A cost effective approach to handle measurement and verification sampling and modelling uncertainties

Abstract

In this study, a measurement and verification (M&V) cost minimisation model is proposed to deal with both the M&V modelling and sampling uncertainties. In order to find the optimal solutions in terms of the modelling accuracy level, and the sample size, the M&V cost that includes the modelling cost, sampling cost, and overhead cost is formulated as the objective function, in which the modelling cost is developed as a function of the modelling accuracy in terms of the coefficient of variation of the room mean square error (CV(RMSE)), and the sampling cost, which is directly related to the sample size. In order to illustrate the effectiveness of the proposed model, an optimal M&V modelling and sampling strategy is designed for a traffic intersection lamp retrofit project. In addition, partial optimal M&V plans designed with optimal sampling but non-optimal modelling solutions, or with optimal modelling but non-optimal sampling solutions are employed as the benchmark. Comparisons between the optimal and non-optimal solutions show advantageous cost savings performance in the execution of sampling and modelling activities for the case study. More precisely, the optimal solutions reduce the sampling cost by 55% and the total M&V cost by 14% against the solutions obtained by optimal modelling but non-optimal sampling solutions. To test the applicability and flexibility of the proposed model for the cost-effective design of similar traffic light retrofit projects, simulations have been carried out to evaluate the model performance when applying the model to M&V projects with different characteristics. The simulation results show that the proposed model is able to offer flexible trade-offs between the modelling and sampling uncertainties; namely, using more accurate baseline models and smaller sample sizes or less accurate baseline models but greater sample sizes to accommodate different practical needs in executing M&V projects with different characteristics. The major contributions of this study can be highlighted as follows: 1) a M&V modelling cost model is developed, which is able to offer a quantitative analysis of the M&V baseline model uncertainty and cost; and, 2) a M&V cost minimisation model is proposed to handle both the M&V modelling and sampling uncertainties cost-effectively. The effectiveness and flexibility of this model are demonstrated by a case study and simulations.