MONOTONIC NEURAL NETWORK: COMBINING DEEP LEARNING WITH DOMAIN KNOWLEDGE FOR CHILLER PLANTS ENERGY OPTIMIZATION

Abstract

In this paper, we are interested in building a domain knowledge based deep learning framework to solve the chiller plants energy optimization problems. Compared to the hotspot applications of deep learning (e.g. image classification and NLP), it is difficult to collect enormous data for deep network training in realworld physical systems. Most existing methods reduce the complex systems into linear model to facilitate the training on small samples. To tackle the small sample size problem, this paper considers domain knowledge in the structure and loss design of deep network to build a nonlinear model with lower redundancy function space. Specifically, the energy consumption estimation of most chillers can be physically viewed as an input-output monotonic problem. Thus, we can design a Neural Network with monotonic constraints to mimic the physical behavior of the system. We verify the proposed method in a cooling system of a data center, experimental results show the superiority of our framework in energy optimization compared to the existing ones.

1. INTRODUCTION

The demand for cooling in data centers, factories, malls, railway stations, airports and other buildings is rapidly increasing, as the global economy develops and the level of informatization improves. According to statistics from the International Energy Agency (IEA, 2018) , cooling energy consumption accounts for 20 of the total electricity used in buildings around the world today. Therefore, it is necessary to perform refined management of the cooling system to reduce energy consumption and improve energy utilization. Chiller plants are one of the main energy-consuming equipment of the cooling system. Due to the non-linear relationship between parameters and energy consumption, and performance changes due to time or age, deep learning is very suitable for modeling chiller plants. In recent years, deep learning (Goodfellow et al., 2016) research has made considerable progress, and algorithms have achieved impressive performance on tasks such as vision (Krizhevsky et al., 2012; He et al., 2016 ), language (Mikolov et al., 2011; Devlin et al., 2018), and speech (Hinton et al., 2012; Oord et al., 2016) , etc. Generally, their success relies on a large amount of labeled data, but real-world physical systems will make data collection limited, expensive, and low-quality due to security constraints, collection costs, and potential failures. Therefore, deep learning applications are extremely difficult to be deployed in real-world systems. There are some researches about few sample learning summarized from Lu et al. (2020) , which focusing on how to apply the knowledge learned in other tasks to few sample tasks, and applications in computer vision, natural language processing, speech and other tasks. Domain Knowledge that has been scientifically demonstrated, however, is more important in few sample learning tasks, especially in the application of physical system optimization. Domain knowledge can provide more derivable and demonstrable information, which is very helpful for physical system optimization tasks that lack samples. We discussed the method of machine learning algorithms combined with domain knowledge and its application in chiller energy optimization in this article. In particular, we propose a monotonic neural network (MNN), which can constrain the input-output of the chiller power model to conform to physical laws and provide accurate function space about chiller plants. Using MNN for system identification can help the subsequent optimization step and improve 1.5% the performance of optimization compared with the state-of-the-art methods.

2. BACKGROUND AND RELATED WORK

Chiller plantsfoot_0 energy optimization is an optimization problem of minimizing energy. In order to simplify the optimization process, the optimized system is usually assumed to be stable, which means that for each input of the system, the corresponding output is assumed to be time-independent. Mostly used methods are model-based optimization (MBOfoot_1 ) (Ma & Wang, 2009; Ma et al., 2011; Huang & Zuo, 2014) . Although Some research using Reinforcement learning model for optimal control (Wei et al., 2017; Li et al., 2019; Ahn & Park, 2020) . However, applying RL to the control of real-world physical systems will be caused by unexpected events, safety constraints, limited observations, and potentially expensive or even catastrophic failures Becomes complicated (Lazic et al., 2018) . MBO has been proven to be a feasible method to improve the operating efficiency of chillers, which uses chiller plants model to estimate the energy consumption with given control parameters under the predicted or measured cooling load and outside weather conditions. The optimization algorithm is then used to get the best value of the control parameter to minimize energy consumption (Malara et al., 2015) . The model can be a physics-based model or a machine learning model. Physics-based models are at the heart of today's engineering and science, however, it is hard to apply due to the complexity of the cooling system. Experts need to spend a lot of time modeling based on domain knowledge (Ma et al., 2008) . When the system changes (structure adjustment, equipment aging, replacement), it needs to be re-adapted. In recent years, the data-driven method has gradually become an optional solution. Its advantage lies in the self-learning ability based on historical data and the ability to adapt to changes. Thanks to its stability and efficiency, linear regression is the mostly used modeling method in real-world cooling system optimal control tasks (Zhang et al., 2011; Lazic et al., 2018) . But ordinary linear models cannot capture nonlinear relationships between parameters and energy consumption, and polynomial regression is very easy to overfit. With the remarkable progress of deep learning research, some studies apply it in cooling system (Gao, 2014; Evans & Gao, 2016; Malara et al., 2015) . Deep learning is very good at nonlinear relationship fitting, but it relies on a large amount of data and is highly nonlinear, which brings great difficulties to subsequent decision-making. Due to the inability to obtain a large amount of data, frontier studies have begun to consider the integration of domain knowledge into the progress of system identification and optimization (Vu et al., 2017; Karpatne et al., 2017; Muralidhar et al., 2018; Jia et al., 2020) . The combination methods made laudable progress, although it is still at a relatively early stage. In conclusion, reinforcement learning approach either requires a detailed system model for simulation or an actual system that can be tested repeatedly. The cooling system is too complex to simulate, the former is impossible. While in actual system design and implementation, the latter may be impractical. The MBO method has been proven to be feasible in optimal control, and the optimization performance is determined by the system identification model. However, physical model is complex and time-consuming, linear model in the machine learning model has poor fitting ability, neural network requires large scale datasets, and its highly nonlinearity is not conducive to subsequent optimization step. Domain knowledge can provide more knowledge for machine learning, in this article, we make a theoretical analysis and methodological description about the combination of domain knowledge and deep networks. In particular, we propose a monotonic neural network, which can capture operation logic of chiller. Compared with the above state of art method, MNN reduces the dependence on amount of data, provides a more accurate function space, facilitates subsequent optimization steps and improves optimization performance.



How chiller plants work can see in appendix A.1. How MBO methods work can see in appendix A.3.

