PCR+ In Diesel Fuels and Emissions Research

LIST OF FIGURES			v
LIST OF TABLES			vii
ACRONYMS AND ABBREVIATIONS			ix
ACKNOWLEDGEMENTS			xi
EXECUTIVE SUMMARY			xiii

1	INTRODUCTION		1
	1.1	BACKGROUND	1
	1.2	BASIC TERMINOLOGY	2
	1.3	ORGANIZATION OF REPORT	3
2	METHODOLOGY AND DATA		5
	2.1	DIESEL FUEL AND EMISSIONS DATABASES	5
	2.2	EPA UNIFIED MODEL	7
3	ISSUES WITH STEPWISE REGRESSION		9
	3.1	RELATIONSHIPS AMONG FUEL PROPERTIES	9
	3.2	THE CONSEQUENCE OF CORRELATIONS	10
	3.3	THE EFFECT OF ALIASING ON REGRESSION COEFFICIENTS	12
	3.4	THE EFFECT OF ALIASING ON PREDICTIVE POWER	15
	3.5	COMMENTS ON THE EPA UNIFIED EMISSION MODELS	20
	3.6	SUMMARY	21
4	APPLICATION OF PCR+ TO DIESEL EMISSIONS		23
	4.1	STATISTICAL BACKGROUND	23
	4.2	EIGENVECTOR REPRESENTATION OF FUELS	24
	4.3	A PCR+ MODEL OF EMISSIONS	26
	4.4	DIESEL FUEL EFFECTS ON EMISSIONS	28
	4.5	PARTITIONING OF THE MODEL SUMS OF SQUARES	34
	4.6	ISSUES OF STATISTICAL BIAS	37
5	DIESEL FUEL EIGENVECTORS		39
	5.1	EIGENFUEL STRUCTURE OF COMMERCIAL DIESEL FUELS	39
	5.2	EIGENFUEL STRUCTURE OF EXPERIMENTAL FUELS	41
	5.3	DISCUSSION AND SUMMARY	45
6	USE OF EIGENFUELS IN EXPERIMENT DESIGN		47
	6.1	METHODOLOGICAL PRINCIPLES OF EXPERIMENT DESIGN	47
	6.2	DEMONSTRATION AND APPLICATION OF PRINCIPLES	48
	6.3	DISCUSSION AND SUMMARY	51
7	EIGENFUELS IN FUELS RESEARCH		53
	7.1	DESIGN OF MONTE CARLO SIMULATIONS	53
	7.2	ESTIMATING THE PROPERTIES OF ALTERNATIVE FUELS	56
8	EIGENFUELS IN FUELS REFORMULATION		59
	8.1	WHAT HAPPENS WHEN EIGENFUELS ARE CHANGED?	59
	8.2	A FRAMEWORK FOR FUEL REFORMULATION	62
9	REFERENCES		65

APPENDIX A: SUPPORTING DATA			67
APPENDIX B: THE MULTIPLICITY OF MULTIPLE REGRESSION			77
APPENDIX C: CALCULATION OF THE ALIAS MATRIX			105
APPENDIX D: PARTITIONING THE MODEL SUM OF SQUARES			113
APPENDIX E: EXPERIMENT DESIGN AND DATA ANALYSIS			129
APPENDIX F: EIGENVECTORS: THEIR ROLE IN EMISSIONS			145