改进使模型训练数据稳定，但是造成污染前后训练结果差别不大
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Modeling and Optimization of Complex Building
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Energy Systems with Deep Neural Networks
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Yize Chen, Yuanyuan Shi and Baosen Zhang∗
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Department of Electrical Engineering, University of Washington, Seattle, WA, USA
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{yizechen, yyshi, zhangbao}@uw.edu
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arXiv:1711.02278v1 [math.OC] 7 Nov 2017 Abstract—Modern buildings encompass complex dynamics of of building systems. While in [8], [9], reinforcement learning
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multiple electrical, mechanical, and control systems. One of the was proposed to learn control policies without any explicit
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biggest hurdles in applying conventional model-based optimiza- modeling assumptions, but computational costs for searching
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tion and control methods to building energy management is through large state and action spaces is hight. Ill-defined
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the huge cost and effort of capturing diverse and temporally reward functions (e.g., sparse, noisy and delayed rewards)
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correlated dynamics. Here we propose an alternative approach could also prevent reinforcement learning algorithm finding
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which is model-free and data-driven. By utilizing high volume of the optimal control solutions [10]. Furthermore, large com-
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data coming from advanced sensors, we train a deep Recurrent mercial buildings may have quality of service constraints that
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Neural Networks (RNN) which could accurately represent the op- prevent the deep exploration of some states in reinforcement
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eration’s temporal dynamics of building complexes. The trained learning.
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network is then directly fitted into a constrained optimization
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problem with finite horizons. By reformulating the constrained (a). RNN Fitting Building Deep Recurrent Neural Network
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optimization as an unconstrained optimization problem, we use Running Pt = fRNN ( Xt − T,..., Xt)
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iterative gradient descents method with momentum to find P t-n
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optimal control inputs. Simulation results demonstrate proposed Pro<72>ile X t P t-n+1
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method’s improved performances over model-based approach on
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both building system modeling and control. RNN T ( X t , H t ) Energy
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Consumption
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Index Terms—Building energy management, deep learning,
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gradient algorithms, HVAC systems Pt
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I. INTRODUCTION
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According to a recent United Nations Environment Pro- P t+n-1
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gramme (UNEP) report, buildings are responsible for 40% of
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the global energy consumption [1]. Consequently, managing Xt c P t+n
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the energy consumption of buildings has significant econom- OriginalControl Inputs
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ical, social, and environmental impacts, and has received RNN T ( X t , H t )
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much attention from researchers. Many approaches have been (b). Inputs Optimization
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proposed to control building systems (e.g., commercial and Constrained Optimization on Xtc
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office buildings, data centers) for energy efficiency, such as
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nonlinear adaptive control, Model Predictive Control (MPC) Pt*
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and decentralized control for building heating, ventilation, Optimal Control Inputs
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and air conditioning (HVAC) systems [2], [3], [4]. However,
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most previous research on building energy management are X c*
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either based on the detailed physics model of buildings [5] or t
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simplified RC circuit models [2], [3], [6]. The former often
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involves tedious and complex modeling processes with a huge Fig. 1. Our model architecture for building energy system modeling
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number of variables and parameters, whereas the latter cannot and optimization based on a deep Recurrent Neural Networks (RNN).
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fully capture the long term dynamics of large commercial
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buildings. In this work, we address these challenges by proposing
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a data-driven method which closes the loop for accurate
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With the advance of sensing, communication and com- predictive model and real-time control. The method is based
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puting, detailed operation data are being collected for many on deep recurrent neural networks that leverage rich volumes
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buildings. These data along with future weather forecasts can of sensor data [11]. Though neural network has previously
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be utilized for data-driven real-time optimization approaches. been adopted as an approach for designing controllers, the lack
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In [7], the authors developed a data predictive control method of large datasets and computation capabilities have prevented
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to replace the traditional MPC controller by using data to it from being deployed in real-time applications [12]. Firstly
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build a regression tree that represent the dynamical model in a supervised learning manner, our Recurrent Neural Net-
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for a building. However, regression trees still results in a works (RNN) firstly learns the complex temporal dynamics
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linear model that can be far away from the true dynamics mapping from various measurements of building operation
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profiles to energy consumption. Next we formulate an op-
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timization problem with the objective of minimizing build-
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ing energy consumption, which is subject to RNN-modeled model with known parameters representing building’s physical
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building dynamics as well as physical constraints over a finite dynamics. f (·) maps past T timestep’s running profile to
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horizon of time. To solve the constrained optimization problem energy consumption at timestep t.
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in a block-splitting approach, we take iterative gradient descent
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steps on the set of controllable inputs (e.g., zone temperature With a model f (·) representing the building dynamics, we
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setpoints, heat rejected/added into each zone) at the current formulate an optimal finite-horizon predictive control prob-
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timestep. It thus finds the control inputs for each timestep. lem, and propose an efficient algorithm to find the group of
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Fig. 1 illustrates our model framework. Our approach does optimal control inputs Xct∗. At timestep t, the control input
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not need analysis on complex interactions within conduction, Xct minimizes the energy consumption of the building for
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convection or radiation processes. In addition, it can be easily future T steps. Meanwhile, previous T steps’ control inputs
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scaled up to large buildings and distributed algorithms. would affect current energy consumption. The objective of
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the controller is to minimize the energy consumption with a
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The main contributions of our paper are: rolling horizon T , while maintaining some variables within
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comfortable intervals. Mathematically, we formulate the gen-
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• We model the building energy dynamics using recurrent eral control problem as
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neural networks, which leverages large volumes of data
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to represent the complex dynamics of buildings. T
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• We propose an input/output optimization algorithm which minimize Pt2+τ (1a)
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efficiently find the optimal control inputs for the model
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represented by RNN. Xtc ,...,Xct+T τ =0
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• The proposed modeling and optimization approaches subject to Pt+τ = f (Xt−T +τ , ..., Xt+τ ), ∀τ (1b)
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open door to the integration of complex system dynamics
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modeling and decision-making. Xtc+τ ≤ Xtc+τ ≤ Xtc+τ , ∀τ (1c)
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The contents of the paper are as follows. The rolling horizon Xut+c τ ≤ Xtu+c τ ≤ Xtu+c τ , ∀τ (1d)
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control problem formulation and model-based method are
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firstly presented in Section. II. In Section. III we show the Xtu+c τ = h(Xt−T +τ , ..., Xt−1+τ , Xct+τ , Xtp+hyτ ),
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design of a deep RNN which models the dynamics of complex
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building systems. We then reformulate the control problem ∀τ
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as an unconstrained optimization problem, and propose the
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algorithm to find optimal control inputs in Section. IV. Fi- (1e)
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nally, simulation results on large building HVAC system are
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evaluated and compared with model-based control method in where (1b) h(·) denotes the rolling horizon predictive model;
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Section. V. (1c) and (1d) are the constraints on controllable and uncontrol-
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lable variables respectively; the h(·) in (1e) denotes a rolling
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horizon predictive function for uncontrollable variables based
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on past T steps’ observations as well as current step control
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inputs and physical forecasts.
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II. PROBLEM FORMULATION & PRELIMINARIES B. First-Order Thermal Dynamic Model
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A. Problem Formulation
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We consider a building energy system which includes sev- For building HVAC system, one popular method used in
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finite-horizon MPC to model the thermal dynamics is the
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eral subsystems and zones with potentially complex interac- reduced Resistance-Capacitance (RC) model [2], [3], [6]. Here
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we use a rolling horizon MPC controller as a benchmark for
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tions between them. No information about the exact system comparison.
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dynamics is known. At time t, we are provided with the Denote N (i) as the neighboring zones for zone i, the first-
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building’s running profile Xt := [Xut c, Xtc, Xtphy]T , where order RC model modeling HVAC dynamics is formulated as
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Xut c denotes a collection of uncontrollable measurements such
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as zone temperature measurements, system node temperature
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measurements, lighting schedule, in-room appliances schedule, CiT˙i,t = To,t − Ti,t + Tj,t − Ti,t + Pi,t (2)
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room occupancies and etc; and Xtc denotes a collection of Ri Rij
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j∈N (i)
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controllable measurements such as zone temperature setpoints,
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appliances working schedule and etc; Xtphy denotes the set of where Ci, Ti are the thermal capacitance and room temperature
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for each zone i, while To is the outside dry bulb temperature,
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physical measurements or forecasts values, such as dry bulb and Ri, Rij are the thermal resistance for zone i against the
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outside and the neighboring zone j. The schematic of RC
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temperature, humidity and radiation volume. There are some
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network for modeling HVAC system is shown in Fig. 2.
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physical constraints on some of Xtc and Xut c, for example
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the temperature setpoints as well as real measurements should Once we find Ci, Ri, Rij for all the zones, we have a 1st-
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order system to model the thermal dynamics. Since Ti ∈
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not fall out of users’ comfort regions. Without loss of gen- Xuc, To ∈ Xphy, by reformulating (2) and taking a sum of
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Xct and Pi for all zones, we reformulate and write the building overall
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erality, we denote the constraints as Xct ≤ Xtc ≤ a group thermal dynamics
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Xtuc ≤ Xtuc ≤ Xut c. Building System operators have
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of past running profile X = {Xt} along with the collection
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of energy consumption metering at each time step P = {Pt}.
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We are interested in firstly learning a model
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f (Xt−T , ..., Xt) = Pt, where f (·) denotes the predictive Pt = fRC (Xt−T , ..., Xt) (3)
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Tj Ci
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Qradiation Rij
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Ti
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Ri
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To
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Ci
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Pi
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Fig. 2. RC network with thermal exchange between different comp.
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which is further used in the optimal control problem defined
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in (1a)-(1e). MPC for building HVAC system under different
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model settings has been implemented in [2], [3]. We focus
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on the performance comparison of RC model to our proposed
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method in both model fitting and optimization tasks.
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III. RECURRENT NEURAL NETWORKS Fig. 3. A graphical model illustrating the RNN which is used for
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modeling T -length input-output sequential data. θh,t, θo,t, θx,t are
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Since the 1st-order thermal dynamic model defined in (2) the neural weights associated with hidden states ht+1, output oˆt, and
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does not either capture complicated nonlinear dynamics, nor input xt respectively.
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model the long-term temporal dependencies of building HVAC
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system, the deep RNN model becomes a good replacement. to be the set of neurons used in modeling the T -length
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temporal data, and wrap up all neural-composed functions of
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RNN is a class of artificial neural networks specially de- {f , f } θx,t,θo,t θh,t,θx,t to get the overall function fRNN , which
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signed for sequential data modeling. Unlike fully-connected utilizes θ to find the output predictions with length T time-
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neural networks where inputs are fed into the neural networks series input:
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as a full vector, RNN feeds input sequentially into a neural
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network with directed connections. It uses its internal memory oˆT = fRNN (x0, ..., xT ) (6)
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to process time-series inputs. In Fig. 3 we show the structure
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of an RNN model. We set up the RNN model and initialize neuron weights θ
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by sampling from a normal distribution. During batch-training
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We specifically design the RNN model to solve a time- process, with a group of sequential input xt, t = 0, ..., T ,
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dependent regression problem. That is to say, we want RNN oˆT is firstly computed, and by doing back-propagation using
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automatically learn the relationship between sequential input stochastic gradient descent (SGD) with respect to all neu-
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xt, t = 0, , ..., T and output oT . At timestep t, RNN is rons [13], θ is optimized to minimize the regression loss
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provided with hidden state vector ht and input vector xt, defined in mean-square-error (MSE) form:
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and outputs its computation vector oˆt. The t-step RNN cell
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is composed of three group of neurons, θx,t, θh,t, θo,t. They Ltraining(θ) = ||oˆT − oT ||22, (7a)
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are associated with input, hidden state and output respectively,
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and are organized in function f , f θx,t, θo,t θh,t,θx,t to complete θ∗ = arg min Ltraining(θ) (7b)
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the following computations:
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oˆt = fθx,t,θo,t (xt, ht), (4a) We then set up a length-T RNN accordingly for our
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ht+1 = fθh,t,θx,t (xt, ht) (4b) building dynamics modeling problem. With the training sets
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of input vectors of historical building operating profiles
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where oˆt is the RNN’s prediction output, while ht+1 is {Xt−T , ..., Xt} and an output energy consumption Pt, our
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passed into next neuron group and takes part in t + 1 step’s RNN model fRNN is trained to represent the system dynamics
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computation.
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Pˆt = fRNN (Xt−T , ..., Xt) (8)
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After concatenating all the neurons cells from 0 to T , we
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get the chain function to compute ht. Thus the RNN compute Our RNN is totally data-driven, and can process and repre-
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the final prediction value oˆT : sent temporal dependencies. With a rich volume of historical
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building operating data X and P provided as the training
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oˆT = fθx,T , θo,T (xT , hT ) (5) datasets, we train a deep RNN, which accurately models the
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nonlinear, complex temporal dynamics of building system. We
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Since ht captures information from past inputs xt−1, we will show in Section V that our deep RNN model outperforms
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trace hidden states back into functions of previous steps’ RC model in fitting the dynamics of a large-scale building
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hidden states and inputs. Thus final output oˆT is eventually HVAC system.
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a function of the sequential inputs xt, t = 0, ..., T . For
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simplicity, let’s denote θ = {θh,t, θo,t, θx,t}, t = 0, ..., T
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IV. INPUTS OPTIMIZATION FOR BUILDING CONTROL of controllable inputs for the finite horizon optimal control
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problem at timestep t.
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In this section we describe our control algorithm which is
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based on our pre-trained deep learning model. We demonstrate The k-step gradient descent method is working as follows:
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how it is able to incorporate (8) into the optimization problem
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(1). We also illustrate how to solve such optimization problem gt+τ,k = η∇Xtc+τ,k Lopti(Xct,k−1, ..., Xtc+T,k−1) (11a)
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to find a collection of optimal control sequential inputs. Xtc+τ,k = Xtc+τ,k−1 − gt+τ,k, τ = 0, ..., T (11b)
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By substituting f (·) in (1) with fRNN , and denote Xvt ar = where η is the learning rate, and Xtc+τ,k denotes the value for
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[Xct , Xtuc],the finite horizon control problem for building en- Xtc+τ after k step’s update.
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ergy management is written as
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Throughout our modeling and optimization approach, we do
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T not make any physical model assumptions, and directly utilize
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a deep RNN to extract the model dynamics as well as finding
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minimize Pt2+τ (9a) the optimal actions to take at each time step to cut down energy
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consumption. We summarize the proposed method in Algo-
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Xtc ,...,Xtc+T τ =0 rithm 1, which closes the loop for building dynamics modeling
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and control inputs optimization. In our implementation, we
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subject to Pt+τ = fRNN (Xt−T +τ , ..., Xt+τ ), ∀τ (9b) improve the algorithm performance by adding momentum to
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gradient descents (MomentumGD), which is shown to get
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Xtv+arτ ≤ Xvt+arτ ≤ Xvt+arτ , ∀τ (9c) over some local minima during optimization iterations as well
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as accelerating the convergence [14]. The MomentumGD is
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Xtu+c τ = h(Xt−T +τ , ..., Xt−1+τ , Xct+τ , Xtp+hyτ ), realized as follows:
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∀τ
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(9d)
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Since Xtu+cτ , τ = 1, ..., T is directly controlled by control in- gt+τ,k = γgt,k−1 + η∇Xtc+τ,k Lopti(Xct,k−1, ..., Xct+T,k−1)
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puts of previous time. For all the uncontrollable variables with (12a)
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constraints we model, they also possess pairing controllable
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variables, e.g., the temperature measurements-temperature set- Xtc+τ,k = Xct+τ,k−1 − gt+τ,k, τ = 0, ..., T (12b)
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points. We then choose Xtu+cτ = Xtc−1+τ , τ = 1, ..., T , since
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such uncontrollable values are the control outputs correspond- where γ is a momentum term determining how much previous
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ing to the previous step’s control inputs. Thus we diminish gradients are incorporated into current step’s update.
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constraint (9d).
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Algorithm 1 Input Optimization for Building Control
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Since the constrained optimization problem (9) includes a
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non-convex deep neural network in the constraints, we use log Input: Pre-trained RNN fRNN , learning rate η, momentum
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barriers functions to rewrite the problem in an unconstrained
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form: γ, input optimization iterations Niter
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min Lopti(Xct , ..., Xtc+T ) = Input: Control window-size T
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Input: Sensor measurements Xut c, weather forecasts Xtphy
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Xtc ,...,Xtc+T Initialize: Xt, ..., Xt+T
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Initialize: Optimal control inputs Xt∗ ← ∅
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T
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for iteration= 0, ..., Niter do
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fR2 NN (Xt−T +τ , ..., Xt+τ ) Update Xct using gradient descent:
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for τ = 0, ..., T do
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τ =0 gt+τ ← ∇Xct+τ Lopti(Xct , ..., Xtc+T )
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Xct+τ ← Xtc+τ − η · M omentumGD(Xct+τ , gt+τ , γ)
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T (10) end for
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Update Xut c using gradient descent:
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− λ log(Xtv+arτ − Xtv+arτ ) for τ = 0, ..., T do
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Xut+c τ = Xtc+τ −1
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τ =0 end for
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T end for
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X∗t .insert(Xct )
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− λ log(Xtv+arτ − Xtv+arτ )
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τ =0
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where λ is a tuning parameter, and Lopti(Xtc, ..., Xct+T ) V. CASE STUDY
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defines a loss function with inputs Xct , ..., Xct+T . We solve
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this loss minimization problem by iteratively taking gradient In this section, we set up a realistic model in standard
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building simulation software EnergyPlus [15]. We demonstrate
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descents of (10). Note that during RNN model training, we the effectiveness of our data-driven approach for both system
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dynamics modeling and building energy management. In order
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are taking gradients ∇θLtraining(θ) with respect to all the
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neurons. Once training is done, Ltraining(θ) is converged.
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The RNN model serves as the temporal physical model, and
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is always modeling the building system dynamics accurately.
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Here we are taking gradients with this fixed, pre-trained RNN
|
||||||
|
model, and find gradients ∇Xct+τ Lopti(Xct , ..., Xtc+T ), τ =
|
||||||
|
0, ..., T with respect to the group of controllable variables.
|
||||||
|
Once Lopti(Xtc, ..., Xct+T ) is converged, and we find Xct∗
|
||||||
|
that is a local optimal solution. Xtc∗ is also the solution
|
||||||
|
to compare with the model-based approach, we focus on the RNN model is able to fit noon values given past 4 hours’
|
||||||
|
HVAC system for a large building complex. But our method input measurements. Moreover, RC model performs poorly on
|
||||||
|
is a general regression and optimization approach, which weekend regression task, which hardly represents the HVAC
|
||||||
|
could be easily applied to overall building energy management dynamics. This inaccurate model would make subsequent
|
||||||
|
problem. MPC algorithm fail to operate on correct model space.
|
||||||
|
|
||||||
|
A. Experimental Setup 9 × 108
|
||||||
|
We set up our EnergyPlus simulations using a 12-storey
|
||||||
|
8 Measurements RC RNN
|
||||||
|
large office building (in Fig. 4) listed in the commercial
|
||||||
|
reference buildings from U.S. Department of Energy (DoE Energy Consumption [J] 7
|
||||||
|
CRB) [16]. The building has a total floor area of 498, 584
|
||||||
|
square feet which is divided into 16 separate zones. We 6
|
||||||
|
simulate the building running through the year of 2004 in
|
||||||
|
Seattle, WA, and record (Xt, Pt) with a resolution of 10 5
|
||||||
|
minutes. We shuffle and separate 2 months’ data as our
|
||||||
|
stand-alone testing dataset for both regression and control 4
|
||||||
|
performance evaluation, while the remaining 10 months’ data
|
||||||
|
is used to for RNN training. The processed datasets have 55 3
|
||||||
|
input features, which include controllable variables such as
|
||||||
|
zone temperature setpoints, and uncontrollable variables such 2
|
||||||
|
as zone occupancies and temperature measurements. Output
|
||||||
|
is a single feature for energy consumption at each timestep. 1
|
||||||
|
We directly use historical weather data records into both RC
|
||||||
|
model and RNN model. For future work, the forecasts model 0
|
||||||
|
should also be considered into the pipeline. A finite horizon
|
||||||
|
of 4 hours is set for both MPC method and proposed method. Days
|
||||||
|
|
||||||
|
We set up our deep learning model using Tensorflow, a Fig. 5. Comparison of building’s real energy consumption measure-
|
||||||
|
Python open-source package. Our RNN model is composed of ments(real), Recurrent Neural Networks’ predicted energy consump-
|
||||||
|
1 recurrent layer with 3 subsequent fully-connected layers. We tion (blue) and RC model prediction (green) on a week of testing
|
||||||
|
adopt rectified linear unit (ReLU) activation functions, dropout data.
|
||||||
|
layers and Stochastic Gradient Descent (SGD) optimizer to
|
||||||
|
improve our neural network training. Next we show the constrained optimization problem for-
|
||||||
|
mulated in (10) is efficient in finding optimal inputs Xct for
|
||||||
|
Fig. 4. Schematic diagram of simulated large commercial building. the HVAC system. In Fig. 6 we show a group of 3 plots cor-
|
||||||
|
responding to different zone temperature setpoint constraints.
|
||||||
|
B. Simulation Results We keep setpoint constraints the same for all the 16 zones.
|
||||||
|
We first compare the model fitting performance for 1st order Compare the results of Xct ∈[18°C,26°C] and the results of
|
||||||
|
Xct ∈[19°C,24°C], we observe that our approach is able to
|
||||||
|
model and RNN model, and the fitting result for two weeks’ find sharper control inputs with less energy consumption when
|
||||||
|
energy consumption is shown in Fig. 5. To quantitatively constraint intervals are bigger. When there is no constraint
|
||||||
|
compare the model fitting error, we calculate the Root-Mean- on temperature, our approach simply finds extreme control
|
||||||
|
Square-Error (RMSE) value for normalized energy consump- inputs such that the energy consumption is nearly same as the
|
||||||
|
tion on test dataset. RMSE for the first-order RC model midnight consumption.
|
||||||
|
is 0.240. The RNN model improves RC model by 68.33%
|
||||||
|
with an RMSE of 0.076. It is also interesting to notice that We then compare the optimization performance for RC
|
||||||
|
this large office building actually has an energy consumption model and RNN model. Fig. 7 illustrates a Monday-Friday
|
||||||
|
dropdown on weekdays’ noon due to the occupancy schedule. energy consumption profile with temperature setpoint con-
|
||||||
|
RC model fails to capture this dynamic characteristics, while straints Xtc ∈[18°C,26°C]. By using RNN model and taking
|
||||||
|
the gradient steps, we find a sequence of control inputs that
|
||||||
|
could reduce 30.74% of energy consumption. On the other
|
||||||
|
hand, the solution found by RC model only gives us a 4.07%
|
||||||
|
reduction of energy consumption. This furthur illustrates that
|
||||||
|
RC model is not good at modeling large-scale building system
|
||||||
|
dynamics.
|
||||||
|
|
||||||
|
Fig. 8 demonstrates how our proposed approach is able to
|
||||||
|
find a group of control inputs for the building system globally.
|
||||||
|
All of four zones’ setpoint schedule exhibit daily patterns.
|
||||||
|
Yet they are set to different values and evolution patterns.
|
||||||
|
These setpoint schedule can provide to building operators, and
|
||||||
|
it remains to be examined in real buildings if such optimized
|
||||||
|
schedules could benefit the complex system as a whole.
|
||||||
|
Energy Consumption [J]9x 108 Measurements Temperature [C] Temperature [C]
|
||||||
|
8 L19H24
|
||||||
|
7 L18H26
|
||||||
|
6 Unconstrained
|
||||||
|
|
||||||
|
5 basement bottom_core
|
||||||
|
top_core top_sub4
|
||||||
|
4
|
||||||
|
|
||||||
|
3 Temperature [C] Temperature [C]
|
||||||
|
|
||||||
|
2
|
||||||
|
|
||||||
|
1
|
||||||
|
|
||||||
|
0 0 6 Time o1f2the day(h) 18 24
|
||||||
|
|
||||||
|
Fig. 6. Effects of constraints interval on optimization performance.
|
||||||
|
|
||||||
|
9x 108 Measurements RC-Opti RNN-Opti Fig. 8. One week temperature setpoint profile for 4 different zones
|
||||||
|
8 of the office building.
|
||||||
|
|
||||||
|
Energy Consumption [J] 7 [3] X. Zhang, W. Shi, B. Yan, A. Malkawi, and N. Li, “Decentralized
|
||||||
|
and distributed temperature control via hvac systems in energy efficient
|
||||||
|
6 buildings,” arXiv preprint arXiv:1702.03308, 2017.
|
||||||
|
|
||||||
|
5 [4] Y. Shi, B. Xu, B. Zhang, and D. Wang, “Leveraging energy storage to
|
||||||
|
optimize data center electricity cost in emerging power markets,” arXiv
|
||||||
|
4 preprint arXiv:1606.01536, 2016.
|
||||||
|
|
||||||
|
3 [5] M. Trcˇka and J. L. Hensen, “Overview of hvac system simulation,”
|
||||||
|
Automation in Construction, vol. 19, no. 2, pp. 93–99, 2010.
|
||||||
|
2
|
||||||
|
[6] Y. Ma, F. Borrelli, B. Hencey, A. Packard, and S. Bortoff, “Model pre-
|
||||||
|
1 dictive control of thermal energy storage in building cooling systems,”
|
||||||
|
in Decision and Control, 2009 held jointly with the 2009 28th Chinese
|
||||||
|
0 Mon Tue Wed Thu Fri Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE
|
||||||
|
Conference on. IEEE, 2009, pp. 392–397.
|
||||||
|
Days
|
||||||
|
[7] A. Jain, M. Behl, and R. Mangharam, “Data predictive control for
|
||||||
|
Fig. 7. Comparison of optimization results of RC model (green) and building energy management,” in BuildSys, 2017.
|
||||||
|
RNN model (blue) with respect to original measurements (red).
|
||||||
|
[8] L. Yang, Z. Nagy, P. Goffin, and A. Schlueter, “Reinforcement learning
|
||||||
|
VI. CONCLUSION for optimal control of low exergy buildings,” Applied Energy, vol. 156,
|
||||||
|
pp. 577–586, 2015.
|
||||||
|
In this work, we are exploiting Recurrent Neural Networks’
|
||||||
|
ability of learning complex temporal interactions among high- [9] T. Wei, Y. Wang, and Q. Zhu, “Deep reinforcement learning for building
|
||||||
|
dimensional building dynamics. Our proposed method consists hvac control,” in The Design and Automation Conference, 2017.
|
||||||
|
Recurrent Neural Networks regression and sequence opti-
|
||||||
|
mization steps, which could both be solved efficiently. Our [10] V. Mnih, K. Kavukcuoglu, D. Silver, A. Graves, I. Antonoglou, D. Wier-
|
||||||
|
proposed approach is easily to be deployed for any building stra, and M. Riedmiller, “Playing atari with deep reinforcement learn-
|
||||||
|
unit provided with rich historical running data. Simulation ing,” arXiv preprint arXiv:1312.5602, 2013.
|
||||||
|
results show that our method outperforms existing ones both
|
||||||
|
in capturing the thermal dynamics of the building as well as [11] K.-i. Funahashi and Y. Nakamura, “Approximation of dynamical systems
|
||||||
|
providing effective control solutions. by continuous time recurrent neural networks,” Neural networks, vol. 6,
|
||||||
|
no. 6, pp. 801–806, 1993.
|
||||||
|
REFERENCES
|
||||||
|
[12] D. H. Nguyen and B. Widrow, “Neural networks for self-learning control
|
||||||
|
[1] C.-C. Cheng, S. Pouffary, N. Svenningsen, and J. M. Callaway, “The systems,” IEEE Control systems magazine, vol. 10, no. 3, pp. 18–23,
|
||||||
|
kyoto protocol, the clean development mechanism and the building and 1990.
|
||||||
|
construction sector: A report for the unep sustainable buildings and
|
||||||
|
construction initiative,” 2008. [13] L. Bottou, “Large-scale machine learning with stochastic gradient de-
|
||||||
|
scent,” in Proceedings of COMPSTAT’2010. Springer, 2010, pp. 177–
|
||||||
|
[2] Y. Ma, A. Kelman, A. Daly, and F. Borrelli, “Predictive control for 186.
|
||||||
|
energy efficient buildings with thermal storage: Modeling, stimulation,
|
||||||
|
and experiments,” IEEE Control Systems, vol. 32, no. 1, pp. 44–64, [14] I. Sutskever, J. Martens, G. Dahl, and G. Hinton, “On the importance
|
||||||
|
2012. of initialization and momentum in deep learning,” in International
|
||||||
|
conference on machine learning, 2013, pp. 1139–1147.
|
||||||
|
|
||||||
|
[15] D. B. Crawley, L. K. Lawrie, F. C. Winkelmann, W. F. Buhl, Y. J.
|
||||||
|
Huang, C. O. Pedersen, R. K. Strand, R. J. Liesen, D. E. Fisher, M. J.
|
||||||
|
Witte et al., “Energyplus: creating a new-generation building energy
|
||||||
|
simulation program,” Energy and buildings, vol. 33, no. 4, pp. 319–331,
|
||||||
|
2001.
|
||||||
|
|
||||||
|
[16] M. Deru, K. Field, D. Studer, K. Benne, B. Griffith, P. Torcellini, B. Liu,
|
||||||
|
M. Halverson, D. Winiarski, M. Rosenberg et al., “Us department of
|
||||||
|
energy commercial reference building models of the national building
|
||||||
|
stock,” 2011.
|
||||||
|
|
||||||
126
main.py
126
main.py
|
|
@ -2,6 +2,10 @@ import pandas as pd
|
||||||
import numpy as np
|
import numpy as np
|
||||||
import tensorflow as tf
|
import tensorflow as tf
|
||||||
import matplotlib.pyplot as plt
|
import matplotlib.pyplot as plt
|
||||||
|
from keras import regularizers
|
||||||
|
from keras.callbacks import TensorBoard, LearningRateScheduler
|
||||||
|
from keras.layers import Dropout
|
||||||
|
from sklearn.preprocessing import MinMaxScaler
|
||||||
|
|
||||||
|
|
||||||
def data_read(data_address):
|
def data_read(data_address):
|
||||||
|
|
@ -16,8 +20,7 @@ def data_read(data_address):
|
||||||
X = np.array(df['Voltage'])
|
X = np.array(df['Voltage'])
|
||||||
Y = np.array(df['Problem'])
|
Y = np.array(df['Problem'])
|
||||||
|
|
||||||
# 归一化处理
|
X = tf.nn.relu(X)
|
||||||
X = (X - np.min(X)) / (np.max(X) - np.min(X))
|
|
||||||
|
|
||||||
# 转换为时间序列数据格式
|
# 转换为时间序列数据格式
|
||||||
time_steps = 34
|
time_steps = 34
|
||||||
|
|
@ -26,7 +29,7 @@ def data_read(data_address):
|
||||||
X_series.append(X[i:(i + time_steps)])
|
X_series.append(X[i:(i + time_steps)])
|
||||||
Y_series.append(Y[i + time_steps - 1])
|
Y_series.append(Y[i + time_steps - 1])
|
||||||
|
|
||||||
return np.array(X_series).reshape(-1, time_steps, 1), np.array(Y_series)
|
return np.array(X_series), np.array(Y_series)
|
||||||
|
|
||||||
|
|
||||||
X_train, Y_train = data_read(
|
X_train, Y_train = data_read(
|
||||||
|
|
@ -34,39 +37,67 @@ X_train, Y_train = data_read(
|
||||||
X_test, Y_test = data_read(
|
X_test, Y_test = data_read(
|
||||||
'Liu/data/VOLTAGE-QUALITY-CLASSIFICATION-MODEL--main/Voltage Quality Test.csv')
|
'Liu/data/VOLTAGE-QUALITY-CLASSIFICATION-MODEL--main/Voltage Quality Test.csv')
|
||||||
|
|
||||||
|
# 归一化
|
||||||
|
sc = MinMaxScaler(feature_range=(0, 1))
|
||||||
|
X_train = sc.fit_transform(X_train)
|
||||||
|
X_test = sc.transform(X_test)
|
||||||
|
|
||||||
|
X_train.reshape(-1, 34, 1)
|
||||||
|
X_test.reshape(-1, 34, 1)
|
||||||
|
|
||||||
|
|
||||||
|
np.random.seed(7)
|
||||||
|
np.random.shuffle(X_train)
|
||||||
|
np.random.seed(7)
|
||||||
|
np.random.shuffle(Y_train)
|
||||||
|
tf.random.set_seed(7)
|
||||||
|
|
||||||
|
|
||||||
# 获取类别数量
|
# 获取类别数量
|
||||||
n_classes = len(np.unique(Y_train))
|
n_classes = len(np.unique(Y_train))
|
||||||
|
|
||||||
# 构建模型
|
|
||||||
model = tf.keras.models.Sequential([
|
|
||||||
tf.keras.layers.LSTM(50, return_sequences=True, input_shape=(34, 1)),
|
|
||||||
tf.keras.layers.LSTM(50),
|
|
||||||
tf.keras.layers.Dense(n_classes, activation='softmax') # 修改为适应多分类
|
|
||||||
])
|
|
||||||
|
|
||||||
# 编译模型
|
|
||||||
model.compile(optimizer='adam',
|
|
||||||
loss='sparse_categorical_crossentropy', metrics=['accuracy'])
|
|
||||||
|
|
||||||
# 训练模型
|
|
||||||
model.fit(X_train, Y_train, epochs=10, validation_split=0.2)
|
|
||||||
|
|
||||||
# 评估模型
|
|
||||||
loss, accuracy = model.evaluate(X_test, Y_test)
|
|
||||||
|
|
||||||
print(X_train.shape)
|
|
||||||
|
|
||||||
|
|
||||||
# 制作扰动数据
|
|
||||||
|
|
||||||
# 损失函数
|
# 损失函数
|
||||||
loss_fn = tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True)
|
loss_fn = tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True)
|
||||||
|
|
||||||
# 定义损失函数
|
# 构建使用 RNN 的模型
|
||||||
loss_fn = tf.keras.losses.SparseCategoricalCrossentropy()
|
model = tf.keras.models.Sequential([
|
||||||
|
tf.keras.layers.SimpleRNN(100, return_sequences=True, input_shape=(34, 1)),
|
||||||
|
Dropout(0.2),
|
||||||
|
tf.keras.layers.SimpleRNN(100),
|
||||||
|
Dropout(0.2),
|
||||||
|
tf.keras.layers.Dense(n_classes, activation='relu',
|
||||||
|
kernel_regularizer=regularizers.l2(0.3)) # 适应多分类
|
||||||
|
])
|
||||||
|
|
||||||
|
# 编译模型
|
||||||
|
model.compile(
|
||||||
|
optimizer='SGD',
|
||||||
|
loss=loss_fn,
|
||||||
|
metrics=['accuracy'])
|
||||||
|
|
||||||
|
# 定义学习率指数递减的函数
|
||||||
|
def lr_schedule(epoch):
|
||||||
|
initial_learning_rate = 0.01
|
||||||
|
decay_rate = 0.1
|
||||||
|
decay_steps = 250
|
||||||
|
new_learning_rate = initial_learning_rate * decay_rate ** (epoch / decay_steps)
|
||||||
|
return new_learning_rate
|
||||||
|
|
||||||
|
# 定义学习率调度器
|
||||||
|
lr_scheduler = LearningRateScheduler(lr_schedule)
|
||||||
|
|
||||||
|
|
||||||
|
# Save initial weights
|
||||||
|
initial_weights = model.get_weights()
|
||||||
|
|
||||||
|
# TensorBoard 回调
|
||||||
|
log_dir = "logs/fit"
|
||||||
|
tensorboard_callback = TensorBoard(log_dir=log_dir, histogram_freq=1)
|
||||||
|
|
||||||
|
# 制作扰动数据
|
||||||
|
|
||||||
# 转换X_train和Y_train为TensorFlow张量
|
# 转换X_train和Y_train为TensorFlow张量
|
||||||
X_train_tensor = tf.convert_to_tensor(X_train, dtype=tf.float32)
|
X_train_tensor = tf.convert_to_tensor(X_train, dtype=tf.float64)
|
||||||
Y_train_tensor = tf.convert_to_tensor(Y_train, dtype=tf.int32)
|
Y_train_tensor = tf.convert_to_tensor(Y_train, dtype=tf.int32)
|
||||||
|
|
||||||
# 使用tf.GradientTape来计算梯度
|
# 使用tf.GradientTape来计算梯度
|
||||||
|
|
@ -81,35 +112,34 @@ with tf.GradientTape() as tape:
|
||||||
# 计算关于输入X的梯度
|
# 计算关于输入X的梯度
|
||||||
gradients = tape.gradient(loss, X_train_tensor)
|
gradients = tape.gradient(loss, X_train_tensor)
|
||||||
|
|
||||||
# 计算每个输入的梯度的L2范数
|
|
||||||
gradient_magnitudes = tf.norm(gradients, axis=1)
|
|
||||||
|
|
||||||
# 创建每个gamma对应的准确率的字典
|
# 创建每个gamma对应的准确率的字典
|
||||||
accuracy_per_gamma = {}
|
accuracy_per_gamma = {}
|
||||||
|
|
||||||
|
|
||||||
# 平坦化梯度
|
# 平坦化梯度
|
||||||
flattened_gradients = tf.reshape(gradients, [-1])
|
flattened_gradients = tf.reshape(gradients, [-1])
|
||||||
|
|
||||||
# 选择最大的γ * |X|个梯度
|
# 选择最大的γ * |X|个梯度
|
||||||
for gamma in [0.05, 0.1, 0.2, 0.4]:
|
for gamma in [0.05, 0.1, 0.2, 0.4]:
|
||||||
num_gradients_to_select = int(gamma * tf.size(flattened_gradients, out_type=tf.dtypes.float32))
|
num_gradients_to_select = int(
|
||||||
top_gradients_indices = tf.argsort(flattened_gradients, direction='DESCENDING')[:num_gradients_to_select]
|
gamma * tf.size(flattened_gradients, out_type=tf.dtypes.float32))
|
||||||
|
top_gradients_indices = tf.argsort(flattened_gradients, direction='DESCENDING')[
|
||||||
|
:num_gradients_to_select]
|
||||||
|
|
||||||
# 创建一个新的梯度张量，初始化为原始梯度的副本
|
# 创建一个新的梯度张量，初始化为原始梯度的副本
|
||||||
updated_gradients = tf.identity(flattened_gradients)
|
updated_gradients = tf.identity(flattened_gradients)
|
||||||
|
|
||||||
# 创建一个布尔掩码，其中选定的最大梯度为False，其他为True
|
# 创建一个布尔掩码，其中选定的最大梯度为False，其他为True
|
||||||
mask = tf.ones_like(updated_gradients, dtype=bool)
|
mask = tf.ones_like(updated_gradients, dtype=bool)
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mask = tf.tensor_scatter_nd_update(mask, tf.expand_dims(top_gradients_indices, 1), tf.zeros_like(top_gradients_indices, dtype=bool))
|
mask = tf.tensor_scatter_nd_update(mask, tf.expand_dims(
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|
top_gradients_indices, 1), tf.zeros_like(top_gradients_indices, dtype=bool))
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|
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# 使用这个掩码更新梯度
|
# 使用这个掩码更新梯度
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updated_gradients = tf.where(mask, tf.zeros_like(updated_gradients), updated_gradients)
|
updated_gradients = tf.where(mask, tf.zeros_like(
|
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|
updated_gradients), updated_gradients)
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|
|
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# 将梯度重构为原始形状
|
# 将梯度重构为原始形状
|
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updated_gradients = tf.reshape(updated_gradients, tf.shape(gradients))
|
updated_gradients = tf.reshape(updated_gradients, tf.shape(gradients))
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|
|
||||||
|
|
||||||
# 创建准确率列表
|
# 创建准确率列表
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accuracy_list = []
|
accuracy_list = []
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|
|
||||||
|
|
@ -118,18 +148,16 @@ for gamma in [0.05, 0.1, 0.2, 0.4]:
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# 应用学习率到梯度
|
# 应用学习率到梯度
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||||||
scaled_gradients = learning_rate * updated_gradients
|
scaled_gradients = learning_rate * updated_gradients
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|
|
||||||
|
|
||||||
# 使用缩放后的梯度更新X_train_tensor
|
# 使用缩放后的梯度更新X_train_tensor
|
||||||
X_train_updated = X_train_tensor - scaled_gradients
|
X_train_updated = tf.add(X_train_tensor, scaled_gradients)
|
||||||
tf.reshape(X_train_updated, (3332,34,1))
|
|
||||||
X_train_updated = X_train_updated.numpy()
|
X_train_updated = X_train_updated.numpy()
|
||||||
|
|
||||||
# 编译模型
|
# Reset model weights to initial weights
|
||||||
model.compile(
|
model.set_weights(initial_weights)
|
||||||
optimizer='adam', loss='sparse_categorical_crossentropy', metrics=['accuracy'])
|
|
||||||
|
|
||||||
# 训练模型
|
# 训练模型，添加 TensorBoard 回调
|
||||||
model.fit(X_train_updated, Y_train, epochs=1500, validation_split=0.2)
|
history = model.fit(X_train_updated, Y_train, epochs=1500,
|
||||||
|
batch_size=32, callbacks=[tensorboard_callback, lr_scheduler])
|
||||||
|
|
||||||
# 评估模型
|
# 评估模型
|
||||||
loss, accuracy = model.evaluate(X_test, Y_test)
|
loss, accuracy = model.evaluate(X_test, Y_test)
|
||||||
|
|
@ -137,9 +165,11 @@ for gamma in [0.05, 0.1, 0.2, 0.4]:
|
||||||
# 记录准确率
|
# 记录准确率
|
||||||
accuracy_list.append(accuracy)
|
accuracy_list.append(accuracy)
|
||||||
|
|
||||||
|
|
||||||
# 记录该gamma下的准确率
|
# 记录该gamma下的准确率
|
||||||
accuracy_per_gamma[gamma] = accuracy_list
|
accuracy_per_gamma[gamma] = accuracy_list
|
||||||
|
|
||||||
|
|
||||||
# 学习率样本
|
# 学习率样本
|
||||||
learning_rates = [0.1, 0.2, 0.3, 0.4, 0.5]
|
learning_rates = [0.1, 0.2, 0.3, 0.4, 0.5]
|
||||||
|
|
||||||
|
|
@ -147,11 +177,12 @@ learning_rates = [0.1, 0.2, 0.3, 0.4, 0.5]
|
||||||
gammas = [0.05, 0.1, 0.2, 0.4]
|
gammas = [0.05, 0.1, 0.2, 0.4]
|
||||||
|
|
||||||
# 创建图像
|
# 创建图像
|
||||||
plt.figure(figsize=(10, 6))
|
last_plt = plt.figure(figsize=(10, 6))
|
||||||
|
|
||||||
# 为每个gamma值绘制曲线
|
# 为每个gamma值绘制曲线
|
||||||
for gamma in gammas:
|
for gamma in gammas:
|
||||||
plt.plot(learning_rates, accuracy_per_gamma[gamma], marker='o', label=f'Gamma={gamma}')
|
plt.plot(learning_rates,
|
||||||
|
accuracy_per_gamma[gamma], marker='o', label=f'Gamma={gamma}')
|
||||||
|
|
||||||
# 添加标题和标签
|
# 添加标题和标签
|
||||||
plt.title('Accuracy vs Learning Rate for Different Gammas')
|
plt.title('Accuracy vs Learning Rate for Different Gammas')
|
||||||
|
|
@ -162,3 +193,4 @@ plt.legend()
|
||||||
# 显示图像
|
# 显示图像
|
||||||
plt.show()
|
plt.show()
|
||||||
|
|
||||||
|
# tensorboard --logdir logs/fit
|
||||||
Loading…
Reference in New Issue