Ref. N Ndark Nbright adark bdark abright bbright pˆcomf Eˆcomf E50,dark E50,bright
3 243 16 3 5.907 -1.253 -10.91 6.653·10−3 0.927 976 111.7 1640
4 244 6 5 16.036 -3.252 -261.068 75.11·10−3 0.999 3282 138.6 3476
6 578 51 2 14.305 -2.662 -7.556 1.413·10−3 0.990 1634 215.8 5348
10 263 14 27 -0.013 -0.388 -2.613 1.623·10−3 0.808 250 1.0 1610
11 384 29 22 1.556 -0.633 -3.327 0.302·10−3 0.905 1608 11.7 11008
16 415 81 43 9.581 -1.816 -4.414 1.424·10−3 0.906 1068 195.8 3100
26 313 30 5 3.698 -0.842 -4.270 0.602·10−3 0.895 1990 80.9 7088
30 410 45 54 7.542 -1.437 -3.756 2.123·10−3 0.787 764 190.4 1769
All 6851 538 433 2.515 -0.750 -3.207 0.627·10−3 0.869 1044 28.5 5116
Table 6.8: Occupant speci c summary of visual comfort probability: total number of answers, number of discomfort answers, logistic regression parameters for discomfort prob-abilities, maximum tted comfort probability, comfort illuminance and characteristic illu-minances for discomfort
However, when less adequate lighting is used, the eect of increased discomfort from ar-ti cial lighting noticed by Laurentin et al. [140] could possibly be modelled by adaptive decrements generated by the absence of daylight.
6.5.3 Individual behaviours
We applied similar criteria to select individual occupants in order to study their speci c probabilities of discomfort, based on the statistical signi cance of their speci cities. Un-fortunately in this case, a much smaller number of individual datasets (just eight) meet our selection requirements from the point of view achieving an acceptable quality of t.
The comfort probabilities for our nine retained occupants are presented in Figure 6.19, for whom the regression parameters are presented in Table 6.8.
Occupants clearly report with very similar probabilities that their environment is un-comfortably dark; which contrasts with signi cant variability with respect to the percep-tion of being uncomfortably bright, some of them being comfortable at high illuminances (Ref. 4, 6, 11, 26 and 38, like many other discarded occupants) while other are more sen-sitive to glare (Ref. 3, 10, 16 and 30), which causes an increase in pbright at intermediate values of Ein.
6.6 Linking actions and comfort
We have studied in detail the probability of action on windows (Chapter 4) and shading devices (Chapter 5), the probability of thermal and visual comfort and the factors in uenc-ing comfort temperature. In this section, we show how these concepts are inter-related in a general formulation of human adaptive actions as a response to environmental discomfort.
In Section 6.6.1 we show how discomfort leads to action, while we discuss in Section 6.6.2 the feedback to perceived comfort in response to occupants' actions.
6.6.1 A general formulation of human adaptive actions
The notion of action inertia. Figure 6.20(a) shows the probability of thermal discom-fort deduced from pcomf together with the probability of actions on windows at arrival and
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Figure 6.19: Fitted visual comfort probabilities (black lines) and discomfort probabili-ties (blue and red lines) with t standard errors (dashed lines), observed proportions of comfortable votes with their binomial 95% con dence intervals and box plots of reported comfortable illuminances
6.6. LINKING ACTIONS AND COMFORT 137
(a) Thermal discomfort probability with probabili-ties of action on windows
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(b) Visual discomfort probability with probabilities of action on blinds
Figure 6.20: Comparing discomfort and action probabilities
during presence10, as derived in Chapter 4. These curves appear to follow a common trend, although the tted action probabilities are lower than the comfort probabilities.
From the observation that as discomfort probability increases, so does action proba-bility, we may hypothesise that discomfort causes action, and we may regard the oset between the two as an inertia towards action, a concept proposed by Robinson [69]. We may de ne this action inertia through some formulation of the discrepancy between action probability and discomfort probability, which can be expressed for example as:
I(θin) = pdiscomf(θin)
pact(θin) . (6.17)
This temperature-dependent estimate of inertia is rather complex, but it is both informative and oers a direct link between discomfort and action, as we directly obtain pact(θin) = (1/I(θin)) · pdiscomf(θin).
Action inertia with respect to thermal comfort. In the case of actions on windows, this inertia is dierent between arrival (lower) and during presence, which corresponds to the observed higher reactivity in this special case. Figure 6.21(a) shows that as pdiscomf(θin) increases the action inertia decreases which is an expected result, while it reaches a maxi-mum around θin= 26◦C.
The intermediate probability of closing actions is based on outdoor temperature, which undermines the meaning of action inertia, as it implies two dierent variables; so we con-sider this no further. We do not study the action inertia for the case of actions on departure, as they are based on predictive rationale rather than on a reaction to recently experienced thermal discomfort.
10For the purposes of this analysis, we consider actions probabilities based on the single most in uential variable: θinfor P01,arr, P10,arrand P01,int, and θoutfor P10,int.
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Indoor temperature(°C) pdiscomfpact
Openings on arrival Openings during presence Closings on arrival
(a) Temperature-dependent inertia for actions on windows
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Indoor illuminance (lx) pdiscomfpact
Lowering on arrival Lowering during presence Raising on arrival Raising during presence
(b) Illuminance-dependent inertia for actions on blinds
Figure 6.21: Behaviour of the stimulus-dependent action inertia, shown on a logarithmic scale
We notice in Figure 6.21(a) that the behaviour of action inertia is very similar between actions on arrival and during presence, with higher values in this latter case; consistent with observed behaviours. Action inertia reaches a maximum at a temperature close to 26◦C, above which it decreases, corresponding to a higher reactivity to discomfort as temperature rises.
Action inertia with respect to visual comfort. A similar reasoning can be applied to study the link between visual comfort and actions on blinds. Figure 6.20(b) shows the probability of visual discomfort with the probabilities of actions on blinds (derived in Chapter 5, using Ein as the sole predictor).
It is noticeable that occupants display signi cant inertia in relatively dark conditions, when they are able to switch on electric lighting to counteract visual discomfort. Therefore, a comprehensive estimation of inertia towards visual stimuli needs also to account for actions on lights. This behaviour may also be caused by the relatively low rate of change of illuminance, as the sky darkens relatively gradually.
We observe a regular decrease of inertia as the illuminance rises (Figure 6.21(b)). It is striking that there is almost continuity between inertia towards dark and bright stimuli when the dominant contribution changes. If switch-on probabilities for lighting were avail-able, we could expect to obtain a strong decrease in action inertia for low illuminances, as for pdark.
6.6.2 Comfort feedback of adaptive actions
We have observed that adaptive actions lead to a shift in comfort temperature that allows occupants to feel comfortable in hotter or colder conditions than would be the case if no action was exercised. In order to account for this phenomenon, we can de ne an
adaptation-6.6. LINKING ACTIONS AND COMFORT 139
22 24 26 28 30 32 34
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Indoor temperature (°C)
Adaptation−corrected temperature (°C)
Without adaptation Partial clothing
Part. clothing, window, fan Full adaptation
Figure 6.22: Adaptation-corrected versus actual indoor temperature for four dierent cases of available adaptive opportunities
corrected temperature θad:
θad = θin− ˜θ(θin) = θin−X
i
p(θin) · βi, (6.18)
where ˜θ(θin) is the adaptive correction de ned from the empirical adaptive increments βi
and p(θin), the probabilities for the controls to be used.
With this de nition, we can study the variation of θad (the perceived temperature accounting for adaptive actions) as θin increases. We observe in Figure 6.22 for example that the dierence between θadand θinincreases for higher temperatures, which corresponds to a higher probability of performing adaptive actions11 and therefore to a bene t from the associated adaptive increments. It is worth noting that some actions considered for the calculation of θad (like the use of a fan or changing the clothing level) alter the temperature at which one is neutral, without altering the actual temperature; while others, such as opening a window, chie y alter the room temperature itself. For this latter case, the deduced increment already accounts both for this physical eect and the non-physical eects dealt with in the previous case.
The four presented curves correspond to dierent available adaptive opportunities. In the case of no possible adaptation, θinand θadcoincide. When actions on windows, fans and clothing are possible, the dierence between adaptation-corrected and actual temperature becomes signi cant; for instance when θin = 28◦C the occupant perceives a temperature θad of 26.5◦C.
11The probability for fans to be switched on is deduced from the expression published by Haldi and Robinson [74]. The derivation of ordinal probabilities for clothing levels is provided in Appendix A.
Environment
Figure 6.23: A proposal for a new perspective to understand the interactions between the environment, occupant comfort and adaptive actions
This estimation of the eect of control actions on thermal comfort enables a more rigor-ous estimation of the acceptable conditions in naturally-ventilated buildings. Furthermore this analysis underlines the positive impact of unconstrained adaptation on occupant com-fort and on target indoor temperatures, which can be set higher or lower provided that occupants have adequate freedom to use windows, fans and to adapt their clothing levels.
This quanti cation of the eects of adaptive actions on occupants' comfort partly
con- rms our preliminary hypothesis (Section 1.2). However, the separation of physical, phys-iological and psychological feedback in this eect remains to be studied.
Finally, our data preclude an examination of the impact of performed actions on sub-sequent actions (the probability of which may depend on feedback from prior actions);
but based on our results, we suggest that θad accounts for this eect, and that subsequent action probabilities should take θad instead of θin as an input variable to account for the feedback from prior actions. This assertion needs con rmation following further detailed measurements. Our analysis of actions on windows and shading devices did not isolate any signi cant interaction between these latter, however various adaptive actions linked to thermal comfort (windows, fans, clothing) are expected to be connected.