Symbolic Aggregate Approximation Research Articles

Smart sewing work measurement system using IoT-based power monitoring device and approximation algorithm

To enable Small and Medium-sized Enterprises (SMEs) level garment manufacturers to measure and monitor the work of individual workers without incurring a large financial burden, a smart sewing work measurement system was developed using an IoT-based power monitoring device and an approximation algorithm. The amount of electric current used in the sewing work was measured, and the measured data was transmitted to a server using Wi-Fi communication. The analysis of the data was conducted through the Symbolic Aggregate approximation (SAX) and Dynamic Time Warping (DTW) methods. The daily workload of each worker derived from the system developed through this study showed an error rate of 8% compared to the actual workload, and the time measured by the sensor was different from the time measured by a manager using a stopwatch. These differences are considered to be due to measurement errors in the stopwatch, human noise from the measurer and the operator, and the relatively few samples relative to the total workload. The IoT-based power monitoring and work measurement system for sewing work developed through this study can be applied to smart garment manufacturing factories at an acceptable cost level, while SMEs can realise high recognition rates and semi-real-time monitoring.

A pattern recognition methodology for analyzing residential customers load data and targeting demand response applications

The availability of smart meter data allows defining innovative applications such as demand response (DR) programs for households. However, the dimensionality of data imposes challenges for the data mining of load patterns. In addition, the inherent variability of residential consumption patterns is a major problem for deciding on the characteristic consumption patterns and implementing proper DR settlements. In this regard, this paper utilizes a data size reduction and clustering methodology to analyze residential consumption behavior. Firstly, the distinctive time periods of household activity during the day are identified. Then, using these time periods, a modified symbolic aggregate approximation (SAX) technique is utilized to transform the load patterns into symbolic representations. In the next step, by applying a clustering method, the major consumption patterns are extracted and analyzed. Finally, the customers are ranked based on their stability over time. The proposed approach is applied on a large dataset of residential customers’ smart meter data and can achieve three main goals: 1) it reduces the dimensionality of data by utilizing the data size reduction, 2) it alleviates the problems associated with the clustering of residential customers, 3) its results are in accordance with the needs of systems operators or demand response aggregators and can be used for demand response targeting. The paper also provides a thorough analysis of different aspects of residential electricity consumption and various approaches to the clustering of households which can inform industry and research activity to optimize smart meter operational use.

SAX-ARM: Deviant event pattern discovery from multivariate time series using symbolic aggregate approximation and association rule mining

The discovery of event patterns from multivariate time series is important to academics and practitioners. In particular, we consider the event patterns related to anomalies such as outliers and deviations, which are important factors in system monitoring for manufacturing processes. In this paper, we propose a method for discovering the rules to describe deviant event patterns from multivariate time series, called SAX-ARM (association rule mining based on symbolic aggregate approximation). Inverse normal transformation (INT) is first adopted for converting the distribution of time series to the normal distribution. Then, symbolic aggregate approximation (SAX) is applied to symbolize time series, and association rule mining (ARM) is used for discovering frequent rules among the symbols of deviant events. The experimental results show the discovery of informative rules among deviant events in a multivariate time series from a die-casting manufacturing process that has ten variables with 1,437 lengths. We also present the results of sensitivity analysis, which demonstrates that significant rules can be discovered with different settings of the SAX parameters. The results describe the usefulness of the proposed method to identify deviant event among multivariate time series with high complexity.

Development and evaluation of HVAC operation schedule detection algorithm

Small- and medium-sized (<5,000 m2 or <50,000 sf) commercial buildings (SMBs) represent over 94% of the U.S. commercial building stock and consume over 1018 kJ (∼1015 Btus) of total site energy. Many of these buildings use rudimentary controls that are mostly manual, with limited scheduling capability and no monitoring or failure management. Therefore, many of the systems in these buildings are operated inefficiently and consume excess energy. SMBs typically use packaged rooftop units (RTUs) that are controlled by an individual thermostat. Studies have shown that managing set points and schedules of the RTUs will result in up to 20% energy/cost savings. Because there is no monitoring infrastructure in these buildings, deviation of actual heating, ventilation and air conditioning (HVAC) set points and schedules from expected cannot be easily inferred or detected. In this paper, a new methodology is proposed to detect HVAC operation schedules using a symbolic aggregate approximation (SAX) technique. This new method only requires a single temperature measurement (zone temperature) to infer the HVAC schedule. The method was tested and validated using field data from a number of RTUs from six buildings in different climate locations. The confusion metric was used to evaluate how well the method is able to identify the operating schedule of RTUs. Overall, the schedule detection method was successful in detecting the daily operating schedule of RTUs under summer (hot) and winter (cold) weather conditions when energy use is highest or when the RTUs are cycling ON/OFF often. The method can also distinguish different schedules and generate clusters of HVAC operating schedules.

SAX Breakpoints for Random Forest Based Real-Time Contrast Control Chart

In the manufacturing process, process monitoring is very important. Real-time contrast (RTC) control chart outperforms existing monitoring methods. However, the performance of RTC control chart depends on the classifier. The existing RTC charts use random forest (RF), support vector machine (SVM), or kernel linear discriminant analysis (KLDA) as a classifier. RF classifier can find cause of faults but the performance is lower than others. Therefore, we suggest the data representation method to improve the RF based RTC control chart. Symbolic aggregate approximation (SAX) is famous method to improve the performance of classification and clustering. We convert the input data by using SAX. We change the parameters of SAX such as alphabet size and breakpoints to improve the performance. Experiment shows that represented data is efficient method to improve the performance of RTC control chart.

Analyzing the relationship between historic canopy dynamics and current plant species diversity in the herb layer of temperate forests using long-term Landsat time series

Current plant species diversity of the forest herb layer is influenced by site conditions, seed banks, stand age and historic canopy dynamics, induced for example by natural and anthropogenic disturbances. Long-term Landsat time series allow for analyzing forest canopy dynamics over several decades at a spatial resolution of 30 m. These dynamics have not been related to plant diversity in the herb layer of forests yet. Here, we related canopy layer dynamics of 132 one hectare temperate forest plots derived from Landsat time series (1985–2015) to herb layer plant species diversity observed in 2015. To quantitatively characterize the dynamics in the canopy over this period, we applied Symbolic Aggregate ApproXimation representation (SAX) to yearly NDVI time series of the plots and calculated the frequency of the representations of similar time series patterns, hereafter called SAX-metrics. We used the SAX-metrics as predictors to estimate with beta regression models the Simpson's diversity index of the herb layer of our forest plots subdivided into six forest types. Models including SAX-metrics, describing abrupt decreases in NDVI, and high, medium, or low NDVI values had pseudo R2 between 0.13 and 0.63. We conclude that disturbances, canopy closure, as well as stand age, as represented in NDVI time series, influence the diversity in the herb layer in five of the six examined forest types. Our study shows that information on historic canopy dynamics, detected from Landsat time series, can contribute to a better understanding of current herb layer diversity in some forest types. This study gives first indications on the potential of temporal metrics of Landsat time series in biodiversity research.

Accelerating pattern-based time series classification: a linear time and space string mining approach

Subsequences-based time series classification algorithms provide interpretable and generally more accurate classification models compared to the nearest neighbor approach, albeit at a considerably higher computational cost. A number of discretized time series-based algorithms have been proposed to reduce the computational complexity of these algorithms; however, the asymptotic time complexity of the proposed algorithms is also cubic or higher-order polynomial. We present a remarkably fast and resource-efficient time series classification approach which employs a linear time and space string mining algorithm for extracting frequent patterns from discretized time series data. Compared to other subsequence or pattern-based classification algorithms, the proposed approach only requires a few parameters, which can be chosen arbitrarily and do not require any fine-tuning for different datasets. The time series data are discretized using symbolic aggregate approximation, and frequent patterns are extracted using a string mining algorithm. An independence test is used to select the most discriminative frequent patterns, which are subsequently used to create a transformed version of the time series data. Finally, a classification model can be trained using any off-the-shelf algorithm. Extensive empirical evaluations demonstrate the competitive classification accuracy of our approach compared to other state-of-the-art approaches. The experiments also show that our approach is at least one to two orders of magnitude faster than the existing pattern-based methods due to the extremely fast frequent pattern extraction, which is the most computationally intensive process in pattern-based time series classification approaches.

A novel feature extraction algorithm for bearing fault diagnosis based on enhanced symbolic aggregate approximation

A novel feature extraction algorithm for bearing fault diagnosis based on enhanced symbolic aggregate approximation

Radar Emitter Signal Identification Based on Multi-scale Information Entropy

With the increasing complexity of radar signals, it is more and more difficult to extract features of the real sequences, but when they are transformed to a symbol sequence, it is usually easier to mine the effective feature parameters. Therefore, a radar signal recognition method based on Multi-Scale Information Entropy (MSIE) is proposed. Firstly, the radar signal is transformed into symbolic sequence by Symbolic Aggregate approXimation (SAX) algorithm under different character number scales. Then, the information entropy of each symbol sequence is combined to form the MSIE feature vector. Finally, the k-Nearest Neighbor (k-NN) is used as a classifier to realize the classification and identification of radar signals. The simulation results of 6 typical radar signals show that using the proposed method the correct recognition rate of different radar signals is greater than 90% when Signal to Noise Ratio (SNR) is 5 dB, and better performance can be obtaned conpared with the traditional identification method based on complexity characteristics (box-dimension and sparseness).

A Relative Entropy Weibull-SAX framework for health indices construction and health stage division in degradation modeling of multivariate time series asset data

Predictive maintenance is the monitoring of an asset’s condition over its life cycle to provide a prognosis for when maintenance is required. Prior to prognosis, an asset’s life cycle is modeled by a health indicator (HI) which is derived from sensor measurements and describes an asset’s degradation over a life cycle. Often an asset’s HI is accompanied by a health stage (HS) division, which describes the asset’s life cycle condition in discrete states. Generally, HSs are discrete representations generated from discrete state transition models, dynamic state space models, or subjectively defined thresholds, which use sensor measurements to provide a HS division related to an asset’s life cycle degradation. HS division methods are often designed for a specific asset in which HS division is based on user assumptions and not generalizable to different asset types or asset data representations. Also, HS division methods are often limited to a bi-state HS division (normal and failure), in which unobservable states are often generalized transition states. As assets become more complex and require multivariate measurements, more advanced methods are required to model an asset’s degradation using HIs and HSs. This work introduces Relative Entropy Weibull-SAX (REWS), a data-driven HI and HS degradation modeling method for multivariate asset data. REWS constructs a HI using relative entropy to represent an asset’s condition as a change of entropy during its life cycle. The relative entropy representation is then discretized into HS divisions using a Weibull distribution based Symbolic Aggregate approXimation. REWS’s utility is demonstrated on the Commercial Modular Aero-Propulsion System Simulation dataset which describes the life cycle observations of multiple aircraft engines.

Observing the Pulse of a City: A Smart City Framework for Real-Time Discovery, Federation, and Aggregation of Data Streams

An increasing number of cities are confronted with challenges resulting from the rapid urbanization and new demands that a rapidly growing digital economy imposes on current applications and information systems. Smart city applications enable city authorities to monitor, manage, and provide plans for public resources and infrastructures in city environments, while offering citizens and businesses to develop and use intelligent services in cities. However, providing such smart city applications gives rise to several issues, such as semantic heterogeneity and trustworthiness of data sources, and extracting up-to-date information in real time from large-scale dynamic data streams. In order to address these issues, we propose a novel framework with an efficient semantic data processing pipeline, allowing for real-time observation of the pulse of a city. The proposed framework enables efficient semantic integration of data streams, and complex event processing on top of real-time data aggregation and quality analysis in a semantic Web environment. To evaluate our system, we use real-time sensor observations that have been published via an open platform called Open Data Aarhus by the City of Aarhus. We examine the framework utilizing symbolic aggregate approximation to reduce the size of data streams, and perform quality analysis taking into account both single and multiple data streams. We also investigate the optimization of the semantic data discovery and integration based on the proposed stream quality analysis and data aggregation techniques.

Data-Driven Modelling of Smart Building Ventilation Subsystem

Considering the advances in building monitoring and control through networks of interconnected devices, effective handling of the associated rich data streams is becoming an important challenge. In many situations, the application of conventional system identification or approximate grey-box models, partly theoretic and partly data driven, is either unfeasible or unsuitable. The paper discusses and illustrates an application of black-box modelling achieved using data mining techniques with the purpose of smart building ventilation subsystem control. We present the implementation and evaluation of a data mining methodology on collected data from over one year of operation. The case study is carried out on four air handling units of a modern campus building for preliminary decision support for facility managers. The data processing and learning framework is based on two steps: raw data streams are compressed using the Symbolic Aggregate Approximation method, followed by the resulting segments being input into a Support Vector Machine algorithm. The results are useful for deriving the behaviour of each equipment in various modi of operation and can be built upon for fault detection or energy efficiency applications. Challenges related to online operation within a commercial Building Management System are also discussed as the approach shows promise for deployment.

Fault diagnosis of bearing based on Symbolic Aggregate approXimation and Lempel-Ziv

Aiming at the problem that the traditional Lempel-Ziv encoding method can’t accurately reflect the bearing modulation information in bearing fault diagnosis, an improved Lempel-Ziv method based on Symbolic Aggregate approXimation is proposed to improve the coding accuracy and the computational efficiency of Lempel-Ziv indicator. According to the Piecewise Aggregate Approximation, the normalized bearing signal is divided into w equal-sized segments. The equal-sized segments are symbolized by determined breakpoints. The complexity value of the symbol sequence is calculated by Lempel-Ziv indicator. The proposed method is verified by a single-point defect dataset and a run-to-failure dataset of bearing, respectively. The results show that the proposed method can effectively reflect the modulation information of bearings. While the proposed method has higher computational efficiency than the traditional Lempel-Ziv method and can realize the early fault diagnosis of bearings.

Motif-based association rule mining and clustering technique for determining energy usage patterns for smart meter data

Nowadays, smart energy meters are being used to record periodic electricity consumption. The real time data produced by smart meters provide the detailed information about the electricity usage of a particular consumer. In this paper, we propose a motif-based association rule mining and clustering technique for determining the energy usage patterns for smart meter data. The association rules of motifs within a specific time window characterizes behaviors of energy consumer. In particular, we focus on an extraction of the temporal information of the smart meter. The process is based on the unique combination of Symbolic Aggregate approximation (SAX), temporal motif discovery and association rule mining to detect the expected and unexpected patterns robustly. Experiments on real world smart meter datasets justify that the proposed model discovers the useful routine behavior of electricity energy consumers, which are helpful for electricity utility experts. Further, in this paper, clustering on the motifs is performed which gives the different consumption behavior of consumers on different days which can help distribution network operator (DNO) for electricity network modeling and management. In future, we can form motif-based signature using the proposed approach for different applications such as anomaly detection and dynamic detection of operating patterns.

Detecting anomalies in sequential data augmented with new features

This paper presents a new weighted local outlier factor method for anomaly detection, which is underpinned with three novel components: (1) a piecewise linear representation defined on the basis of the important points that consist of extreme points and additional points; (2) a set of new features which are used to identify anomalies given the new piecewise linear representation; (3) a weighting schema, assigning different weights to different features by accounting for the discriminant power of the features. The underlying idea of the proposed method is to characterize a time series with a set of four features and then discover abnormal changes by taking account of the closeness of any data points augmented with the new features. The comparative experiments demonstrate that the proposed piecewise representation method has performed well in sequential time series data, and the weighted local outlier factor method has achieved better accuracy and RankPower in detecting anomalies from the same data sets in comparison with the conventional local outlier factor, normalized local outlier factor and HOT symbolic aggregate approximation methods.

A New Time Series Similarity Measurement Method Based on the Morphological Pattern and Symbolic Aggregate Approximation

Aiming at the problem that the traditional similarity measurement methods cannot effectively measure the similarity of the time series with the difference both in the trend and detail, this paper proposes a new time series similarity measurement method (MP-SAX) based on the morphological pattern (MP) and symbolic aggregate approximation (SAX). According to the empirical mode decomposition (EMD), the time series are decomposed and reconstructed into the trend component and the detail component. Then, the similarity of the trend component under morphological pattern coding and that of the detail component under symbolic aggregate approximation coding are respectively calculated by the longest common subsequence (LCS). Finally, the similarity of the time series is obtained by weighted aggregation of the similarity of trend component and detail component. The MP-SAX is verified by the simulation time series and the time series from UCR Time Series Classification/Clustering Homepage. The results show that the MP-SAX can effectively measure the similarity of the time series with the changes both in trend and detail.

Perceptual Vibration Hashing by Sub-Band Coding: An Edge Computing Method for Condition Monitoring

High data throughput during real-time vibration monitoring can easily lead to network congestion, insufficient data storage space, heavy computing burden, and high communication costs. As a new computing paradigm, edge computing is deemed to be a good solution to these problems. In this paper, perceptual hashing is proposed as an edge computing form, aiming not only to reduce the data dimensionality but also to extract and represent the machine condition information. A sub-band coding method based on wavelet packet transform, two-dimensional discrete cosine transform, and symbolic aggregate approximation is developed for perceptual vibration hashing. When the sub-band coding method is implemented on a monitoring terminal, the acquired kilobyte-long vibration signal can be transformed into a machine condition hash occupying only a few bytes. Therefore, the efficiency of condition monitoring can benefit from the compactness of the machine condition hash, while comparable diagnostic and prognostic results can still be achieved. The effectiveness of the developed method is verified with two benchmark bearing datasets. Considerations on practical condition monitoring applications are also presented.

Symbolic Aggregate approXimation-Local Binary Pattern Feature Descriptor Combination for Automatic Facial Expression Recognition

Automatic identification of facial expression is a significant research area which is anticipated for real time processing in Human-Computer Interaction domain. Along with an efficient classifier for assigning the class label to each of the input face image, it is very necessary to have a strong feature vector for training the classifier. This paper proposes an effectual combination of Local Binary Pattern and Symbolic Aggregate approXimation method for the feature vector generation for the classifier. Twenty one facial patches are extracted from the face image and the LBP value and SAX string for these twenty one patches are utilised for feature vector generation. The feature vectors of images are submitted to the Ensemble Bag classifier for training purpose. Images which were not used for training is used for testing. An average accuracy of 98.7% was obtained when tested on JAFFE data set for seven expressions and an accuracy of 96.96% was obtained for nine expressions on fused database. A detailed analysis of the testing conducted on images with partial occlusion and illumination variance are presented here.

Anomaly detection in ECG based on trend symbolic aggregate approximation.

ECG anomaly detection is a necessary approach to detect disease Electrocardiography( ECG) signals before the detail diagnosis process in medical field to gauge the health of the human heart. Nowadays, there are many anomaly detection methods for ECG detection including supervised learning and unsupervised learning. For supervised learning, it requires the knowledge of expert and different types of Arrhythmia data for training. However, since the anomalies are less and unknown in many cases which are di cult to distinguish and be labeled, unsupervised methods are more suitable to detect the ECG anomalies. Furthermore, the existing unsupervised learning studies do not take ECG shape into account where different diseases have different shapes. In this paper, a novel simple trend aggregate approximation method is proposed, the relative binary trend representation are used to record the shape feature in original time series and to detect the anomaly heart signals by similarity comparison. We use the ECG dataset in UCR Time Series Classification Archive to obtain ECG time series data and the experiment results are assessed by means of sensitivity, specificity, false alarm rate measures which is robust and promising with high accuracy.

A Modified IP-Based NILM Approach Using Appliance Characteristics Extracted by 2-SAX

Deregulation on the delivery side of the power market has continuously been moving forward worldwide, which make bidirectional flow and interactions between customers and grids needs to be more refined and in-depth. Large-scale coverage of the advanced metering infrastructure (AMI) brings in skyrocketing of an immense amount of fine-grained, real-time consumption data and causes communication traffic congestion between meters and a cloud computing center. To tackle these two challenges, this paper proposes a modified IP-based non-intrusive load monitoring approach using appliance characteristics extracted by quadratic symbolic aggregate approximation (2-SAX). A 2-SAX algorithm is implemented to carry out dimensionality reduction on equipment load data and extracted the state's transition behavior characteristics and operation probability characteristics of each device. The extracted features can use to modify the disaggregation results of integer programming for overcoming the shortcomings of the previous IP approach. The developed method is tested with AMPds dataset. The results of experiments illustrate the 2-SAX consequences in 38.82%, 52.46%, and 13.41% reduction in MAE, MAPE, and RMSE on the heat pump and achieves similar performance on the other appliances, compared with normal SAX. Meanwhile, the proposed method MIP-AC2S delivers significant accuracy advantage and competitive performance over IP, ALIP, and MIP disaggregation method.