A Study on Several Machine Learning Methods for Estimating Cabin

Occupant Equivalent Temperature

Diana Hintea, James Brusey and Elena Gaura

Coventry University, Priory Lane, Coventry, CV1 5FB, U.K.

Keywords:

Equivalent Temperature, HVAC Control, Machine Learning, Parameter Estimation.

Abstract:

Occupant comfort oriented Heating, Ventilation and Air Conditioning (HVAC) control rises to the challenge

of delivering comfort and reducing the energy budget. Equivalent temperature represents a more accurate

predictor for thermal comfort than air temperature in the car cabin environment, as it integrates radiant heat and

airﬂow. Several machine learning methods were investigated with the purpose of estimating cabin occupant

equivalent temperature from sensors throughout the cabin, namely Multiple Linear Regression, MultiLayer

Perceptron, Multivariate Adaptive Regression Splines, Radial Basis Function Network, REPTree, K-Nearest

Neighbour and Random Forest. Experimental equivalent temperature and cabin data at 25 points was gathered

in a variety of environmental conditions. A total of 30 experimental hours were used for training and evaluating

the estimators’ performance. Most machine learning tehniques provided a Root Mean Square Error (RMSE)

between 1.51 °C and 1.85 °C, while the Radial Basis Function Network performed the worst, with an average

RMSE of 3.37 °C. The Multiple Linear Regression had an average RMSE of 1.60 °C over the eight body

part equivalent temperatures and also had the fastest processing time, enabling a straightforward real-time

implementation in a car’s engine control unit.

1 INTRODUCTION

Vehicle HVAC systems aim to ensure that passengers

are thermally comfortable. However, thermal comfort

is inﬂuenced by a large number of environmental vari-

ables and, furthermore, thermal preferences can vary

greatly between individuals due to physiological, be-

havioural and cultural factors.

Nilsson’s equivalent temperature-based model

was shown to provide the highest correlation scores

with subjective occupant comfort data in Hintea et.

al (Hintea et al., 2014). Although equivalent temper-

ature is shown to be necessary for estimating ther-

mal comfort, it cannot feasibly be measured in real-

time in a manufactured vehicle. A solution to this is

virtual sensing. Virtual sensing is applied in a vari-

ety of domains (Wenzel et al., 2007; Way and Sri-

vastava, 2006; Srivastava et al., 2005) and the idea

behind the concept of vehicular virtual thermal com-

fort sensing is that, based on data from a set of cabin

environmental sensors, readings from virtual sensors

(equivalent temperature sensors in this case) are in-

ferred. Therefore, a method that estimates occupant

body part equivalent temperatures from a minimalis-

tic set of inexpensive cabin environmental sensors is

proposed, consisting of two stages. First, using a mu-

tual information-based approach, the set of cabin en-

vironmental sensors that correlate well with the body

part equivalent temperatures is selected. Second, a

machine learning approach is applied to infer the oc-

cupant body part equivalent temperatures from the

previously selected cabin environmental sensors.

The purpose of this paper is to establish, based

on empirical data, which of seven different ma-

chine learning methods (Multiple Linear Regression

(MLR), MultiLayer Perceptron (MLP), Multivariate

Adaptive Regression Splines (MARS), Radial Ba-

sis Function Network (RBF), REPTree, K-Nearest

Neighbor (KNN) and Random Forest (RF)) is the

most suitable for cabin occupant equivalent tempera-

ture estimation based on the estimation accuracy pro-

vided and the processing time required for the estima-

tion.

The paper is structured as follows: Section 2 re-

views the machine learning techniques used for es-

timating occupant equivalent temperature. Section 3

presents the experimental data sets gathered for eval-

uation purposes, while Section 4 presents the results

obtained through training and testing of the presented

estimators and a comparison of their performance. Fi-

629

Hintea D., Brusey J. and Gaura E..

A Study on Several Machine Learning Methods for Estimating Cabin Occupant Equivalent Temperature.

DOI: 10.5220/0005573606290634

In Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2015), pages 629-634

ISBN: 978-989-758-122-9

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

nally, Section 5 concludes the paper.

2 MACHINE LEARNING

ALGORITHMS

Several machine learning methods were implemented

and evaluated for estimating equivalent temperature,

namely MLR, MLP, MARS, RBF, REPTree, KNN

and RF. They are presented in the following subsec-

tions.

2.1 Multiple Linear Regression

MLR (Draper and Smith, 1981) models the relation-

ship between a response variable (the variable we

want to provide an estimate for) and two or more ex-

planatory variables (the variables from which the es-

timate is performed) by ﬁtting a linear equation to the

observed data. MLR was implemented in Python.

2.2 Multilayer Perceptron

MLP (Haykin, 1998) is a feed-forward artiﬁcial neu-

ral network model that consists of multiple layers of

nodes and maps the input data onto an appropriate

output. The back-propagation technique is used for

training the network. The estimator was implemented

in Python using WEKA libraries.

2.3 K-Nearest Neighbour

KNN (Cover and Hart, 1967) represents an instance-

based lazy learning method considering the closest

training examples in the feature space. The method

relies in classifying an object by the majority vote

of its neighbours. The object is assigned to the most

common class amongst its k nearest neighbours, with

k being a positive (typically small) integer. In the case

of k = 1, the object is assigned to the class of the

single nearest neighbour. The estimator was imple-

mented in Python using the Orange software libraries.

2.4 Multivariate Adaptive Regression

Splines

MARS (Friedman, 1991; Hastie et al., 2009) is a

non-parametric regression technique that models non-

linearities and interactions between variables. The

basis functions, together with the model parameters

(estimated with the least squares estimation method),

are combined to predict the inputs. The estimator was

implemented in Python using the Orange software li-

braries.

2.5 Radial Basis Function Network

RBF (Haykin, 1998) is an Artiﬁcial Neural Network

that uses radial basis functions as activation functions.

A RBF network consists of inputs, a hidden layer of

basis functions and outputs. At the input of each neu-

ron, the distance between the neuron centre and the

input vector is calculated. The output of the neu-

ron is then formed by applying the basis function to

this distance. The RBF network output is formed by

a weighted sum of the neuron outputs and the unity

bias. Usually, RBF networks are complemented with

a linear part. This corresponds to additional direct

connections from the inputs to the output neuron. The

estimator was implemented in Python using WEKA

libraries.

2.6 Reduced Error Pruning Tree

REPTree (Witten and Frank, 2005; Quinlan, 1986) is

a fast decision tree learner that builds a regression tree

using information gain reduction and pruning. REP-

Tree yields a sub-optimal tree under the restriction

that a sub-tree can only be pruned if it does not con-

tain a sub-tree with a lower classiﬁcation error than it-

self. More accurate performance can be obtained at a

higher computational cost. The estimator was imple-

mented in Python using WEKA libraries. REPTree

is usually used as a classiﬁer, however it allows the

selection of numerical outputs and, therefore, be used

as an estimator.

2.7 Random Forest

RF (Breiman, 2001) is an ensemble classiﬁer that con-

sists of multiple decision trees and outputs the class

produced by the largest number of individual trees.

The estimator was implemented in Python using the

Orange software libraries.

3 EXPERIMENTAL DATA SETS

GATHERING

The test car used for the experimental data gather-

ing was a Jaguar XJ (2010 model year). The IN-

NOVA Flatman support manikin

was placed in the

front passenger seat. Throughout the experimental

trials, equivalent temperature was measured in real-

time at eight locations (corresponding to head, chest,

LumaSense Technologies The INNOVA "Flatman"

Manikin: http://www.lumasenseinc.com/EN/products/

thermal-comfort/ﬂatman/the-manikin-innova-ﬂatman.html

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630

left lower arm, right lower arm, left upper arm, right

upper arm, thigh and calf) using dry heat loss sensors

attached to the Flatman and connected to an INNOVA

thermal comfort data logger.

For the development and evaluation of the estima-

tion methods, cabin environmental parameters were

also measured, as follows:

1. Air temperature and relative humidity at six points

(head, chest and feet level of the occupants, both

on the left and right side) using type T thermo-

couples and Honeywell S&C HIH-5031 humidity

sensors

2. Solar loading at the driver sunroof using automo-

tive solar sensors.

3. Cabin air and surface temperatures at 19 cabin

points using type K thermocouples.

4. Driver centre and outboard face vent air tempera-

tures using type K thermocouples.

Three types of trials (a total of 70 individual trials)

were performed, as described below.

3.1 Variable Cabin Temperatures with

Steady State External Conditions

The trials were performed within an enclosed space,

characterised by stable ambient air temperature, in or-

der to avoid the effects of wind and sun. The sub-

jects were pre-conditioned to 22 °C in a separate

room for 20 minutes. The test car cabin was also

pre-conditioned to 22 °C. The subject entered the car

and remained in static conditions (HVAC set-point of

22 °C and air ﬂow set on medium or high as per trial)

for 10 minutes. The HVAC set-point temperature was

then increased by 1 °C every 3 minutes until it reached

28 °C.

The subject then left the car and was again pre-

conditioned to 22 °C, as was the car cabin. The sub-

ject entered the car, again remaining in static condi-

tions (HVAC set-point of 22 °C) for 10 minutes. The

HVAC set-point temperature was decreased by 1 °C

every three minutes until it reached 16 °C. This proce-

dure was performed four times per subject, with each

combination of medium and high air ﬂow and with

and without solar loading on the driver side of the car.

3.2 User Control with Steady State

External Conditions

The purpose of these trials was to gain knowledge of

Sensirion SHT75 - Digital Humidity Sensor (RH&T):

http://www.sensirion.com/en/01_humidity_sensors/

06_humidity_sensor_sht75.html

the HVAC inputs performed by the subjects in order

to reach a comfortable temperature, starting with sev-

eral pre-conditioning temperatures. These trials were

also performed with the vehicle in an enclosed space,

characterised by stable ambient air temperature and

shielded from the wind and sun. The car cabin and

the subjects were pre-conditioned to a neutral (22 °C),

hot (28 °C), or cold (16 °C) temperature for 20 min-

utes prior to the trial. The subject entered the car and

remained inside for 15 minutes, during which they

were permitted to adjust the air conditioning at will

in order to make themselves comfortable. The control

adjustments performed were logged by the observer.

These trials were performed both with and without

simulated solar loading on the driver side of the car,

with each condition tested once per subject.

3.3 User Control During Short Journeys

The trials consisted of subjects driving the test car

on private roads. The car and the subjects were pre-

conditioned to a neutral (22 °C), hot (28 °C), or cold

(16 °C) temperature. The subjects entered the car and

drove for 15 minutes, during which they were per-

mitted to adjust the air conditioning at will in order

to make themselves comfortable. The subjects were

required to turn and change speed at frequent inter-

vals in order to simulate daily driving routines. The

hot and cold tests were performed twice per subject,

while the neutral tests were performed once. The ad-

justments made to the HVAC inputs were also logged

by the observer.

4 EQUIVALENT TEMPERATURE

ESTIMATION PERFORMANCE

EVALUATION

To implement the machine learning methods the au-

thor used Python (van Rossum and Drake, 2001), the

WEKA software libraries (Hall et al., 2009) and the

open-source Orange software libraries (Demsar et al.,

2013). As a result of an empirical investigation, the

parameters corresponding to each machine learning

method were set as follows: for MLP – the number

of hidden layers is 2, the learning rate is 0.2, the mo-

mentum is 0.2 and the training time corresponds to

500 epochs; for KNN – k is 5; for MARS – the max-

imum degree of the terms in the model is 2 and the

maximum number of terms in the forward pass is 10;

for RBF – the minimum standard deviation for the

clusters is 0.1, the learning rate is 0.2 and the num-

ber of clusters for K-Means corresponds to 2 epochs;

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631

for REPTree there is no restriction on the maximum

depth, the minimum total weight of the instances in a

leaf is 2 and the number of data folds used for pruning

is 3 and for RF – the number of trees in the forest is

100.

Cross Validation (CV) was used to evaluate each

estimator’s performance on the full set of experimen-

tal data, indicating how well the algorithm gener-

alised to unseen data. Both K-fold CV (presented in

Algorithm 1) (with k = 10) and Leave One Out Cross

Validation (LOTOCV) (presented in Algorithm 2)

were applied. The author also used LOTOCV, not

just 10-fold CV, to better cope with the tendency of

autocorrelation for time series data and, also, with

the existing trial-to-trial variation. The outputs of the

estimators were compared to the original measured

equivalent temperature and Root Mean Square Error

(RMSE) was used as an accuracy measure. The esti-

mation was performed using the best two cabin sen-

sors selected as described by Hintea et. al (Hintea

et al., 2011)

Algorithm 1: K-fold Cross-Validation process.

1. The whole dataset is randomly partitioned into k

samples of equal size.

2. One sample out of the k is selected as the valida-

tion data.

3. The remaining k − 1 samples are used as training

data.

4. The process is repeated k times, with each sample

set used once as validation data.

5. The k results are averaged to provide a mean error

over the individual cross-validation processes.

Algorithm 2: Leave-One-Trial-Out-Cross-Validation pro-

cess.

1. The whole dataset is partitioned into n individual

experimental trials.

2. One trial out of the n is selected as the validation

data.

3. The remaining n − 1 trials are used as training

data.

4. The process is repeated n times, with each trial set

used once as validation data.

5. The n results are averaged to provide a mean error

over the individual cross-validation processes.

Tables 1 and 2 present the estimation errors

(RMSE) using both LOTOCV and 10-fold CV for all

seven different machine learning methods.

For KNN, the results of the evaluation show that

the RMSE varied between 1.52 °C and 2.15 °C (for

chest and head, respectively) when LOTOCV was ap-

plied and between 0.42 °C and 0.71 °C (for thigh

and head, respectively) when 10-fold CV was ap-

plied. The results of the 10-fold CV are more accurate

than the ones corresponding to LOTOCV due to over-

ﬁtting (results are not representative for unseen data)

the model.

For MARS, the RMSE varied between 1.27 °C

and 1.70 °C (for thigh and head, respectively) when

LOTOCV was applied and between 1.07 °C and

1.55 °C (for thigh and head, respectively) when 10-

fold CV was applied.

For MLP, the results of the evaluation show that

the RMSE varied between 1.40 °C and 1.87 °C (for

chest and head, respectively) when LOTOCV was ap-

plied and between 1.76 °C and 2.98 °C (for thigh and

head, respectively) when 10-fold CV was applied.

For MLR, the RMSE varied between 1.30 °C and

1.91 °C (for thigh and head, respectively) when LO-

TOCV was applied and between 1.33 °C and 1.81 °C

(for thigh and head, respectively) when 10-fold CV

was applied.

For RBF, the results of the evaluation show that

the RMSE varied between 2.93 °C and 4.47 °C (for

chest and head, respectively) when LOTOCV was ap-

plied and between 3.09 °C and 4.54 °C (for thigh

and head, respectively) when 10-fold CV was applied.

These results are worse than the ones produced by all

other learning-based approaches.

For REPTree, the RMSE varied between 1.47 °C

and 2.09 °C (for chest and head, respectively) when

LOTOCV was applied and between 0.99 °C and

1.91 °C (for calf and head, respectively) when 10-

fold CV was applied. The results of the 10-fold CV

are signiﬁcantly better than the ones corresponding to

LOTOCV because of over-ﬁtting (results are not rep-

resentative for unseen data).

For RF, the results of the evaluation show that the

RMSE varied between 0.95 °C and 1.45 °C (for thigh

and head, respectively) when LOTOCV was applied

and between 1.40 °C and 1.96 °C (for thigh and head,

respectively) when 10-fold CV was applied. The re-

sults of the 10-fold CV are signiﬁcantly better than

the ones corresponding to LOTOCV because of over-

ﬁtting (results are not representative for unseen data).

P-values were generated through paired t-tests for

each combination of models in order to establish the

signiﬁcance of these results. MLR is signiﬁcantly bet-

ter than KNN (p-value of 3.12e-023), RBF (p-value

of 5.10e-009), REPTree (p-value of 6.82e-012) and

RF (p-value of 4.89e-078). The models MLP and

MARS perform better than MLR with low conﬁdence

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Table 1: Equivalent temperature estimation results (RMSE) using Leave One Trial Out Cross Validation (LOTOCV) using

different machine learning methods.

Equivalent Temperature Estimation

Target KNN MARS MLP MLR RBF REPTree RF

Head 2.15 °C 1.70 °C 1.87 °C 1.91 °C 4.47 °C 2.09 °C 1.96 °C

Chest 1.52 °C 1.37 °C 1.40 °C 1.41 °C 2.93 °C 1.47 °C 1.42 °C

Lower arm left 2.08 °C 1.57 °C 1.56 °C 1.85 °C 3.15 °C 1.97 °C 1.79 °C

Lower arm right 1.87 °C 1.54 °C 1.59 °C 1.59 °C 3.31 °C 2.01 °C 1.78 °C

Upper arm left 1.76 °C 1.56 °C 1.48 °C 1.65 °C 3.26 °C 1.73 °C 1.67 °C

Upper arm right 2.00 °C 1.56 °C 1.74 °C 1.77 °C 3.76 °C 1.67 °C 1.78 °C

Thigh 1.58 °C 1.27 °C 1.18 °C 1.30 °C 3.01 °C 1.48 °C 1.40 °C

Calf 1.88 °C 1.49 °C 1.48 °C 1.81 °C 3.08 °C 1.82 °C 1.39 °C

Average 1.85 °C 1.51 °C 1.53 °C 1.66 °C 3.37 °C 1.78 °C 1.64 °C

Table 2: Equivalent temperature estimation results (RMSE) using 10-fold Cross Validation (10-fold CV) using different

machine learning methods.

Equivalent Temperature Estimation

Target KNN MARS MLP MLR RBF REPTree RF

Head 0.71 °C 1.55 °C 2.98 °C 1.81 °C 4.54 °C 1.91 °C 1.45 °C

Chest 0.46 °C 1.20 °C 1.87 °C 1.42 °C 3.13 °C 1.03 °C 1.06 °C

Lower arm left 0.59 °C 1.48 °C 2.23 °C 1.78 °C 3.36 °C 1.07 °C 1.20 °C

Lower arm right 0.64 °C 1.41 °C 2.25 °C 1.49 °C 3.36 °C 1.43 °C 1.23 °C

Upper arm left 0.46 °C 1.31 °C 2.08 °C 1.61 °C 3.22 °C 1.07 °C 1.12 °C

Upper arm right 0.63 °C 1.47 °C 2.62 °C 1.70 °C 3.74 °C 1.61 °C 1.25 °C

Thigh 0.42 °C 1.07 °C 1.76 °C 1.33 °C 3.09 °C 1.00 °C 0.95 °C

Calf 0.58 °C 1.31 °C 2.48 °C 1.91 °C 3.48 °C 0.99 °C 1.20 °C

Average 0.56 °C 1.35 °C 2.28 °C 1.63 °C 3.49 °C 1.26 °C 1.18 °C

Table 3: Classiﬁcation time for all equivalent temperature estimators using LOCOTV.

Method MARS MLP MLR REPTree KNN RF RBF

Classiﬁcation time (seconds) 3.06 18.16 0.23 7.45 64.34 59.11 4.12

(p-values of 0.08 and 0.09, respectively). However,

the improvement of these models over MLR is of only

0.13 °C average RMSE.

At this stage, another factor to be taken into con-

sideration is the processing time, the time required to

perform the estimation on an unseen data set. This is

an important factor to consider prior to integrating the

estimation method within a control unit. Table 3 pro-

vides a summary of the processing time required by

the machine learning approaches.

MLR provided the fastest processing time, of

0.23 seconds, outperforming all other methods (sig-

niﬁcance: p-value of 2e-021 when combined with any

of the other models). The MLR processing time was,

therefore, the fastest for each individual trial. The

classiﬁcation time for MLR was lower than for all

other estimation techniques, while the estimation er-

ror obtained was outperformed by two models, the

MLP and MARS. The improvement in accuracy of

the latter two methods is not signiﬁcant, therefore the

MLR approach is concluded to be the most suitable

estimation approach.

5 CONCLUSIONS

This paper studied several machine learning methods

for estimating cabin occupant equivalent temperature

from a minimalistic set of inexpensive cabin envi-

ronmental sensors. Seven different machine learning

approaches were implemented and evaluated: Multi-

ple Linear Regression (MLR), MultipleLayer Percep-

tron (MLP), K-Nearest Nighbour (KNN), Multivari-

ate Adaptive Regression Splines (MARS), Radial Ba-

sis Function Network (RBF), REPTree and Random

Forest (RF).

Most learning tehniques provided a RMSE be-

tween 1.51 °C (for MARS) and 1.85 °C (for KNN).

RBF performed the worst, with an average RMSE of

3.37 °C. MLR had an average RMSE of 1.60 °C over

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the eight body part equivalent temperatures. MLR

outperformed all other estimation techniques with re-

gard to fast processing time (of 0.23 seconds). These

two factors combined would enable a straightforward

real-time implementation in a car’s engine control

unit in comparison to the other machine learning tech-

niques evaluated.

ACKNOWLEDGEMENTS

The Low Carbon Vehicle Technology Project

(LCVTP) was a collaborative research project be-

tween leading automotive companies and research

partners, revolutionising the way vehicles are pow-

ered and manufactured. The project partners included

Jaguar Land Rover, Tata Motors European Techni-

cal Centre, Ricardo, MIRA LTD., Zytek, WMG and

Coventry University. The project included 15 au-

tomotive technology development work-streams that

will deliver technological and socio-economic out-

puts that will beneﬁt the West Midlands Region. The

£19 million project was funded by Advantage West

Midlands (AWM) and the European Regional Devel-

opment Fund (ERDF).

The authors would like to thank the anonymous

reviewers for their insightful comments.

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