Lean Energy Analysis: Identifying, Discovering and Tracking
Energy Savings Potential
Introduction
This chapter discusses a technique for the statistical and graphical analysis of energy, weather
and production data. It is an important part of the effort to understand baseline energy use.
The technique is called lean energy analysis, LEA, because of its synergy with the principles of
lean manufacturing. In terms of lean manufacturing, “any activity that does not add value to the
product is waste”. Similarly, energy that does not add value to a product is also waste. LEA
quickly quantifies how much energy adds value to the product and facility, and how much is
waste. Thus, LEA provides direct insight to the minimum energy requirements and the steps
required to improve overall energy efficiency.
The statistical LEA models presented here disaggregate electricity and fuel use into the following
components:



Weather-dependent energy use
Production-dependent energy use
Independent energy use
This quick but accurate disaggregation of energy use:




Accurately quantifies the energy not adding value to the product or the facility
Improves calibration of energy use models with utility billing data
Focuses attention on the most promising areas for reducing energy use
Provides an accurate baseline for measuring the effectiveness of energy management
efforts over time.
Source Data
The source data for LEA models are monthly electricity use, fuel use, production and outdoor air
temperature. Altogether, only 60 data points are required to analyze one year of electricity and
fuel use. The electricity and fuel use data can be extracted from utility bills. Average
temperatures for the energy billing periods are available from many sources including the
UD/EPA Average Daily Temperature Archive, which posts average daily temperatures from 1995
to present for over 300 cities around the world (http://www.engr.udayton.edu/weather/).
Production data are carefully measured and logged by most companies. Thus, the data for LEA
are readily available.
The techniques shown here can also be applied to sub-metered or interval data. Increasing the
spatial or time resolution of the data often lends additional insight. However, the use of submetered data may not capture interaction and synergistic effects between systems. Moreover,
the use short time-interval data in place of monthly data in regression models, rarely increases
insight into the monthly energy use patterns that ultimately determine utility costs. Thus, it is
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recommended that the LEA techniques shown here be applied to monthly whole plant
production and energy use data even if sub-metered or interval data are available.
Software
The software used to develop the models is Energy Explorer (Kissock, 2000). Energy Explorer
integrates the previously laborious tasks of data processing, graphing and statistical modeling in
a user-friendly, graphical interface. The multivariable change-point models described above are
included in Energy Explorer. These models enable users to quickly and accurately determine
baseline energy use, predict future energy use, understand factors that influence energy use,
calculate retrofit savings, and identify operational and maintenance problems.
The LEA Concept
LEA uses least-square regression models to create an energy signature of plant energy use. The
resulting energy signature model represents a concise and accurate summary of energy use as a
function of primary drivers. It can be used to disaggregate energy use, identify energy saving
opportunities and as a baseline for measuring the effectiveness of energy management efforts
over time. In LEA models, fuel and electricity use are regressed against outdoor air temperature
and production data using multivariate change-point models.
A three-parameter heating multivariate (3PH-MVR) model is appropriate for plants that use fuel
for space heating and production (Equation 1). The model coefficients are weatherindependent fuel use (Fi), heating change-point temperature (Tcph), heating slope (HS) and the
fuel production coefficient (FPC). Using these coefficients, fuel use (F) can be estimated as a
function of outdoor air temperature (Toa) and production (P). The superscript + indicates that
the value of the parenthetic quantity is zero when it evaluates to a negative quantity.
F = Fi + HS (Tcph – Toa)+ + FPC P
(1)
The model allows fuel use to be disaggregated into weather-dependent, production-dependent
and independent components as shown in Figure 1.
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Fuel
Weather
Production
Independent
Temperature
Figure 1. Fuel use disaggregation using 3PH-MVR model.
Similarly, a three-parameter cooling multivariate (3PC-MVR) model is appropriate for plants that
use electricity for space cooling and production (Equation 2). The model coefficients are the
model coefficients are weather-independent electricity use (Ei), cooling change-point
temperature (Tcpc), cooling slope (CS) and electricity production coefficient (EPC). Using these
coefficients, electricity use (E) can be estimated as a function of outdoor air temperature (Toa)
and production (P). The superscript + indicates that the value of the parenthetic quantity is zero
when it evaluates to a negative quantity.
E = Ei + CS (Toa – Tcpc)+ + EPC P
(2)
The model allows electricity use to be disaggregated into weather-dependent, productiondependent and independent components as shown in Figure 2.
Electricity
Weather
Production/Sales
Independent
Temperature
Figure 2. Electricity use disaggregation using 3PC-MVR model.
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LEA Score
With proper control, energy use should vary with production and weather. For example, the run
time, and hence the electricity consumption, of electrical production machinery should increase
at high levels of production. Similarly, the run time, and hence the fuel consumption, of space
heating equipment should increase during cold weather when more heat is lost through the
building envelope. Thus, energy use that does not vary with production or weather is a target
for energy savings potential, since it is likely that the energy using equipment is not being
properly controlled. The ‘independent’ component of energy use determined by the LEA
statistical analysis quantifies this savings potential. One way to quickly understand this potential
is to calculate the ‘LEA score’ of electricity and fuel use as:
LEA score = 1 – Percent Independent
Example
Calculate the LEA score if the weather-dependent component of energy is 20%,
production-dependent component of energy is 10%, and independent component
of energy is 70%.
LEA score = 1 – 70% = 30%
This relatively low LEA score indicates significant potential for energy savings from
improved control and/or insulation.
Our analysis of LEA scores from 28 manufacturing facilities shows the following electricity and
fuel LEA scores.
Thus, electricity LEA scores were as low as 5% and as high as 95%. Fuel LEA scores ranged from
5% to 78%. The magnitude of the variation indicates widely varying levels of energy waste and
control among manufacturing plants. The mean electricity LEA scores were:
Mean Electricity LEA = 39%
Mean Fuel LEA = 58%
Thus, the average fraction of plant electricity use that does not vary with production or weather
is 61% and the average fraction of plant fuel use that does not vary with production or weather
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is 42%. These relatively low LEA scores indicate that most manufacturing plants have significant
opportunities to reduce leaks and heat loss and improve the control of energy using equipment
so that energy consumption follows load more directly.
Case Study LEA of Natural Gas Use
Figure 3 shows monthly natural gas use and average outdoor air temperature during 2002. The
graph shows that natural gas use increases during cold months and decreases during warm
months, however, some natural gas is used even during summer. Thus, outdoor air temperature
appears to have some influence on natural gas use, but does not appear to be the sole
influential variable.
Figure 3. Monthly natural gas use and outdoor air temperature.
Figure 4 shows monthly natural gas use and number of units produced during 2002. The graph
shows some correlation between production and natural gas use. For example, gas use declines
during low-production months such as July and December.
Figure 4. Monthly natural gas use and quantity of units produced.
The natural gas use and weather data are then regressed to produce an energy-signature model.
For plants that use fuel for space heating and production, the best model is a three-parameter
heating (3PH) model. In a 3PH model, the model coefficients are the weather-independent fuel
use (Fi), the heating change-point temperature (Tcph), and the heating slope (HS). Using these
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coefficients, fuel use (F) can be estimated as a function of outdoor air temperature (Toa) using
Equation 3. The superscript + indicates that the value of the parenthetic quantity is zero when it
evaluates to a negative quantity.
F = Fi + HS (Tcph – Toa)+
(3)
Figure 5 shows a three-parameter heating (3PH) change-point model of monthly natural gas use
as a function of outdoor air temperature. In Figure 10, the flat section of the model on the right
indicates temperature-independent natural gas use, Fi, when no space heating is needed. At
outdoor air temperatures below the change-point temperature, Tcph, of about 66 F, natural gas
use begins to increase with decreasing outdoor air temperature and increasing space-heating
load. The slope of the line, HS, indicates the how much additional natural gas is consumed as
the outdoor air temperature decreases. The model’s R2 of 0.92 indicates that temperature is
indeed an influential variable. The model’s CV-RMSE of 7.5% indicates that the model provides
a good fit to the data.
Figure 5. Three-parameter heating (3PH) change-point model of monthly natural gas use as a
function of outdoor air temperature.
Despite the relatively good fit of the outdoor air temperature model shown in Figure 5,
inspection of Figure 5 indicates that production also influences natural gas use. Figure 6 shows a
two-parameter model of natural gas use as a function of number of units produced. The model
shows a trend of decreasing natural gas use with production, and a very low R2 = 0.02. This
indicates that production alone is a poor indicator of natural gas use.
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Figure 6. Two-parameter model of monthly natural gas use as a function of quantity of units
produced.
Figure 7 shows the regression results of a three-parameter heating model of natural gas use as a
function of outdoor air temperature, that also includes production as an additional independent
variable, PC1. This model is called a 3PH-MVR model since it includes the capabilities of both a
three-parameter heating model of energy use versus temperature, plus a multivariableregression model (MVR). The model’s R2 of 0.97 and CV-RMSE of 5.1% are improvements over
either of the previous models that attempted to predict natural gas use using air temperature of
production independently. Thus, this model provides a very good fit to the data. In addition,
note that when combined with temperature data, the model coefficient for production (FPC =
0.0199) is now positive, indicating that gas use does indeed increase with increased production.
Figure 7. Results of three-parameter heating model of natural gas use as function of both
outdoor air temperature and production (3PH-MVR). Measured natural gas use (light squares)
and predicted natural gas use (bold squares) are plotted against outdoor air temperature.
Using the regression coefficients from Figure 7, the equation for predicting natural gas fuel use,
F, as a function of outdoor air temperature Toa and quantity of units produced, P, with a 3PHMVR model (Equation 1) is:
F = 59.58 (mcf/dy) + 9.372 (mcf/dy-F) x [62.06 (F) - Toa (F)]+ + 0.0199 (mcf/dy-unit) x P (units)
Thus, natural gas use can be broken down into the following components:
Independent fuel use = 59.58 (mcf/dy)
Weather-dependent fuel use = 9.372 (mcf/dy-F) x [62.06 (F) - Toa (F)]+
Production-dependent fuel use = 0.0199 (mcf/dy-unit) x P (units)
These coefficients can be used to calculate natural gas use by each component. Figure 8 shows
the breakdown of natural gas use using these equations. Inspection of Figure 8b shows
excellent agreement between actual natural gas use and natural gas use predicted using
Equation 1.
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300
Independent
14%
Nat Gas
(mcf/dy)
250
200
Production
150
Weather
100
Independent
Weather
28%
Production
58%
50
0
1
2
3
4
5
6
7
8
9 10 11 12
Month
Figure 8. Time trends and pie chart of disaggregated fuel use.
600
Nat Gas
(mcf/dy)
500
400
Actual
300
Predicted
200
100
0
1
2
3
4
5
6
7
8
9 10 11 12
Month
Figure 8b. Time trends of actual and predicted natural gas use.
The fuel LEA score is:
LEA score = 1 – Percent Independent = 1 – 14% = 86%
This relatively high LEA score indicates that fuel use is relatively well controlled; however, the
potential for fuel savings from improved control and/or insulation is still about 14% of fuel use.
Case Study of LEA of Electricity Use
Figure 9 shows monthly electricity use and average outdoor air temperature during 2002. The
graph shows that electricity is slightly higher during summer and early fall, when the outdoor air
temperatures are higher and air conditioning loads are greatest. In the fall, electricity use
declines steeply; however, it is unlikely that the dramatic reduction in electricity use is caused
solely by the cooler air temperatures since electricity use during the first part of the year
remained relatively high despite similarly cold temperatures. Thus, outdoor air temperature
appears to have some influence on electricity use, but does not appear to be the sole influential
variable.
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Figure 9. Monthly electricity use and average daily temperatures during 2002.
Figure 10 shows monthly electricity use and the quantity of units produced each month during
2002. The two trends appear to be relatively well correlated, frequently rising and falling in
unison. However, summer electricity use is distinctly higher than electricity use during the rest
of the year. Thus, both production and outdoor air temperature appear to significantly
influence electricity use.
Figure 10. Monthly electricity use and number of units produced during 2002.
The electricity use and weather data are then regressed to derive an energy-signature model.
For plants that use electricity for air conditioning and other purposes, the best model is a threeparameter cooling (3PC) model. In a 3PC model, the model coefficients are the weatherindependent electricity use (Ei), the cooling change-point temperature (Tcpc), and the cooling
slope (CS). Electricity use (E) can be estimated using Equation 4.
E = Ei + CS (Toa – Tcpc)+
(4)
Figure 11 shows a three-parameter cooling (3PC) change-point model of monthly electricity use
as a function of outdoor air temperature. In Figure 11, the flat section of the model on the left
indicates temperature-independent electricity use, Ei, when no air conditioning is needed. At
outdoor air temperatures above the change-point temperature, Tcpc, of about 32 F, electricity
use begins to increase with increasing outdoor air temperature and air conditioning load. The
slope of the line, CS, indicates the how much additional electricity is consumed as the outdoor
air temperature increases.
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The model’s R2 of 0.67 indicates that temperature is indeed an influential variable. CV-RMSE is
a non-dimensional measure of the scatter of data around the model. The model’s CV-RMSE of
6.4% indicates that the model provides a good fit to the data.
Figure 11. Three-parameter cooling (3PC) change-point model of monthly electricity use as a
function of outdoor air temperature.
Despite the relatively good fit of the outdoor air temperature model shown in Figure 11,
inspection of Figure 12 indicates that production also influences electricity use. Figure 12 shows
a two-parameter model of electricity use as a function of number of units produced. The model
shows a trend of increasing electricity use with increased production. However, the model R2 is
0.32, which indicates that production alone is a poor indicator of electricity use.
Figure 12. Two-parameter model of monthly electricity use as a function of quantity of units
produced.
Clearly, the best model for predicting electricity use would include both outdoor air
temperature and production. Figure 13 shows the regression results of a three-parameter
cooling model of electricity use as a function of outdoor air temperature, that also includes
production as an additional independent variable. This model is called a 3PC-MVR model since
it includes the capabilities of both a three-parameter cooling model of energy use versus
temperature, plus a multivariable-regression model (MVR). In Figure 13, the measured
electricity use (light squares) and predicted electricity use (bold squares) are plotted against
outdoor air temperature. It is seen that the measured and predicted electricity use are almost
on top of each other for each monthly temperature, which graphically indicates that the model
is a good predictor of electricity use. The model’s R2 of 0.82 and CV-RMSE of 5.1% are
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improvements over the previous models that attempted to predict natural gas use using air
temperature of production independently. In addition, the coefficient that describes electricity
use per unit of production, EPC, is now positive as expected. Thus, this model provides a very
good fit to the data.
Figure 13. Results of three-parameter cooling model of electricity use as function of both
outdoor air temperature and production. Measured electricity use (light squares) and predicted
electricity use (bold squares) are plotted against outdoor air temperature.
Using the regression coefficients from Figure 13, the equation for predicting electricity use, E, as
a function of outdoor air temperature Toa and quantity of units produced, P, with a 3PC-MVR
model (Equations 2) is:
E (kWh/dy) = 41,589 (kWh/dy) + 361.159 (kWh/dy-F) x [Toa (F) – 30.7093 (F)]+
+ 2.4665 (kWh/dy-unit) x P1 (units)
Thus, electricity use can be broken down into the following components.
Independent electricity use = 41,589 (kWh/dy)
Weather-dependent electricity use = 361.16 (kWh/dy-F) x [Toa (F) – 30.71 (F)]+
Production-dependent electricity use = 2.4665 (kWh/dy-unit) x P (units)
These coefficients can be used to estimate electricity use by each component (Figure14).
Inspection of Figure 14b indicates excellent agreement between actual electricity use and the
electricity use predicted using Equation 2.
50,000
Elec (kWh/dy)
40,000
Independent
30,000
Production
20,000
Production
39%
Weather
Independent
51%
10,000
0
1
2
3
4
5
6
7
8
9 10 11 12
Weather
10%
Month
Figure 14. Time trends and pie chart of disaggregated electricity use.
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Elec (kWh/dy)
100,000
75,000
Actual
50,000
Predicted
25,000
0
1
2
3
4
5
6
7
8
9 10 11 12
Month
Figure 14b. Time trends actual and predicted electricity use.
In an ideal plant, all electricity use would be proportional to production or devoted to space
conditioning; independent electricity use, which is unrelated to production or space
conditioning, would tend toward zero. In terms of the well-known principles of lean production,
any activity that does not directly add value to the product is waste. Seen in this light, the goal
is to reduce independent electricity use as low as possible.
The electricity LEA score for this facility is:
LEA score = 1 – Percent Independent = 1 – 51% = 49%
This LEA score indicates that the potential for electricity savings from improved control is over
half of all electricity use. Several recommendations could address the high independent
electricity use such as improved procedures to shut down equipment when it is not in
production and improving the control of the air compressors so that electricity use follows
compressed air output more directly. With diligence, even tasks that are thought to be nonproduction related such as lighting and air compression can become more related to production.
For example, turning off lights in areas where production has stopped would decrease the
fraction of independent electricity use and increase the fraction of production-dependent
electricity use. Similarly, fixing compressed air leaks would both save energy use and increase
the fraction of production-dependent electricity use.
Using LEA To Discover Savings Opportunities
LEA indicators of savings opportunities include:
•
Departure from expected shape
•
High independent energy use
•
High data scatter
Identification of these savings opportunities using LEA is demonstrated in the following
examples.
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Departure from Expected Shape
The five-parameter model of electricity as a function of outdoor air temperature shown in
Figure 15 identified a previously unknown and unnecessary air conditioning load. The air
conditioner was subsequently turned off.
Figure 15. Five-parameter model of electricity as a function of outdoor air temperature.
The two-parameter model of electricity as a function of outdoor air temperature shown in
Figure 16 identified malfunctioning economizers. The expected shape of electricity as a function
of outdoor air temperature with functioning economizers would be a 3PC model, since the
economizers should replace air conditioning electricity use during cold weather. After discussing
the issue with plant maintenance personnel, it was discovered that the economizer dampers
remained closed during winter. A highly cost-effective recommendation was made to fix the
economizers.
Figure 16. Two-parameter model of electricity as a function of outdoor air temperature. A
three-parameter model was expected if the economizers were properly functioning.
High Independent Energy Use
Figure 17 shows monthly electricity use graphed verses production. While production varies
greatly, electricity use does not. Nearly the same amount of electricity used to make 250 parts
is also used to make 25 parts. Statistically, this is shown by the very low R2 value of 0.01,
indicating that production has almost no affect on electricity use. This suggests that the major
electricity uses in the plant do not vary with production. The full LEA analysis shows that 65% of
plant electricity use does not vary with production: plant lighting (37%), air compressors (17%),
and three 60-hp dust collection systems (11%).
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Figure 17. Two-parameter model of electricity as a function of outdoor air temperature. A
three-parameter model was expected if the economizers were properly functioning.
Electricity use for all three of these systems could be varied with production. Lighting could be
controlled by motion sensors, to turn off lights in areas when not in use. The air compressor
mode of operation could be easily switched from “hand” to “load/unload” mode, allowing the
compressors to unload when compressed air is not needed. Dampers could shut off dustcollection drops when not in use, varying the amount of air collected by the system. A variablespeed drive could be installed on the dust-collector motor to allow the power draw of the dustcollector motor to vary with varying dust collection. Thus, identifying non-production
dependent energy use helped identify several energy savings opportunities.
Similarly, a low fuel LEA score, which indicates that fuel use that does not vary with production
or weather often indicates that a significant quantity of heat is continually leaking from process
equipment. Thus, low fuel LEA scores often indicate opportunities for insulation upgrades.
Figure 18. Two-parameter model of fuel as a function of production. The high fuel use at zero
production causes a low fuel LEA score and indicates the potential for significant fuel savings
from reducing heat leakage from process heating equipment.
High Data Scatter
High data scatter indicates that loads are not varying with weather or production, and/or that
the energy consumption is not varying with the loads. Alternately, low data scatter indicates
that loads vary with weather or production and energy consumption varies with load.
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For example, Figure 19 shows a three-parameter model of natural gas use as a function of
outdoor air temperature at a plant that used natural gas only for space heating. While a 3PH
model was the best regression fit, the high amount of scatter in the model is visually apparent;
during some months, heating energy use varies by a factor of three at the same outdoor air
temperature! This scatter is reflected in a CV-RMSE of 67.6%, which indicates that other factors
influence gas use in addition to outdoor temperature. Discussions with plant personnel
revealed that the shipping doors were frequently left open. Subsequent investigation showed a
strong correlation between gas use and shipping-door open time. As a result, management
installed a plastic strip doors to form a wind barrier when shipping doors were open.
Figure 19. Three-parameter model of natural gas use as a function of outdoor air temperature.
In comparison, Figure20 shows a model of natural gas use as a function of outdoor air
temperature in a well-controlled heat-treating plant. The CV-RMSE for this model is a relatively
low 5.2%. The right slope shows the variation of fuel use with outside air temperature in the
heat treat ovens, due to the variation in the temperature of the incoming product and
combustion air and air leaking through the ovens. The left slope shows the additional fuel use
required to heat the facility at very low air temperatures. Certainly fuel use could be reduced by
reducing heat loss from the facility or the quantity of air leaking through the ovens. These
measures would reduce the slopes of the lines. However, the relatively tight fits between data
points and model lines shows that loads vary with temperature and energy use varies with load.
Figure 20. Four-parameter model of natural gas use as a function of outdoor air temperature in
a well-controlled heat treating plant.
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Using LEA For Budgeting, Costing And Tracking Savings
Equations 1 and 2 model plant energy use as a function of production and outdoor air
temperature. These equations can predict future fuel and electricity use for budgeting or other
purposes. For example, if production is expected to change in the future, then future gas and
electricity use as a function of the new levels of production could be predicted. In addition, it is
relatively easy to bracket projected weather –related energy use by driving the models with
temperature data from years with above-average and below-average temperatures.
The fuel and electricity production coefficients quantify plant energy use per unit of production.
Thus, these coefficients and be used to quantify the actual cost of energy per unit. This
information is useful in determining manufacturing costs, and subsequently the selling price, of
energy-intensive products.
Equations 1 and 2 can also be used as a baseline for measuring savings from energy
conservation retrofits. To “measure” retrofit savings, compare actual electricity use from after
the retrofit to the electricity use predicted by Equations 1 and 2 when driven with the
temperatures and production data from after the retrofit.
For example, Figure 21 shows three-parameter models of natural gas use as a function of
outdoor air temperature before (upper blue line) and after (lower red line) a temperature
setback retrofit. The savings are the differences between the upper blue line, which represents
how much energy the facility would have used given the outdoor air temperatures that actually
occurred, and the lower red data points which are the actual energy use after the retrofit.
Figure 21. Three-parameter models of natural gas use as a function of outdoor air temperature
before (upper blue line) and after (lower red line) a temperature setback retrofit.
References
Haberl. J., Sreshthaputra, A., Claridge, D.E. and Kissock, J.K., 2003. “Inverse Modeling Toolkit
(1050RP): Application and Testing”, ASHRAE Transactions, Vol. 109, Part 2.
Kissock, K., Reddy, A. and Claridge, D., 1998a. "Ambient-Temperature Regression Analysis for
Estimating Retrofit Savings in Commercial Buildings", ASME Journal of Solar Energy Engineering,
Vol. 120, No. 3, pp. 168-176.
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Kissock, J.K., 2000, “Energy Explorer Data Analysis Software”, Version 1.0, Dayton, OH.
Kissock, J.K., Haberl. J. and Claridge, D.E., 2003. “Inverse Modeling Toolkit (1050RP): Numerical
Algorithms”, ASHRAE Transactions, Vol. 109, Part 2.
Kissock, J.K. and Seryak, J., 2004, “Understanding Manufacturing Energy Use Through Statistical
Analysis”, Proceedings of National Industrial Energy Technology Conference, Houston, TX, April
20-23, 2004.
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