Cost function for sub-agent elements in multi-agent energy management system

Distributed generation plays a key role in reducing CO2 emissions and losses in transmission of power. However, due to the nature of renewable resources, distributed generation requires suitable control strategies to assure reliability and optimality for the grid. Multi-agent systems are perfect candidates for providing distributed control of distributed generation stations as well as providing reliability and flexibility for the grid integration. The proposed multi-agent energy management system consists of single-type agents who control one or more gird entities, which are represented as generic sub-agent elements. The agent applies one control algorithm across all elements and uses a cost function to evaluate the suitability of the element as a supplier. The behavior set by the agent's user defines which parameters of an element have greater weight in the cost function, which allows the user to specify the preference on suppliers dynamically. This study shows the ability of the multi-agent energy management system to select suppliers according to the selection behavior given by the user. The optimality of the supplier for the required demand is ensured by the cost function based on the parameters of the element.

Aircraft routing with minimal climate impact: the REACT4C climate cost function modelling approach (V1.0)

In addition to CO2, the climate impact of aviation is strongly influenced by non-CO2 emissions, such as nitrogen oxides, influencing ozone and methane, and water vapour, which can lead to the formation of persistent contrails in ice-supersaturated regions. Because these non-CO2 emission effects are characterised by a short lifetime, their climate impact largely depends on emission location and time; that is to say, emissions in certain locations (or times) can lead to a greater climate impact (even on the global average) than the same emission in other locations (or times). Avoiding these climate-sensitive regions might thus be beneficial to climate. Here, we describe a modelling chain for investigating this climate impact mitigation option. This modelling chain forms a multi-step modelling approach, starting with the simulation of the fate of emissions released at a certain location and time (time-region grid points). This is performed with the chemistry–climate model EMAC, extended via the two submodels AIRTRAC (V1.0) and CONTRAIL (V1.0), which describe the contribution of emissions to the composition of the atmosphere and to contrail formation, respectively. The impact of emissions from the large number of time-region grid points is efficiently calculated by applying a Lagrangian scheme. EMAC also includes the calculation of radiative impacts, which are, in a second step, the input to climate metric formulas describing the global climate impact of the emission at each time-region grid point. The result of the modelling chain comprises a four-dimensional data set in space and time, which we call climate cost functions and which describes the global climate impact of an emission at each grid point and each point in time. In a third step, these climate cost functions are used in an air traffic simulator (SAAM) coupled to an emission tool (AEM) to optimise aircraft trajectories for the North Atlantic region. Here, we describe the details of this new modelling approach and show some example results. A number of sensitivity analyses are performed to motivate the settings of individual parameters. A stepwise sanity check of the results of the modelling chain is undertaken to demonstrate the plausibility of the climate cost functions.

The full-spectrum correlated-k method for longwave atmospheric radiative transfer using an effective Planck function

The correlated k-distribution (CKD) method is widely used in the radiative transfer schemes of atmospheric models and involves dividing the spectrum into a number of bands and then reordering the gaseous absorption coefficients within each one. The fluxes and heating rates for each band may then be computed by discretizing the reordered spectrum into of order 10 quadrature points per major gas and performing a monochromatic radiation calculation for each point. In this presentation it is shown that for clear-sky longwave calculations, sufficient accuracy for most applications can be achieved without the need for bands: reordering may be performed on the entire longwave spectrum. The resulting full-spectrum correlated k (FSCK) method requires significantly fewer monochromatic calculations than standard CKD to achieve a given accuracy. The concept is first demonstrated by comparing with line-by-line calculations for an atmosphere containing only water vapor, in which it is shown that the accuracy of heating-rate calculations improves approximately in proportion to the square of the number of quadrature points. For more than around 20 points, the root-mean-squared error flattens out at around 0.015 K/day due to the imperfect rank correlation of absorption spectra at different pressures in the profile. The spectral overlap of m different gases is treated by considering an m-dimensional hypercube where each axis corresponds to the reordered spectrum of one of the gases. This hypercube is then divided up into a number of volumes, each approximated by a single quadrature point, such that the total number of quadrature points is slightly fewer than the sum of the number that would be required to treat each of the gases separately. The gaseous absorptions for each quadrature point are optimized such that they minimize a cost function expressing the deviation of the heating rates and fluxes calculated by the FSCK method from line-by-line calculations for a number of training profiles. This approach is validated for atmospheres containing water vapor, carbon dioxide, and ozone, in which it is found that in the troposphere and most of the stratosphere, heating-rate errors of less than 0.2 K/day can be achieved using a total of 23 quadrature points, decreasing to less than 0.1 K/day for 32 quadrature points. It would be relatively straightforward to extend the method to include other gases.

Weak constraints in four-dimensional variational data assimilation

The formulation of four-dimensional variational data assimilation allows the incorporation of constraints into the cost function which need only be weakly satisfied. In this paper we investigate the value of imposing conservation properties as weak constraints. Using the example of the two-body problem of celestial mechanics we compare weak constraints based on conservation laws with a constraint on the background state.We show how the imposition of conservation-based weak constraints changes the nature of the gradient equation. Assimilation experiments demonstrate how this can add extra information to the assimilation process, even when the underlying numerical model is conserving.

A tractable means of correcting sector level TFP calculations in the face of biased technological change.

The measurement of the impact of technical change has received significant attention within the economics literature. One popular method of quantifying the impact of technical change is the use of growth accounting index numbers. However, in a recent article Nelson and Pack (1999) criticise the use of such index numbers in situations where technical change is likely to be biased in favour of one or other inputs. In particular they criticise the common approach of applying observed cost shares, as proxies for partial output elasticities, to weight the change in quantities which they claim is only valid under Hicks neutrality. Recent advances in the measurement of product and factor biases of technical change developed by Balcombe et al (2000) provide a relatively straight-forward means of correcting product and factor shares in the face of biased technical progress. This paper demonstrates the correction of both revenue and cost shares used in the construction of a TFP index for UK agriculture over the period 1953 to 2000 using both revenue and cost function share equations appended with stochastic latent variables to capture the bias effect. Technical progress is shown to be biased between both individual input and output groups. Output and input quantity aggregates are then constructed using both observed and corrected share weights and the resulting TFPs are compared. There does appear to be some significant bias in TFP if the effect of biased technical progress is not taken into account when constructing the weights

Consumer welfare and the loss induced by withholding information: The case of BSE in Italy

The paper develops a measure of consumer welfare losses associated with withholding it formation about a possible link between BSE and vCJD. The Cost of Ignorance (COI) is measured by comparing the utility of the informed choice with the utility of the uninformed choice, under conditions of improved information. Unlike previous work that is largely based on a single equation demand model, the measure is obtained retrieving a cost,function from a dynamic Almost Ideal Demand System. The estimated perceived loss for Italian consumers due to delayed information ranges from 12 percent to 54 percent of total meat expenditure, depending on the month assumed to embody correct beliefs about the safety level of beef.

Estimation of Hidden Markov Models parameters using differential evolution

Hidden Markov Models (HMMs) have been successfully applied to different modelling and classification problems from different areas over the recent years. An important step in using HMMs is the initialisation of the parameters of the model as the subsequent learning of HMM’s parameters will be dependent on these values. This initialisation should take into account the knowledge about the addressed problem and also optimisation techniques to estimate the best initial parameters given a cost function, and consequently, to estimate the best log-likelihood. This paper proposes the initialisation of Hidden Markov Models parameters using the optimisation algorithm Differential Evolution with the aim to obtain the best log-likelihood.

Multiple-model fault tolerant control of terminal unites of HVAC Systems

In this work, a fault-tolerant control scheme is applied to a air handling unit of a heating, ventilation and air-conditioning system. Using the multiple-model approach it is possible to identify faults and to control the system under faulty and normal conditions in an effective way. Using well known techniques to model and control the process, this work focuses on the importance of the cost function in the fault detection and its influence on the reconfigurable controller. Experimental results show how the control of the terminal unit is affected in the presence a fault, and how the recuperation and reconfiguration of the control action is able to deal with the effects of faults.

Planning rigid body motions using elastic curves

This paper tackles the problem of computing smooth, optimal trajectories on the Euclidean group of motions SE(3). The problem is formulated as an optimal control problem where the cost function to be minimized is equal to the integral of the classical curvature squared. This problem is analogous to the elastic problem from differential geometry and thus the resulting rigid body motions will trace elastic curves. An application of the Maximum Principle to this optimal control problem shifts the emphasis to the language of symplectic geometry and to the associated Hamiltonian formalism. This results in a system of first order differential equations that yield coordinate free necessary conditions for optimality for these curves. From these necessary conditions we identify an integrable case and these particular set of curves are solved analytically. These analytic solutions provide interpolating curves between an initial given position and orientation and a desired position and orientation that would be useful in motion planning for systems such as robotic manipulators and autonomous-oriented vehicles.

Optimal kinematic control of an autonomous underwater vehicle

This note investigates the motion control of an autonomous underwater vehicle (AUV). The AUV is modeled as a nonholonomic system as any lateral motion of a conventional, slender AUV is quickly damped out. The problem is formulated as an optimal kinematic control problem on the Euclidean Group of Motions SE(3), where the cost function to be minimized is equal to the integral of a quadratic function of the velocity components. An application of the Maximum Principle to this optimal control problem yields the appropriate Hamiltonian and the corresponding vector fields give the necessary conditions for optimality. For a special case of the cost function, the necessary conditions for optimality can be characterized more easily and we proceed to investigate its solutions. Finally, it is shown that a particular set of optimal motions trace helical paths. Throughout this note we highlight a particular case where the quadratic cost function is weighted in such a way that it equates to the Lagrangian (kinetic energy) of the AUV. For this case, the regular extremal curves are constrained to equate to the AUV's components of momentum and the resulting vector fields are the d'Alembert-Lagrange equations in Hamiltonian form.

Sparse model identification using orthogonal forward regression with basis pursuit and D-optimality

An efficient model identification algorithm for a large class of linear-in-the-parameters models is introduced that simultaneously optimises the model approximation ability, sparsity and robustness. The derived model parameters in each forward regression step are initially estimated via the orthogonal least squares (OLS), followed by being tuned with a new gradient-descent learning algorithm based on the basis pursuit that minimises the l(1) norm of the parameter estimate vector. The model subset selection cost function includes a D-optimality design criterion that maximises the determinant of the design matrix of the subset to ensure model robustness and to enable the model selection procedure to automatically terminate at a sparse model. The proposed approach is based on the forward OLS algorithm using the modified Gram-Schmidt procedure. Both the parameter tuning procedure, based on basis pursuit, and the model selection criterion, based on the D-optimality that is effective in ensuring model robustness, are integrated with the forward regression. As a consequence the inherent computational efficiency associated with the conventional forward OLS approach is maintained in the proposed algorithm. Examples demonstrate the effectiveness of the new approach.

A-optimality orthogonal forward regression algorithm using branch and bound

In this brief, we propose an orthogonal forward regression (OFR) algorithm based on the principles of the branch and bound (BB) and A-optimality experimental design. At each forward regression step, each candidate from a pool of candidate regressors, referred to as S, is evaluated in turn with three possible decisions: 1) one of these is selected and included into the model; 2) some of these remain in S for evaluation in the next forward regression step; and 3) the rest are permanently eliminated from S. Based on the BB principle in combination with an A-optimality composite cost function for model structure determination, a simple adaptive diagnostics test is proposed to determine the decision boundary between 2) and 3). As such the proposed algorithm can significantly reduce the computational cost in the A-optimality OFR algorithm. Numerical examples are used to demonstrate the effectiveness of the proposed algorithm.

Robust neurofuzzy rule base knowledge extraction and estimation using subspace decomposition combined with regularization and D-optimality

A new robust neurofuzzy model construction algorithm has been introduced for the modeling of a priori unknown dynamical systems from observed finite data sets in the form of a set of fuzzy rules. Based on a Takagi-Sugeno (T-S) inference mechanism a one to one mapping between a fuzzy rule base and a model matrix feature subspace is established. This link enables rule based knowledge to be extracted from matrix subspace to enhance model transparency. In order to achieve maximized model robustness and sparsity, a new robust extended Gram-Schmidt (G-S) method has been introduced via two effective and complementary approaches of regularization and D-optimality experimental design. Model rule bases are decomposed into orthogonal subspaces, so as to enhance model transparency with the capability of interpreting the derived rule base energy level. A locally regularized orthogonal least squares algorithm, combined with a D-optimality used for subspace based rule selection, has been extended for fuzzy rule regularization and subspace based information extraction. By using a weighting for the D-optimality cost function, the entire model construction procedure becomes automatic. Numerical examples are included to demonstrate the effectiveness of the proposed new algorithm.

Automatic nonlinear predictive model-construction algorithm using forward regression and the PRESS statistic

An automatic nonlinear predictive model-construction algorithm is introduced based on forward regression and the predicted-residual-sums-of-squares (PRESS) statistic. The proposed algorithm is based on the fundamental concept of evaluating a model's generalisation capability through crossvalidation. This is achieved by using the PRESS statistic as a cost function to optimise model structure. In particular, the proposed algorithm is developed with the aim of achieving computational efficiency, such that the computational effort, which would usually be extensive in the computation of the PRESS statistic, is reduced or minimised. The computation of PRESS is simplified by avoiding a matrix inversion through the use of the orthogonalisation procedure inherent in forward regression, and is further reduced significantly by the introduction of a forward-recursive formula. Based on the properties of the PRESS statistic, the proposed algorithm can achieve a fully automated procedure without resort to any other validation data set for iterative model evaluation. Numerical examples are used to demonstrate the efficacy of the algorithm.

Modelling sediment supply and transport in the River Lugg: strategies for controlling sediment loads

The River Lugg has particular problems with high sediment loads that have resulted in detrimental impacts on ecology and fisheries. A new dynamic, process-based model of hydrology and sediments (INCA- SED) has been developed and applied to the River Lugg system using an extensive data set from 1995–2008. The model simulates sediment sources and sinks throughout the catchment and gives a good representation of the sediment response at 22 reaches along the River Lugg. A key question considered in using the model is the management of sediment sources so that concentrations and bed loads can be reduced in the river system. Altogether, five sediment management scenarios were selected for testing on the River Lugg, including land use change, contour tillage, hedging and buffer strips. Running the model with parameters altered to simulate these five scenarios produced some interesting results. All scenarios achieved some reduction in sediment levels, with the 40% land use change achieving the best result with a 19% reduction. The other scenarios also achieved significant reductions of between 7% and 9%. Buffer strips produce the best result at close to 9%. The results suggest that if hedge introduction, contour tillage and buffer strips were all applied, sediment reductions would total 24%, considerably improving the current sediment situation. We present a novel cost-effectiveness analysis of our results where we use percentage of land removed from production as our cost function. Given the minimal loss of land associated with contour tillage, hedges and buffer strips, we suggest that these management practices are the most cost-effective combination to reduce sediment loads.