David K. Ruch

A four-parameter change-point model for predicting energy consumption in commercial buildings

This paper develops a four-parameter change-point model of energy consumption as a function of dry-bulb temperature, along with accompanying error diagnostics for the models parameters. The model is a generalization of the widely used three-parameter, or variable-base degree-day method. The model is applied to data from a case study grocery store, is compared to the three-parameter PRISM CO model of the store data, and is shown to provide a statistically better fit to consumption data below about 15{degrees}C. This model appears to be useful for diagnosing unexpected energy use in some buildings and should be useful for determining retrofit energy savings from monitored pre-retrofit and post-retrofit data for the class of buildings whose pre-retrofit consumption is fit by a four-parameter linear change-point model.

Wavelet theory : an elementary approach with applications

Preface. Acknowledgments. 1 The Complex Plane and the Space L 2 (R). 1.1 Complex Numbers and Basic Operations. Problems. 1.2 The Space L 2 (R). Problems. 1.3 Inner Products. Problems. 1.4 Bases and Projections. Problems. 2 Fourier Series and Fourier Transformations. 2.1 Eulers Formula and the Complex Exponential Function. Problems. 2.2 Fourier Series. Problems. 2.3 The Fourier Transform. Problems. 2.4 Convolution and B-Splines. Problems. 3 Haar Spaces. 3.1 The Haar Space V 0 . Problems. 3.2 The General Haar Space V j . Problems. 3.3 The Haar Wavelet Space W 0 . Problems. 3.4 The General Haar Wavelet Space W j . Problems. 3.5 Decomposition and Reconstruction. Problems. 3.6 Summary. 4 The Discrete Haar Wavelet Transform and Applications. 4.1 The One-Dimensional Transformation. Problems. 4.2 The Two-Dimensional Transformation. Problems. 4.3 Edge Detection and Naive Image Compression. 5 Multiresolution Analysis. 5.1 Multiresolution Analysis. Problems. 5.2 The View from the Transform Domain. Problems. 5.3 Examples of Multiresolution Analyses. Problems. 5.4 Summary. 6 Daubechies Scaling Functions and Wavelets. 6.1 Constructing the Daubechies Scaling Functions. Problems. 6.2 The Cascade Algorithm. Problems. 6.3 Orthogonal Translates, Coding and Projections. Problems. 7 The Discrete Daubechies Transformation and Applications. 7.1 The Discrete Daubechies Wavelet Transform. Problems. 7.2 Projections and Signal and Image Compression. Problems. 7.3 Naive Image Segmentation. Problems. 8 Biorthogonal Scaling Functions and Wavelets. 8.1 A Biorthogonal Example and Duality. Problems. 8.2 Biorthogonality Conditions for Symbols and Wavelet Spaces. Problems. 8.3 Biorthogonal Spline Filter Pairs and the CDF97 Filter Pair. Problems. 8.4 Decomposition and Reconstruction. Problems. 8.5 The Discrete Biorthogonal Wavelet Transformation. Problems. 8.6 Riesz Basis Theory. Problems. 9 Wavelet Packets. 9.1 Constructing Wavelet Packet Functions. Problems. 9.2 Wavelet Packet Spaces. Problems. 9.3 The Discrete Packet Transform and Best Basis Algorithm. Problems. 9.4 The FBI Fingerprint Compression Standard. Appendix A: Huffman Coding. Problems. References. Topic Index. Author Index.

Uncertainty in Baseline Regression Modeling and in Determination of Retrofit Savings

The objective of this paper is to discuss the various sources of uncertainty inherent in the estimation of actual measured energy savings from baseline regression models, and to present pertinent statistical concepts and formulae to determine this uncertainty. Regression models of energy use in commercial buildings are not of the standard type addressed in textbooks because of the changepoint behavior of the models and the effect of patterned and non-constant variance residuals (largely as a result of changes in operating modes of the building and the HVAC system). This paper also addresses such issues as how model prediction is impacted by both improper model residuals and models identified from data periods which do not encompass the entire range of variation of both climatic conditions and the different building operating modes.

A development and comparison of NAC estimates for linear and change-point energy models for commercial buildings

Abstract The normalized annual consumption (NAC) index has proved useful in energy analysis using the PRISM model. This paper develops NAC with rigorous statistical error diagnostics for linear and four-parameter change-point energy models. The models are applied to daily data from several case study commercial/institutional buildings, and the NAC estimates are analyzed and compared. The importance of goodness-of-fit for a model toward producing an accurate NAC estimate is examined. A new statistics, NSR, designed to measure goodness-of-fit over temperature regions of long-term significance, is introduced and tested on the case study buildings.

Prediction Uncertainty of Linear Building Energy Use Models With Autocorrelated Residuals

Autocorrelated residuals from regression models of building energy use present problems when attempting to estimate retrofit energy savings and the uncertainty of the savings. This paper discusses the causes of autocorrelation in energy use models and proposes a method to deal with autocorrelation. A hybrid of ordinary least squares (OLS) and autoregressive (AR) models is developed to accurately predict energy use and give reasonable uncertainty estimates, Only linear models are considered because both the data and the physical theory for many commercial buildings support this choice (Kissock, 1993). A procedure for model selection is presented and tested on data from three commercial buildings participating in the Texas LoanSTAR program. In every case examined, the hybrid OLS-AR model provided the best estimate of energy use and the most robust estimate of uncertainty.

On Multipower Equations: Some Iterative Solutions and Applications

A generalization of McFarlands iterative scheme [12] for solving quadratic equations in Banach spaces is reported. The notion of a uniformly contractive system is introduced and subsequently employed to investigate the convergence of a new iterative method for approximating solutions to this wider class of multipower equations. Existence and uniqueness of solutions are addressed within the framework of a uniformly contractive system. To illustrate the use of the new iterative scheme, we employ it when approximating solutions to a Hammerstein equation and a Chandrashekar equation. Due to the nature of the examples, we have found that wavelet/scaling function bases are a natural choice for the implementation of our iterative method.

Completely continuous and related multilinear operators

Completely continuous multilinear operators are defined and their properties investigated. This class of operators is shown to form a closed multi-ideal. Unlike the linear case, compact multilinear operators need not be completely continuous. The completely continuous maps are shown to be the closure of a subspace of the finite rank operators. Hilbert-Schmidt operators are also considered. An application to finding error bounds for solutions of multipower equations is presented.

On uniformly contractive systems and quadratic equations in Banach space

The solution of quadratic equations using the contraction mapping principle is considered. A uniqueness result extending that given by Argyros is proved. Uniformly contractive systems theory is used to find approximate solutions and convergence criteria are given. In particular, only pointwise convergence of approximating operators is required to guarantee convergence of the approximate solutions. A theorem and algorithm for a continuation method are presented, and illustrated on Chandrasekhars equation.

Solving polynomic operator equations in ordered banach spaces

An iterative method for solving polynomic operator equations is considered. Existence and uniqueness results are proven for decreasing polynomic operators. The method is applied to a pair of integral equations, improving known results about their solutions. Another approach is then used to extend these results.