Efficient longitudinal population survival survey sampling for the measurement and verification of lighting retrofit projects

Abstract

A method is presented for reducing the required sample sizes for reporting energy savings with predetermined statistical accuracy in lighting retrofit measurement and verification projects, where the population of retrofitted luminaires is to be tracked over time. The method uses a Dynamic Generalised Linear Model with Bayesian forecasting to account for past survey sample sizes and survey results and forecast future population decay, while quantifying estimation uncertainty. A genetic algorithm is used to optimise multiyear sampling plans, and distributions are convolved using a new method of moments technique using the Mellin transform instead of a Monte Carlo simulation. Two cases studies are investigated: single population designs, and stratified population designs, where different kinds of lights are replaced in the same retrofit study. Results show significant cost reductions and increased statistical efficiency when using the proposed Bayesian framework.

Efficient metering and surveying sampling designs in longitudinal Measurement and Verification for lighting retrofit

“…The first is population survival: establishing how many of the originally installed (retrofitted) units are still effective at a given point in time. This entails survey sampling and has been the focus of previous works [14][15][16][17][18][19][20]. The second factor is the average annual energy use per unit.…”

“…Last, the earlier method assumes that proportion of lamps surviving at a given point in time is known with certainty, and does not combine this survey sampling uncertainty 245 with the meter-sampling uncertainty. Survey sampling uncertainty was characterised in previous work [14], and will be incorporated in Section 4.…”

“…The method proposed in this paper seeks to improve on the areas above by providing a Bayesian approach to the lighting 250 retrofit monitoring problem, which has been suggested for energy monitoring as far back as 1991 [43]. This Bayesian approach extends previous work [14] from only population survival survey sampling to also include metering placement and overall M&V study design -which has not been done before 255 to our knowledge. Bayesian statistics allows for the use of information from prior meter-samples to be incorporated in a mathematically consistent manner.…”

Bayesian Energy Measurement and Verification Analysis

“…This has been done successfully for energy projects [22][23][24][25]. Prior information is also useful in longitudinal studies, where measurements or samples from previous years can be taken into account [20,21]. 12.…”

“…10. Bayesian approaches allow real-time or online updating of estimates [19][20][21]. For many other machine learning techniques, the data need to be split into testing and training sets, the model trained on the training set, and then used to predict the testing set period.…”