Duality Based A Posteriori Error Estimation for Quasi-Periodic Solutions Using Time Averages

We propose an a posteriori error estimation technique for the computation of average functionals of solutions for nonlinear time dependent problems based on duality techniques. The exact solution is assumed to have a periodic or quasi-periodic behavior favoring a fixed mesh strategy in time. We show how to circumvent the need of solving time dependent dual problems. The estimator consists of an averaged residual weighted by sensitivity factors coming from a stationary dual problem and an additional averaging error term coming from nonlinearities of the operator considered. In order to illustrate this technique the resulting adaptive algorithm is applied to several model problems: a linear scalar parabolic problem with known exact solution, the nonsteady Navier–Stokes equations with known exact solution, and finally to the well-known benchmark problem for Navier–Stokes (flow behind a cylinder) in order to verify the modeling assumptions

Calibrating Energy Performance Model of a Hospital Building: Dealing with Practical Issues of Data Availability and Granularity in a Case Study Building in the UK

Calibration of energy models is mathematically a highly-parameterized and under-determined problem. Hospitals are energy intensive buildings that have complex and varying specifications for their functions and operations. Calibration of energy models of hospitals is further challenging due to difficulties such as base-load estimation and end-use disaggregation of a 24-hour running facility’s measured energy use (specially end-uses such as specialist equipment and plug loads). This paper attempts to calibrate the energy model of a hospital building in the UK. Along with design stage building construction documentation, on-site observations and semi-structured stakeholder interviews, energy and Indoor Environmental Quality (IEQ) data is collected for a period of one year. A calibrated energy model is then used to quantify the effects of the observed energy performance gap issues found in the building. The energy and IEQ for the building are compared against design stage targets and industry benchmarks. The paper also reflects on practicalities of data collection such as shortcomings in metering, monitoring and observations that could be addressed for model calibration in hospitals

Towards net-zero carbon performance: using demand side management and a low carbon grid to reduce operational carbon emissions in a UK public office

This paper investigates the performance of an office building that has achieved a low carbon performance in practice thanks to a performance contract and Soft Landings approach. The findings show the potential of this building for further de-carbonisation as a result of electrification of heating and load shifting to take advantage of a low carbon electricity grid. Whilst retrospective modelling based on the past carbon intensity data shows the effectiveness of demand-side management, assessment of the existing smart readiness of the building revealed that the building services and control strategy are not fully equipped with the data analytics and carbon or price signal responsiveness required to facilitate grid integration. The environmental strategy and procurement method used for this building combined with an effective grid integration strategy can serve as a prototype for low carbon design to achieve the ever stringent carbon emissions objectives set out for the non-domestic buildings

Managing energy performance in buildings from design to operation using modelling and calibration

To manage the concerns regarding the energy performance gap in buildings, a structured and longitudinal performance assessment of buildings, covering design through to operation, is necessary. Modelling can form an integral part of this process by ensuring that a good practice design stage modelling is followed by an ongoing evaluation of operational stage performance using a robust calibration protocol. In this paper, we demonstrate, via a case study of an office building, how a good practice design stage model can be fine-tuned for operational stage using a new framework that helps validate the causes for deviations of actual performance from design intents. This paper maps the modelling based process of tracking building performance from design to operation, identifying the various types of performance gaps. Further, during the operational stage, the framework provides a systematic way to separate the effect of (i) operating conditions that are driven by the building’s actual function and occupancy as compared with the design assumptions, and (ii) the effect of potential technical issues that cause underperformance. As the identification of issues is based on energy modelling, the process requires use of advanced and well-documented simulation tools. The paper concludes with providing an outline of the software platform requirements needed to generate robust design models and their calibration for operational performance assessments. PRACTICAL APPLICATION: The paper’s findings are a useful guide for building industry professionals to manage the performance gap with appropriate accuracy through a robust methodology in an easy to use workflow. The methodological framework to analyse building energy performance in-use links best practice design stage modelling guidance with a robust operational stage investigation. It helps designers, contractors, building managers and other stakeholders with an understanding of procedures to follow to undertake an effective measurement and verification exercise

Weakly Consistent Regularisation Methods for Ill-Posed Problems

This Chapter takes its origin in the lecture notes for a 9 h course at the Institut Henri Poincaré in September 2016. The course was divided in three parts. In the first part, which is not included herein, the aim was to first recall some basic aspects of stabilised finite element methods for convection-diffusion problems. We focus entirely on the second and third parts which were dedicated to ill-posed problems and their approximation using stabilised finite element methods. First we introduce the concept of conditional stability. Then we consider the elliptic Cauchy-problem and a data assimilation problem in a unified setting and show how stabilised finite element methods may be used to derive error estimates that are consistent with the stability properties of the problem and the approximation properties of the finite element space. Finally, we extend the result to a data assimilation problem subject to the heat equation

Cross-sectoral assessment of the performance gap using calibrated building energy performance simulation

The energy performance gap in buildings is a well-known phenomenon. However, its actual definition and extent is dependent on the baseline used for defining the gap. In this paper a calibration-based methodology is used to identify and validate the root causes of the performance gap. Following analysis of the performance of four case studies in the UK, from different building sectors, cross sectoral learnings that are applicable in the wider industry context are uncovered. Through the model calibration process and in the overall performance assessment, Indoor Environmental Quality (IEQ) parameters have been used to improve the robustness of validation of the calibrated models and to highlight the interrelationship of energy and IEQ. The study shows the importance of contractual accountability to minimise performance issues, building a case for having IEQ in energy performance contracts to manage the trade-offs of IEQ against energy performance that leads to unintended health consequences for the occupants

Moving beyond energy, towards "total" performance: Managing issues in UK school buildings

The policy-driven focus, at present, is to improve the energy performance of buildings. However, energy-related issues alone do not capture the full impact of buildings on occupants and the wider environment. The performance of a building also includes occupant wellbeing and indoor environmental quality (IEQ). Specifically, for schools, there is a strong association between IEQ (temperature, ventilation rates, and indoor CO2 concentrations) with cognitive performance. Traffic-related external pollutants such as particulate matter and nitrogen dioxide are linked to adverse health impacts, especially in dense urban environments. This paper assesses the performance issues and inter-relationships between energy and IEQ in a newly-built and partly-refurbished school campus in London. Based on the evidence gathered from this case study, larger endemic issues and constraints within the construction industry are explored and lessons for improved performance in the design and operation of school buildings are highlighted