Afrooz Ebadat

Estimation of building occupancy levels through environmental signals deconvolution

We address the problem of estimating the occupancy levels in rooms using the information available in standard HVAC systems. Instead of employing dedicated devices, we exploit the significant statistical correlations between the occupancy levels and the CO2 concentration, room temperature, and ventilation actuation signals in order to identify a dynamic model. The building occupancy estimation problem is formulated as a regularized deconvolution problem, where the estimated occupancy is the input that, when injected into the identified model, best explains the currently measured CO2 levels. Since occupancy levels are piecewise constant, the zero norm of occupancy is plugged into the cost function to penalize non-piecewise constant inputs. The problem then is seen as a particular case of fused-lasso estimator by relaxing the zero norm into the ℓ1 norm. We propose both online and offline estimators; the latter is shown to perform favorably compared to other data-based building occupancy estimators. Results on a real testbed show that the MSE of the proposed scheme, trained on a one-week-long dataset, is half the MSE of equivalent Neural Network (NN) or Support Vector Machine (SVM) estimation strategies.

Regularized Deconvolution-Based Approaches for Estimating Room Occupancies

We address the problem of estimating the number of people in a room using information available in standard HVAC systems. We propose an estimation scheme based on two phases. In the first phase, we assume the availability of pilot data and identify a model for the dynamic relations occurring between occupancy levels, CO2 concentration and room temperature. In the second phase, we make use of the identified model to formulate the occupancy estimation task as a deconvolution problem. In particular, we aim at obtaining an estimated occupancy pattern by trading off between adherence to the current measurements and regularity of the pattern. To achieve this goal, we employ a special instance of the so-called fused lasso estimator, which promotes piecewise constant estimates by including an ℓ1 norm-dependent term in the associated cost function. We extend the proposed estimator to include different sources of information, such as actuation of the ventilation system and door opening/closing events. We also provide conditions under which the occupancy estimator provides correct estimates within a guaranteed probability. We test the estimator running experiments on a real testbed, in order to compare it with other occupancy estimation techniques and assess the value of having additional information sources. Note to Practitioners - Home automation systems benefit from automatic recognition of human presence in the built environment. Since dedicated hardware is costly, it may be preferable to detect occupancy with software-based systems which do not require the installation of additional devices. The object of this study is the reconstruction of occupancy patterns in a room using measurements of concentration, temperature, fresh air inflow, and door opening/closing events. All these signals are information sources often available in HVAC systems of modern buildings and homes. We assess the value of such information sources in terms of their relevance in detecting occupancy in small and medium-sized rooms. The proposed estimation scheme is composed of two distinct phases. The first is a training phase where the goal is to derive a mathematical model relating the number of occupants with the concentration. It is required to record the actual occupants in the room for a time period spanning few days, a task that can be performed either with manual logging or with temporary dedicated hardware counting systems. In a second phase, we use the derived model to design an online software which collects measurements of the environmental signals and provides the number of people currently in the room. The estimated occupancy levels can then be employed to enhance the efficiency of the HVAC system of the building. We notice that, in modern residential buildings composed by structurally equal flats, the training phase can be run in one flat only, since the obtained model will be reasonably valid for the other flats.

Application set approximation in optimal input design for model predictive control

This contribution considers one central aspect of experiment design in system identification, namely application set approximation. When a control design is based on an estimated model, the achievable performance is related to the quality of the estimate. The degradation in control performance due to plant-modeling missmatch is quantified by an application cost function. A convex approximation of the set of models that satisfy the control specification is typically required in optimal input design. The standard approach is to use a quadratic approximation of the application cost function, where the main computational effort is to find the corresponding Hessian matrix. Our main contribution is an alternative approach for this problem, which uses the structure of the underlying optimal control problem to considerably reduce the computations needed to find the application set. This technique allows the use of applications oriented input design for MPC on much more complex plants. The approach is numerically evaluated on a distillation control problem.

Blind identification strategies for room occupancy estimation

We propose and test on real data a two-tier estimation strategy for inferring occupancy levels from measurements of CO2 concentration and temperature levels. The first tier is a blind identification step, based either on a frequentist Maximum Likelihood method, implemented using non-linear optimization, or on a Bayesian marginal likelihood method, implemented using a dedicated Expectation-Maximization algorithm. The second tier resolves the ambiguity of the unknown multiplicative factor, and returns the final estimate of the occupancy levels. The overall procedure addresses some practical issues of existing occupancy estimation strategies. More specifically, first it does not require the installation of special hardware, since it uses measurements that are typically available in many buildings. Second, it does not require apriori knowledge on the physical parameters of the building, since it performs system identification steps. Third, it does not require pilot data containing measured real occupancy patterns (i.e., physically counting people for some periods, a typically expensive and time consuming step), since the identification steps are blind.

An application-oriented approach to dual control with excitation for closed-loop identification

Identification of systems operating in closed loop is an important problem in industrial applications, where model-based control is used to an increasing extent. For model-based controllers, plant changes over time eventually result in a mismatch between the dynamics of any initial model in the controller and the actual plant dynamics. When the mismatch becomes too large, control performance suffers and it becomes necessary to re-identify the plant to restore performance. Often the available data are not informative enough when the identification is performed in closed loop and extra excitation needs to be injected. This paper considers the problem of generating such excitation with the least possible disruption to the normal operations of the plant. The methods explicitly take time domain constraints into account. The formulation leads to optimal control problems which are in general very difficult optimization problems. Computationally tractable solutions based on Markov decision processes and model predictive control are presented. The performance of the suggested algorithms is illustrated in two simulation examples comparing the novel methods and algorithms available in the literature.

Multi-room occupancy estimation through adaptive gray-box models

We consider the problem of estimating the occupancy level in buildings using indirect information such as CO2 concentrations and ventilation levels. We assume that one of the rooms is temporarily equipped with a device measuring the occupancy. Using the collected data, we identify a gray-box model whose parameters carry information about the structural characteristics of the room. Exploiting the knowledge of the same type of structural characteristics of the other rooms in the building, we adjust the gray-box model to capture the CO2 dynamics of the other rooms. Then the occupancy estimators are designed using a regularized deconvolution approach which aims at estimating the occupancy pattern that best explains the observed CO2 dynamics. We evaluate the proposed scheme through extensive simulation using a commercial software tool, IDA-ICE, for dynamic building simulation.

the KTH open testbed for smart HVAC control

To facilitate the assessment of the feasibility, opportunities and weaknesses of advanced Heating, Ventilation and Air Conditioning (HVAC) control schemes we propose the remotely accessible KTH open testbed for smart HVAC control. This testbed allows researchers from all over the world to test estimators and controllers on a real facility, and aims to become a benchmark for the evaluation of the effectiveness of the control schemes proposed in the literature. This demo describes the testbed through a series of videos and Graphical User Interfaces (GUIs), and illustrates the potentialities and limitations of the remotely accessible hardware.

Applications Oriented Input Design in Time-Domain Through Cyclic Methods

In this paper we propose a method for applications oriented input design for linear systems in open-loop under time-domain constraints on the amplitude of input and output signals. The method guara ...

Input Signal Generation for Constrained Multiple-Input Multple-Output Systems

In this paper we extend a recent method for generating an input signal with a desired auto-correlation function while satisfying both input and output constraints for the system it is to be applied ...

Applications oriented input design for closed-loop system identification: a graph-theory approach

A new approach to experimental design for identification of closed-loop models is presented. The method considers the design of an experiment by minimizing experimental cost, subject to probabilistic bounds on the input and output signals, and quality constraints on the identified model. The input and output bounds are common in many industrial processes due to physical limitations of actuators. The aforementioned constraints make the problem non-convex. By assuming that the experiment is a realization of a stationary process with finite memory and finite alphabet, we use results from graph-theory to relax the problem. The key feature of this approach is that the problem becomes convex even for non-linear feedback systems. A numerical example shows that the proposed technique is an attractive alternative for closed-loop system identification.