ASHRAE G2 10:2010 Edition

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ASHRAE Guideline 2-2010 Engineering Analysis of Experimental Data

Published By	Publication Date	Number of Pages
ASHRAE	2010	30

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4	ForEwOrd ForEwOrd 1. Purpose 1. Purpose 2. Scope 2. Scope 3. Definitions 3. Definitions
5	4. Types of Measurements 4. Types of Measurements 4.1 Types of Measurements. Measurements are categorized as either primary measurements or derived measurements. 4.1 Types of Measurements. Measurements are categorized as either primary measurements or derived measurements. 4.2 Categories of Data. There are two primary categories of data: type and sample. 4.2 Categories of Data. There are two primary categories of data: type and sample. 5. The Experimental Process 5. The Experimental Process 5.1 The intent of this section is to provide a general overview of the relationship between equipment selection, data analysis, and reporting of results obtained from engineering experiments. A well-planned experiment requires that the experimental e… 5.1 The intent of this section is to provide a general overview of the relationship between equipment selection, data analysis, and reporting of results obtained from engineering experiments. A well-planned experiment requires that the experimental e… 5.2 Identify Experimental Goals and Acceptable Accuracy 5.2 Identify Experimental Goals and Acceptable Accuracy 5.3 Identify Variables and Relationships 5.3 Identify Variables and Relationships
6	5.4 Establish Measured Variables and Limits 5.4 Establish Measured Variables and Limits 5.5 Select Preliminary Instrumentation 5.5 Select Preliminary Instrumentation 5.6 Document Uncertainty of Each Measured Variable 5.6 Document Uncertainty of Each Measured Variable 5.7 Perform Preliminary Uncertainty Analysis 5.7 Perform Preliminary Uncertainty Analysis 5.8 Final Instrument Selection and Methods 5.8 Final Instrument Selection and Methods 5.9 Install Instrumentation 5.9 Install Instrumentation
7	5.10 Perform Initial Data Quality Verification 5.10 Perform Initial Data Quality Verification 5.11 Collect Data 5.11 Collect Data 5.12 Accomplish Data Reduction and Analysis 5.12 Accomplish Data Reduction and Analysis 5.13 Perform Final Uncertainty Analysis 5.13 Perform Final Uncertainty Analysis 5.14 Report Results 5.14 Report Results
8	5.15 Other Considerations 5.15 Other Considerations 6. Uncertainty Analysis Methods and Techniques 6. Uncertainty Analysis Methods and Techniques 6.1 The intent of this section is to provide an overview of the steps needed to perform an uncertainty analysis. Details on completing an uncertainty analysis are included in Informative Annex A, with examples included in Informative Annex B. 6.1 The intent of this section is to provide an overview of the steps needed to perform an uncertainty analysis. Details on completing an uncertainty analysis are included in Informative Annex A, with examples included in Informative Annex B. 6.2 Preliminary Uncertainty Analysis 6.2 Preliminary Uncertainty Analysis 6.3 Final Uncertainty Analysis 6.3 Final Uncertainty Analysis 7. Data Validation 7. Data Validation 7.1 Data validation involves processes undertaken to ensure that both individual data and ensembles of data are reasonable and accurate. An important component of analyzing engineering experimental data is the process of validating both raw and proce… 7.1 Data validation involves processes undertaken to ensure that both individual data and ensembles of data are reasonable and accurate. An important component of analyzing engineering experimental data is the process of validating both raw and proce…
9	7.2 Limit Checks. Fortunately, many of the measurements made in conjunction with HVAC&R systems have identifiable limits. Limits are useful in a number of experimental phases such as establishing a basis for appropriate instrumentation and measuremen… 7.2 Limit Checks. Fortunately, many of the measurements made in conjunction with HVAC&R systems have identifiable limits. Limits are useful in a number of experimental phases such as establishing a basis for appropriate instrumentation and measuremen…
10	7.3 Independent Checks (Mass and Energy Balances). In a number of cases, independent checks can be used as a method to establish viability of data. Examples of independent checks include comparison of measured (or calculated) values with those of oth… 7.3 Independent Checks (Mass and Energy Balances). In a number of cases, independent checks can be used as a method to establish viability of data. Examples of independent checks include comparison of measured (or calculated) values with those of oth… 7.4 Checks on Outliers. The nature and complexity of making experimental measurements can occasionally lead to observations quite different from expected values. A number of different terms have been used to describe such observations or data points,… 7.4 Checks on Outliers. The nature and complexity of making experimental measurements can occasionally lead to observations quite different from expected values. A number of different terms have been used to describe such observations or data points,… Figure 7-1 Stationary data set including an outlier at a part- load ratio of 40%. Figure 7-1 Stationary data set including an outlier at a part- load ratio of 40%. Figure 7-2 Time-dependent data set with single outlier near hour 14 (2 p.m.). Figure 7-2 Time-dependent data set with single outlier near hour 14 (2 p.m.). 7.5 Chauvenet’s Criterion for Rejecting Data Points. A statistics-based method that can be used as a basis for rejecting outliers is Chauvenet’s criterion. Chauvenet’s criterion states that a suspect data point or reading can be rejected if the p… 7.5 Chauvenet’s Criterion for Rejecting Data Points. A statistics-based method that can be used as a basis for rejecting outliers is Chauvenet’s criterion. Chauvenet’s criterion states that a suspect data point or reading can be rejected if the p…
11	8. REGRESSION ANALYSIS 8. REGRESSION ANALYSIS 8.1 Overview 8.1 Overview 8.2 Regression Model Development 8.2 Regression Model Development
12	8.3 Types of Models 8.3 Types of Models
13	Figure 8-1 Example of heat transfer data. Figure 8-1 Example of heat transfer data. Figure 8-2 Example of heat transfer data including first-order curve fit for all data in the flow rate range from 10 to 50 L/s (159 to 793 gpm). Figure 8-2 Example of heat transfer data including first-order curve fit for all data in the flow rate range from 10 to 50 L/s (159 to 793 gpm). Figure 8-3 Example of heat transfer data including second-order curve fit for all data in the flow rate range from 10 to 100 L/s (159 to 1590 gpm). Figure 8-3 Example of heat transfer data including second-order curve fit for all data in the flow rate range from 10 to 100 L/s (159 to 1590 gpm).
14	8.4 Model Selection. Section 8.3 provided an introduction to the types of regression models that are commonly used as well as general guidance to formulation of a regression-based model. There are a number of formal procedures available to methodical… 8.4 Model Selection. Section 8.3 provided an introduction to the types of regression models that are commonly used as well as general guidance to formulation of a regression-based model. There are a number of formal procedures available to methodical…
15	8.5 Model Diagnostics 8.5 Model Diagnostics Figure 8-4 Overall or histogram plot of the residuals that resulted from the quadratic curve fit shown in Figure 8-3. Figure 8-4 Overall or histogram plot of the residuals that resulted from the quadratic curve fit shown in Figure 8-3. Figure 8-5 Residuals plotted in order of observation. Figure 8-5 Residuals plotted in order of observation.
16	Figure 8-6a Residuals exhibitng acceptable behavior. Figure 8-6a Residuals exhibitng acceptable behavior. 9. REFERENCES 9. REFERENCES INFORmative ANNEX A—UNCERTAINTY ANALYSIS/ PROPAGATION OF ERROR INFORmative ANNEX A—UNCERTAINTY ANALYSIS/ PROPAGATION OF ERROR A.1 Need for Uncertainty Analysis. Any measurement exhibits some difference between the measured value and the true value, and therefore has an associated uncertainty. A statement of measured value without an accompanying uncertainty statement has li… A.1 Need for Uncertainty Analysis. Any measurement exhibits some difference between the measured value and the true value, and therefore has an associated uncertainty. A statement of measured value without an accompanying uncertainty statement has li…
17	A.2 Basic Uncertainty Concepts: Random and Fixed Errors. The degree of inaccuracy of a measurement is quantified using Equation A-1: A.2 Basic Uncertainty Concepts: Random and Fixed Errors. The degree of inaccuracy of a measurement is quantified using Equation A-1: A.3 Uncertainty of a Measured Variable A.3 Uncertainty of a Measured Variable
18	A.4 Propagation of Errors of Single-Sample Data A.4 Propagation of Errors of Single-Sample Data
20	A.5 Errors Associated with Regression Analysis. There are three separate sources of uncertainty when using observed data to develop a predictive model. Consider a model such as the following: y = a0 + a1 x1 + a2 x2, where the x’s are the predictor … A.5 Errors Associated with Regression Analysis. There are three separate sources of uncertainty when using observed data to develop a predictive model. Consider a model such as the following: y = a0 + a1 x1 + a2 x2, where the x’s are the predictor …
21	A.6 References A.6 References
22	informative Annex B— HVAC&R SYSTEM Examples informative Annex B— HVAC&R SYSTEM Examples B.1 Individual Measurement Uncertainty Calculation B.1 Individual Measurement Uncertainty Calculation B.2 Propagation of Error in Heat Transfer B.2 Propagation of Error in Heat Transfer B.3 Propagation of Error in Power Measurement B.3 Propagation of Error in Power Measurement
23	B.4 Propagation of Error for the Coefficient of Performance of a Chiller B.4 Propagation of Error for the Coefficient of Performance of a Chiller
24	B.5 Propagation of Error in a Mass Balance B.5 Propagation of Error in a Mass Balance Figure B-1 Preliminary uncertainty analysis of chiller COP. Figure B-1 Preliminary uncertainty analysis of chiller COP. Figure B-2 Illustration of a mixing valve. Figure B-2 Illustration of a mixing valve. B.6 Propagation of Error in an Energy Balance B.6 Propagation of Error in an Energy Balance Figure B-3 Illustration of a simple heat exchanger. Figure B-3 Illustration of a simple heat exchanger.
26	Figure B-4 “Measured” hot-side and cold-side heat exchanger loads in kW, including respective uncertainties as a range. Figure B-4 “Measured” hot-side and cold-side heat exchanger loads in kW, including respective uncertainties as a range. INFORMATIVE Annex C— Reporting of Results INFORMATIVE Annex C— Reporting of Results
27	Figure C-1 Thermal resistance vs. mean temperature for a 10.16-cm-thick layer of expanded polystyrene foam. Figure C-1 Thermal resistance vs. mean temperature for a 10.16-cm-thick layer of expanded polystyrene foam.
28	INFORMATIVE annex d— bibliography INFORMATIVE annex d— bibliography