Grey-box radial basis function modelling: the art of incorporating prior knowledge

A basic principle in data modelling is to incorporate available a priori information regarding the underlying data generating mechanism into the modelling process. We adopt this principle and consider grey-box radial basis function (RBF) modelling capable of incorporating prior knowledge. Specifically, we show how to explicitly incorporate the two types of prior knowledge: the underlying data generating mechanism exhibits known symmetric property and the underlying process obeys a set of given boundary value constraints. The class of orthogonal least squares regression algorithms can readily be applied to construct parsimonious grey-box RBF models with enhanced generalisation capability.

A fast identification algorithm for Box-Cox transformation based radial basis function neural network

In this letter, a Box-Cox transformation-based radial basis function (RBF) neural network is introduced using the RBF neural network to represent the transformed system output. Initially a fixed and moderate sized RBF model base is derived based on a rank revealing orthogonal matrix triangularization (QR decomposition). Then a new fast identification algorithm is introduced using Gauss-Newton algorithm to derive the required Box-Cox transformation, based on a maximum likelihood estimator. The main contribution of this letter is to explore the special structure of the proposed RBF neural network for computational efficiency by utilizing the inverse of matrix block decomposition lemma. Finally, the Box-Cox transformation-based RBF neural network, with good generalization and sparsity, is identified based on the derived optimal Box-Cox transformation and a D-optimality-based orthogonal forward regression algorithm. The proposed algorithm and its efficacy are demonstrated with an illustrative example in comparison with support vector machine regression.

NOx and O3 above a tropical rainforest: an analysis with a global and box model

A cross-platform field campaign, OP3, was conducted in the state of Sabah in Malaysian Borneo between April and July of 2008. Among the suite of observations recorded, the campaign included measurements of NOx and O3 – crucial outputs of any model chemistry mechanism. We describe the measurements of these species made from both the ground site and aircraft. We then use the output from two resolutions of the chemistry transport model p-TOMCAT to illustrate the ability of a global model chemical mechanism to capture the chemistry at the rainforest site. The basic model performance is good for NOx and poor for ozone. A box model containing the same chemical mechanism is used to explore the results of the global model in more depth and make comparisons between the two. Without some parameterization of the nighttime boundary layer – free troposphere mixing (i.e. the use of a dilution parameter), the box model does not reproduce the observations, pointing to the importance of adequately representing physical processes for comparisons with surface measurements. We conclude with a discussion of box model budget calculations of chemical reaction fluxes, deposition and mixing, and compare these results to output from p-TOMCAT. These show the same chemical mechanism behaves similarly in both models, but that emissions and advection play particularly strong roles in influencing the comparison to surface measurements.

Evaluation of a Lagrangian box model using field measurements from EASE (Eastern Atlantic Summer Experiment) 1996

The Cambridge Tropospheric Trajectory model of Chemistry and Transport (CiTTyCAT), a Lagrangian chemistry model, has been evaluated using atmospheric chemical measurements collected during the East Atlantic Summer Experiment 1996 (EASE '96). This field campaign was part of the UK Natural Environment Research Council's (NERC) Atmospheric Chemistry Studies in the Oceanic Environment (ACSOE) programme, conducted at Mace Head, Republic of Ireland, during July and August 1996. The model includes a description of gas-phase tropospheric chemistry, and simple parameterisations for surface deposition, mixing from the free troposphere and emissions. The model generally compares well with the measurements and is used to study the production and loss of O3 under a variety of conditions. The mean difference between the hourly O3 concentrations calculated by the model and those measured is 0.6 ppbv with a standard deviation of 8.7 ppbv. Three specific air-flow regimes were identified during the campaign – westerly, anticyclonic (easterly) and south westerly. The westerly flow is typical of background conditions for Mace Head. However, on some occasions there was evidence of long-range transport of pollutants from North America. In periods of anticyclonic flow, air parcels had collected emissions of NOx and VOCs immediately before arriving at Mace Head, leading to O3 production. The level of calculated O3 depends critically on the precise details of the trajectory, and hence on the emissions into the air parcel. In several periods of south westerly flow, low concentrations of O3 were measured which were consistent with deposition and photochemical destruction inside the tropical marine boundary layer.

Grey-box radial basis function modelling

A fundamental principle in data modelling is to incorporate available a priori information regarding the underlying data generating mechanism into the modelling process. We adopt this principle and consider grey-box radial basis function (RBF) modelling capable of incorporating prior knowledge. Specifically, we show how to explicitly incorporate the two types of prior knowledge: (i) the underlying data generating mechanism exhibits known symmetric property, and (ii) the underlying process obeys a set of given boundary value constraints. The class of efficient orthogonal least squares regression algorithms can readily be applied without any modification to construct parsimonious grey-box RBF models with enhanced generalisation capability.

Thinking out of the box – skills for work

Since the Dearing Report .1 there has been an increased emphasis on the development of employability and transferable (‘soft’) skills in undergraduate programmes. Within STEM subject areas, recent reports concluded that universities should offer ‘greater and more sustainable variety in modes of study to meet the changing demands of industry and students’.2 At the same time, higher education (HE) institutions are increasingly conscious of the sensitivity of league table positions on employment statistics and graduate destinations. Modules that are either credit or non-credit bearing are finding their way into the core curriculum at HE. While the UK government and other educational bodies argue the way forward over A-level reform, universities must also meet the needs of their first year cohorts in terms of the secondary to tertiary transition and developing independence in learning.

Inside the black box: unravelling the development viability appraisal process

Over the last decade issues related to the financial viability of development have become increasingly important to the English planning system. As part of a wider shift towards the compartmentalisation of planning tasks, expert consultants are required to quantify, in an attempt to rationalise, planning decisions in terms of economic ‘viability’. Often with a particular focus on planning obligations, the results of development viability modelling have emerged as a key part of the evidence base used in site-specific negotiations and in planning policy formation. Focussing on the role of clients and other stakeholders, this paper investigates how development viability is tested in practice. It draws together literature on the role of calculative practices in policy formation, client feedback and influence in real estate appraisals and stakeholder engagement and consultation in the planning literature to critically evaluate the role of clients and other interest groups in influencing the production and use of development viability appraisal models. The paper draws upon semi-structured interviews with the main producers of development viability appraisals to conclude that, whilst appraisals have the potential to be biased by client and stakeholder interests, there are important controlling influences on potential opportunistic behaviour. One such control is local authorities’ weak understanding of development viability appraisal techniques which limits their capacity to question the outputs of appraisal models. However, this also is of concern given that viability is now a central feature of the town planning system.

An experiment on energy-saving competition with socially responsible consumers: opening the black box

We present results from experimental price-setting oligopolies in which green firms undertake different levels of energy-saving investments motivated by public subsidies and demand-side advantages. We find that consumers reveal higher willingness to pay for greener sellers’ products. This observation in conjunction to the fact that greener sellers set higher prices is compatible with the use and interpretation of energy-saving behaviour as a differentiation strategy. However, sellers do not exploit the resulting advantage through sufficiently high price-cost margins, because they seem trapped into “run to stay still” competition. Regarding the use of public subsidies to energy-saving sellers we uncover an undesirable crowding-out effect of consumers’ intrinsic tendency to support green manufacturers. Namely, consumers may be less willing to support a green seller whose energy-saving strategy yields a direct financial benefit. Finally, we disentangle two alternative motivations for consumer’s attractions to pro-social firms; first, the self-interested recognition of the firm’s contribution to the public and private welfare and, second, the need to compensate a firm for the cost entailed in each pro-social action. Our results show the prevalence of the former over the latter.

Coupling an aerosol box model with one-dimensional flow: a tool for understanding observations of new particle formation events

Field observations of new particle formation and the subsequent particle growth are typically only possible at a fixed measurement location, and hence do not follow the temporal evolution of an air parcel in a Lagrangian sense. Standard analysis for determining formation and growth rates requires that the time-dependent formation rate and growth rate of the particles are spatially invariant; air parcel advection means that the observed temporal evolution of the particle size distribution at a fixed measurement location may not represent the true evolution if there are spatial variations in the formation and growth rates. Here we present a zero-dimensional aerosol box model coupled with one-dimensional atmospheric flow to describe the impact of advection on the evolution of simulated new particle formation events. Wind speed, particle formation rates and growth rates are input parameters that can vary as a function of time and location, using wind speed to connect location to time. The output simulates measurements at a fixed location; formation and growth rates of the particle mode can then be calculated from the simulated observations at a stationary point for different scenarios and be compared with the ‘true’ input parameters. Hence, we can investigate how spatial variations in the formation and growth rates of new particles would appear in observations of particle number size distributions at a fixed measurement site. We show that the particle size distribution and growth rate at a fixed location is dependent on the formation and growth parameters upwind, even if local conditions do not vary. We also show that different input parameters used may result in very similar simulated measurements. Erroneous interpretation of observations in terms of particle formation and growth rates, and the time span and areal extent of new particle formation, is possible if the spatial effects are not accounted for.