This research focuses on the lightweight topology optimization method for structures under the premise of meeting the requirements of stability and vibration characteristics. A new topology optimization model with the...This research focuses on the lightweight topology optimization method for structures under the premise of meeting the requirements of stability and vibration characteristics. A new topology optimization model with the constraints of natural frequencies and critical buckling loads and the objective of minimizing the structural volume is established and solved based on the independent continuous mapping method. The eigenvalue equations and composite exponential filter functions are applied to convert the optimization formulation into a continuous, solvable mathematical programming model. In the process of topology optimization, suitable initial values of the filter functions are chosen to avoid local modes, and the dynamic frequency gap constraints are added in the optimal model to prevent mode switches. Furthermore, for the optimal structures with grey elements obtained by the continuous optimization model, the bisection-inverse iteration is applied to search the optimal discrete structures. Finally, a detailed scheme is given for the buckling and frequency topology optimization problem. Numerical examples illustrate that the modelling method of minimizing the economic index with given performance requirements is practical and feasible for multi-performance topology optimization problems.展开更多
It is an important topic to improve the redundancy of optimized configuration to resist the local failure in topology optimization of continuum structures.Such a fail-safe topology optimization problem has been solved...It is an important topic to improve the redundancy of optimized configuration to resist the local failure in topology optimization of continuum structures.Such a fail-safe topology optimization problem has been solved effectively in the ficld of statics.In this paper,the fail-safe topology optimization problem is extended to the field of frequency topology optimization.Based on the independent continuous mapping(ICM)method,the model of fail-safe topology optimization is established with the objective of minimal weight integrating with the discrete condition of topological variables and the constraint of the fundamental frequency.The fail-safe optimization model established above is substituted by a sequence of subproblems in the form of the quadratic program with exact second-order information and solved efficiently by the dual sequence quadratic programming(DSQP)algorithm.The numerical result reveals that the optimized fail-safe structure has more complex configuration and preserved materials than the structure obtained from the traditional frequency topology optimization,which means that the optimized fail-safe structure has higher redundancy.Moreover,the optimized fail-safe structure guarantees that the natural frequency meets the constraint of fundamental frequency when the local failure ocurs,which can avoid the structural frequency to be sensitive to local failure.The fail-safe optimirzation topology model is proved effective and feasible by four numerical examples.展开更多
In actual power systems,most of the high-voltage buses of the transformers are zero injection buses without load or generation.Power injections into these buses are strictly 0,so based on Kirchhoff's current law(K...In actual power systems,most of the high-voltage buses of the transformers are zero injection buses without load or generation.Power injections into these buses are strictly 0,so based on Kirchhoff's current law(KCL),equality constraints should be used to handle these buses in a state estimation model.It is a challenge to ensure that these zero injection constraints can be strictly satisfied without losing computational efficiency.展开更多
This paper presents a novel topology optimization method to design graded lattice structures to minimize the volume subject to displacement constraints based on the independent continuous mapping(ICM)method.First,the ...This paper presents a novel topology optimization method to design graded lattice structures to minimize the volume subject to displacement constraints based on the independent continuous mapping(ICM)method.First,the effective elastic properties of graded unit cells are analyzed by the strain energy-based homogenization method.A surrogate model using quartic polynomial interpolation is built to map the independent continuous topological variable to the effective elastic matrix of the unit cell and set up the relationship between the macroscale structure and microscale unit cells.Second,a lightweight topology optimization model is established,which can be transformed into an explicitly standard quadratic programming problem by sensitivity analysis and solved by dual sequential quadratic programming.Third,several numerical examples demonstrate that graded lattice structures have a better lightweight effect than uniform lattice structures,which validates the effectiveness and feasibility of the proposed method.The results show that graded lattice structures become lighter with increasing displacement constraints.In addition,some diverse topological configurations are obtained.This method provides a reference for the graded lattice structure design and expands the application of the ICM method.展开更多
A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years.The method has yielded many new analytic solutions due to its rigorousness.In this study,the first e...A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years.The method has yielded many new analytic solutions due to its rigorousness.In this study,the first endeavor is made to further developed the symplectic superposition method for the free vibration of rectangular thin plates with mixed boundary constraints on an edge.The Hamiltonian system-based governing equation is first introduced such that the mathematical techniques in the symplectic space are applied.The solution procedure incorporates separation of variables,symplectic eigen solution and superposition.The analytic solution of an original problem is finally obtained by a set of equations via the equivalence to the superposition of some elaborated subproblems.The natural frequency and mode shape results for representative plates with both clamped and simply supported boundary constraints imposed on the same edge are reported for benchmark use.The present method can be extended to more challenging problems that cannot be solved by conventional analytic methods.展开更多
Traditional topology optimization methods may lead to a great reduction in the redundancy of the optimized structure due to unexpected material removal at the critical components.The local failure in critical componen...Traditional topology optimization methods may lead to a great reduction in the redundancy of the optimized structure due to unexpected material removal at the critical components.The local failure in critical components can instantly cause the overall failure in the structure.More and more scholars have taken the fail-safe design into consideration when conducting topology optimization.A lot of good designs have been obtained in their research,though limited regarding minimizing structural compliance(maximizing stiffness)with given amount of material.In terms of practical engineering applications considering fail-safe design,it is more meaningful to seek for the lightweight structure with enough stiffness to resist various component failures and/or to meet multiple design requirements,than the stiffest structure only.Thus,this paper presents a fail-safe topology optimization model for minimizing structural weight with respect to stress and displacement constraints.The optimization problem is solved by utilizing the independent continuous mapping(ICM)method combined with the dual sequence quadratic programming(DSQP)algorithm.Special treatments are applied to the constraints,including converting local stress constraints into a global structural strain energy constraint and expressing the displacement constraint explicitly with approximations.All of the constraints are nondimensionalized to avoid numerical instability caused by great differences in constraint magnitudes.The optimized results exhibit more complex topological configurations and higher redundancy to resist local failures than the traditional optimization designs.This paper also shows how to find the worst failure region,which can be a good reference for designers in engineering.展开更多
Combining the vector level set model,the shape sensitivity analysis theory with the gradient projection technique,a level set method for topology optimization with multi-constraints and multi-materials is presented in...Combining the vector level set model,the shape sensitivity analysis theory with the gradient projection technique,a level set method for topology optimization with multi-constraints and multi-materials is presented in this paper.The method implicitly describes structural material in- terfaces by the vector level set and achieves the optimal shape and topology through the continuous evolution of the material interfaces in the structure.In order to increase computational efficiency for a fast convergence,an appropriate nonlinear speed mapping is established in the tangential space of the active constraints.Meanwhile,in order to overcome the numerical instability of general topology opti- mization problems,the regularization with the mean curvature flow is utilized to maintain the interface smoothness during the optimization process.The numerical examples demonstrate that the approach possesses a good flexibility in handling topological changes and gives an interface representation in a high fidelity,compared with other methods based on explicit boundary variations in the literature.展开更多
By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constra...By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constraints in Karush-Kuhn-Tucker necessary conditions are removed. For constructing the Lagrange neural network and Lagrange multiplier method, it is no longer necessary to convert inequality constraints into equality constraints by slack variables in order to reuse those results dedicated to equality constraints, and they can be similarly proved with minor modification. Utilizing this technique, a new type of Lagrange neural network and a new type of Lagrange multiplier method are devised, which both handle inequality constraints directly. Also, their stability and convergence are analyzed rigorously.展开更多
The accuracy of parameter estimation is critical when digitally modeling a ship. A parameter estimation method with constraints was developed, based on the variational method. Performance functions and constraint equa...The accuracy of parameter estimation is critical when digitally modeling a ship. A parameter estimation method with constraints was developed, based on the variational method. Performance functions and constraint equations in the variational method are constructed by analyzing input and output equations of the system. The problem of parameter estimation was transformed into a problem of least squares estimation. The parameter estimation equation was analyzed in order to get an optimized estimation of parameters based on the Lagrange multiplication operator. Simulation results showed that this method is better than the traditional least squares estimation, producing a higher precision when identifying parameters. It has very important practical value in areas of application such as system identification and parameter estimation.展开更多
this paper,we propose a class of smoothing-regularization methods for solving the mathematical programming with vanishing constraints.These methods include the smoothing-regularization method proposed by Kanzow et al....this paper,we propose a class of smoothing-regularization methods for solving the mathematical programming with vanishing constraints.These methods include the smoothing-regularization method proposed by Kanzow et al.in[Comput.Optim.Appl.,2013,55(3):733-767]as a special case.Under the weaker conditions than the ones that have been used by Kanzow et al.in 2013,we prove that the Mangasarian-Fromovitz constraint qualification holds at the feasible points of smoothing-regularization problem.We also analyze that the convergence behavior of the proposed smoothing-regularization method under mild conditions,i.e.,any accumulation point of the stationary point sequence for the smoothing-regularization problem is a strong stationary point.Finally,numerical experiments are given to show the efficiency of the proposed methods.展开更多
In this paper, a new method for solving a mathematical programming problem with linearly complementarity constraints (MPLCC) is introduced, which applies the Levenberg-Marquardt (L-M) method to solve the B-stationary ...In this paper, a new method for solving a mathematical programming problem with linearly complementarity constraints (MPLCC) is introduced, which applies the Levenberg-Marquardt (L-M) method to solve the B-stationary condition of original problem. Under the MPEC-LICQ, the proposed method is proved convergent to B-stationary point of MPLCC.展开更多
The impact dynamics of a flexible multibody system is investigated. By using a partition method, the system is divided into two parts, the local impact region and the region away from the impact. The two parts are con...The impact dynamics of a flexible multibody system is investigated. By using a partition method, the system is divided into two parts, the local impact region and the region away from the impact. The two parts are connected by specific boundary conditions, and the system after partition is equivalent to the original system. According to the rigid-flexible coupling dynamic theory of multibody system, system＇s rigid-flexible coupling dynamic equations without impact are derived. A local impulse method for establishing the initial impact conditions is proposed. It satisfies the compatibility con- ditions for contact constraints and the actual physical situation of the impact process of flexible bodies. Based on the contact constraint method, system＇s impact dynamic equa- tions are derived in a differential-algebraic form. The contact/separation criterion and the algorithm are given. An impact dynamic simulation is given. The results show that system＇s dynamic behaviors including the energy, the deformations, the displacements, and the impact force during the impact process change dramatically. The impact makes great effects on the global dynamics of the system during and after impact.展开更多
Rotor airfoil design is investigated in this paper. There are many difficulties for this highdimensional multi-objective problem when traditional multi-objective optimization methods are used. Therefore, a multi-layer...Rotor airfoil design is investigated in this paper. There are many difficulties for this highdimensional multi-objective problem when traditional multi-objective optimization methods are used. Therefore, a multi-layer hierarchical constraint method is proposed by coupling principal component analysis(PCA) dimensionality reduction and e-constraint method to translate the original high-dimensional problem into a bi-objective problem. This paper selects the main design objectives by conducting PCA to the preliminary solution of original problem with consideration of the priority of design objectives. According to the e-constraint method, the design model is established by treating the two top-ranking design goals as objective and others as variable constraints. A series of bi-objective Pareto curves will be obtained by changing the variable constraints, and the favorable solution can be obtained by analyzing Pareto curve spectrum. This method is applied to the rotor airfoil design and makes great improvement in aerodynamic performance. It is shown that the method is convenient and efficient, beyond which, it facilitates decision-making of the highdimensional multi-objective engineering problem.展开更多
In this paper,the 3D leader–follower formation control problem,which focuses on swarms of fixed-wing Unmanned Aerial Vehicles(UAVs)with motion constraints and disturbances,has been investigated.Original formation err...In this paper,the 3D leader–follower formation control problem,which focuses on swarms of fixed-wing Unmanned Aerial Vehicles(UAVs)with motion constraints and disturbances,has been investigated.Original formation errors of the follower UAVs have been transformed into the Frenet-Serret frame.Formation control laws satisfying five motion constraints(i.e.,linear velocity,linear acceleration,heading rate,climb rate and climb angle)have been designed.The convergence of the control laws has been discussed via the Lyapunov stability tool.In addition,to address the unknown disturbances,an adaptive disturbance observer is exploited.Furthermore,formation control laws involving estimated disturbances are presented as well.The collision avoidance between UAVs is achieved with the artificial potential method.Simulation results obtained using four scenarios verify the effectiveness of the proposed method in situations with constant disturbances and varying disturbances,as well as without disturbances.展开更多
The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the ...The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.展开更多
In this paper,the application of an algorithm for precipitation retrieval based on Himawari-8 (H8) satellite infrared data is studied.Based on GPM precipitation data and H8 Infrared spectrum channel brightness tempera...In this paper,the application of an algorithm for precipitation retrieval based on Himawari-8 (H8) satellite infrared data is studied.Based on GPM precipitation data and H8 Infrared spectrum channel brightness temperature data,corresponding "precipitation field dictionary" and "channel brightness temperature dictionary" are formed.The retrieval of precipitation field based on brightness temperature data is studied through the classification rule of k-nearest neighbor domain (KNN) and regularization constraint.Firstly,the corresponding "dictionary" is constructed according to the training sample database of the matched GPM precipitation data and H8 brightness temperature data.Secondly,according to the fact that precipitation characteristics in small organizations in different storm environments are often repeated,KNN is used to identify the spectral brightness temperature signal of "precipitation" and "non-precipitation" based on "the dictionary".Finally,the precipitation field retrieval is carried out in the precipitation signal "subspace" based on the regular term constraint method.In the process of retrieval,the contribution rate of brightness temperature retrieval of different channels was determined by Bayesian model averaging (BMA) model.The preliminary experimental results based on the "quantitative" evaluation indexes show that the precipitation of H8 retrieval has a good correlation with the GPM truth value,with a small error and similar structure.展开更多
Plastic wrinkling predictions and shear enforced wrinkling characteristics of Ti-alloy thin-walled tubes under combination die constraints have become key problems urgently in need of solutions in order to improve for...Plastic wrinkling predictions and shear enforced wrinkling characteristics of Ti-alloy thin-walled tubes under combination die constraints have become key problems urgently in need of solutions in order to improve forming quality in their shear bending processes under differential temperature fields. To address this, a wrinkling wave function was developed by considering their shear bend deformation characteristics. Based on this wave function and the thin shell theory, an energy prediction model for this type of wrinkling was established. This model enables consideration of the effects of shear deformation zone ranges, material parameters, loading modes, and friction coefficients between tube and dies on the minimum wrinkling energy. Tube wrinkling sensitive zones(WSZs) can be revealed by combining this wrinkling prediction model with a thermalmechanical coupled finite element model for simulating these bending processes. The reliability of this wrinkling prediction model was verified, and an investigation into the tube wrinkling characteristics was carried out based on the experimental conditions. This found that the WSZs are located on either a single side or both sides of the maximum shear stress zone. When the friction coefficients between the tube and the various dies coincide, the WSZs are located on both sides.The larger the value of the tube inner corner radius and/or the smaller the value of the outer cornerradius, the smaller the wrinkling probability. With an increase in the value of the moving die displacement, the wrinkling probability increases at first, and then decreases.展开更多
This paper considers dealing with path constraints in the framework of the improved control vector iteration （CVI） approach. Two available ways for enforcing equality path constraints are presented, which can be dir...This paper considers dealing with path constraints in the framework of the improved control vector iteration （CVI） approach. Two available ways for enforcing equality path constraints are presented, which can be directly incorporated into the improved CVI approach. Inequality path constraints are much more difficult to deal with, even for small scale problems, because the time intervals where the inequality path constraints are active are unknown in advance. To overcome the challenge, the ll penalty function and a novel smoothing technique are in-troduced, leading to a new effective approach. Moreover, on the basis of the relevant theorems, a numerical algo-rithm is proposed for nonlinear dynamic optimization problems with inequality path constraints. Results obtained from the classic batch reaCtor operation problem are in agreement with the literature reoorts, and the comoutational efficiency is also high.展开更多
A oanstructive method is presented to design controllers that force the output of nonlinear systems in a strict feedback form to track a bounded and sufficient smooth reference trajectory asymptotically. Under suitabl...A oanstructive method is presented to design controllers that force the output of nonlinear systems in a strict feedback form to track a bounded and sufficient smooth reference trajectory asymptotically. Under suitable condition with the initial output tracking error, the proposed controllers guarantee the output tracking error within a symmtric or an asymmetric pre-specified limit range, and boundedness of all signals of the closed loop system. A transformation is inmxuced to take care of the output tracking error constraint. Smooth and/or p -times differentiable step functions are propsed and incor- porated in the output tracking error transformation to overcome difficulties due to the asynxnetric limit range on the output tracking error. As a result, there are no switchings in the proposed controllers despite of the asymmnetric limit range.展开更多
Background:The purpose of the study is to understand the role of cash flow sensitivity to investment as a measure of financial constraints among listed Indian manufacturing firms.It also analyses the role of tangibili...Background:The purpose of the study is to understand the role of cash flow sensitivity to investment as a measure of financial constraints among listed Indian manufacturing firms.It also analyses the role of tangibility in alleviating financial constraints.Further,the role of other financial factors in investment decisions is explored.Methods:The study is conducted using the generalized method of moments(GMM)estimator on dynamic panel data for the period of(2009–2015)on 768 listed manufacturing firms.Results:The analysis finds that cash flow sensitivity is a valid measure of financial constraints in the Indian manufacturing sector.Results according to splitting criteria found that investment decisions of standalone firms are more sensitive to cash flow than group affiliated firms.Further,splitting the firms according to market capitalization and tangible net worth reveals a higher degree of cash flow sensitivity by firms with lower market capitalization and asset tangibility.The results for the effects of tangibility of assets on easing financial constraint were found significant only in the case of firms with low tangible net worth and medium market capitalization.Conclusions:The study confirms cash flow sensitivity to investment as a valid measure of financial constraints.It will confirm pooling of internal funds by financially constrained firms to accept profitable investment opportunities in future.Further,it also reports that asset tangibility eases the financial constraints faced by firms.展开更多
基金the National Natural Science Foundation of China (11872080, 11172013)Natural Science Foundation of Beijing Municipality (3192005)Beijing Education Committee Development Project (SQKM201610005001).
文摘This research focuses on the lightweight topology optimization method for structures under the premise of meeting the requirements of stability and vibration characteristics. A new topology optimization model with the constraints of natural frequencies and critical buckling loads and the objective of minimizing the structural volume is established and solved based on the independent continuous mapping method. The eigenvalue equations and composite exponential filter functions are applied to convert the optimization formulation into a continuous, solvable mathematical programming model. In the process of topology optimization, suitable initial values of the filter functions are chosen to avoid local modes, and the dynamic frequency gap constraints are added in the optimal model to prevent mode switches. Furthermore, for the optimal structures with grey elements obtained by the continuous optimization model, the bisection-inverse iteration is applied to search the optimal discrete structures. Finally, a detailed scheme is given for the buckling and frequency topology optimization problem. Numerical examples illustrate that the modelling method of minimizing the economic index with given performance requirements is practical and feasible for multi-performance topology optimization problems.
基金the National Natural Science Foundation of China(Grant 11872080).
文摘It is an important topic to improve the redundancy of optimized configuration to resist the local failure in topology optimization of continuum structures.Such a fail-safe topology optimization problem has been solved effectively in the ficld of statics.In this paper,the fail-safe topology optimization problem is extended to the field of frequency topology optimization.Based on the independent continuous mapping(ICM)method,the model of fail-safe topology optimization is established with the objective of minimal weight integrating with the discrete condition of topological variables and the constraint of the fundamental frequency.The fail-safe optimization model established above is substituted by a sequence of subproblems in the form of the quadratic program with exact second-order information and solved efficiently by the dual sequence quadratic programming(DSQP)algorithm.The numerical result reveals that the optimized fail-safe structure has more complex configuration and preserved materials than the structure obtained from the traditional frequency topology optimization,which means that the optimized fail-safe structure has higher redundancy.Moreover,the optimized fail-safe structure guarantees that the natural frequency meets the constraint of fundamental frequency when the local failure ocurs,which can avoid the structural frequency to be sensitive to local failure.The fail-safe optimirzation topology model is proved effective and feasible by four numerical examples.
文摘In actual power systems,most of the high-voltage buses of the transformers are zero injection buses without load or generation.Power injections into these buses are strictly 0,so based on Kirchhoff's current law(KCL),equality constraints should be used to handle these buses in a state estimation model.It is a challenge to ensure that these zero injection constraints can be strictly satisfied without losing computational efficiency.
基金the National Natural Science Foundation of China(Grant No.11872080)Beijing Natural Science Foundation(Grant No.3192005)Taishan University Youth Teacher Science Foundation(Grant No.QN-01-201901).
文摘This paper presents a novel topology optimization method to design graded lattice structures to minimize the volume subject to displacement constraints based on the independent continuous mapping(ICM)method.First,the effective elastic properties of graded unit cells are analyzed by the strain energy-based homogenization method.A surrogate model using quartic polynomial interpolation is built to map the independent continuous topological variable to the effective elastic matrix of the unit cell and set up the relationship between the macroscale structure and microscale unit cells.Second,a lightweight topology optimization model is established,which can be transformed into an explicitly standard quadratic programming problem by sensitivity analysis and solved by dual sequential quadratic programming.Third,several numerical examples demonstrate that graded lattice structures have a better lightweight effect than uniform lattice structures,which validates the effectiveness and feasibility of the proposed method.The results show that graded lattice structures become lighter with increasing displacement constraints.In addition,some diverse topological configurations are obtained.This method provides a reference for the graded lattice structure design and expands the application of the ICM method.
基金the support from the National Natural Science Foundation of China(Grants 12022209,11972103,and 11825202)the Liaoning Revitalization Talents Program of China(Grant XLYC1807126)the Fundamental Research Funds for the Central Universities(Grant DUT21LAB124).
文摘A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years.The method has yielded many new analytic solutions due to its rigorousness.In this study,the first endeavor is made to further developed the symplectic superposition method for the free vibration of rectangular thin plates with mixed boundary constraints on an edge.The Hamiltonian system-based governing equation is first introduced such that the mathematical techniques in the symplectic space are applied.The solution procedure incorporates separation of variables,symplectic eigen solution and superposition.The analytic solution of an original problem is finally obtained by a set of equations via the equivalence to the superposition of some elaborated subproblems.The natural frequency and mode shape results for representative plates with both clamped and simply supported boundary constraints imposed on the same edge are reported for benchmark use.The present method can be extended to more challenging problems that cannot be solved by conventional analytic methods.
基金This work showed in this paper has been supported by the National Natural Science Foundation of China(Grant 11872080).
文摘Traditional topology optimization methods may lead to a great reduction in the redundancy of the optimized structure due to unexpected material removal at the critical components.The local failure in critical components can instantly cause the overall failure in the structure.More and more scholars have taken the fail-safe design into consideration when conducting topology optimization.A lot of good designs have been obtained in their research,though limited regarding minimizing structural compliance(maximizing stiffness)with given amount of material.In terms of practical engineering applications considering fail-safe design,it is more meaningful to seek for the lightweight structure with enough stiffness to resist various component failures and/or to meet multiple design requirements,than the stiffest structure only.Thus,this paper presents a fail-safe topology optimization model for minimizing structural weight with respect to stress and displacement constraints.The optimization problem is solved by utilizing the independent continuous mapping(ICM)method combined with the dual sequence quadratic programming(DSQP)algorithm.Special treatments are applied to the constraints,including converting local stress constraints into a global structural strain energy constraint and expressing the displacement constraint explicitly with approximations.All of the constraints are nondimensionalized to avoid numerical instability caused by great differences in constraint magnitudes.The optimized results exhibit more complex topological configurations and higher redundancy to resist local failures than the traditional optimization designs.This paper also shows how to find the worst failure region,which can be a good reference for designers in engineering.
基金The project supported by the National Natural Science Foundation of China (59805001,10332010) and Key Science and Technology Research Project of Ministry of Education of China (No.104060)
文摘Combining the vector level set model,the shape sensitivity analysis theory with the gradient projection technique,a level set method for topology optimization with multi-constraints and multi-materials is presented in this paper.The method implicitly describes structural material in- terfaces by the vector level set and achieves the optimal shape and topology through the continuous evolution of the material interfaces in the structure.In order to increase computational efficiency for a fast convergence,an appropriate nonlinear speed mapping is established in the tangential space of the active constraints.Meanwhile,in order to overcome the numerical instability of general topology opti- mization problems,the regularization with the mean curvature flow is utilized to maintain the interface smoothness during the optimization process.The numerical examples demonstrate that the approach possesses a good flexibility in handling topological changes and gives an interface representation in a high fidelity,compared with other methods based on explicit boundary variations in the literature.
文摘By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constraints in Karush-Kuhn-Tucker necessary conditions are removed. For constructing the Lagrange neural network and Lagrange multiplier method, it is no longer necessary to convert inequality constraints into equality constraints by slack variables in order to reuse those results dedicated to equality constraints, and they can be similarly proved with minor modification. Utilizing this technique, a new type of Lagrange neural network and a new type of Lagrange multiplier method are devised, which both handle inequality constraints directly. Also, their stability and convergence are analyzed rigorously.
基金Supported by the Navy Equipment Department Foundation under Grant No. 2009(189)
文摘The accuracy of parameter estimation is critical when digitally modeling a ship. A parameter estimation method with constraints was developed, based on the variational method. Performance functions and constraint equations in the variational method are constructed by analyzing input and output equations of the system. The problem of parameter estimation was transformed into a problem of least squares estimation. The parameter estimation equation was analyzed in order to get an optimized estimation of parameters based on the Lagrange multiplication operator. Simulation results showed that this method is better than the traditional least squares estimation, producing a higher precision when identifying parameters. It has very important practical value in areas of application such as system identification and parameter estimation.
基金Supported in part by NSFC(No.11961011)Guangxi Science and Technology Base and Talents Special Project(No.2021AC06001).
文摘this paper,we propose a class of smoothing-regularization methods for solving the mathematical programming with vanishing constraints.These methods include the smoothing-regularization method proposed by Kanzow et al.in[Comput.Optim.Appl.,2013,55(3):733-767]as a special case.Under the weaker conditions than the ones that have been used by Kanzow et al.in 2013,we prove that the Mangasarian-Fromovitz constraint qualification holds at the feasible points of smoothing-regularization problem.We also analyze that the convergence behavior of the proposed smoothing-regularization method under mild conditions,i.e.,any accumulation point of the stationary point sequence for the smoothing-regularization problem is a strong stationary point.Finally,numerical experiments are given to show the efficiency of the proposed methods.
文摘In this paper, a new method for solving a mathematical programming problem with linearly complementarity constraints (MPLCC) is introduced, which applies the Levenberg-Marquardt (L-M) method to solve the B-stationary condition of original problem. Under the MPEC-LICQ, the proposed method is proved convergent to B-stationary point of MPLCC.
基金supported by the National Natural Science Foundation of China(Nos.11132007,11272155,and 10772085)the Fundamental Research Funds for the Central Universities(No.30920130112009)the 333 Project of Jiangsu Province of China(No.BRA2011172)
文摘The impact dynamics of a flexible multibody system is investigated. By using a partition method, the system is divided into two parts, the local impact region and the region away from the impact. The two parts are connected by specific boundary conditions, and the system after partition is equivalent to the original system. According to the rigid-flexible coupling dynamic theory of multibody system, system＇s rigid-flexible coupling dynamic equations without impact are derived. A local impulse method for establishing the initial impact conditions is proposed. It satisfies the compatibility con- ditions for contact constraints and the actual physical situation of the impact process of flexible bodies. Based on the contact constraint method, system＇s impact dynamic equa- tions are derived in a differential-algebraic form. The contact/separation criterion and the algorithm are given. An impact dynamic simulation is given. The results show that system＇s dynamic behaviors including the energy, the deformations, the displacements, and the impact force during the impact process change dramatically. The impact makes great effects on the global dynamics of the system during and after impact.
基金supported by the National Natural Science Foundation of China (No. 11402288 and 11372254)the National Basic Research Program of China (No. 2014CB744804)
文摘Rotor airfoil design is investigated in this paper. There are many difficulties for this highdimensional multi-objective problem when traditional multi-objective optimization methods are used. Therefore, a multi-layer hierarchical constraint method is proposed by coupling principal component analysis(PCA) dimensionality reduction and e-constraint method to translate the original high-dimensional problem into a bi-objective problem. This paper selects the main design objectives by conducting PCA to the preliminary solution of original problem with consideration of the priority of design objectives. According to the e-constraint method, the design model is established by treating the two top-ranking design goals as objective and others as variable constraints. A series of bi-objective Pareto curves will be obtained by changing the variable constraints, and the favorable solution can be obtained by analyzing Pareto curve spectrum. This method is applied to the rotor airfoil design and makes great improvement in aerodynamic performance. It is shown that the method is convenient and efficient, beyond which, it facilitates decision-making of the highdimensional multi-objective engineering problem.
基金co-supported by the National Natural Science Foundation of China(Nos.61803353 and U19B2029)the China Postdoctoral Science Foundation(No.2017M620858)。
文摘In this paper,the 3D leader–follower formation control problem,which focuses on swarms of fixed-wing Unmanned Aerial Vehicles(UAVs)with motion constraints and disturbances,has been investigated.Original formation errors of the follower UAVs have been transformed into the Frenet-Serret frame.Formation control laws satisfying five motion constraints(i.e.,linear velocity,linear acceleration,heading rate,climb rate and climb angle)have been designed.The convergence of the control laws has been discussed via the Lyapunov stability tool.In addition,to address the unknown disturbances,an adaptive disturbance observer is exploited.Furthermore,formation control laws involving estimated disturbances are presented as well.The collision avoidance between UAVs is achieved with the artificial potential method.Simulation results obtained using four scenarios verify the effectiveness of the proposed method in situations with constant disturbances and varying disturbances,as well as without disturbances.
基金supported by the National Natural Science Foundation of China,Grant Nos.42174011,41874001 and 41664001Innovation Found Designated for Graduate Students of ECUT,Grant No.DHYC-202020。
文摘The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.
基金Supported by National Natural Science Foundation of China(41805080)Natural Science Foundation of Anhui Province,China(1708085QD89)+1 种基金Key Research and Development Program Projects of Anhui Province,China(201904a07020099)Open Foundation Project Shenyang Institute of Atmospheric Environment,China Meteorological Administration(2016SYIAE14)
文摘In this paper,the application of an algorithm for precipitation retrieval based on Himawari-8 (H8) satellite infrared data is studied.Based on GPM precipitation data and H8 Infrared spectrum channel brightness temperature data,corresponding "precipitation field dictionary" and "channel brightness temperature dictionary" are formed.The retrieval of precipitation field based on brightness temperature data is studied through the classification rule of k-nearest neighbor domain (KNN) and regularization constraint.Firstly,the corresponding "dictionary" is constructed according to the training sample database of the matched GPM precipitation data and H8 brightness temperature data.Secondly,according to the fact that precipitation characteristics in small organizations in different storm environments are often repeated,KNN is used to identify the spectral brightness temperature signal of "precipitation" and "non-precipitation" based on "the dictionary".Finally,the precipitation field retrieval is carried out in the precipitation signal "subspace" based on the regular term constraint method.In the process of retrieval,the contribution rate of brightness temperature retrieval of different channels was determined by Bayesian model averaging (BMA) model.The preliminary experimental results based on the "quantitative" evaluation indexes show that the precipitation of H8 retrieval has a good correlation with the GPM truth value,with a small error and similar structure.
基金support of National Natural Science Foundation of China (No. 51305415)
文摘Plastic wrinkling predictions and shear enforced wrinkling characteristics of Ti-alloy thin-walled tubes under combination die constraints have become key problems urgently in need of solutions in order to improve forming quality in their shear bending processes under differential temperature fields. To address this, a wrinkling wave function was developed by considering their shear bend deformation characteristics. Based on this wave function and the thin shell theory, an energy prediction model for this type of wrinkling was established. This model enables consideration of the effects of shear deformation zone ranges, material parameters, loading modes, and friction coefficients between tube and dies on the minimum wrinkling energy. Tube wrinkling sensitive zones(WSZs) can be revealed by combining this wrinkling prediction model with a thermalmechanical coupled finite element model for simulating these bending processes. The reliability of this wrinkling prediction model was verified, and an investigation into the tube wrinkling characteristics was carried out based on the experimental conditions. This found that the WSZs are located on either a single side or both sides of the maximum shear stress zone. When the friction coefficients between the tube and the various dies coincide, the WSZs are located on both sides.The larger the value of the tube inner corner radius and/or the smaller the value of the outer cornerradius, the smaller the wrinkling probability. With an increase in the value of the moving die displacement, the wrinkling probability increases at first, and then decreases.
基金Supported by the National Natural Science Foundation of China(U1162130)the National High Technology Research and Development Program of China(2006AA05Z226)Outstanding Youth Science Foundation of Zhejiang Province(R4100133)
文摘This paper considers dealing with path constraints in the framework of the improved control vector iteration （CVI） approach. Two available ways for enforcing equality path constraints are presented, which can be directly incorporated into the improved CVI approach. Inequality path constraints are much more difficult to deal with, even for small scale problems, because the time intervals where the inequality path constraints are active are unknown in advance. To overcome the challenge, the ll penalty function and a novel smoothing technique are in-troduced, leading to a new effective approach. Moreover, on the basis of the relevant theorems, a numerical algo-rithm is proposed for nonlinear dynamic optimization problems with inequality path constraints. Results obtained from the classic batch reaCtor operation problem are in agreement with the literature reoorts, and the comoutational efficiency is also high.
文摘A oanstructive method is presented to design controllers that force the output of nonlinear systems in a strict feedback form to track a bounded and sufficient smooth reference trajectory asymptotically. Under suitable condition with the initial output tracking error, the proposed controllers guarantee the output tracking error within a symmtric or an asymmetric pre-specified limit range, and boundedness of all signals of the closed loop system. A transformation is inmxuced to take care of the output tracking error constraint. Smooth and/or p -times differentiable step functions are propsed and incor- porated in the output tracking error transformation to overcome difficulties due to the asynxnetric limit range on the output tracking error. As a result, there are no switchings in the proposed controllers despite of the asymmnetric limit range.
基金This research received no specific grant from any funding agency in the public,commercial,or not-for-profit sectors。
文摘Background:The purpose of the study is to understand the role of cash flow sensitivity to investment as a measure of financial constraints among listed Indian manufacturing firms.It also analyses the role of tangibility in alleviating financial constraints.Further,the role of other financial factors in investment decisions is explored.Methods:The study is conducted using the generalized method of moments(GMM)estimator on dynamic panel data for the period of(2009–2015)on 768 listed manufacturing firms.Results:The analysis finds that cash flow sensitivity is a valid measure of financial constraints in the Indian manufacturing sector.Results according to splitting criteria found that investment decisions of standalone firms are more sensitive to cash flow than group affiliated firms.Further,splitting the firms according to market capitalization and tangible net worth reveals a higher degree of cash flow sensitivity by firms with lower market capitalization and asset tangibility.The results for the effects of tangibility of assets on easing financial constraint were found significant only in the case of firms with low tangible net worth and medium market capitalization.Conclusions:The study confirms cash flow sensitivity to investment as a valid measure of financial constraints.It will confirm pooling of internal funds by financially constrained firms to accept profitable investment opportunities in future.Further,it also reports that asset tangibility eases the financial constraints faced by firms.
