatory maintenance checks. This constitutes the aircraft routing problem.We introduce a novel approach to aircraft routing problem, by infusing traditional methodologies with insightful customer feedback to create a more responsive and customer-centric model. Unlike conventional techniques of constructing routes, in our work, we construct maintenance feasible strings. Traditional aircraft routing methodologies typically concentrate on minimizing propagated delay. However, by integrating customer feedback, more effective prioritization to minimize delays for flight legs with higher customer dissatisfaction can be achieved. We propose an optimization model that strives to minimize propagated delay while prioritizing flights based on customer feedback, thus resulting in customer-aware routes. To solve the proposed optimization model, we design an iterative alternating optimization scheme where feasible strings are first constructed from the pool of available flight legs using a string generation procedure, followed by solving an integer linear optimization problem over only the feasible set of strings obtained in the first stage. To construct feasible strings of flights at each iteration, we use two different methods. The first method is based on a dynamic programming approach which is useful for mean delay information. To handle practical cases where delays are uncertain, we propose a reinforcement learning (RL) approach to construct the strings. We provide experiments of our proposed methods on synthetic and real data sets and demonstrate the effectiveness of our RL model in comparison to dynamic programming based model. Our experiments affirm that routing decisions informed by customer feedback prioritize minimizing delays for specific flight legs, resulting in routes that are inherently customer-friendly.

Nonlinear vibration analysis of thin plate with periodically distributed tunable-stiffness nonlinear oscillators in subsonic flow

This paper provides a new passive control method for nonlinear vibration of subsonic thin plates. The control method uses periodically distributed tunable-stiffness nonlinear oscillators (NLO). By using von Karman’s nonlinear plate theory and subsonic aerodynamic model, the nonlinear dynamic model of thin plate is established based on Hamilton’s principle. Through analyzing the system’s nonlinear dynamics bifurcation, the impact of periodic distribution on the stability is discussed. The amplitude-frequency responses are discussed under different NLO installation modes and design parameters by using Matcont software. The results show that the periodically distributed tunable-stiffness nonlinear oscillators can improve the stability of the system and have a remarkable suppression effect. The optimal control scheme for vibration suppression by periodically distributed tunable-stiffness nonlinear oscillators is obtained. The results obtained from this research can offer a valuable understanding of nonlinear vibration control, thereby enabling the identification of various control approaches that can be implemented in practical applications during future design endeavors.

Optimal Voltage Recovery Learning Control for Microgrids with N-Distributed Generations via Hybrid Iteration Algorithm

Considering that the nonlinearity and uncertainty of the microgrid model complicate the derivation and design of the optimal controller, an adaptive dynamic programming (ADP) algorithm is designed to solve the model-free non-zero-sum game. By combining the advantages of policy iteration and value iteration, an optimal learning control scheme based on hybrid iteration is constructed to provide stringent real power sharing for the nonlinear and coupled microgrid systems with N-distributed generations. First, using non-zero-sum differential game strategy, a novel distributed secondary voltage recovery consensus optimal control protocol is built using a hybrid iteration method to realize the voltage recovery of microgrids. Then, the data of the system state and input are gathered along a dynamic system trajectory and a data-driven optimal controller learns the game solution without microgrid physics information, enhancing convenience and efficiency in practical applications. Furthermore, the convergence analysis is given in detail, and it is proved that the control protocol can converge to the optimal solution so as to ensure the stability of the voltage recovery of the microgrid system. Convergence analysis proves the convergence of the the protocol to the optimal solution, ensuring voltage recovery stability. Simulation results validate the feasibility and effectiveness of the proposed scheme.

Hybrid optimization schemes for solving the piezoresistive inversion problem in self-sensing materials

Materials with electrically conductive nanofillers have the ability to ‘sense’ changes to their mechanical state. When these materials are deformed, the embedded nanofiller networks are disturbed causing a measurable change in the electrical conductivity of the material. This self-sensing property, known as piezoresistivity, has been leveraged in numerous engineering venues. Although this property has been thoroughly explored, prevailing self-sensing techniques provide little-to-no information about the underlying mechanical state of the material, such as the displacement and strain. This information must be indirectly obtained from the conductivity change. This limitation exists because obtaining mechanics from conductivity is an under-determined inverse problem with many possible mathematically feasible solutions. Previous work in this area used metaheuristic algorithms and imposed mechanics-based constraints to solve the piezoresistive inversion problem. Although this approach was successful, it was computationally inefficient due to the stochastic search process and the need to perform multiple searches to find a converged solution. To overcome this limitation, we herein propose a hybrid optimization scheme for solving the piezoresistive inversion problem. This scheme is implemented in two steps. In the first step, a metaheuristic algorithm performs a single search for a suitable solution to the inverse problem. In the second step, a gradient descent algorithm searches for the final solution using the solution from the previous step as the starting point. We explore different norms for the fitness function of the metaheuristic search and demonstrate using experimental data that the proposed hybrid optimization scheme can accurately and efficiently calculate displacements and strains from conductivity changes. This exploration significantly advances the state of the art by enabling computationally efficient and highly accurate predictions of full-field mechanical condition in self-sensing materials for the first time, thereby paving the way for greater use of these principles in practice.

Analytic rotation-invariant modelling of anisotropic finite elements

Anisotropic hyperelastic distortion energies are used to solve many problems in fields like computer graphics and engineering with applications in shape analysis, deformation, design, mesh parameterization, biomechanics and more. However, formulating a robust anisotropic energy that is low-order and yet sufficiently non-linear remains a challenging problem for achieving the convergence promised by Newton-type methods in numerical optimization. In this paper, we propose a novel analytic formulation of an anisotropic energy that is smooth everywhere, low-order, rotationally-invariant and at-least twice differentiable. At its core, our approach utilizes implicit rotation factorizations with invariants of the Cauchy-Green tensor that arises from the deformation gradient. The versatility and generality of our analysis is demonstrated through a variety of examples, where we also show that the constitutive law suggested by the anisotropic version of the well-known As-Rigid-As-Possible energy is the foundational parametric description of both passive and active elastic materials. The generality of our approach means that we can systematically derive the force and force-Jacobian expressions for use in implicit and quasistatic numerical optimization schemes, and we can also use our analysis to rewrite, simplify and speedup several existing anisotropic and isotropic distortion energies with guaranteed inversion-safety.

Application of Hydrus-2D Model in Subsurface Drainage of Saline Soil in Coastal Forest Land—A Case Example of Fengxian, Shanghai

The study aims to explore saline drainage modeling in coastal saline soils, particularly focusing on subsurface pipe drainage in the Shanghai coastal area. Utilizing Hydrus-2D/3D-2.05 software, dynamic changes in soil–water–salt under various subsurface pipe laying conditions in forested areas were simulated to identify optimal schemes. Indoor and outdoor experiments demonstrated the Hydrus model’s ability to effectively simulate soil–water–salt transport processes under complex conditions. Subsequent simulations under different parameters of underground pipe laying, including burial depths (D = 0.5/0.7/0.9/1.1/1.3/1.5 m) and pipe diameters (Ø = 8/10/12 cm), further corroborated model validation. Among the analyzed schemes, those with burial depths around 0.7 m and pipe diameters under 12 cm exhibited the most substantial salinity improvement. Regression analysis highlighted a significant impact of burial depth D on cumulative salt discharge, with a coefficient of 12.812, outweighing that of pipe diameter Ø. Furthermore, subsurface pipe laying schemes demonstrated long-term benefits and cost advantages, obviating the need for additional irrigation infrastructure. These findings underscore the significance of subsurface pipe drainage in enhancing soil quality, reducing construction expenses, and optimizing land utilization, providing a valuable foundation for the Shanghai Green Corridor development and related initiatives.

Topology optimization for the design of manufacturable piezoelectric energy harvesters using dual-MMC method

Abstract This paper presents a new topology optimization scheme for the manufacturable piezoelectric energy harvesters (PEHs). Most of the existing topology optimization schemes for the design for PEHs are difficult to cope with manufacturing constraints producing design results that pose serious challenges for the local poling of the piezoelectric materials. In this work, dual-Moving Morphable Component (dual-MMC) scheme for explicit topology optimization for the design of PEHs is presented. In dual-MMC scheme, two independent sets of MMC are employed to describe the structural topology of the PEH and polarization profile in piezoelectric material in an explicit manner. With the use of the scheme, the shape of electrodes and the opposite polarization directions in the local poling process can be effectively treated as a constraint making the realization of the PEH an easy task. Several examples for the design of cantilever-type PEH are provided to demonstrate the effectiveness of the proposed approach. Furthermore, a designed PEH actually manufactured for demonstration of the production process.

Effect of Biochar on Apple Yield and Quality in Aged Apple Orchards on the Loess Plateau (China)

Apples are not only a foodstuff, but also a raw material for many industrial production fields, and the market demand is constantly increasing. The Loess Plateau is one of the world’s largest apple-producing areas, with about 85% are aged orchards (more than 20 years old), facing problems such as poor soil water retention, degradation of tree strength, and declining yield and quality, etc, so do aged orchards in other regions of the world, and study on improving quality and increasing yield of aged orchards is of great significance to the sustainable development of the apple industry. Here, 6 treatments (2, 4, 6, 8, 10 and 12 kg/plant) were designed in the experiment to study the effects of biochar on yield and quality in aged apple orchards. The study showed that: biochar could improve soil water retention, but caused the soil alkalization; biochar could improve apple quality and increase yield, T3 and T4 were of better quality, and T3 had the highest yield. Comprehensive analysis, T3 is the optimal scheme. The results not only provide a reference for aged orchards worldwide, but also have great significance for the sustainable development of the apple industry.

Research on dynamic balance optimization method of flexible rotor based on GWO

Abstract Aiming at the problem that the dynamic balance process of a flexible rotor needs to start and stop frequently to add test weight, which is time-consuming and labor-consuming, and the balance accuracy is difficult to guarantee, a dynamic balance optimization method of flexible rotor based on Grey Wolf Optimizer(GWO) is proposed. In this paper, a virtual prototype model is established based on a power turbine rotor for a certain type of turboshaft engine, and a rotor test platform is built. The transfer function is used to find the relationship between unbalance and vibration response, and the equilibrium equations are established to solve the problem. In the process of solving the problem that the equilibrium equations are mostly contradictory, GWO is used to solve the contradictory equations to obtain the optimal counterweight scheme at the full working speed of the rotor. The results show that the method proposed in this paper eliminates the tedious test weight process of traditional dynamic balance, and the vibration reduction effect is better than the conventional on-site dynamic balance. The work of this paper can improve the efficiency and accuracy of flexible rotor dynamic balance and provide technical reference for the vibration control of aero-engine.

Harmonic impedance optimization scheme for multi‐resonance systems to suppress resonance

AbstractHarmonic resonance is caused by harmonic source matching resonance frequency and presents the characteristics of decentralization and whole network in modern grids. The current resonance suppression methods mainly focus on reducing the harmonic source, and are suitable for single‐site and small‐scale grids. This paper presents a new method for suppressing parallel resonance at system level. The holistic harmonic resonance is suppressed by reducing the harmonic impedance. In addition, new resonances are prevented by weakening the coupling between resonance and non‐resonance frequencies. The resonance modal analysis and resonance frequency shift (RFS) are employed to optimize harmonic impedance. Simulation results indicate that the capacitance parameter has higher sensitivity and is theoretically more suitable for RFS. Considering the accuracy of modal frequency sensitivity, a variable‐limit genetic algorithm for iteration is proposed. The validity of the proposed method was verified using an IEEE 14‐bus test network.

Constraint programming for reservoir operation optimization of Bhumibol dam

The modern constraint programming (CP) was adopted to minimize water scarcity and excessive water which are the critical issues in reservoir operation of Bhumibol Dam (BB) to solve consecutive droughts in the Chao Phraya River Basin (CPYRB), Thailand. The situations of the severe droughts have been frequently occurred in a broad area of CPYRB due to an extremely low rainfall leading to unusually low water levels and inflow in major reservoirs. Therefore, multi-objective optimization was conducted to characterize the actual operation and physical reservoir system of BB Dam. Two different CP models with seasonal and yearly constraints were manipulated using MiniZinc programming language and the constraint solver IPOPT to find the optimal daily release scheme from 2000 to 2018 of BB Dam. The potential of downstream flow conditions was also considered to partially supply downstream water demand and store savable water in a reservoir for subsequent use during possible future droughts. The results reveal that CP models can diminish some extent of yearly reservoir release, while daily long-term release scheme conforms well with the actual operation particularly during dry and wet seasons in specific drought years. These mean that amount of reservoir water of approximately 47.12–103.83 MCM/year can be saved and stored in reservoir for subsequent use in CPYRB when CP models are deployed. This results in a reservoir storage increase of 7.10–7.94% at the end of the wet season for seasonal and yearly CP models, respectively. When potential side flow is considered, the increase climbs up to 10.49%. This envisages the higher possibility of supplying reservoir water for agricultural water needs over the dry season in the Greater Chao Phraya Irrigation Scheme. As the potential hydraulic head is subject to increased reservoir water storage, therefore, the increase in hydropower production is definitely found of ranging from + 6.10% to + 13.79% by these two sorts of CP models. In addition, handling with huge volumes of flood and drought by CP models is well managed as the specific release constraints during refilled and drawdown periods are used to define the constraint satisfaction problem.

Data-driven constrained reinforcement learning algorithm for path tracking control of hovercraft

This paper presents a novel Constrained Backstepping Reinforcement Learning (CBRL) approach designed for path tracking of hovercraft. The approach addresses the challenges posed by complex modeling, multiple constraints, and large sideslip angles during high-speed maneuvers of underactuated hovercraft. Initially, a unique state constraint function is formulated, incorporating constraint boundaries related to navigation speed and path curvature. Additionally, transformations are applied to the yaw angular velocity and virtual yaw control law, ensuring that the yaw angular velocity remains within safety limits. Subsequently, a data-driven backstepping reinforcement learning optimal approach, coupled with a line-of-sight guidance law, is employed to guide the hovercraft along the intended path by regulating its yaw angle. Simultaneously, the backstepping reinforcement learning optimal control scheme is used to regulate the surge speed of the hovercraft above the resistance peak speed, thereby preventing excessive sideslip angles during path tracking. Neural network observers are integrated into the design process of both the yaw and surge controllers to monitor system dynamics in the presence of interference. Through simulation, the effectiveness and feasibility of the proposed CBRL algorithm are demonstrated.

Data-driven traffic sensor location and path flow estimation using Wasserstein metric

This paper introduces link information value obtained by the traffic sensors and presents a traffic sensor location and flow estimation joint optimization model in an urban road network. In contrast to most previous studies, this paper adds new traffic sensors into the existing sensor network and proposes a data-driven path flow measurement method based on Wasserstein metric, which is utilized to measure the distance between the estimated traffic flow distribution and the actual distribution. Furthermore, this paper develops a customized greedy algorithm by combining a search strategy for the link information value to obtain the optimal sensor location scheme and perform traffic flow estimation under different budget conditions. Numerical experiments are conducted on Sioux-Falls test network and Eastern Massachusetts interstate highway subnetwork to verify the accuracy and effectiveness of the proposed model based on Wasserstein metric and the developed solution method. Computational results show that the sensor location scheme generated by the model based on Wasserstein metric can reduce the estimation error of the traffic flow compared with KL divergence model under the same deployment cost. Additionally, the customized greedy algorithm can achieve the better performance than the Brute force algorithm in terms of computing time and solution quality.

Optimization of the Coupling between Water and Energy Consumption in a Smart Integrated Photovoltaic Pumping Station System

Agricultural irrigation requires significant consumption of freshwater resources and energy. The integration of photovoltaic power generation into irrigation systems has been extensively investigated in order to save the cost of energy. However, current research often neglects the coupling relationship between photovoltaic power generation and irrigation schemes. This study presented a novel smart integrated photovoltaic pump station system to effectively address the issue associated with water and energy consumption in irrigation. An optimization model was proposed to synchronize the energy consumption of irrigation pump stations with photovoltaic power generation, accurately meeting the irrigation water demand while maximizing solar energy utilization. The optimization model incorporates power balance, grid-connected power, and total water demand as constraints while considering pump speed as the decision variable and aiming to minimize daily operational costs. Finally, a high-standard farmland was used as a case study to validate the efficacy of the optimization strategy through two photovoltaic grid-connected policies—one allowing for the sale of surplus power and the other prohibiting it. An improved dynamic programming method was employed to solve for optimal energy consumption schemes under different water demand conditions; the results were compared against traditional methods, revealing potential cost savings ranging from 6.2% to 30.5%. The optimization model and method propose a new operational concept for the irrigation system with photovoltaic generation, effectively utilizing the distinctive features of both irrigation and photovoltaics to optimize water and energy resources.

Research on multi-objective optimisation of product form design based on kansei engineering

It is crucial to understand and meet the multi-dimensional affective image needs of users for product form in a user demand-oriented product development model. Multi-objective evolutionary algorithms based on decomposition will be introduced into the field of kansei engineering to carry out research on product form optimisation design based on multi-objective evolutionary algorithms. A constrained multi-objective discrete optimisation model was established using the kansei engineering prediction model constructed through machine learning techniques as the objective function, and a reference vector guided evolutionary algorithm was used to solve it. The superiority of this method was verified by comparing it with other commonly used solving methods in this field. Combining entropy weight method and TOPSIS, select the optimisation design scheme that best meets the multi-dimensional affective needs of users from the obtained pareto set. Taking the train as an example, the proposed method was explained. The results indicate that the optimisation scheme obtained by this method can achieve the improvement and optimisation of product form in multiple affective dimensions. Meanwhile, a comparative study on the applicability of multi-objective evolutionary algorithms in the form optimisation problem of different affective dimensions is carried out to provide reference and suggestions for subsequent product design research.