Actual engineering systems will be inevitably affected by uncertain factors.Thus,the Reliability-Based Multidisciplinary Design Optimization(RBMDO)has become a hotspot for recent research and application in complex en...Actual engineering systems will be inevitably affected by uncertain factors.Thus,the Reliability-Based Multidisciplinary Design Optimization(RBMDO)has become a hotspot for recent research and application in complex engineering system design.The Second-Order/First-Order Mean-Value Saddlepoint Approximate(SOMVSA/-FOMVSA)are two popular reliability analysis strategies that are widely used in RBMDO.However,the SOMVSA method can only be used efficiently when the distribution of input variables is Gaussian distribution,which significantly limits its application.In this study,the Gaussian Mixture Model-based Second-Order Mean-Value Saddlepoint Approximation(GMM-SOMVSA)is introduced to tackle above problem.It is integrated with the Collaborative Optimization(CO)method to solve RBMDO problems.Furthermore,the formula and procedure of RBMDO using GMM-SOMVSA-Based CO(GMM-SOMVSA-CO)are proposed.Finally,an engineering example is given to show the application of the GMM-SOMVSA-CO method.展开更多
We apply the second-order Born-Oppenheimer （BO） approximation to investigate the dynamics of the Rabi model, which describes the interaction between a two-level system and a single bosonic mode beyond the rotating w...We apply the second-order Born-Oppenheimer （BO） approximation to investigate the dynamics of the Rabi model, which describes the interaction between a two-level system and a single bosonic mode beyond the rotating wave approxi- mation. By comparing with the numerical results, we find that our approach works well when the frequency of the two-level system is much smaller than that of the bosonic mode.展开更多
Although the genetic algorithm (GA) has very powerful robustness and fitness, it needs a large size of population and a large number of iterations to reach the optimum result. Especially when GA is used in complex str...Although the genetic algorithm (GA) has very powerful robustness and fitness, it needs a large size of population and a large number of iterations to reach the optimum result. Especially when GA is used in complex structural optimization problems, if the structural reanalysis technique is not adopted, the more the number of finite element analysis (FEA) is, the more the consuming time is. In the conventional structural optimization the number of FEA can be reduced by the structural reanalysis technique based on the approximation techniques and sensitivity analysis. With these techniques, this paper provides a new approximation model-segment approximation model, adopted for the GA application. This segment approximation model can decrease the number of FEA and increase the convergence rate of GA. So it can apparently decrease the computation time of GA. Two examples demonstrate the availability of the new segment approximation model.展开更多
This paper presents an adaptive rationalized Haar function approximation method to obtain the optimal injection strategy for alkali-surfactant-polymer(ASP) flooding. In this process, the non-uniform control vector par...This paper presents an adaptive rationalized Haar function approximation method to obtain the optimal injection strategy for alkali-surfactant-polymer(ASP) flooding. In this process, the non-uniform control vector parameterization is introduced to convert original problem into a multistage optimization problem, in which a new normalized time variable is adopted on the combination of the subinterval length. Then the rationalized Haar function approximation method, in which an auxiliary function is introduced to dispose path constraints, is used to transform the multistage problem into a nonlinear programming. Furthermore, an adaptive strategy proposed on the basis of errors is adopted to regulate the order of Haar function vectors. Finally, the nonlinear programming for ASP flooding is solved by sequential quadratic programming. To illustrate the performance of proposed method,the experimental comparison method and control vector parameterization(CVP) method are introduced to optimize the original problem directly. By contrastive analysis of results, the accuracy and efficiency of proposed method are confirmed.展开更多
To increase the efficiency of the multidisciplinary optimization of aircraft, an aerodynamic approximation model is improved. Based on the study of aerodynamic approximation model constructed by the scaling correction...To increase the efficiency of the multidisciplinary optimization of aircraft, an aerodynamic approximation model is improved. Based on the study of aerodynamic approximation model constructed by the scaling correction model, case-based reasoning technique is introduced to improve the approximation model for optimization. The aircraft case model is constructed by utilizing the plane parameters related to aerodynamic characteristics as attributes of cases, and the formula of case retrieving is improved. Finally, the aerodynamic approximation model for optimization is improved by reusing the correction factors of the most similar aircraft to the current one. The multidisciplinary optimization of a civil aircraft concept is carried out with the improved aerodynamic approximation model. The results demonstrate that the precision and the efficiency of the optimization can be improved by utilizing the improved aerodynamic approximation model with ease-based reasoning technique.展开更多
In this paper, a model averaging method is proposed for varying-coefficient models with response missing at random by establishing a weight selection criterion based on cross-validation. Under certain regularity condi...In this paper, a model averaging method is proposed for varying-coefficient models with response missing at random by establishing a weight selection criterion based on cross-validation. Under certain regularity conditions, it is proved that the proposed method is asymptotically optimal in the sense of achieving the minimum squared error.展开更多
In this paper, a computational approach is proposed for solving the discrete-time nonlinear optimal control problem, which is disturbed by a sequence of random noises. Because of the exact solution of such optimal con...In this paper, a computational approach is proposed for solving the discrete-time nonlinear optimal control problem, which is disturbed by a sequence of random noises. Because of the exact solution of such optimal control problem is impossible to be obtained, estimating the state dynamics is currently required. Here, it is assumed that the output can be measured from the real plant process. In our approach, the state mean propagation is applied in order to construct a linear model-based optimal control problem, where the model output is measureable. On this basis, an output error, which takes into account the differences between the real output and the model output, is defined. Then, this output error is minimized by applying the stochastic approximation approach. During the computation procedure, the stochastic gradient is established, so as the optimal solution of the model used can be updated iteratively. Once the convergence is achieved, the iterative solution approximates to the true optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, an example on a continuous stirred-tank reactor problem is studied, and the result obtained shows the applicability of the approach proposed. Hence, the efficiency of the approach proposed is highly recommended.展开更多
A new reliability-based multidisciplinary design optimization （RBMDO） framework is proposed by combining the single-loop-based reliability analysis （SLBRA） method with multidisciplinary feasible （MDF） method. Th...A new reliability-based multidisciplinary design optimization （RBMDO） framework is proposed by combining the single-loop-based reliability analysis （SLBRA） method with multidisciplinary feasible （MDF） method. The Kriging approximate model with updating is introduced to reduce the computational cost of MDF caused by the complex structure. The computational efficiency is remarkably improved as the lack of iterative process during reliability analysis. Special attention is paid to a turbine blade design optimization by adopting the proposed method. Results show that the method is much more efficient than the commonly used double-loop based RBMDO method. It is feasible and efficient to apply the method to the engineering design.展开更多
In density-based topological design, one expects that the final result consists of elements either black （solid material） or white （void）, without any grey areas. Moreover, one also expects that the optimal topolo...In density-based topological design, one expects that the final result consists of elements either black （solid material） or white （void）, without any grey areas. Moreover, one also expects that the optimal topology can be obtained by starting from any initial topology configuration. An improved structural topological optimization method for multidisplacement constraints is proposed in this paper. In the proposed method, the whole optimization process is divided into two optimization adjustment phases and a phase transferring step. Firstly, an optimization model is built to deal with the varied displacement limits, design space adjustments, and reasonable relations between the element stiffness matrix and mass and its element topology variable. Secondly, a procedure is proposed to solve the optimization problem formulated in the first optimization adjustment phase, by starting with a small design space and advancing to a larger deign space. The design space adjustments are automatic when the design domain needs expansions, in which the convergence of the proposed method will not be affected. The final topology obtained by the proposed procedure in the first optimization phase, can approach to the vicinity of the optimum topology. Then, a heuristic algorithm is given to improve the efficiency and make the designed structural topology black/white in both the phase transferring step and the second optimization adjustment phase. And the optimum topology can finally be obtained by the second phase optimization adjustments. Two examples are presented to show that the topologies obtained by the proposed method are of very good 0/1 design distribution property, and the computational efficiency is enhanced by reducing the element number of the design structural finite model during two optimization adjustment phases. And the examples also show that this method is robust and practicable.展开更多
In the process of multidisciplinary design optimization, there exits the calculation complexity problem due to frequently calling high fidelity system analysis models. The high fidelity system analysis models can be s...In the process of multidisciplinary design optimization, there exits the calculation complexity problem due to frequently calling high fidelity system analysis models. The high fidelity system analysis models can be surrogated by approximate models. The sensitivity analysis and numerical noise filtering can be done easily by coupling approximate models to optimization. Approximate models can reduce the number of executions of the problem's simulation code during optimization, so the solution efficiency of the multidisciplinary design optimization problem can be improved. Most optimization methods are based on gradient. The gradients of the objective and constrain functions are gained easily. The gra- dient-based Kriging (GBK) approximate model can be constructed by using system response value and its gradients. The gradients can greatly improve prediction precision of system response. The hybrid optimization method is constructed by coupling GBK approximate models to gradient-based optimiza- tion methods. An aircraft aerodynamics shape optimization design example indicates that the methods of this paper can achieve good feasibility and validity.展开更多
Control parameter optimization is an efficient way to improve the endurance of underwater gliders(UGs),which influences their gliding efficiency and energy consumption.This paper analyzes the optimal matching between ...Control parameter optimization is an efficient way to improve the endurance of underwater gliders(UGs),which influences their gliding efficiency and energy consumption.This paper analyzes the optimal matching between the net buoyancy and the pitching angle and proposes a segmented control strategy of Petrel-L.The optimization of this strategy is established based on the gliding range model of UG,which is solved based on the approximate model,and the variations of the optimal control parameters with the hotel load are obtained.The optimization results indicate that the segmented control strategy can significantly increase the gliding range when the optimal matching between the net buoyancy and the pitching angle is reached,and the increase rate is influenced by the hotel load.The gliding range of the underwater glider can be increased by 10.47%at a hotel load of 0.5 W.The optimal matching analysis adopted in this study can be applied to other UGs to realize endurance improvement.展开更多
According to time-sharing valuation principle (TSVP) of power supply, the relationships of current density and current efficiency at different acidities are obtained based on the processed data of electrolytic deposit...According to time-sharing valuation principle (TSVP) of power supply, the relationships of current density and current efficiency at different acidities are obtained based on the processed data of electrolytic deposition process of zinc (EDPZ) with the least square method (LSM). Thus an optimal model of time-sharing power supply system for EDPZ is established, which has been optimized by use of an improved efficient simulated annealing algorithm (SAA). Practical results show that industrial and mining enterprises can obtain enormous economic benefits every year.展开更多
We consider optimal control problems for the flow of gas in a pipe network. The equations of motions are taken to be represented by a semi-linear model derived from the fully nonlinear isothermal Euler gas equations. ...We consider optimal control problems for the flow of gas in a pipe network. The equations of motions are taken to be represented by a semi-linear model derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a given network and introduce a time discretization thereof. We then study the well-posedness of the corresponding time-discrete optimal control problem. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a non-overlapping domain decomposition of the semi-linear elliptic optimal control problem on the graph into local problems on a small part of the network, ultimately on a single edge.展开更多
The problem of correcting simultaneously mass and stiffness matrices of finite element model of undamped structural systems using vibration tests is considered in this paper.The desired matrix properties,including sat...The problem of correcting simultaneously mass and stiffness matrices of finite element model of undamped structural systems using vibration tests is considered in this paper.The desired matrix properties,including satisfaction of the characteristic equation,symmetry,positive semidefiniteness and sparsity,are imposed as side constraints to form the optimal matrix pencil approximation problem.Using partial Lagrangian multipliers,we transform the nonlinearly constrained optimization problem into an equivalent matrix linear variational inequality,develop a proximal point-like method for solving the matrix linear variational inequality,and analyze its global convergence.Numerical results are included to illustrate the performance and application of the proposed method.展开更多
In the research on spatial hearing and virtual auditory space,it is important to effectively model the head-related transfer functions(HRTFs).Based on the analysis of the HRTFs’spectrum and some perspectives of psych...In the research on spatial hearing and virtual auditory space,it is important to effectively model the head-related transfer functions(HRTFs).Based on the analysis of the HRTFs’spectrum and some perspectives of psychoacoustics,this paper applied multiple demes’parallel and real-valued coding genetic algorithm(GA)to approxi-mate the HRTFs’zero-pole model.Using the logarithmic magnitude’s error criterion for the human auditory sense,the results show that the performance of the GA is on the average 39%better than that of the traditional Prony method,and 46%better than that of the Yule-Walker algo-rithm.展开更多
Optimal Power Flow (OPF) plays a crucial role in optimization and operation of the bipolar DC distribution network (Bi-DCDN). However, existing OPF models encounter difficulties in the power optimization of Bi-DCDNs d...Optimal Power Flow (OPF) plays a crucial role in optimization and operation of the bipolar DC distribution network (Bi-DCDN). However, existing OPF models encounter difficulties in the power optimization of Bi-DCDNs due to the optimal power expressed as a product form, i.e., the product of voltage and current. Hence, this brief formulates the OPF problem of Bi-DCDNs using the branch flow model (BFM). The BFM employs power, instead of current, to account for the unique structure of Bi-DCDNs. Convex relaxation and linear approximation are sequentially applied to reformulate the BFM-based OPF, presenting it as a second-order cone programming (SOCP) problem. Further, the effectiveness of the proposed OPF model is verified in case studies. The numerical results demonstrate that the BFM-based OPF is a feasible and promising approach for Bi-DCDNs.展开更多
基金support from the National Natural Science Foundation of China(Grant No.52175130)the Sichuan Science and Technology Program(Grant No.2021YFS0336)+4 种基金the China Postdoctoral Science Foundation(Grant No.2021M700693)the 2021 Open Project of Failure Mechanics and Engineering Disaster Prevention,Key Lab of Sichuan Province(Grant No.FMEDP202104)the Fundamental Research Funds for the Central Universities(Grant No.ZYGX2019J035)the Sichuan Science and Technology Innovation Seedling Project Funding Project(Grant No.2021112)the Sichuan Special Equipment Inspection and Research Institute(YNJD-02-2020)are gratefully acknowledged.
文摘Actual engineering systems will be inevitably affected by uncertain factors.Thus,the Reliability-Based Multidisciplinary Design Optimization(RBMDO)has become a hotspot for recent research and application in complex engineering system design.The Second-Order/First-Order Mean-Value Saddlepoint Approximate(SOMVSA/-FOMVSA)are two popular reliability analysis strategies that are widely used in RBMDO.However,the SOMVSA method can only be used efficiently when the distribution of input variables is Gaussian distribution,which significantly limits its application.In this study,the Gaussian Mixture Model-based Second-Order Mean-Value Saddlepoint Approximation(GMM-SOMVSA)is introduced to tackle above problem.It is integrated with the Collaborative Optimization(CO)method to solve RBMDO problems.Furthermore,the formula and procedure of RBMDO using GMM-SOMVSA-Based CO(GMM-SOMVSA-CO)are proposed.Finally,an engineering example is given to show the application of the GMM-SOMVSA-CO method.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10975181 and 11175247)the National Basic Research Program of China(Grant No.2012CB922104)
文摘We apply the second-order Born-Oppenheimer （BO） approximation to investigate the dynamics of the Rabi model, which describes the interaction between a two-level system and a single bosonic mode beyond the rotating wave approxi- mation. By comparing with the numerical results, we find that our approach works well when the frequency of the two-level system is much smaller than that of the bosonic mode.
文摘Although the genetic algorithm (GA) has very powerful robustness and fitness, it needs a large size of population and a large number of iterations to reach the optimum result. Especially when GA is used in complex structural optimization problems, if the structural reanalysis technique is not adopted, the more the number of finite element analysis (FEA) is, the more the consuming time is. In the conventional structural optimization the number of FEA can be reduced by the structural reanalysis technique based on the approximation techniques and sensitivity analysis. With these techniques, this paper provides a new approximation model-segment approximation model, adopted for the GA application. This segment approximation model can decrease the number of FEA and increase the convergence rate of GA. So it can apparently decrease the computation time of GA. Two examples demonstrate the availability of the new segment approximation model.
基金Supported by the National Natural Science Foundation of China(61573378)the Fundamental Research Funds for the Central Universities(15CX06064A)
文摘This paper presents an adaptive rationalized Haar function approximation method to obtain the optimal injection strategy for alkali-surfactant-polymer(ASP) flooding. In this process, the non-uniform control vector parameterization is introduced to convert original problem into a multistage optimization problem, in which a new normalized time variable is adopted on the combination of the subinterval length. Then the rationalized Haar function approximation method, in which an auxiliary function is introduced to dispose path constraints, is used to transform the multistage problem into a nonlinear programming. Furthermore, an adaptive strategy proposed on the basis of errors is adopted to regulate the order of Haar function vectors. Finally, the nonlinear programming for ASP flooding is solved by sequential quadratic programming. To illustrate the performance of proposed method,the experimental comparison method and control vector parameterization(CVP) method are introduced to optimize the original problem directly. By contrastive analysis of results, the accuracy and efficiency of proposed method are confirmed.
文摘To increase the efficiency of the multidisciplinary optimization of aircraft, an aerodynamic approximation model is improved. Based on the study of aerodynamic approximation model constructed by the scaling correction model, case-based reasoning technique is introduced to improve the approximation model for optimization. The aircraft case model is constructed by utilizing the plane parameters related to aerodynamic characteristics as attributes of cases, and the formula of case retrieving is improved. Finally, the aerodynamic approximation model for optimization is improved by reusing the correction factors of the most similar aircraft to the current one. The multidisciplinary optimization of a civil aircraft concept is carried out with the improved aerodynamic approximation model. The results demonstrate that the precision and the efficiency of the optimization can be improved by utilizing the improved aerodynamic approximation model with ease-based reasoning technique.
文摘In this paper, a model averaging method is proposed for varying-coefficient models with response missing at random by establishing a weight selection criterion based on cross-validation. Under certain regularity conditions, it is proved that the proposed method is asymptotically optimal in the sense of achieving the minimum squared error.
文摘In this paper, a computational approach is proposed for solving the discrete-time nonlinear optimal control problem, which is disturbed by a sequence of random noises. Because of the exact solution of such optimal control problem is impossible to be obtained, estimating the state dynamics is currently required. Here, it is assumed that the output can be measured from the real plant process. In our approach, the state mean propagation is applied in order to construct a linear model-based optimal control problem, where the model output is measureable. On this basis, an output error, which takes into account the differences between the real output and the model output, is defined. Then, this output error is minimized by applying the stochastic approximation approach. During the computation procedure, the stochastic gradient is established, so as the optimal solution of the model used can be updated iteratively. Once the convergence is achieved, the iterative solution approximates to the true optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, an example on a continuous stirred-tank reactor problem is studied, and the result obtained shows the applicability of the approach proposed. Hence, the efficiency of the approach proposed is highly recommended.
基金Supported by the National High Technology Research and Development Program of China("863" Program) (2009AA04Z418, 2007AA04Z404)the National "111" Project(B07050)~~
文摘A new reliability-based multidisciplinary design optimization （RBMDO） framework is proposed by combining the single-loop-based reliability analysis （SLBRA） method with multidisciplinary feasible （MDF） method. The Kriging approximate model with updating is introduced to reduce the computational cost of MDF caused by the complex structure. The computational efficiency is remarkably improved as the lack of iterative process during reliability analysis. Special attention is paid to a turbine blade design optimization by adopting the proposed method. Results show that the method is much more efficient than the commonly used double-loop based RBMDO method. It is feasible and efficient to apply the method to the engineering design.
基金supported by the National Natural Science Foundation of China (10872036)the High Technological Research and Development Program of China (2008AA04Z118)the Airspace Natural Science Foundation (2007ZA23007)
文摘In density-based topological design, one expects that the final result consists of elements either black （solid material） or white （void）, without any grey areas. Moreover, one also expects that the optimal topology can be obtained by starting from any initial topology configuration. An improved structural topological optimization method for multidisplacement constraints is proposed in this paper. In the proposed method, the whole optimization process is divided into two optimization adjustment phases and a phase transferring step. Firstly, an optimization model is built to deal with the varied displacement limits, design space adjustments, and reasonable relations between the element stiffness matrix and mass and its element topology variable. Secondly, a procedure is proposed to solve the optimization problem formulated in the first optimization adjustment phase, by starting with a small design space and advancing to a larger deign space. The design space adjustments are automatic when the design domain needs expansions, in which the convergence of the proposed method will not be affected. The final topology obtained by the proposed procedure in the first optimization phase, can approach to the vicinity of the optimum topology. Then, a heuristic algorithm is given to improve the efficiency and make the designed structural topology black/white in both the phase transferring step and the second optimization adjustment phase. And the optimum topology can finally be obtained by the second phase optimization adjustments. Two examples are presented to show that the topologies obtained by the proposed method are of very good 0/1 design distribution property, and the computational efficiency is enhanced by reducing the element number of the design structural finite model during two optimization adjustment phases. And the examples also show that this method is robust and practicable.
基金Supported by the National High Technology Research and Development Program of China ("863" Program)
文摘In the process of multidisciplinary design optimization, there exits the calculation complexity problem due to frequently calling high fidelity system analysis models. The high fidelity system analysis models can be surrogated by approximate models. The sensitivity analysis and numerical noise filtering can be done easily by coupling approximate models to optimization. Approximate models can reduce the number of executions of the problem's simulation code during optimization, so the solution efficiency of the multidisciplinary design optimization problem can be improved. Most optimization methods are based on gradient. The gradients of the objective and constrain functions are gained easily. The gra- dient-based Kriging (GBK) approximate model can be constructed by using system response value and its gradients. The gradients can greatly improve prediction precision of system response. The hybrid optimization method is constructed by coupling GBK approximate models to gradient-based optimiza- tion methods. An aircraft aerodynamics shape optimization design example indicates that the methods of this paper can achieve good feasibility and validity.
基金jointly supported by the National Key R&D Program of Chinathe National Natural Science Foundation of China (Grant Nos. 11902219 and 51721003)the Natural Science Foundation of Tianjin City (Grant No. 18JCJQJC46400)。
文摘Control parameter optimization is an efficient way to improve the endurance of underwater gliders(UGs),which influences their gliding efficiency and energy consumption.This paper analyzes the optimal matching between the net buoyancy and the pitching angle and proposes a segmented control strategy of Petrel-L.The optimization of this strategy is established based on the gliding range model of UG,which is solved based on the approximate model,and the variations of the optimal control parameters with the hotel load are obtained.The optimization results indicate that the segmented control strategy can significantly increase the gliding range when the optimal matching between the net buoyancy and the pitching angle is reached,and the increase rate is influenced by the hotel load.The gliding range of the underwater glider can be increased by 10.47%at a hotel load of 0.5 W.The optimal matching analysis adopted in this study can be applied to other UGs to realize endurance improvement.
文摘According to time-sharing valuation principle (TSVP) of power supply, the relationships of current density and current efficiency at different acidities are obtained based on the processed data of electrolytic deposition process of zinc (EDPZ) with the least square method (LSM). Thus an optimal model of time-sharing power supply system for EDPZ is established, which has been optimized by use of an improved efficient simulated annealing algorithm (SAA). Practical results show that industrial and mining enterprises can obtain enormous economic benefits every year.
文摘We consider optimal control problems for the flow of gas in a pipe network. The equations of motions are taken to be represented by a semi-linear model derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a given network and introduce a time discretization thereof. We then study the well-posedness of the corresponding time-discrete optimal control problem. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a non-overlapping domain decomposition of the semi-linear elliptic optimal control problem on the graph into local problems on a small part of the network, ultimately on a single edge.
基金The work was supported by the National Natural Science Foundation of China(No.11571171)。
文摘The problem of correcting simultaneously mass and stiffness matrices of finite element model of undamped structural systems using vibration tests is considered in this paper.The desired matrix properties,including satisfaction of the characteristic equation,symmetry,positive semidefiniteness and sparsity,are imposed as side constraints to form the optimal matrix pencil approximation problem.Using partial Lagrangian multipliers,we transform the nonlinearly constrained optimization problem into an equivalent matrix linear variational inequality,develop a proximal point-like method for solving the matrix linear variational inequality,and analyze its global convergence.Numerical results are included to illustrate the performance and application of the proposed method.
基金supported by the National Basic Research of China(No.2002CB312102)。
文摘In the research on spatial hearing and virtual auditory space,it is important to effectively model the head-related transfer functions(HRTFs).Based on the analysis of the HRTFs’spectrum and some perspectives of psychoacoustics,this paper applied multiple demes’parallel and real-valued coding genetic algorithm(GA)to approxi-mate the HRTFs’zero-pole model.Using the logarithmic magnitude’s error criterion for the human auditory sense,the results show that the performance of the GA is on the average 39%better than that of the traditional Prony method,and 46%better than that of the Yule-Walker algo-rithm.
文摘Optimal Power Flow (OPF) plays a crucial role in optimization and operation of the bipolar DC distribution network (Bi-DCDN). However, existing OPF models encounter difficulties in the power optimization of Bi-DCDNs due to the optimal power expressed as a product form, i.e., the product of voltage and current. Hence, this brief formulates the OPF problem of Bi-DCDNs using the branch flow model (BFM). The BFM employs power, instead of current, to account for the unique structure of Bi-DCDNs. Convex relaxation and linear approximation are sequentially applied to reformulate the BFM-based OPF, presenting it as a second-order cone programming (SOCP) problem. Further, the effectiveness of the proposed OPF model is verified in case studies. The numerical results demonstrate that the BFM-based OPF is a feasible and promising approach for Bi-DCDNs.
