In order to obtain Mg alloys with fine microstructures and high mechanical performances,a novel friction-based processing method,name as“constrained friction processing(CFP)”,was investigated.Via CFP,defect-free Mg-...In order to obtain Mg alloys with fine microstructures and high mechanical performances,a novel friction-based processing method,name as“constrained friction processing(CFP)”,was investigated.Via CFP,defect-free Mg-Zn-Ca rods with greatly refined grains and high mechanical properties were produced.Compared to the previous as-cast microstructure,the grain size was reduced from more than 1 mm to around 4μm within 3 s by a single process cycle.The compressive yield strength was increased by 350%while the ultimate compressive strength by 53%.According to the established material flow behaviors by“tracer material”,the plastic material was transported by shear deformation.From the base material to the rod,the material experienced three stages,i.e.deformation by the tool,upward flow with additional tilt,followed by upward transportation.The microstructural evolution was revealed by“stop-action”technique.The microstructural development at regions adjacent to the rod is mainly controlled by twinning,dynamic recrystallization(DRX)as well as particle stimulated nucleation,while that within the rod is related to DRX combined with grain growth.展开更多
In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However,...In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly finetuned strategy or technique might overfit some problem types,resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties.First, the constrained Pareto front(CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance(i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search,which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.展开更多
Flexible damping technology considering aseismic materials and aseismic structures seems be a good solution for engineering structures.In this study,a constrained damping structure for underground tunnel lining,using ...Flexible damping technology considering aseismic materials and aseismic structures seems be a good solution for engineering structures.In this study,a constrained damping structure for underground tunnel lining,using a rubber-sand-concrete(RSC)as the aseismic material,is proposed.The aseismic performances of constrained damping structure were investigated by a series of hammer impact tests.The damping layer thickness and shape effects on the aseismic performance such as effective duration and acceleration amplitude of time-domain analysis,composite loss factor and damping ratio of the transfer function analysis,and total vibration level of octave spectrum analysis were discussed.The hammer impact tests revealed that the relationship between the aseismic performance and damping layer thickness was not linear,and that the hollow damping layer had a better aseismic performance than the flat damping layer one.The aseismic performances of constrained damping structure under different seismicity magnitudes and geological conditions were investigated.The effects of the peak ground acceleration(PGA)and tunnel overburden depth on the aseismic performances such as the maximum principal stress and equivalent plastic strain(PEEQ)were discussed.The numerical results show the constrained damping structure proposed in this paper has a good aseismic performance,with PGA in the range(0.2-1.2)g and tunnel overburden depth in the range of 0-300 m.展开更多
The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient f...The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient flows(FxTGFs).First,a general class of nonlinear functions in designing FxTGFs is provided.A unified method for designing first-order FxTGFs is shown under Polyak-Łjasiewicz inequality assumption,a weaker condition than strong convexity.When there exist both bounded and vanishing disturbances in the gradient flow,a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented.Under the strict convexity assumption,Newton-based FxTGFs is given and further extended to solve time-varying optimization.Besides,the proposed FxTGFs are further used for solving equation-constrained optimization.Moreover,an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization.To show the effectiveness of various FxTGFs,the static regret analyses for several typical FxTGFs are also provided in detail.Finally,the proposed FxTGFs are applied to solve two network problems,i.e.,the network consensus problem and solving a system linear equations,respectively,from the perspective of optimization.Particularly,by choosing component-wisely sign-preserving functions,these problems can be solved in a distributed way,which extends the existing results.The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications.展开更多
This paper investigates the consensus control of multi-agent systems(MASs) with constrained input using the dynamic event-triggered mechanism(ETM).Consider the MASs with small-scale networks where a centralized dynami...This paper investigates the consensus control of multi-agent systems(MASs) with constrained input using the dynamic event-triggered mechanism(ETM).Consider the MASs with small-scale networks where a centralized dynamic ETM with global information of the MASs is first designed.Then,a distributed dynamic ETM which only uses local information is developed for the MASs with large-scale networks.It is shown that the semi-global consensus of the MASs can be achieved by the designed bounded control protocol where the Zeno phenomenon is eliminated by a designable minimum inter-event time.In addition,it is easier to find a trade-off between the convergence rate and the minimum inter-event time by an adjustable parameter.Furthermore,the results are extended to regional consensus of the MASs with the bounded control protocol.Numerical simulations show the effectiveness of the proposed approach.展开更多
Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention.Various constrained multi-objective optimization evolutionary algorithms(CMOEAs)have been dev...Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention.Various constrained multi-objective optimization evolutionary algorithms(CMOEAs)have been developed with the use of different algorithmic strategies,evolutionary operators,and constraint-handling techniques.The performance of CMOEAs may be heavily dependent on the operators used,however,it is usually difficult to select suitable operators for the problem at hand.Hence,improving operator selection is promising and necessary for CMOEAs.This work proposes an online operator selection framework assisted by Deep Reinforcement Learning.The dynamics of the population,including convergence,diversity,and feasibility,are regarded as the state;the candidate operators are considered as actions;and the improvement of the population state is treated as the reward.By using a Q-network to learn a policy to estimate the Q-values of all actions,the proposed approach can adaptively select an operator that maximizes the improvement of the population according to the current state and thereby improve the algorithmic performance.The framework is embedded into four popular CMOEAs and assessed on 42 benchmark problems.The experimental results reveal that the proposed Deep Reinforcement Learning-assisted operator selection significantly improves the performance of these CMOEAs and the resulting algorithm obtains better versatility compared to nine state-of-the-art CMOEAs.展开更多
The gun-track launch system is a new special launch device that connects the track outside the muzzle.Because it is constrained by the track,the characteristics of development of the muzzle jet differ from those of th...The gun-track launch system is a new special launch device that connects the track outside the muzzle.Because it is constrained by the track,the characteristics of development of the muzzle jet differ from those of the traditional muzzle jet.Specifically,it changes from freely developing to doing so in a constrained manner,where this results in an asymmetric direction of flow as well as spatio-temporal coupling-induced interference between various shock waves and the formation of vortices.In this background,the authors of this article formulate and consider the development and characteristics of evolution of the muzzle jet as it impacts a constrained moving body.We designed simulations to test the gun-track launch system,and established a numerical model based on the dynamic grid method to explore the development and characteristics of propagation of disturbances when the muzzle jet impacted a constrained moving body.We also considered models without a constrained track for the sake of comparison.The results showed that the muzzle jet assumed a circumferential asymmetric shape,and tended to develop in the area above the muzzle.Because the test platform was close to the ground,the muzzle jet was subjected to reflections from it that enhanced the development and evolution of various forms of shock waves and vortices in the muzzle jet to exacerbate its rate of distortion and asymmetric characteristics.This in turn led to significant differences in the changes in pressure at symmetric points that would otherwise have been identical.The results of a comparative analysis showed that the constrained track could hinder the influence of reflections from the ground on the muzzle jet to some extent,and could reduce the velocity of the shock waves inducing the motion of the muzzle as well as the Mach number of the moving body.The work here provides a theoretical basis and the requisite technical support for applications of the gun-track launch system.It also sheds light on the technical bottlenecks that need to be considered to recover high-value warheads.展开更多
Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they prop...Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they propose serious challenges for solvers.Among all constraints,some constraints are highly correlated with optimal feasible regions;thus they can provide effective help to find feasible Pareto front.However,most of the existing constrained multi-objective evolutionary algorithms tackle constraints by regarding all constraints as a whole or directly ignoring all constraints,and do not consider judging the relations among constraints and do not utilize the information from promising single constraints.Therefore,this paper attempts to identify promising single constraints and utilize them to help solve CMOPs.To be specific,a CMOP is transformed into a multitasking optimization problem,where multiple auxiliary tasks are created to search for the Pareto fronts that only consider a single constraint respectively.Besides,an auxiliary task priority method is designed to identify and retain some high-related auxiliary tasks according to the information of relative positions and dominance relationships.Moreover,an improved tentative method is designed to find and transfer useful knowledge among tasks.Experimental results on three benchmark test suites and 11 realworld problems with different numbers of constraints show better or competitive performance of the proposed method when compared with eight state-of-the-art peer methods.展开更多
To efficiently predict the mechanical parameters of granular soil based on its random micro-structure,this study proposed a novel approach combining numerical simulation and machine learning algorithms.Initially,3500 ...To efficiently predict the mechanical parameters of granular soil based on its random micro-structure,this study proposed a novel approach combining numerical simulation and machine learning algorithms.Initially,3500 simulations of one-dimensional compression tests on coarse-grained sand using the three-dimensional(3D)discrete element method(DEM)were conducted to construct a database.In this process,the positions of the particles were randomly altered,and the particle assemblages changed.Interestingly,besides confirming the influence of particle size distribution parameters,the stress-strain curves differed despite an identical gradation size statistic when the particle position varied.Subsequently,the obtained data were partitioned into training,validation,and testing datasets at a 7:2:1 ratio.To convert the DEM model into a multi-dimensional matrix that computers can recognize,the 3D DEM models were first sliced to extract multi-layer two-dimensional(2D)cross-sectional data.Redundant information was then eliminated via gray processing,and the data were stacked to form a new 3D matrix representing the granular soil’s fabric.Subsequently,utilizing the Python language and Pytorch framework,a 3D convolutional neural networks(CNNs)model was developed to establish the relationship between the constrained modulus obtained from DEM simulations and the soil’s fabric.The mean squared error(MSE)function was utilized to assess the loss value during the training process.When the learning rate(LR)fell within the range of 10-5e10-1,and the batch sizes(BSs)were 4,8,16,32,and 64,the loss value stabilized after 100 training epochs in the training and validation dataset.For BS?32 and LR?10-3,the loss reached a minimum.In the testing set,a comparative evaluation of the predicted constrained modulus from the 3D CNNs versus the simulated modulus obtained via DEM reveals a minimum mean absolute percentage error(MAPE)of 4.43%under the optimized condition,demonstrating the accuracy of this approach.Thus,by combining DEM and CNNs,the variation of soil’s mechanical characteristics related to its random fabric would be efficiently evaluated by directly tracking the particle assemblages.展开更多
Constrained Friction Processing(CFP)is a novel solid-state processing technique suitable for lightweight materials,such Mg-and Al-alloys.The technique enables grain size refinement to fine or even ultrafine scale.In t...Constrained Friction Processing(CFP)is a novel solid-state processing technique suitable for lightweight materials,such Mg-and Al-alloys.The technique enables grain size refinement to fine or even ultrafine scale.In this study,the effect of CFP on the microstructural refinement of AM50 rods is investigated in terms of particle size and morphology of the eutectic and secondary phases originally present in the base material,in particular the eutecticβ-Mg_(17)Al_(12)and Al-Mn phases.For that purpose,as-cast and solution heat-treated base material and processed samples were analyzed.The Al_(8)Mn_(5) intermetallic phase was identified as the main secondary phase present in all samples before and after the processing.A notorious refinement of these particles was observed,starting from particles with an average equivalent length of a few micrometers to around 560 nm after the processing.The refinement of the secondary phase refinement is attributed to a mechanism analogous to the attrition comminution,where the combination of temperature increase and shearing of the material enables the continuous breaking of the brittle intermetallic particles into smaller pieces.As for the eutectic phase,the results indicate the presence of the partially divorcedβ-Mg_(17)Al_(12)particles exclusively in the as-cast base material,indicating that no further phase transformations regarding the eutectic phase,such as dynamic precipitation,occurred after the CFP.In the case of the processed as-cast material analyzed after the CFP,the thermal energy generated during the processing led to temperature values above the solvus limit of the eutectic phase,which associated with the mechanical breakage of the particles,enabled the complete dissolution of this phase.Therefore,CFP was successfully demonstrated to promote an extensive microstructure refinement in multiple aspects,in terms of grain sizes of theα-Mg phase and presence and morphology of the Al-Mn and eutecticβ-Mg_(17)Al_(12).展开更多
Mozambique's continental margin in East Africa was formed during the break-off stage of the east and west Gondwana lands. Studying the geological structure and division of continent-ocean boundary(COB) in Mozambiq...Mozambique's continental margin in East Africa was formed during the break-off stage of the east and west Gondwana lands. Studying the geological structure and division of continent-ocean boundary(COB) in Mozambique's continental margin is considered of great significance to rebuild Gondwana land and understand its movement mode. Along these lines, in this work, the initial Moho was fit using the known Moho depth from reflection seismic profiles, and a 3D multi-point constrained gravity inversion was carried out. Thus, highaccuracy Moho depth and crustal thickness in the study area were acquired. According to the crustal structure distribution based on the inversion results, the continental crust at the narrowest position of the Mozambique Channel was detected. According to the analysis of the crustal thickness, the Mozambique ridge is generally oceanic crust and the COB of the whole Mozambique continental margin is divided.展开更多
In this study,a novel residential virtual power plant(RVPP)scheduling method that leverages a gate recurrent unit(GRU)-integrated deep reinforcement learning(DRL)algorithm is proposed.In the proposed scheme,the GRU-in...In this study,a novel residential virtual power plant(RVPP)scheduling method that leverages a gate recurrent unit(GRU)-integrated deep reinforcement learning(DRL)algorithm is proposed.In the proposed scheme,the GRU-integrated DRL algorithm guides the RVPP to participate effectively in both the day-ahead and real-time markets,lowering the electricity purchase costs and consumption risks for end-users.The Lagrangian relaxation technique is introduced to transform the constrained Markov decision process(CMDP)into an unconstrained optimization problem,which guarantees that the constraints are strictly satisfied without determining the penalty coefficients.Furthermore,to enhance the scalability of the constrained soft actor-critic(CSAC)-based RVPP scheduling approach,a fully distributed scheduling architecture was designed to enable plug-and-play in the residential distributed energy resources(RDER).Case studies performed on the constructed RVPP scenario validated the performance of the proposed methodology in enhancing the responsiveness of the RDER to power tariffs,balancing the supply and demand of the power grid,and ensuring customer comfort.展开更多
A method for determining the extrema of a real-valued and differentiable function for which its dependent variables are subject to constraints and that avoided the use of Lagrange multipliers was previously presented ...A method for determining the extrema of a real-valued and differentiable function for which its dependent variables are subject to constraints and that avoided the use of Lagrange multipliers was previously presented (Corti and Fariello, Op. Res. Forum 2 (2021) 59). The method made use of projection matrices, and a corresponding Gram-Schmidt orthogonalization process, to identify the constrained extrema. Furthermore, information about the second-derivatives of the given function with constraints was generated, from which the nature of the constrained extrema could be determined, again without knowledge of the Lagrange multipliers. Here, the method is extended to the case of functional derivatives with constraints. In addition, constrained first-order and second-order derivatives of the function are generated, in which the derivatives with respect to a given variable are obtained and, concomitantly, the effect of the variations of the remaining chosen set of dependent variables are strictly accounted for. These constrained derivatives are valid not only at the extrema points, and also provide another equivalent route for the determination of the constrained extrema and their nature.展开更多
Constrained multi-objective optimization problems(CMOPs) include the optimization of objective functions and the satisfaction of constraint conditions, which challenge the solvers.To solve CMOPs, constrained multi-obj...Constrained multi-objective optimization problems(CMOPs) include the optimization of objective functions and the satisfaction of constraint conditions, which challenge the solvers.To solve CMOPs, constrained multi-objective evolutionary algorithms(CMOEAs) have been developed. However, most of them tend to converge into local areas due to the loss of diversity. Evolutionary multitasking(EMT) is new model of solving complex optimization problems, through the knowledge transfer between the source task and other related tasks. Inspired by EMT, this paper develops a new EMT-based CMOEA to solve CMOPs, in which the main task, a global auxiliary task, and a local auxiliary task are created and optimized by one specific population respectively. The main task focuses on finding the feasible Pareto front(PF), and global and local auxiliary tasks are used to respectively enhance global and local diversity. Moreover, the global auxiliary task is used to implement the global search by ignoring constraints, so as to help the population of the main task pass through infeasible obstacles. The local auxiliary task is used to provide local diversity around the population of the main task, so as to exploit promising regions. Through the knowledge transfer among the three tasks, the search ability of the population of the main task will be significantly improved. Compared with other state-of-the-art CMOEAs, the experimental results on three benchmark test suites demonstrate the superior or competitive performance of the proposed CMOEA.展开更多
Effective constrained optimization algorithms have been proposed for engineering problems recently.It is common to consider constraint violation and optimization algorithm as two separate parts.In this study,a pbest s...Effective constrained optimization algorithms have been proposed for engineering problems recently.It is common to consider constraint violation and optimization algorithm as two separate parts.In this study,a pbest selection mechanism is proposed to integrate the current mutation strategy in constrained optimization problems.Based on the improved pbest selection method,an adaptive differential evolution approach is proposed,which helps the population jump out of the infeasible region.If all the individuals are infeasible,the top 5%of infeasible individuals are selected.In addition,a modified truncatedε-level method is proposed to avoid trapping in infeasible regions.The proposed adaptive differential evolution approach with an improvedεconstraint processmechanism(IεJADE)is examined on CEC 2006 and CEC 2010 constrained benchmark function series.Besides,a standard IEEE-30 bus test system is studied on the efficiency of the IεJADE.The numerical analysis verifies the IεJADE algorithm is effective in comparisonwith other effective algorithms.展开更多
This paper concerns the position optimization problem of a mobile relay over a whole horizontal plane.This problem is important because the position of a mobile relay directly affects the end-to-end performance,e.g.,r...This paper concerns the position optimization problem of a mobile relay over a whole horizontal plane.This problem is important because the position of a mobile relay directly affects the end-to-end performance,e.g.,reliability,connectivity,and data rate.In this paper,we propose a new position optimization scheme of a mobile relay over a whole horizontal plane based on the one-bit feedback information from the destination node,which improves the performance over the prior scheme whose position of the mobile relay is optimized over a fixed orbit.In the proposed scheme,the mobile relay is equipped with merely one single onboard antenna.Moreover,no prior information about the positions of both the source node and the destination node is required.Thus,the proposed scheme can work at low network resources scenario,which is particularly suitable for mobile relay communication with constrained energy,e.g.,the communications in a disaster area where the infrastructure is heavily damaged,volcano monitoring,and wireless powered communication networking.According to the characteristics of the proposed scheme,we further design two heuristic implementations to calculate the optimal position of a mobile relay over a whole horizontal plane.The first implementation has better steady performance whereas the second implementation has better convergence speed.We implement the proposed scheme and conduct an extensive performance comparison between the proposed scheme and prior schemes to verify the advantages of the proposed scheme.展开更多
This paper investigates vibration control of beam through electro-magnetic constrained layer damping （EMCLD） which consists of electromagnet layer, permanent magnet layer and viscoelastic damping layer. When the coi...This paper investigates vibration control of beam through electro-magnetic constrained layer damping （EMCLD） which consists of electromagnet layer, permanent magnet layer and viscoelastic damping layer. When the coil of the electromagnet is electrified with proper control strategy, the electromagnet can exert magnetic force opposite to the direction of structural deformation so that the structural vibration is attenuated. A mathematical model is developed based on the equivalent current method to calculate the electromagnetic control force produced by EMCLD. The governing equations of the system are obtained using Hamilton＇s Principle and then reduced with the assumed-mode method. A simulation on vibration control of a cantilever beam is conducted under the velocity proportional feedback to demonstrate the energy dissipation capability of EMCLD, and the beam system with the same parameter is experimented. The results of experiment and simulation are compared and the results show that the EMCLD is an effective means for suppressing modal vibration. The results also indicate that the beam system has better control performance for larger control current. The EMCLD method presented in this paper provides an applicable and efficient tool for the vibration control of structures.展开更多
In order to overcome the shortcomings that the reconstructed spectral reflectance may be negative when using the classic principal component analysis （PCA）to reduce the dimensions of the multi-spectral data, a nonne...In order to overcome the shortcomings that the reconstructed spectral reflectance may be negative when using the classic principal component analysis （PCA）to reduce the dimensions of the multi-spectral data, a nonnegative constrained principal component analysis method is proposed to construct a low-dimensional multi-spectral space and accomplish the conversion between the new constructed space and the multispectral space. First, the reason behind the negative data is analyzed and a nonnegative constraint is imposed on the classic PCA. Then a set of nonnegative linear independence weight vectors of principal components is obtained, by which a lowdimensional space is constructed. Finally, a nonlinear optimization technique is used to determine the projection vectors of the high-dimensional multi-spectral data in the constructed space. Experimental results show that the proposed method can keep the reconstructed spectral data in [ 0, 1 ]. The precision of the space created by the proposed method is equivalent to or even higher than that by the PCA.展开更多
To overcome some drawbacks of Viterbi algorithm （VA）, such as exponential growing complexity of decoding, and its poor performance under bad channel conditions, some available known information must be used as cons...To overcome some drawbacks of Viterbi algorithm （VA）, such as exponential growing complexity of decoding, and its poor performance under bad channel conditions, some available known information must be used as constrained condition and apriori knowledge for decoding. A new constrained VA is proposed by adding con- straint bits directly for conventional codec. Compared with the conventional VA, under the bad channel condi- tion, the proposed scheme can improve the peak signal to noise ratio （PSNR） of the decoding image 2--10 dB by changing the number of constrained bits. Experimental results show that it is an efficient error-controlling way for the transmission of set partitioning in hierarchical trees （SPIHT） coded image.展开更多
No attempt has been made to date to model growth in girth of rubber tree （Hevea brasiliansis）. We evaluated the few widely used growth functions to identify the most parsimonious and biologically reasonable model fo...No attempt has been made to date to model growth in girth of rubber tree （Hevea brasiliansis）. We evaluated the few widely used growth functions to identify the most parsimonious and biologically reasonable model for describing the girth growth of young rubber trees based on an incomplete set of young age measurements. Monthly data for girth of immature trees （age 2 to 12 yearsi from two locations were sub- jected to modelling. Re-parameterized, unconstrained and constrained growth functions,of Richards （RM）, Gompertz （GM） and the monomo- lecular ＇model ^（MM） were fitted to data. Duration of growth was the firsf constraint introduced. In the stagel We attempted a population aver- age （PA） model to capture the trend in growth. The best PA model was fitted as a subject specific （SS） model. We used appropriate error vari- ance-covariance structure to account for correlation due to repeated measurements over time. Unconstrainecl functions underestimated the asymptotic maximum that did not reflective carrying capacity of the locations. Underestimafions were attributed to the partial set＇ of meas- urements made during the early growth phase of the trees. MM proved superior to RM and GM. In the randomcoefficient models, both Gf and Go appeared to be influenced by tree level effects. Inclusion of diagonal definite positive matrix removed the correlation between random effects. The results were similar at both locations. In the overall assessment MM appeared as the candidate model for studying the girth-age relationships in Hevea trees. Based on the fitted model we conclude that, in Hevea trees, growth rate is maintained at maximum value at to, then decreases until the final state at dG/dt 〉 0, resulting in yield curve with no period of accelerating growth. One physiological explanation is that photosynthetic activity in Hevea trees decreases as girth increases and constructive metabolism is larger than destructive metabolism.展开更多
基金the China Scholarship Council for the award of fellowship and funding(No.202006230137)。
文摘In order to obtain Mg alloys with fine microstructures and high mechanical performances,a novel friction-based processing method,name as“constrained friction processing(CFP)”,was investigated.Via CFP,defect-free Mg-Zn-Ca rods with greatly refined grains and high mechanical properties were produced.Compared to the previous as-cast microstructure,the grain size was reduced from more than 1 mm to around 4μm within 3 s by a single process cycle.The compressive yield strength was increased by 350%while the ultimate compressive strength by 53%.According to the established material flow behaviors by“tracer material”,the plastic material was transported by shear deformation.From the base material to the rod,the material experienced three stages,i.e.deformation by the tool,upward flow with additional tilt,followed by upward transportation.The microstructural evolution was revealed by“stop-action”technique.The microstructural development at regions adjacent to the rod is mainly controlled by twinning,dynamic recrystallization(DRX)as well as particle stimulated nucleation,while that within the rod is related to DRX combined with grain growth.
基金partly supported by the National Natural Science Foundation of China(62076225)。
文摘In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly finetuned strategy or technique might overfit some problem types,resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties.First, the constrained Pareto front(CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance(i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search,which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.
基金supported by the National Natural Science Foundation of China(No.52079133)CRSRI Open Research Program(Program SN:CKWV2019746/KY)+1 种基金the project of Key Laboratory of Water Grid Project and Regulation of Ministry of Water Resources(QTKS0034W23291)the Youth Innovation Promotion Association CAS.
文摘Flexible damping technology considering aseismic materials and aseismic structures seems be a good solution for engineering structures.In this study,a constrained damping structure for underground tunnel lining,using a rubber-sand-concrete(RSC)as the aseismic material,is proposed.The aseismic performances of constrained damping structure were investigated by a series of hammer impact tests.The damping layer thickness and shape effects on the aseismic performance such as effective duration and acceleration amplitude of time-domain analysis,composite loss factor and damping ratio of the transfer function analysis,and total vibration level of octave spectrum analysis were discussed.The hammer impact tests revealed that the relationship between the aseismic performance and damping layer thickness was not linear,and that the hollow damping layer had a better aseismic performance than the flat damping layer one.The aseismic performances of constrained damping structure under different seismicity magnitudes and geological conditions were investigated.The effects of the peak ground acceleration(PGA)and tunnel overburden depth on the aseismic performances such as the maximum principal stress and equivalent plastic strain(PEEQ)were discussed.The numerical results show the constrained damping structure proposed in this paper has a good aseismic performance,with PGA in the range(0.2-1.2)g and tunnel overburden depth in the range of 0-300 m.
基金supported by the National Key Research and Development Program of China(2020YFA0714300)the National Natural Science Foundation of China(62003084,62203108,62073079)+3 种基金the Natural Science Foundation of Jiangsu Province of China(BK20200355)the General Joint Fund of the Equipment Advance Research Program of Ministry of Education(8091B022114)Jiangsu Province Excellent Postdoctoral Program(2022ZB131)China Postdoctoral Science Foundation(2022M720720,2023T160105).
文摘The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient flows(FxTGFs).First,a general class of nonlinear functions in designing FxTGFs is provided.A unified method for designing first-order FxTGFs is shown under Polyak-Łjasiewicz inequality assumption,a weaker condition than strong convexity.When there exist both bounded and vanishing disturbances in the gradient flow,a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented.Under the strict convexity assumption,Newton-based FxTGFs is given and further extended to solve time-varying optimization.Besides,the proposed FxTGFs are further used for solving equation-constrained optimization.Moreover,an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization.To show the effectiveness of various FxTGFs,the static regret analyses for several typical FxTGFs are also provided in detail.Finally,the proposed FxTGFs are applied to solve two network problems,i.e.,the network consensus problem and solving a system linear equations,respectively,from the perspective of optimization.Particularly,by choosing component-wisely sign-preserving functions,these problems can be solved in a distributed way,which extends the existing results.The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications.
基金supported in part by the National Natural Science Foundation of China(51939001,61976033,62273072)the Natural Science Foundation of Sichuan Province (2022NSFSC0903)。
文摘This paper investigates the consensus control of multi-agent systems(MASs) with constrained input using the dynamic event-triggered mechanism(ETM).Consider the MASs with small-scale networks where a centralized dynamic ETM with global information of the MASs is first designed.Then,a distributed dynamic ETM which only uses local information is developed for the MASs with large-scale networks.It is shown that the semi-global consensus of the MASs can be achieved by the designed bounded control protocol where the Zeno phenomenon is eliminated by a designable minimum inter-event time.In addition,it is easier to find a trade-off between the convergence rate and the minimum inter-event time by an adjustable parameter.Furthermore,the results are extended to regional consensus of the MASs with the bounded control protocol.Numerical simulations show the effectiveness of the proposed approach.
基金the National Natural Science Foundation of China(62076225,62073300)the Natural Science Foundation for Distinguished Young Scholars of Hubei(2019CFA081)。
文摘Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention.Various constrained multi-objective optimization evolutionary algorithms(CMOEAs)have been developed with the use of different algorithmic strategies,evolutionary operators,and constraint-handling techniques.The performance of CMOEAs may be heavily dependent on the operators used,however,it is usually difficult to select suitable operators for the problem at hand.Hence,improving operator selection is promising and necessary for CMOEAs.This work proposes an online operator selection framework assisted by Deep Reinforcement Learning.The dynamics of the population,including convergence,diversity,and feasibility,are regarded as the state;the candidate operators are considered as actions;and the improvement of the population state is treated as the reward.By using a Q-network to learn a policy to estimate the Q-values of all actions,the proposed approach can adaptively select an operator that maximizes the improvement of the population according to the current state and thereby improve the algorithmic performance.The framework is embedded into four popular CMOEAs and assessed on 42 benchmark problems.The experimental results reveal that the proposed Deep Reinforcement Learning-assisted operator selection significantly improves the performance of these CMOEAs and the resulting algorithm obtains better versatility compared to nine state-of-the-art CMOEAs.
文摘The gun-track launch system is a new special launch device that connects the track outside the muzzle.Because it is constrained by the track,the characteristics of development of the muzzle jet differ from those of the traditional muzzle jet.Specifically,it changes from freely developing to doing so in a constrained manner,where this results in an asymmetric direction of flow as well as spatio-temporal coupling-induced interference between various shock waves and the formation of vortices.In this background,the authors of this article formulate and consider the development and characteristics of evolution of the muzzle jet as it impacts a constrained moving body.We designed simulations to test the gun-track launch system,and established a numerical model based on the dynamic grid method to explore the development and characteristics of propagation of disturbances when the muzzle jet impacted a constrained moving body.We also considered models without a constrained track for the sake of comparison.The results showed that the muzzle jet assumed a circumferential asymmetric shape,and tended to develop in the area above the muzzle.Because the test platform was close to the ground,the muzzle jet was subjected to reflections from it that enhanced the development and evolution of various forms of shock waves and vortices in the muzzle jet to exacerbate its rate of distortion and asymmetric characteristics.This in turn led to significant differences in the changes in pressure at symmetric points that would otherwise have been identical.The results of a comparative analysis showed that the constrained track could hinder the influence of reflections from the ground on the muzzle jet to some extent,and could reduce the velocity of the shock waves inducing the motion of the muzzle as well as the Mach number of the moving body.The work here provides a theoretical basis and the requisite technical support for applications of the gun-track launch system.It also sheds light on the technical bottlenecks that need to be considered to recover high-value warheads.
基金supported in part by the National Key Research and Development Program of China(2022YFD2001200)the National Natural Science Foundation of China(62176238,61976237,62206251,62106230)+3 种基金China Postdoctoral Science Foundation(2021T140616,2021M692920)the Natural Science Foundation of Henan Province(222300420088)the Program for Science&Technology Innovation Talents in Universities of Henan Province(23HASTIT023)the Program for Science&Technology Innovation Teams in Universities of Henan Province(23IRTSTHN010).
文摘Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they propose serious challenges for solvers.Among all constraints,some constraints are highly correlated with optimal feasible regions;thus they can provide effective help to find feasible Pareto front.However,most of the existing constrained multi-objective evolutionary algorithms tackle constraints by regarding all constraints as a whole or directly ignoring all constraints,and do not consider judging the relations among constraints and do not utilize the information from promising single constraints.Therefore,this paper attempts to identify promising single constraints and utilize them to help solve CMOPs.To be specific,a CMOP is transformed into a multitasking optimization problem,where multiple auxiliary tasks are created to search for the Pareto fronts that only consider a single constraint respectively.Besides,an auxiliary task priority method is designed to identify and retain some high-related auxiliary tasks according to the information of relative positions and dominance relationships.Moreover,an improved tentative method is designed to find and transfer useful knowledge among tasks.Experimental results on three benchmark test suites and 11 realworld problems with different numbers of constraints show better or competitive performance of the proposed method when compared with eight state-of-the-art peer methods.
基金supported by the National Key R&D Program of China (Grant No.2022YFC3003401)the National Natural Science Foundation of China (Grant Nos.42041006 and 42377137).
文摘To efficiently predict the mechanical parameters of granular soil based on its random micro-structure,this study proposed a novel approach combining numerical simulation and machine learning algorithms.Initially,3500 simulations of one-dimensional compression tests on coarse-grained sand using the three-dimensional(3D)discrete element method(DEM)were conducted to construct a database.In this process,the positions of the particles were randomly altered,and the particle assemblages changed.Interestingly,besides confirming the influence of particle size distribution parameters,the stress-strain curves differed despite an identical gradation size statistic when the particle position varied.Subsequently,the obtained data were partitioned into training,validation,and testing datasets at a 7:2:1 ratio.To convert the DEM model into a multi-dimensional matrix that computers can recognize,the 3D DEM models were first sliced to extract multi-layer two-dimensional(2D)cross-sectional data.Redundant information was then eliminated via gray processing,and the data were stacked to form a new 3D matrix representing the granular soil’s fabric.Subsequently,utilizing the Python language and Pytorch framework,a 3D convolutional neural networks(CNNs)model was developed to establish the relationship between the constrained modulus obtained from DEM simulations and the soil’s fabric.The mean squared error(MSE)function was utilized to assess the loss value during the training process.When the learning rate(LR)fell within the range of 10-5e10-1,and the batch sizes(BSs)were 4,8,16,32,and 64,the loss value stabilized after 100 training epochs in the training and validation dataset.For BS?32 and LR?10-3,the loss reached a minimum.In the testing set,a comparative evaluation of the predicted constrained modulus from the 3D CNNs versus the simulated modulus obtained via DEM reveals a minimum mean absolute percentage error(MAPE)of 4.43%under the optimized condition,demonstrating the accuracy of this approach.Thus,by combining DEM and CNNs,the variation of soil’s mechanical characteristics related to its random fabric would be efficiently evaluated by directly tracking the particle assemblages.
文摘Constrained Friction Processing(CFP)is a novel solid-state processing technique suitable for lightweight materials,such Mg-and Al-alloys.The technique enables grain size refinement to fine or even ultrafine scale.In this study,the effect of CFP on the microstructural refinement of AM50 rods is investigated in terms of particle size and morphology of the eutectic and secondary phases originally present in the base material,in particular the eutecticβ-Mg_(17)Al_(12)and Al-Mn phases.For that purpose,as-cast and solution heat-treated base material and processed samples were analyzed.The Al_(8)Mn_(5) intermetallic phase was identified as the main secondary phase present in all samples before and after the processing.A notorious refinement of these particles was observed,starting from particles with an average equivalent length of a few micrometers to around 560 nm after the processing.The refinement of the secondary phase refinement is attributed to a mechanism analogous to the attrition comminution,where the combination of temperature increase and shearing of the material enables the continuous breaking of the brittle intermetallic particles into smaller pieces.As for the eutectic phase,the results indicate the presence of the partially divorcedβ-Mg_(17)Al_(12)particles exclusively in the as-cast base material,indicating that no further phase transformations regarding the eutectic phase,such as dynamic precipitation,occurred after the CFP.In the case of the processed as-cast material analyzed after the CFP,the thermal energy generated during the processing led to temperature values above the solvus limit of the eutectic phase,which associated with the mechanical breakage of the particles,enabled the complete dissolution of this phase.Therefore,CFP was successfully demonstrated to promote an extensive microstructure refinement in multiple aspects,in terms of grain sizes of theα-Mg phase and presence and morphology of the Al-Mn and eutecticβ-Mg_(17)Al_(12).
基金The National Natural Science Foundation of China under contract No. 42076078China–Mozambique Joint Cruise under contract No. GASI-01-DLJHJ-CM。
文摘Mozambique's continental margin in East Africa was formed during the break-off stage of the east and west Gondwana lands. Studying the geological structure and division of continent-ocean boundary(COB) in Mozambique's continental margin is considered of great significance to rebuild Gondwana land and understand its movement mode. Along these lines, in this work, the initial Moho was fit using the known Moho depth from reflection seismic profiles, and a 3D multi-point constrained gravity inversion was carried out. Thus, highaccuracy Moho depth and crustal thickness in the study area were acquired. According to the crustal structure distribution based on the inversion results, the continental crust at the narrowest position of the Mozambique Channel was detected. According to the analysis of the crustal thickness, the Mozambique ridge is generally oceanic crust and the COB of the whole Mozambique continental margin is divided.
基金supported by the Sichuan Science and Technology Program(grant number 2022YFG0123).
文摘In this study,a novel residential virtual power plant(RVPP)scheduling method that leverages a gate recurrent unit(GRU)-integrated deep reinforcement learning(DRL)algorithm is proposed.In the proposed scheme,the GRU-integrated DRL algorithm guides the RVPP to participate effectively in both the day-ahead and real-time markets,lowering the electricity purchase costs and consumption risks for end-users.The Lagrangian relaxation technique is introduced to transform the constrained Markov decision process(CMDP)into an unconstrained optimization problem,which guarantees that the constraints are strictly satisfied without determining the penalty coefficients.Furthermore,to enhance the scalability of the constrained soft actor-critic(CSAC)-based RVPP scheduling approach,a fully distributed scheduling architecture was designed to enable plug-and-play in the residential distributed energy resources(RDER).Case studies performed on the constructed RVPP scenario validated the performance of the proposed methodology in enhancing the responsiveness of the RDER to power tariffs,balancing the supply and demand of the power grid,and ensuring customer comfort.
文摘A method for determining the extrema of a real-valued and differentiable function for which its dependent variables are subject to constraints and that avoided the use of Lagrange multipliers was previously presented (Corti and Fariello, Op. Res. Forum 2 (2021) 59). The method made use of projection matrices, and a corresponding Gram-Schmidt orthogonalization process, to identify the constrained extrema. Furthermore, information about the second-derivatives of the given function with constraints was generated, from which the nature of the constrained extrema could be determined, again without knowledge of the Lagrange multipliers. Here, the method is extended to the case of functional derivatives with constraints. In addition, constrained first-order and second-order derivatives of the function are generated, in which the derivatives with respect to a given variable are obtained and, concomitantly, the effect of the variations of the remaining chosen set of dependent variables are strictly accounted for. These constrained derivatives are valid not only at the extrema points, and also provide another equivalent route for the determination of the constrained extrema and their nature.
基金supported in part by the National Natural Science Fund for Outstanding Young Scholars of China (61922072)the National Natural Science Foundation of China (62176238, 61806179, 61876169, 61976237)+2 种基金China Postdoctoral Science Foundation (2020M682347)the Training Program of Young Backbone Teachers in Colleges and Universities in Henan Province (2020GGJS006)Henan Provincial Young Talents Lifting Project (2021HYTP007)。
文摘Constrained multi-objective optimization problems(CMOPs) include the optimization of objective functions and the satisfaction of constraint conditions, which challenge the solvers.To solve CMOPs, constrained multi-objective evolutionary algorithms(CMOEAs) have been developed. However, most of them tend to converge into local areas due to the loss of diversity. Evolutionary multitasking(EMT) is new model of solving complex optimization problems, through the knowledge transfer between the source task and other related tasks. Inspired by EMT, this paper develops a new EMT-based CMOEA to solve CMOPs, in which the main task, a global auxiliary task, and a local auxiliary task are created and optimized by one specific population respectively. The main task focuses on finding the feasible Pareto front(PF), and global and local auxiliary tasks are used to respectively enhance global and local diversity. Moreover, the global auxiliary task is used to implement the global search by ignoring constraints, so as to help the population of the main task pass through infeasible obstacles. The local auxiliary task is used to provide local diversity around the population of the main task, so as to exploit promising regions. Through the knowledge transfer among the three tasks, the search ability of the population of the main task will be significantly improved. Compared with other state-of-the-art CMOEAs, the experimental results on three benchmark test suites demonstrate the superior or competitive performance of the proposed CMOEA.
基金supported by National Natural Science Foundation of China under Grant Nos.52005447,72271222,71371170,71871203,L1924063Zhejiang Provincial Natural Science Foundation of China underGrant No.LQ21E050014Foundation of Zhejiang Education Committee under Grant No.Y201840056.
文摘Effective constrained optimization algorithms have been proposed for engineering problems recently.It is common to consider constraint violation and optimization algorithm as two separate parts.In this study,a pbest selection mechanism is proposed to integrate the current mutation strategy in constrained optimization problems.Based on the improved pbest selection method,an adaptive differential evolution approach is proposed,which helps the population jump out of the infeasible region.If all the individuals are infeasible,the top 5%of infeasible individuals are selected.In addition,a modified truncatedε-level method is proposed to avoid trapping in infeasible regions.The proposed adaptive differential evolution approach with an improvedεconstraint processmechanism(IεJADE)is examined on CEC 2006 and CEC 2010 constrained benchmark function series.Besides,a standard IEEE-30 bus test system is studied on the efficiency of the IεJADE.The numerical analysis verifies the IεJADE algorithm is effective in comparisonwith other effective algorithms.
基金partially supported by the Natural Science Foundation of China(No.61972262)Natural Science Foundation of Guangdong,China(No.2021A1515011344)+2 种基金Key Project of Education Ministry of Guangdong Province(No.2021ZDZX3001)Fundamental Research Programs of Shenzhen City(No.JCYJ20210324093809024,No.JCYJ20180305124648757)China Scholarship Council(No.201908440031).
文摘This paper concerns the position optimization problem of a mobile relay over a whole horizontal plane.This problem is important because the position of a mobile relay directly affects the end-to-end performance,e.g.,reliability,connectivity,and data rate.In this paper,we propose a new position optimization scheme of a mobile relay over a whole horizontal plane based on the one-bit feedback information from the destination node,which improves the performance over the prior scheme whose position of the mobile relay is optimized over a fixed orbit.In the proposed scheme,the mobile relay is equipped with merely one single onboard antenna.Moreover,no prior information about the positions of both the source node and the destination node is required.Thus,the proposed scheme can work at low network resources scenario,which is particularly suitable for mobile relay communication with constrained energy,e.g.,the communications in a disaster area where the infrastructure is heavily damaged,volcano monitoring,and wireless powered communication networking.According to the characteristics of the proposed scheme,we further design two heuristic implementations to calculate the optimal position of a mobile relay over a whole horizontal plane.The first implementation has better steady performance whereas the second implementation has better convergence speed.We implement the proposed scheme and conduct an extensive performance comparison between the proposed scheme and prior schemes to verify the advantages of the proposed scheme.
基金National Natural Science Foundation of China (50275114)
文摘This paper investigates vibration control of beam through electro-magnetic constrained layer damping （EMCLD） which consists of electromagnet layer, permanent magnet layer and viscoelastic damping layer. When the coil of the electromagnet is electrified with proper control strategy, the electromagnet can exert magnetic force opposite to the direction of structural deformation so that the structural vibration is attenuated. A mathematical model is developed based on the equivalent current method to calculate the electromagnetic control force produced by EMCLD. The governing equations of the system are obtained using Hamilton＇s Principle and then reduced with the assumed-mode method. A simulation on vibration control of a cantilever beam is conducted under the velocity proportional feedback to demonstrate the energy dissipation capability of EMCLD, and the beam system with the same parameter is experimented. The results of experiment and simulation are compared and the results show that the EMCLD is an effective means for suppressing modal vibration. The results also indicate that the beam system has better control performance for larger control current. The EMCLD method presented in this paper provides an applicable and efficient tool for the vibration control of structures.
基金The Pre-Research Foundation of National Ministries andCommissions (No9140A16050109DZ01)the Scientific Research Program of the Education Department of Shanxi Province (No09JK701)
文摘In order to overcome the shortcomings that the reconstructed spectral reflectance may be negative when using the classic principal component analysis （PCA）to reduce the dimensions of the multi-spectral data, a nonnegative constrained principal component analysis method is proposed to construct a low-dimensional multi-spectral space and accomplish the conversion between the new constructed space and the multispectral space. First, the reason behind the negative data is analyzed and a nonnegative constraint is imposed on the classic PCA. Then a set of nonnegative linear independence weight vectors of principal components is obtained, by which a lowdimensional space is constructed. Finally, a nonlinear optimization technique is used to determine the projection vectors of the high-dimensional multi-spectral data in the constructed space. Experimental results show that the proposed method can keep the reconstructed spectral data in [ 0, 1 ]. The precision of the space created by the proposed method is equivalent to or even higher than that by the PCA.
文摘To overcome some drawbacks of Viterbi algorithm （VA）, such as exponential growing complexity of decoding, and its poor performance under bad channel conditions, some available known information must be used as constrained condition and apriori knowledge for decoding. A new constrained VA is proposed by adding con- straint bits directly for conventional codec. Compared with the conventional VA, under the bad channel condi- tion, the proposed scheme can improve the peak signal to noise ratio （PSNR） of the decoding image 2--10 dB by changing the number of constrained bits. Experimental results show that it is an efficient error-controlling way for the transmission of set partitioning in hierarchical trees （SPIHT） coded image.
文摘No attempt has been made to date to model growth in girth of rubber tree （Hevea brasiliansis）. We evaluated the few widely used growth functions to identify the most parsimonious and biologically reasonable model for describing the girth growth of young rubber trees based on an incomplete set of young age measurements. Monthly data for girth of immature trees （age 2 to 12 yearsi from two locations were sub- jected to modelling. Re-parameterized, unconstrained and constrained growth functions,of Richards （RM）, Gompertz （GM） and the monomo- lecular ＇model ^（MM） were fitted to data. Duration of growth was the firsf constraint introduced. In the stagel We attempted a population aver- age （PA） model to capture the trend in growth. The best PA model was fitted as a subject specific （SS） model. We used appropriate error vari- ance-covariance structure to account for correlation due to repeated measurements over time. Unconstrainecl functions underestimated the asymptotic maximum that did not reflective carrying capacity of the locations. Underestimafions were attributed to the partial set＇ of meas- urements made during the early growth phase of the trees. MM proved superior to RM and GM. In the randomcoefficient models, both Gf and Go appeared to be influenced by tree level effects. Inclusion of diagonal definite positive matrix removed the correlation between random effects. The results were similar at both locations. In the overall assessment MM appeared as the candidate model for studying the girth-age relationships in Hevea trees. Based on the fitted model we conclude that, in Hevea trees, growth rate is maintained at maximum value at to, then decreases until the final state at dG/dt 〉 0, resulting in yield curve with no period of accelerating growth. One physiological explanation is that photosynthetic activity in Hevea trees decreases as girth increases and constructive metabolism is larger than destructive metabolism.
