Heat Recovery Unit Failure Detection in Air Handling Unit

. Maintenance is a complicated task that encompasses various activities including fault detection, fault diagnosis, and fault reparation. With advancement of Computer Aided Engineering (CAE), maintenance task becomes even more challenging as modern assets became complex mixes of systems and sub systems with complex interaction. Among maintenance activities, fault diagnosis is particularly cumbersome as the reason of failures on the system are often neither obvious in terms of their source nor unique. Early detection and diagnosis of such fault is turning to one of the key requirements for economical and functional e � ciency of assets. Several methods have been studied to detect machine faults for a number of years and were relevant for many application domains. In this paper, we present process-history based method utilising nominal e � ciency of Air Handling Unit (AHU) to detect heat recovery failure using Principle Component Analysis (PCA) in combination of logistic regression method.


Introduction
Air Handling Unit (AHU) is one of the integral parts of any modern house and building that contributes to well-being of its occupants.As energy prices sore up, operating these devices become costly.As a result of ever increasing energy prices along with environmental concerns, building owners have become more and more interested in reducing energy consumption of their buildings.Nowadays in modern AHU, it is common to have Heat Recovery Units (HRU), especially in countries with cold climate like Finland.HRU helps to reduce energy consumption by extracting heat from waste air and utilising it to heat supply air.Energy savings are closely related to a proper maintenance of these equipments in order to guarantee their fault-free operation, as well as a su cient level of comfort for their residents [1].
By advancement of Computer Aided Engineering (CAE), manufacturing companies are producing complex AHU with capabilities of computing, sensing, and actuating.Using these capabilities, maintenance of AHU is even more challenging as this equipment became complex combination of systems and subsystems with complex interactions.Fault diagnosis is considered a complicated maintenance activity since there might be multiple reasons behind each failure and the failure reasons are also often ambiguous in terms of their sources.By identifying and diagnosing faults to be repaired, building owners can benefit by reducing energy consumption and improving operational performance.However, no matter how reliable products (or equipment) are, they tend to deteriorate over time and also occasionally fail due to real-world operating conditions under various degrees of stress.In order to make such assets economically and functionally e cient, it is necessary to detect and diagnose such faults in the early stage.Various methods were applied in many application domains to detect machine faults for several years.Among these methods, this paper utilises process-history based method to detect one type of failure to improve the e ciency of AHU.Using machine learning solutions, the failure is predicted with high performance.

Fault Diagnosis in Air Handling Unit
Fault detection and diagnosis is a well-researched area.Several researchers studied and identified di↵erent techniques to detect and diagnosis fault condition in AHU.Typically, these techniques broadly classified into three categories [2], quantitative model based methods, qualitative model based methods, and process history based methods.These methods belong to the same generic class, namely data-driven methods.But, in general, extensive prior knowledge is required to apply quantitative and qualitative model based methods.They are also often device specific and are hard to be applied to other devices.Therefore, process-history based methods are the focus of this study.Process-history based methods are also known as black box models.Unlike model-based methods that are based on physical principles, these methods are based on actual data that had been generated during usage.The relation between input and output are discovered during learning phase of these methods.Several researchers have contributed to develop methods to detect and diagnose di↵erent kinds of failures on AHU.Process-history based methods are according to di↵erent machine learning techniques such as neural network, Markov model, Principle Component Analysis (PCA), and Support Vector Machine (SVM).
Lee et al. [3] presented Artificial Neural Network (ANN) backward propagation method to detect fault of cooling coil subsystem of AHU based on dominant residual signature.Similarly, in 2012, Yonghua et al. [4] proposed a method to diagnose sensor failure based on regression neural network with combination of wavelet and fractal dimension.In this method, three-level wavelet analysis was applied to decompose the measurement data of sensor, and then fractal dimensions of each frequency band are extracted and used to depict the failure characteristics of the sensors which are then used to train neural network to diagnose sensor faults.Du et al. [5] introduced a detecting method for drifting biases of sensors in an AHU using combination of wavelet analysis along with neural network.PCA is another widely used technique to detect and diagnose fault in AHU.For instance, Wang et al. [6] could present a PCA-based strategy to detect and diagnose sensor faults of the AHU.This strategy employed squared prediction error as indices of fault detection and uses the Q-contribution plot to isolate faults in AHU.Similarly, Du et al. [7] employed PCA with Joint Angle Analysis (JAA) to detect and diagnose both fixed and drifting biases of sensors in Variable Air Volume (VAV) systems.The Squared Prediction Error (SPE) plot based on PCA is used to detect the sensor fixed and drifting biases.Then, the JAA plot instead of conventional contribution plot is applied to diagnose the faults.Chen et al. [8] also proposed a method using PCA for detecting and identifying sensor bias, drifting, and failure in AHU.In his method, PCA is employed to identify correlation of measured variables in heating/cooling billing system and reduce the dimension of measured data and SPE statistic is used to detect sensor faults in the system.Xiao et al. in [9] presented an expert-based multivariate coupling method by enhancing capabilities of PCA-based method in fault diagnosis by taking advantage of expert knowledge about the process concerned.This method develops unique fault patterns of typical sensor faults by analysing the physical cause-e↵ect relations among variables which is compared to fault symptoms reflected by the residual vectors of the PCA models with fault patterns to isolate sensor fault.Similarly, several other researchers such as West et al. [10] and Liang et al. [11] used Hidden Markov and SVM to detect faulty condition from the normal operation.
3 Theoretical Background

System description
A typical AHU with balanced air ventilation system, as shown in Fig. 1, includes the HRU, supply fan, extract fan, air filters, controllers, and sensors.The system circulates the fresh air from outside to the building by utilising two fans (supply side and extract side) and two ducts (fresh air supply and exhaust vents).Fresh air supply and exhaust vents can be installed in every room, but typically this system is designed to supply fresh air to bedrooms and living rooms where occupants spend their most of time.A filter is employed to remove dust and pollen from outside air before pushing it into the house.The system also extracts air from rooms where moisture and pollutants are most often generated (e.g.kitchen and bathroom).One of the major component of the AHU is HRU which is used to save energy consumption.The principle behind the HRU is to extract heat from extracted air (before it is removed as waste air) from house and utilise it to heat fresh air that is entering into the house.HRU is a fundamental component of AHU which helps to recycle extracted heat.The main controllers included in the system are supply air temperature controller which adjusts the temperature of the supply air entering into house and Hru output which controls the heat recovery rate.In order to measure e ciency of HRU, five temperature sensors are installed in AHU which measure the temperature of circulating air at di↵erent part of AHU (detailed in Table 1).In addition to data from sensors, HRU control state, supply fan speed, and extract fan speed can be collected from system.Principal Component Analysis (PCA) is defined as statistical procedure mostly used for dimension reduction and orthogonal decomposition.A Principal Component (PC) is defined as a linear transformation of the original variables, which are normally correlated, into a new set of variables, which are uncorrelated or orthogonal to each other [12].If there are n observations with p variables, then the number of distinct PCs is min(n 1, p).This transformation is defined in such a way that the first PC has the largest possible variance, and each succeeding component in turn has the highest variance possible under the constraint that it is orthogonal to the preceding components.The resulting vectors are an uncorrelated orthogonal basis set.The first PC Y 1 is given by the linear combination of the variables X 1 ,X 2 ,X 3 ,.....,X p as shown in equation 1. Collectively, all of these transformations of the original variables to the PCs is given by equation 2. The rows of matrix A (loading matrix) are called the eigenvectors of matrix S x (equation 3), the variance-covariance matrix of the original data.The elements of an eigenvector are the weights a ij , and are known as loadings.The elements in the diagonal of matrix S y (equation 4), the variance-covariance matrix of the PC, are known as the eigenvalues.
S y = AS x A T (4)

Logistic Regression (LR)
Logistic Regression (LR) was developed by David Cox in 1958 [13].It is a statistical method to determine dependent dichotomous (True or False) variable using one or more independent variables.It is a variation of ordinary regression method that is used when the dependent variable is a dichotomous.The goal of the LR is to find the best fitting model to describe the relationship between the dichotomous characteristic of the dependent variable and a set of independent variables [14].LR generates the coe cients, standard errors, and significance levels of a formula to predict a logit transformation of the probability of presence of the characteristic of interest.The logit model of multiple LRs can be shown in equation 5 and the logit transformation are defined as the logged odds shown in equation 6 and equation 7.

Methodology
The method of detection and diagnosis for HRU failure is depicted in Fig. 2.This binary classification method is based on the nominal e ciency of AHU to detect failure of HRU using PCA and LR method.The rationale behind such methodology is the fact that there are high number of dimensions and detecting faulty operation (HRU Failure) from normal operation is quite di cult.The nominal e ciency (µ nom ) of the HRU is a function of air temperatures in AHU which is given by equation 8 [15].To develop this model, dataset contains 26700 instances of data with two types of information which were collected during "Normal" and "No Heat Recovery" state.One information is regarding class label (i.e "Normal": 18882 instances and "No Heat Recovery": 7818 instances) and the other contains di↵erent kinds of air temperature circulated by AHU (detailed in Table 1).Since Hru output is set to "max" (i.e. it is a constant parameter) and HRU nominal e ciency is a function of air temperatures associated with AHU (as shown in equation 8), only temperature dimensions are considered in this analysis.In other words, these dimensions can be combined together to measure the performance of HRU.
As the first step, collected dataset is split into "Train" and "Test" datasets then PCA model, based on nominal e ciency, is set up through training dataset with five temperature dimensions.The corresponding matrix is denoted as: The primary PCs are identified based on eigenvalue which is calculated based on variance-covariance matrix of PCs (equation 4) and eigenvector are used to project "Train" and "Test" datasets into principle component subspace.The eigenvectors are computed based on variance-covariance matrix of original data (equation 3).Since dependent variable (i.e class) are dichotomous in nature, these data are used to train the LR model by merging associated class with each instance of data.The LR model is trained with di↵erent cuto↵ values in order to improve its predictive performance.The cuto↵ value is defined threshold probability of sample is belongs to particular class or not.Once the optimal cuto↵ value is selected, the "Test" dataset are used to evaluate the performance of model.Di↵erent performance metrics and results are presented in the next chapter.

Table 1 :
Air Handling Unit Sensor Details As stated, detection and diagnosis of HRU failure is carried out by using "Test" dataset.The accuracy of our proposed method for "Train" and "Test" at di↵erent cuto↵ values is shown in Fig.3 (a).It is clearly seen that accuracy of the model is increased from 95% to 97% when the cuto↵ is changed from 0.3 to 0.8 .Detailed performance metrics such as Sensitivity, Specificity of method is presented in table2.It worth noticing change in cuto↵ value has its e↵ects on Sensitivity, Specificity.Fig.3(b)depicts the tradeo↵ choosing a reasonable cuto↵.If we increase the cuto↵ value, the number of True Negative (TN) increases and the number of True Positive (TP) decreases or in order word, if we increase the cuto↵'s value, the number of False Positive (FP) is lowered, while the number of False Negative (FN) rises.In this study, our main objective is to e↵ectively detect failure of HRU for immediate maintenance, thus we chose 0.8 as the final cuto↵ where faulty HRU unit can be detected with 97% of accuracy while maintaining perfect specificity of 100% along with 91% sensitivity.

Table 2 :
Performance metrics of proposed methodology to detect HRU failure In this paper, we presented application of PCA with combination of LR method to detect the HRU failure of the AHU based on nominal e ciency parameters.This method helps quick detection of faulty HRU which aids to take quick action (such as maintenance of AHU) to avoid further damage.If such faults remain undetected, it may result unwanted consequences such as wasting of energy and establishing an unhealthy living space.This study is focused on fault detection of a single component (i.e.HRU) of AHU using nominal e ciency.In future, we plan to extend this study to detect other types of fault that might occur in other components during operation of AHU.