Adaptive Dynamic Method Research Articles

A sparse stiff chemistry solver based on dynamic adaptive integration for efficient combustion simulations

A sparse stiff chemistry solver based on dynamic adaptive hybrid integration (AHI-S) is developed and demonstrated for efficient combustion simulations. In a previous study, a dynamic adaptive method for hybrid integration (AHI) was developed to speed up the time integration of chemically reacting flows with detailed chemistry. The AHI method solves the fast subcomponent of chemistry implicitly and the slow subcomponent of chemistry and transport explicitly, and it was shown that AHI is more accurate and efficient than the operator-splitting schemes when there are significant radical sources from the transport term. In the present study, the AHI method is first improved to minimize the number of nontrivial entries in the Jacobian. Sparse matrix techniques are further integrated into AHI to achieve high computational efficiency. The performance of the new AHI-S solver is investigated in constant-pressure auto-ignition systems using different mechanisms that consist of 9–2878 species. It is shown that the computational cost of the AHI-S solver is overall linearly proportional to the mechanism size and is comparable to that of evaluating reaction rates using CHEMKIN-II subroutines. The AHI-S solver achieves speed-up factors ranging from approximately 10, for the 9-species hydrogen mechanism, to approximately 3000, for the 2878-species biodiesel mechanism, compared with the fully implicit VODE solver with Jacobian evaluated through numerical perturbations and factorized with dense matrix operations. It is further found that for mechanisms with less than approximately 100 species, the time saving of AHI-S is primarily attributed to the reduced size of the implicit core of the governing equations, while for mechanisms with more than 100 species, the computational cost of VODE is dominated by the dense LU factorization, such that the time saving of AHI-S is mostly attributed to the sparse LU factorization. The AHI-S solver is then applied to unsteady perfectly stirred reactors involving extinction and re-ignition. Speed-up factors from 50 to 30,000 are achieved compared with the Strang splitting scheme with the chemistry substeps implicitly integrated with VODE, while speed-up factors of 10–100 are achieved compared with the Strang splitting scheme implemented with the sparse stiff LSODES solver. In the end, the performance of AHI-S is investigated in one-dimensional (1-D) unsteady freely propagating laminar premixed flames for a methane/air mixture, for which the time step size in AHI-S is limited by the fastest transport process. A speed-up factor of approximately 200 is achieved compared with the Strang splitting scheme for fixed time step sizes between 10−8s and 10−6s.

Real Time Adaptive Stream-oriented Geo-data Filtering

The cutting-edge engineering maintenance software systems of various objects are aimed at processing of geo-location data coming from the employees’ mobile devices in real time. To reduce the amount of transmitted data such systems, usually, use various filtration methods of geo-coordinates recorded directly on mobile devices. The paper identifies the reasons for errors of geo-data coming from different sources, and proposes an adaptive dynamic method to filter geo-location data. Compared with the static method previously described in the literature [1] the approach offers to align adaptively the filtering threshold with changing characteristics of coordinates from many sources of geo-location data. To evaluate the efficiency of the developed filter method have been involved about 400 thousand points, representing motion paths of different type (on foot, by car and high-speed train) and parking (indoors, outdoors, near high-rise buildings) to take data from different mobile devices. Analysis of results has shown that the benefits of the proposed method are the more precise location of long parking (up to 6 hours) and coordinates when user is in motion, the capability to provide steam-oriented filtering of data from different sources that allows to use the approach in geo-information systems, providing continuous monitoring of the location in streamoriented data processing in real time. The disadvantage is a little bit more computational complexity and increasing amount of points of the final track as compared to other filtration techniques. In general, the developed approach enables a significant quality improvement of displayed paths of moving mobile objects.

On the evolution of patch-type dependent immigration

Empirical studies of dispersal indicate that decisions to immigrate are patch-type dependent; yet theoretical models usually ignore this fact. Here, we investigate the evolution of patch-type dependent immigration of a population inhabiting and dispersing in a heterogeneous landscape, which is structured by patches of low and high reward. We model the decision to immigrate in detail from a mechanistic underpinning. With the methods of adaptive dynamics, we derive both analytical and numerical results for the evolution of immigration when life-history traits are patch-type dependent. The model exhibits evolutionary branching in a wide parameter range and the subsequent coevolution can lead to a stable coexistence of a generalist, settling in patches of any type, and a specialist that only immigrates into patches of high reward. We find that individuals always settle in the patches of high reward, in which survival until maturation, relative fecundity and emigration probability are high. We investigate how the probability to immigrate into patches of low reward changes with model parameters. For example, we show that immigration into patches of low reward increases when the emigration probability in these patches increases. Further, immigration into patches of low reward decreases when the patches of high reward become less safe during the dispersal season.

Attitude stabilization of rigid spacecraft with disturbance generated by time varying uncertain exosystems

This paper is concerned with the problem of attitude stabilization of rigid spacecraft in the presence of parameter uncertainty and external disturbance generated by some time varying uncertain exosystems. A time varying internal model that is free of the uncertain parameter is proposed to compensate the disturbance. An adaptive attitude controller is presented by incorporating time varying dynamic coordinate transformation, semi-tensor product and adaptive control method. Especially, the parameter uncertainties caused by the inertia matrix and uncertain exosystems are tackled by combining the semi-tensor product and adaptive control method. Finally, a simulation example is presented to illustrate the effectiveness of the proposed method.

Siderophore production and the evolution of investment in a public good: An adaptive dynamics approach to kin selection

Like many other bacteria, Pseudomonas aeruginosa sequesters iron from the environment through the secretion, and subsequent uptake, of iron-binding molecules. As these molecules can be taken up by other bacteria in the population than those who secreted them, this is a form of cooperation through a public good. Traditionally, this problem has been studied by comparing the relative fitnesses of siderophore-producing and non-producing strains, but this gives no information about the fate of strains that do produce intermediate amounts of siderophores. Here, we investigate theoretically how the amount invested in this form of cooperation evolves. We use a mechanistic description of the laboratory protocols used in experimental evolution studies to describe the competition and cooperation of the bacteria. From this dynamical model we derive the fitness following the adaptive dynamics method. The results show how selection is driven by local siderophore production and local competition. Because siderophore production reduces the growth rate, local competition decreases with the degree of relatedness (which is a dynamical variable in our model).Our model is not restricted to the analysis of small phenotypic differences and allows for theoretical exploration of the effects of large phenotypic differences between cooperators and cheats. We predict that an intermediate ESS level of cooperation (molecule production) should exist. The adaptive dynamics approach allows us to assess evolutionary stability, which is often not possible in other kin-selection models. We found that selection can lead to an intermediate strategy which in our model is always evolutionarily stable, yet can allow invasion of strategies that are much more cooperative. Our model describes the evolution of a public good in the context of the ecology of the microorganism, which allows us to relate the extent of production of the public good to the details of the interactions.

An Application Adaptation Approach to Mitigate the Impact of Dynamic Thermal Management on Video Encoding

Due to limitations of cooling methods such as using fan and heat sink, dynamic thermal management (DTM) is being widely adopted to manage the temperature of computing systems. However, application of DTM can reduce the system performance and thereby affect the quality of real-time applications. Real-time video encoding, which has high computational need and hard deadlines, is a commonly used application that can be severely affected by the usage of DTM. We study the effect of DTM on a widely used H.264 video encoder and formulate a multidimensional optimization problem to maximize video quality and minimize bit rate while ensuring that the video encoder can run in real time in spite of DTM effects. We model the effects of adapting encoding parameters on video quality, bit rate, and encoder speed. We propose a dynamic application adaptation method to efficiently solve the optimization problem by optimally adapting the encoding parameters in response to DTM effects. In addition, we show that the proposed dynamic application adaptation method would reduce the need for cooling methods such as forced convection cooling. We implement the proposed approach on an Intel® Core™ 2 Duo platform where dynamic voltage and frequency scaling (DVFS) is used for DTM. Our measurements with several videos reveal that when DTM is applied, the video quality is affected significantly. However, using the proposed adaptation algorithm, the encoder can run in real time, and the quality loss is minimized with only a marginal increase in the bit rate.

Adaptive dynamics analysis of a predator–prey model with selective disturbance

Evolution problem is always a hot topic in the mathematical biology field. In this paper, we investigate the evolutionary effects of selective disturbance on an evolving trait (e.g. body size and maturation age) of the predator individuals in one-predator two-prey community. By using methods of adaptive dynamics and population dynamics we construct an invasion fitness function and obtain the conditions for evolutionary branching and evolutionary stability under selective disturbance in both monomorphic and dimorphic populations. We further conduct a size-selective disturbance function founded on chi-square distribution to study evolutionary stable coexistence, and considering the evolutionary branching and evolutionary stability by using theoretic analysis and numerical simulations. The evolutionary results from a biological point of view show that (1) two strategies could gradually evolve to form a single ancestral strategy, moreover, higher levels of polymorphism cannot build up during evolution, that is, following first evolutionary branching two species will eventually evolve into two generalist species and reach an evolutionary stable coexistence; (2) smaller disturbance could touch off higher levels of dimorphism during evolution, while large disturbance can go against evolutionary branching and advance evolutionary stability.

A Dynamic Adaptive Wavelet Method for Solution of the Schrodinger Equation

In this paper, we present a dynamically adaptive wavelet method for solving Schrodinger equation on one-dimensional, two-dimensional and on the sphere. Solving one-dimensional and two-dimensional Schrodinger equations are based on Daubechies wavelet with finite difference method on an arbitrary grid, and for spherical Schrodinger equation is based on spherical wavelet over an optimal spherical geodesic grid. The method is applied to the solution of Schrodinger equation for computational efficiency and achieve accuracy with controlling spatial grid adaptation — high resolution computations are performed only in regions where a solution varies greatly (i.e., near steep gradients, or near-singularities) and a much coarser grid where the solution varies slowly. Thereupon the dynamic adaptive wavelet method is useful to analyze local structure of solution with very less number of computational cost than any other methods. The prowess and computational efficiency of the adaptive wavelet method is demonstrated for the solution of Schrodinger equation on one-dimensional, two-dimensional and on the sphere.

Dynamic parameter adaptation in particle swarm optimization using interval type-2 fuzzy logic

In this paper, we propose a new method for dynamic parameter adaptation in particle swarm optimization (PSO). PSO is an optimization method inspired in social behavior, which has been applied to different optimization problems obtaining good results. In this paper, we propose an improvement to the convergence and diversity of the swarm in PSO using interval type-2 fuzzy logic. Simulation results show that the proposed approach improves the performance of PSO. A comparison of the proposed method using type-2 fuzzy logic with the original PSO approach, and with PSO using type-1 fuzzy logic for dynamic parameter adaptation is presented.

Multi-scale modeling of dynamics and ignition to flame transitions of high pressure stratified n-heptane/toluene mixtures

The transitions from ignition to flames as well as the combustion dynamics in stratified n-heptane and toluene mixtures are numerically modeled by a correlated dynamic adaptive chemistry method coupled with a hybrid multi-timescale method (HMTS/CO-DAC) in a one-dimensional constant volume chamber. The study attempts to answer how the kinetic difference between n-alkanes and aromatics leads to different ignition to flame transitions and knocking-like acoustic wave formation at low temperature and engine pressure conditions with fuel stratification. It is found that the low temperature chemistry (LTC) and fuel stratification of n-heptane leads to the formation of multiple ignition fronts. Four different combustion wave fronts, a low temperature ignition (LTI) front followed by a high temperature ignition (HTI) front, a premixed flame (PF) front, and a diffusion flame (DF) front, are demonstrated. The fast LTI and HTI wave front propagation leads to a shock-like strong acoustic wave propagation, thus strongly modifying the dynamics of the subsequent diffusion and premixed flame fronts. On the other hand, for the toluene mixture, due to the lack of LTC, only two combustion wave fronts are formed, a HTI front and a premixed flame front, exhibiting stable flow field and no formation of shock-like acoustic wave. The dynamics of transition from combustion to shock waves is further analyzed by using a modified Burgers’ equation. The analysis for n-heptane/air mixture indicates that both the onset of LTI and the strong dependency of HTI on the equivalence ratio can either promote or attenuate the transition from strong acoustic wave to shock wave. However, the toluene/air mixture exhibits no coupling with acoustic wave, suggesting that the rich LTC reactivity with fuel stratification, specific to the n-alkane chemistry, can lead to knocking and acoustic formation.

Dynamic Model Adaptation for Multiscale Simulation of Hyperbolic Systems with Relaxation

In numerous industrial CFD applications, it is usual to use two (or more) different codes to solve a physical phenomenon: where the flow is a priori assumed to have a simple behavior, a code based on a coarse model is applied, while a code based on a fine model is used elsewhere. This leads to a complex coupling problem with fixed interfaces. The aim of the present work is to provide a numerical indicator to optimize to position of these coupling interfaces. In other words, thanks to this numerical indicator, one could verify if the use of the coarser model and of the resulting coupling does not introduce spurious effects. In order to validate this indicator, we use it in a dynamical multiscale method with moving coupling interfaces. The principle of this method is to use as much as possible a coarse model instead of the fine model in the computational domain, in order to obtain an accuracy which is comparable with the one provided by the fine model. We focus here on general hyperbolic systems with stiff relaxation source terms together with the corresponding hyperbolic equilibrium systems. Using a numerical Chapman---Enskog expansion and the distance to the equilibrium manifold, we construct the numerical indicator. Based on several works on the coupling of different hyperbolic models, an original numerical method of dynamic model adaptation is proposed. We prove that this multiscale method preserves invariant domains and that the entropy of the numerical solution decreases with respect to time. The reliability of the adaptation procedure is assessed on various 1D and 2D test cases coming from two-phase flow modeling.

A dynamic adaptive method for hybrid integration of stiff chemistry

The operator-splitting schemes for integration of stiff diffusion–reaction systems were found to fail in error control, i.e. incurring O(1) relative errors, with splitting time steps larger than that required for fully explicit integration, when significant non-chemical radical sources are present. It was shown that, by excluding the transport term from the chemistry integration, errors by orders of magnitude may occur in radical concentrations solved in the chemistry sub-step, resulting in significant errors in the major species. The failing scenario is demonstrated with a toy problem and an unsteady perfectly-stirred reactor (PSR) for hydrogen/air with significant H radical concentration at inlet. A dynamic adaptive method for hybrid integration (AHI) of stiff chemistry is then proposed as a substitute for the operator-splitting schemes in such cases. The AHI method can obtain accurate solutions by integrating the fast species and reactions implicitly and the non-stiff terms, including slow reactions and non-chemical source terms, explicitly. Specifically, fast species and reactions are identified on-the-fly based on their analytically derived timescales, the rates of slow variables are evaluated explicitly and those of fast species are evaluated partial-implicitly. As such, the number of variables to be implicitly solved at each integration time step is reduced to the number of the fast species, resulting in a smaller Jacobian matrix and consequently lower computational cost compared with the fully implicit solvers. The hybrid method is validated in auto-ignition for hydrogen/air with different equivalence ratios and initial temperatures, and compared with the Strang splitting scheme for the toy problem and the unsteady PSR. Results show significant improvement in accuracy using the AHI method.

Adaptive dynamics for a non-autonomous Lotka–Volterra model with size-selective disturbance

This paper intends to develop a theoretical framework for investigating the evolutionary impact of size-selective disturbance on an evolving trait of individuals in a non-autonomous Lotka–Volterra competition model. We first construct an invasion fitness function, which involves the average growth rate and settles in a nonequilibrium attractor. Then using methods of adaptive dynamics and critical function analysis we investigate the evolution of body size related traits in a competitive community, and when having size-selective disturbance we obtain the conditions for continuously stable strategy and evolutionary branching. Our results show that (1) heavy harvesting can lead to rapidly stable evolution towards smaller body size, but planting has an opposite effect; (2) smaller harvest pressure can give rise to high levels of polymorphism during evolution; (3) planting can make for evolutionary branching, while harvesting can go against evolutionary branching and promote evolutionary stability. Thus we can conclude, from an evolutionary point of view, that planting can promote species diversity and spatial differentiation among populations; however, harvesting does the opposite.

The Automatic Checkout Method of Balloon-Tracking Data at Unequal Intervals of Time

By tracking a beacon ball with theodolite and radar synchronously to inspect the accuracy of ra-dar data is one of the common calibrating methods without calibration towers at sea. Relied on some com-plications, the theodolite which acts as the standard in the precision test can not following the track of a d-ynamic target continuously for a long time. So the present processing methods based on isochronal interv-als can just make use of less continuous data. Upon that a new dynamic adaptive checkout method is introduced. It solves the problem of outliers-eliminating automatically among a great deal of data at unequal in-terval time by three culling steps. The results indicate that this method can eliminate outliers in beacon ball tracking data and make batch processing base on uncontinuous data implemented effectively. Not only the data quantity has been increased, but also the data process efficiency has been improved.

The Automatic Checkout Method of Balloon-Tracking Data at Unequal Intervals of Time

By tracking a beacon ball with theodolite and radar synchronously to inspect the accuracy of ra-dar data is one of the common calibrating methods without calibration towers at sea. Relied on some com-plications, the theodolite which acts as the standard in the precision test can not following the track of a d-ynamic target continuously for a long time. So the present processing methods based on isochronal interv-als can just make use of less continuous data. Upon that a new dynamic adaptive checkout method is introduced. It solves the problem of outliers-eliminating automatically among a great deal of data at unequal in-terval time by three culling steps. The results indicate that this method can eliminate outliers in beacon ball tracking data and make batch processing base on uncontinuous data implemented effectively. Not only the data quantity has been increased, but also the data process efficiency has been improved.

Error analysis of a dynamic model adaptation procedure for nonlinear hyperbolic equations

We propose a dynamic model adaptation method for a nonlinear conservation law coupled with an ordinary differential equation. This called the ''fine model, involves a small time scale and setting this time scale to 0 leads to a classical conservation law, called the ''coarse model, with a flux which depends on the unknown and on space and time. The dynamic model adaptation consists in detecting the regions where the fine model can be replaced by the coarse one in an automatic way, without deteriorating the accuracy of the result. To do so, we provide an error estimate between the solution of the fine model and the solution of the adaptive method, enabling a sharp control of the different parameters. This estimate rests upon stability results for conservation laws with respect to the flux function. Numerical results are presented at the end and show that our estimate is optimal.

Adaptive evolution of attack ability promotes the evolutionary branching of predator species

In this paper, with the methods of adaptive dynamics and critical function analysis, we investigate the evolutionary branching phenomenon of predator species. We assume that both the prey and predators are density-dependent and the predator’s attack ability can adaptively evolve, but this has a cost in terms of its death rate. First, we identify the general properties of trade-off relationships that allow for a continuously stable strategy and evolutionary branching in the predator strategy. It is found that if the trade-off curve is weakly concave near the singular strategy, then the singular strategy may be an evolutionary branching point. Second, we find that after the branching has occurred in the predator strategy, if the trade-off curve is convex–concave–convex, the predator species will eventually evolve into two different types, which can stably coexist on the much longer evolutionary timescale and no further branching is possible.

Coupling analysis of electrocardiogram and electroencephalogram based on improved symbolic transfer entropy

Exploration of the coupling relationship in dynamical system has always been a hot topic of many scholars at home and abroad, the traditional symbolic dynamics analysis method may lead to the results from the serious effect of non-stationary time series. This paper employs coarse graining extraction based on research of original transfer entropy. Through theoretical and experimental analysis, we find that the results of transfer entropy have different distribution trend under different extraction conditions in the coupling analysis of electroencephalogram and electrocardiogram. We choose the best effect of signal data extraction method and apply it to the later application analysis. Furthermore, this paper proposes improvement on the method of time series symbolization, using dynamic adaptive segmentation method. The experimental results show that the whether waking period or sleeping stage, coupling between electroencephalogram and electrocardiogram is more significant when using improved symbolic transfer entropy algorithm. It is also better to capture the dynamic information of the signal and the change of complexity of system dynamics, which is more conductive to clinical testing in practical application and has a better effect on the analysis of non-stationary time series.

Optimal design of fuzzy classification systems using PSO with dynamic parameter adaptation through fuzzy logic

In this paper a new method for dynamic parameter adaptation in particle swarm optimization (PSO) is proposed. PSO is a metaheuristic inspired in social behaviors, which is very useful in optimization problems. In this paper we propose an improvement to the convergence and diversity of the swarm in PSO using fuzzy logic. Simulation results show that the proposed approach improves the performance of PSO. First, benchmark mathematical functions are used to illustrate the feasibility of the proposed approach. Then a set of classification problems are used to show the potential applicability of the fuzzy parameter adaptation of PSO.

An adaptive online safety assessment method for mechanical system with pre-warning function

The safety status of a dynamic mechanical system is determined by its historical, current and future states together. Therefore the safety assessment process of such system should have dynamic and diachronic characteristics, which helps to track the dynamic states of system and predict future probable danger in advance. In order to overcome the disadvantages of traditional static safety assessment approaches, the results from which are often delayed and prone to produce false alarms, an adaptive online safety assessment method is proposed in this paper, which consists of two steps. A dynamic adaptive weighting method is first introduced and an aggregation scheme based on “3-D” time perspective is further presented to integrate system’s historical, current and future safety performance in a unit framework, considering both of assessment and pre-warning functions. The proposed method is able to track and predict the safety status of system dynamically and discover the potential fault in time. Its feasibility and benefits are investigated with a field case study of gas turbine compressor system, which validates that the proposed method improves the accuracy of safety assessment in dynamic conditions, and finally helps to restrain the fault symptom by proactive maintenance successfully.