Integration of chaos theory and mathematical models in building simulation: Part I: Literature review

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasingly complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I) reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develops conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to building simulation scientists, initiates a dialogue and builds bridges between scientists and engineers, and stimulates future research about a wide range of issues on building environmental systems.

Integration of chaos theory and mathematical models in building simulation: Part II: Conceptual frameworks

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasing complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I), published in the previous issue, reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develop conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to (1) building simulation scientists and designers (2) initiating a dialogue between scientists and engineers, and (3) stimulating future research on a wide range of issues involved in designing and managing building environmental systems.

Bifurcation Analysis of Eigenstructure Assignment Control in a Simple Nonlinear Aircraft Model

Aircraft systems are highly nonlinear and time varying. High-performance aircraft at high angles of incidence experience undesired coupling of the lateral and longitudinal variables, resulting in departure from normal controlled � ight. The construction of a robust closed-loop control that extends the stable and decoupled � ight envelope as far as possible is pursued. For the study of these systems, nonlinear analysis methods are needed. Previously, bifurcation techniques have been used mainly to analyze open-loop nonlinear aircraft models and to investigate control effects on dynamic behavior. Linear feedback control designs constructed by eigenstructure assignment methods at a � xed � ight condition are investigated for a simple nonlinear aircraft model. Bifurcation analysis, in conjunction with linear control design methods, is shown to aid control law design for the nonlinear system.

Closed loop design for a simple nonlinear aircraft model using eigenstructure assignment

Aircraft systems are highly nonlinear and time varying. High-performance aircraft at high angles of incidence experience undesired coupling of the lateral and longitudinal variables, resulting in departure from normal controlled flight. The aim of this work is to construct a robust closed-loop control that optimally extends the stable and decoupled flight envelope. For the study of these systems nonlinear analysis methods are needed. Previously, bifurcation techniques have been used mainly to analyze open-loop nonlinear aircraft models and investigate control effects on dynamic behavior. In this work linear feedback control designs calculated by eigenstructure assignment methods are investigated for a simple aircraft model at a fixed flight condition. Bifurcation analysis in conjunction with linear control design methods is shown to aid control law design for the nonlinear system.

Indirect population dynamic benefits of altered life-history trade-offs in response to egg harvesting

Variations in demographic rates due to differential resource allocation between individuals are important considerations in the development of accurate population dynamic models. Systematic harvesting can alter age structure and/or reduce population density, conferring indirect positive benefits on the source population as a result of a consequent redistribution of resources between the remaining individuals. Independently of effects mediated through changes in density and competition, demographic rates can also be influenced by within-individual competition for resources. Harvesting dependent life stages can reduce an individual's current reproductive costs, allowing increased investment in its future fecundity and survival. Although such changes in demographic rates are well known, there has been little exploration of the potential impact on population dynamics. We use empirical data collected from a successfully reintroduced population of the Mauritius kestrel Falco punctatus to explore the population consequences of manipulating reproductive effort through harvesting. Consequent increases in an individual's future fecundity and survival allow source populations to withstand longer and more intensive harvesting regimes without being exposed to an increase in extinction risk, increasing maximum sustainable yields. These effects may also buffer populations against the impacts of stochastic events, but directional shifts in environmental conditions that increase reproductive costs may have detrimental population-level effects.

A perspective on chaos theory: Potential applications to intelligent buildings

Mathematical models have been vitally important in the development of technologies in building engineering. A literature review identifies that linear models are the most widely used building simulation models. The advent of intelligent buildings has added new challenges in the application of the existing models as an intelligent building requires learning and self-adjusting capabilities based on environmental and occupants' factors. It is therefore argued that the linearity is an impropriate basis for any model of either complex building systems or occupant behaviours for control or whatever purpose. Chaos and complexity theory reflects nonlinear dynamic properties of the intelligent systems excised by occupants and environment and has been used widely in modelling various engineering, natural and social systems. It is proposed that chaos and complexity theory be applied to study intelligent buildings. This paper gives a brief description of chaos and complexity theory and presents its current positioning, recent developments in building engineering research and future potential applications to intelligent building studies, which provides a bridge between chaos and complexity theory and intelligent building research.

Towards dynamical system models of language-related brain potentials

Event-related brain potentials (ERP) are important neural correlates of cognitive processes. In the domain of language processing, the N400 and P600 reflect lexical-semantic integration and syntactic processing problems, respectively. We suggest an interpretation of these markers in terms of dynamical system theory and present two nonlinear dynamical models for syntactic computations where different processing strategies correspond to functionally different regions in the system's phase space.

Neural networks for identification of nonlinear systems under random piecewise polynomial disturbances

The problem of identification of a nonlinear dynamic system is considered. A two-layer neural network is used for the solution of the problem. Systems disturbed with unmeasurable noise are considered, although it is known that the disturbance is a random piecewise polynomial process. Absorption polynomials and nonquadratic loss functions are used to reduce the effect of this disturbance on the estimates of the optimal memory of the neural-network model.

Steady state and dynamic modelling of nitrogen in the River Kennet: impacts of land use change since the 1930s

Steady state and dynamic models have been developed and applied to the River Kennet system. Annual nitrogen exports from the land surface to the river have been estimated based on land use from the 1930s and the 1990s. Long term modelled trends indicate that there has been a large increase in nitrogen transport into the river system driven by increased fertiliser application associated with increased cereal production, increased population and increased livestock levels. The dynamic model INCA Integrated Nitrogen in Catchments. has been applied to simulate the day-to-day transport of N from the terrestrial ecosystem to the riverine environment. This process-based model generates spatial and temporal data and reproduces the observed instream concentrations. Applying the model to current land use and 1930s land use indicates that there has been a major shift in the short term dynamics since the 1930s, with increased river and groundwater concentrations caused by both non-point source pollution from agriculture and point source discharges. �

Complex-valued B-spline neural networks for modeling and inverting Hammerstein systems

Many communication signal processing applications involve modelling and inverting complex-valued (CV) Hammerstein systems. We develops a new CV B-spline neural network approach for efficient identification of the CV Hammerstein system and effective inversion of the estimated CV Hammerstein model. Specifically, the CV nonlinear static function in the Hammerstein system is represented using the tensor product from two univariate B-spline neural networks. An efficient alternating least squares estimation method is adopted for identifying the CV linear dynamic model’s coefficients and the CV B-spline neural network’s weights, which yields the closed-form solutions for both the linear dynamic model’s coefficients and the B-spline neural network’s weights, and this estimation process is guaranteed to converge very fast to a unique minimum solution. Furthermore, an accurate inversion of the CV Hammerstein system can readily be obtained using the estimated model. In particular, the inversion of the CV nonlinear static function in the Hammerstein system can be calculated effectively using a Gaussian-Newton algorithm, which naturally incorporates the efficient De Boor algorithm with both the B-spline curve and first order derivative recursions. The effectiveness of our approach is demonstrated using the application to equalisation of Hammerstein channels.

Modeling the Stream Water Nitrate Dynamics in 60,000-km(2) European Catchment, the Garonne, Southwest France

The spatial and temporal dynamics in the stream water NO3-N concentrations in a major European river-system, the Garonne (62,700 km(2)), are described and related to variations in climate, land management, and effluent point-sources using multivariate statistics. Building on this, the Hydrologiska Byrans Vattenbalansavdelning (HBV) rainfall-runoff model and the Integrated Catchment Model of Nitrogen (INCA-N) are applied to simulate the observed flow and N dynamics. This is done to help us to understand which factors and processes control the flow and N dynamics in different climate zones and to assess the relative inputs from diffuse and point sources across the catchment. This is the first application of the linked HBV and INCA-N models to a major European river system commensurate with the largest basins to be managed tinder the Water Framework Directive. The simulations suggest that in the lowlands, seasonal patterns in the stream water NO3-N concentrations emerge and are dominated by diffuse agricultural inputs, with an estimated 75% of the river load in the lowlands derived from arable farming. The results confirm earlier European catchment studies. Namely, current semi-distrubuted catchment-scale dynamic models, which integrate variations in land cover, climate, and a simple representation of the terrestrial and in-stream N cycle, are able to simulate seasonal NO3-N patterns at large spatial (> 300 km(2)) and temporal (>= monthly) scales using available national datasets.