Model predictive control of non-domestic heating using genetic programming dynamic models
Introduction
Model predictive control (MPC) [1] is a powerful control methodology well-suited to systems in which there is an appreciable delay between an input being applied and any observable response, and which may also have control constraints; large (non-domestic) buildings are among such systems. Central to MPC is a predictive model of the dynamics of the system being controlled. Given a prediction horizon extending some number of discrete time steps into the future, the controller optimises the sequence of future inputs by minimising some objective function. Typically, this objective comprises a weighted sum over the prediction horizon of the deviations from a desired setpoint together with the control effort, the magnitudes of the control changes. This latter term is designed to penalise rapid switching of the input and hence minimise actuator wear. At every time step, the future input sequence is optimised, the first of this input sequence applied to the system and the whole process repeated at the next time step. This forever advancing prediction interval gives the technique its alternative name of receding horizon control.
Although MPC has been widely employed in the chemical process industries, where it had its origins, applications to buildings are currently only at the research stage — see, for example, Rockett and Hathway [2] for a review. Critical to MPC, whatever its domain of application, is the performance of the predictive model.
The generally superior climate control of MPC in buildings compared to conventional rule-based approaches appears to offer the potential for significant energy savings – maybe up to 25% [2] – and makes buildings MPC worth pursuing in order to reduce CO2 emissions and to improve internal environmental quality. However, at a round table discussion at a workshop on MPC in buildings held in Montréal in 2011, Henze [3] noted attendees estimated 70% of total costs for MPC implementation were consumed by the creation and calibration of the predictive model that lies at the heart of MPC. In fact, this figure agrees with the 75% often quoted by the wider process-control community [4]. Traditionally, such models are produced by extensive fine-tuning by highly skilled control engineers. Although the high cost of predictive model creation may be tolerable in the highly-capital intensive environment of petrochemicals, Rockett and Hathway [2] have pointed out that such high costs currently make MPC economically unviable for the control of buildings. It is, therefore, critical for the economic uptake of MPC in buildings to create predictive models of the system dynamics using machine learning-based methods that can learn from data obtained from the building in operation rather than be hand-crafted by experts. Further, the characteristics of buildings change over time, either due to changes in use, internal alterations, or indeed external factors, such as the erection/demolition of adjacent buildings that change the solar gains or façade wind pressures on the building under control. Such changes will change the dynamics of the building and necessitate a recalibration of the predictive model in order to maintain optimised control. Rapid and low-cost recalibration without human intervention is thus also essential to maximise the ongoing benefits of MPC in buildings.
Buildings are widely acknowledged to exhibit non-linear dynamics and therefore require a non-linear predictive model. For example, in the situation described in the present paper (see Section 3.2), the heat transfer from a conventional hydronic radiator to the room space is non-linear [5], [6]; the solar energy entering a building via a window was found to be non-linear function of incident radiation by Sturzenegger et al. [7]. The problem of formulating a non-linear predictive model has been discussed in a seminal paper by Sjöberg et al. [8]. Assuming sampling at discrete, equally-spaced time steps, the one-step-ahead (OSA) prediction of a dynamical system at time is given by: where is a vector of inputs, or so-called exogenous variables. The problem is to identify i) , the non-linear function, (ii) the value of dictating how many of the previous inputs need to be considered, and (iii) the value of , the number of previous (autoregressive) outputs to be included. The sets of delayed variables and are usually termed lag sets and compactly incorporate the ‘inertia’ of the controlled system. To implement MPC we generally need a model that produces a set of accurate future predictions over the so-called prediction horizon, that is, time steps into the future.
In principal, the search for in (1) is over the set of all possible functions, but in practice is often restricted to families, such as Volterra functions or neural networks [9]. Identification of the lag sets (i.e. the best combination of values of and ) is typically performed iteratively in a manner highly dependent on the expertise of a control engineer.
Neural networks (NNs) have been widely used for nonlinear dynamic system identification. In order to enhance the accuracy while minimising the model size, an architectural refinement stage is often required. For instance, NeuroEvolution of Augmenting Topologies (NEAT) [10] uses a genetic algorithm (GA) to evolve both model structure and the associated parameters of neural network models.
A further consideration with Volterra approximators and, especially, neural networks is the large number of parameters that have to be estimated during training, which implies a requirement for a large amount of training data. Moreover, with reference to (1), while training NNs can approximate the function , determining the lag sets specified by and usually requires the embedding of the NN training within some global search for the network inputs determined by , the so-called feature selection problem, i.e. a search problem embedded within another search problem.
To address the challenge specified by (1), an increasing number of researchers have applied genetic programming (GP) to nonlinear dynamic systems identification problems [11], [12] due to the advantage of being able to automatically optimise both model structure and its parameters simultaneously during evolution. Basic GP, however, has often been used to evolve the function either as a simple regression problem (i.e. without the autoregressive terms ), or using pre-defined lags sets, that is, pre-specification of and in (1).
Rodríguez-Vázquez and Fleming [13] used GP to identify a number of dynamical systems. Grosman and Lewin [11] used GP to generate an empirical dynamic model of a process, a mixing tank, and then applied it in a nonlinear model predictive control (NMPC) strategy. The results show that the GP method provided significantly better regulatory and servo performance than more traditional control approaches. Recently, Feng et al. [12] also investigated the performance of GP on non-linear dynamical systems and NMPC, and claimed that a GP based predictive controller can obtain satisfactory performance.
In the model training stage, however, Rodríguez-Vázquez and Fleming, Grosman and Lewin [11], and Feng et al. [12] employed user-specified, pre-determined lag sets, which are normally very time-consuming to determine manually in practical applications.
Hinchliffe and Willis [14] also used GP to evolve discrete-time models of dynamic processes, however, evolution of the appropriate lag set of input variables was included by adding unary back-shift (i.e. time lag) operators to the GP’s function set. The experimental results suggest that the performance of GP shows little difference with filter-based neural networks in terms of model accuracy on an extruder case study. The significant point in Hinchliffe and Willis’ [14] work is that their GP formulation is not only able to approximate model structure (), but also construct appropriate lag sets and not require their pre-specification.
Taking advantage of the fact that the Hinchliffe and Willis GP scheme is able to evolve both model structure and lag sets automatically during the evolution process, in this paper, we describe the use of genetic programming for creating the dynamic model necessary for buildings MPC. We believe this to be the first report of the demonstration of buildings MPC using learned GP models. As is common in the control field, we have considered a system simulation in order to rapidly and comprehensively explore the issues involved.
To further underscore the advance made in this paper, it is worth briefly reviewing the process currently used for constructing a grey-box predictive models of buildings. Following the much-cited paper by Hazyuk et al. [6], typically analogous resistor–capacitor (RC) linear networks comprising various numbers of R’s and C’s, each network representing the different physical elements (walls, floors, rooves, etc.), are manually assembled from expert knowledge of the building. This overall composite RC network is combined with injected heat gains from the heating system, solar radiation through windows, etc. (modelled as voltage or current sources) to produce an overall state–space model. It is important to note that the heating and solar inputs are non-linear functions of their controllable variables. For example, energy transfer from a hydronic radiator is a non-linear function of the mean water temperature in the radiator — see [6] for details. Having hand-assembled a model structure, it is necessary to identify the model’s parameter values, a task which is generally regarded as “difficult” [6, p. 385], and requires input/output response data from the building; this process is typically performed using non-linear least-squares fitting. Unfortunately, parameter identification is sometimes problematic due to unidentifiability — the inability to sufficiently accurately determine a parameter’s value due to numerical deficiencies of the model [15]. Overcoming unidentifiability requires judicious modifications to the model followed by re-estimation until the conditions for identifiability are met. At that point, the calibrated model can be validated against data from the building independent of that used for parameter calibration; if the predictive ability of the model is insufficient, the whole process is iterated until a satisfactory model structure is found. The amount of highly-skilled human intervention at every stage of this process directly motivates the automation of the construction of predictive models to render MPC economically-viable for buildings. A credible route to this automation is the principal contribution of the present paper.
In Section 2, we describe genetic programming for modelling dynamical systems and give an example for a benchmark problem from the chemical engineering literature. We describe the building control methodology we have used in Section 3 together with the procedures necessary for successfully identifying a predictive GP model of the test building. In Section 4 we report typical results of the performance of the predictive GP model as well as the performance of the model predictive control scheme. In this paper, we present only representative, typical results and defer detailed discussion of parameter settings, etc. to a future publication. We do, however, consider these issues together with future work in Section 5. We conclude the paper with Section 6.
Section snippets
Genetic programming
Inspired by biological evolution processes, evolutionary algorithms (EA) solve problems by applying the theory of natural selection to a population of individuals with the expectation of evolving fitter models. Genetic algorithms (GA) are one class of EA. Basically, a GA consists of a reproductive strategy for generating offspring with better fitness using the principal genetic operators of crossover and mutation. GP is a subset or an extension of GA. The essential principles of GA and GP are
Building control methodology
In this section, we describe the procedures employed for the MPC of buildings using predictive models obtained through a GP-based system identification. Fig. 5 depicts the components of the simulation system used in this work. We used an industry-grade simulator for building physics, described in Section 3.1, to simulate the responses of a test building. This simulator provides a standardised interface – the Functional Mockup Interface (FMI) [23] – that allows the interconnection of external
Results
In Section 4.1 we describe the results of training the GP predictive model using the open-loop system identification data produced using the procedure set-out in Section 3.3. Section 4.2 presents the control results from using the trained GP predictive models in an MPC controller to regulate the zone temperature of the building model described in Section 3.2.
Discussion and future work
As stated above, scope of this paper is to present what we believe to be the first report of buildings MPC using a predictive model learned data acquired from the building. Our aim here has been to present and document the methodology we have used although a great deal of work remains to be done both in terms of ‘fine tuning’ this, and in extending it. One area that does needs to be explicitly discussed is comparator methods. Since the GP-controller regulates the zone temperature generally
Conclusions
In this paper, we have reported the first use of genetic programming to obtain predictive models for the model predictive control (MPC) of internal building temperatures. Currently, the large-scale adoption of MPC in buildings is rendered uneconomic by the time and cost involved in the design and tuning of predictive models by expert control engineers. We have shown that GP is able to automate this process using an open-loop excitation experiment. The resulting MPC simulation is able to
CRediT authorship contribution statement
Tiantian Dou: Software, Validation, Investigation, Writing - review & editing. Yuri Kaszubowski Lopes: Methodology, Software, Validation, Writing - original draft, Investigation, Writing - review & editing, Visualization. Peter Rockett: Conceptualization, Methodology, Investigation, Writing - original draft, Writing - review & editing, Supervision, Funding acquisition. Elizabeth A. Hathway: Conceptualization, Methodology, Investigation, Writing - review & editing, Supervision, Funding
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
We gratefully acknowledge the financial support of the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/N022351/1.
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Current address: Civil & Building Services Engineering Division, School of the Built Environment and Architecture, London South Bank University, London SE1 0AA, UK.