Detection Of Anomalous Data Research Articles

Generalized Time‐Series Analysis for In Situ Spacecraft Observations: Anomaly Detection and Data Prioritization Using Principal Components Analysis and Unsupervised Clustering

AbstractIn situ spacecraft observations are critical to our study and understanding of the various phenomena that couple mass, momentum, and energy throughout near‐Earth space and beyond. However, on‐orbit telemetry constraints can severely limit the capability of spacecraft to transmit high‐cadence data, and missions are often only able to telemeter a small percentage of their captured data at full rate. This presents a programmatic need to prioritize intervals with the highest probability of enabling the mission's science goals. Larger missions such as the Magnetospheric Multiscale mission (MMS) aim to solve this problem with a Scientist‐In‐The‐Loop (SITL), where a domain expert flags intervals of time with potentially interesting data for high‐cadence data downlink and subsequent study. Although suitable for some missions, the SITL solution is not always feasible, especially for low‐cost missions such as CubeSats and NanoSats. This manuscript presents a generalizable method for the detection of anomalous data points in spacecraft observations, enabling rapid data prioritization without substantial computational overhead or the need for additional infrastructure on the ground. Specifically, Principal Components Analysis and One‐Class Support Vector Machines are used to generate an alternative representation of the data and provide an indication, for each point, of the data's potential for scientific utility. The technique's performance and generalizability is demonstrated through application to intervals of observations, including magnetic field data and plasma moments, from the CASSIOPE e‐POP/Swarm‐Echo and MMS missions.

Towards Efficient Cross-Modal Anomaly Detection Using Triple-Adaptive Network and Bi-Quintuple Contrastive Learning

Cross-modal anomaly detection is a relatively new and challenging research topic in machine learning field, which aims at identifying the anomalies whose patterns are disparate across different modalities. As far as we know, this topic has yet to be well studied, and existing works often suffer from the incomplete anomalous data detection and low data utilization problems. To alleviate these limitations, this paper proposes an efficient deep cross-modal anomaly detection approach via Triple-adaptive Network and Bi-quintuple Contrastive Learning (TN-BCL), which lies among the earliest attempt to detect various cross-modal anomalies within the heterogeneous multi-modal data. To be specific, a triple-adaptive network is explicitly designed to identify various anomalies, whose patterns are disparate in both single-modal scenario and cross-modal scenario. On the one hand, the top branch network is utilized to adaptively detect the attribute anomalies and part of mixed anomalies in multi-modal data samples. On the other hand, the bottom two-branch network, with shared residual blocks, is leveraged to learn the discriminative cross-modal embeddings. At the same time, an efficient bi-quintuple contrastive learning method is designed to enhance the feature correlation between the same attribute data, while maximally enlarging the feature difference between different attribute data. Besides that, the bidirectional learning scheme is employed to significantly improve the data utilization. Through the joint exploitation of the above, different kinds of anomalous samples can be well detected across different modalities. Extensive experiments show that the proposed framework outperforms the state-of-the-art competing methods, with a large improvement margin.

Anomalous data detection in cognitive IoT sensor network

Anomalous data detection in cognitive IoT sensor network

Anomaly detection in internet of medical things with artificial intillegence

Internet of things (IoT) becomes the most popular term in the recent advances in Healthcare devices. The healthcare data in the IoT process and structure is very sensitive and critical in terms of healthy and technical considerations. Outlier detection approaches are considered as principal tool or stage of any IoT system and are mainly categorized in statistical and probabilistic, clustering and classification-based outlier detection. Recently, fuzzy logic (FL) system is used in ensemble and cascade systems with other ML-based tools to enhance outlier detection performance but its limitation involves the false detection of outliers. In this paper, we propose a fuzzy logic system that uses the anomaly score of each point using local outlier factor (LOF), connectivity-based outlier factor (COF) and generalized LOF to eliminate the confusion in classifying points as outliers or inliers. Regarding human activity recognition (HAR) dataset, the FL achieved a value of 98.2 %. Compared to the performance of LOF, COF, and GLOF individually, the accuracy increased slightly, but the increase in precision and recall indicates an increase in correctly classified data and that neither true nor abnormal data is classified wrongly. The results show the increase in precision and recall which indicates an increase in correctly classified data. Thus, it can be confirmed that fuzzy logic with input of scores achieved the desired goal in terms of mitigating cases of false detection of anomalous data. By comparing the proposed ensemble of fuzzy logic and different types of local density scores in this study, the outcomes of fuzzy logic presents a new way of elaborating or fusing the different tools of the same purpose to enhance detection performance

Research on DUAL-ADGAN Model for Anomaly Detection Method in Time-Series Data.

In recent years, anomaly detection techniques in time-series data have been widely used in manufacturing, cybersecurity, and other fields. Meanwhile, various anomaly detection models based on generative adversarial networks (GAN) are gradually used in time-series anomaly detection tasks. However, there are problems of unstable generator training, missed detection of anomalous data, and inconsistency between the discriminator's discriminant and the anomaly detection target in GAN networks. Aiming at the above problems, the paper proposes a DUAL-ADGAN (Dual Anomaly Detection Generative Adversarial Networks) model for the detection of anomalous data in time series. First, the Wasserstein distance satisfying the Lipschitz constraint is used as the loss function of the data reconstruction module, which improves the stability of the traditional GAN network training. Second, by adding a data prediction module to the DUAL-ADGAN model, the distinction between abnormal and normal samples is increased, and the rate of missing abnormal data in the model is reduced. Third, by introducing the Fence-GAN loss function, the discriminator is aligned with the anomaly detection target, which effectively reduces the anomaly data false detection rate of the DUAL-ADGAN model. Finally, anomaly scores derived from the DUAL-ADGAN model are compared with dynamic thresholds to detect anomalies. The experimental results show that the average F1 of the DUAL-ADGAN model is 0.881, which is better than the other nine baseline models. The conclusions demonstrate that the DUAL-ADGAN model proposed in the paper is more stable in training while effectively solving the problems of anomaly miss detection and discriminator inconsistency with the anomaly detection target in the anomaly detection task.

An Applied Variation Anomaly Technique for Detection of Irregular Values in Data Mining

Information superiority is significant to organizations. With the use of data mining, Anomalous data values detection is a most important step in many data related applications. Anomalous data make the performance of data analysis difficult. The presence of anomalous data value can also pose serious problems for researchers. In fact, in appropriate handling of the Anomalous data values in the analysis may introduce bias and can result in misleading conclusions being drawn from a research study and can also limit the generalize ability of the research findings. There are numerous techniques for Anomalous data detection, while using Inliers and Outlier techniques and their different measures in data mining. This article introduces anomalous data detection algorithm that should be used in data mining systems. Basic approaches currently used for solving this Anomalous data values finding, problem are considered, and their results are discussed using table.

Adaptive Anomaly Detection for Internet of Things in Hierarchical Edge Computing: A Contextual-Bandit Approach

The advances in deep neural networks (DNN) have significantly enhanced real-time detection of anomalous data in IoT applications. However, the complexity-accuracy-delay dilemma persists: Complex DNN models offer higher accuracy, but typical IoT devices can barely afford the computation load, and the remedy of offloading the load to the cloud incurs long delay. In this article, we address this challenge by proposing an adaptive anomaly detection scheme with hierarchical edge computing (HEC). Specifically, we first construct multiple anomaly detection DNN models with increasing complexity and associate each of them to a corresponding HEC layer. Then, we design an adaptive model selection scheme that is formulated as a contextual-bandit problem and solved by using a reinforcement learning policy network . We also incorporate a parallelism policy training method to accelerate the training process by taking advantage of distributed models. We build an HEC testbed using real IoT devices and implement and evaluate our contextual-bandit approach with both univariate and multivariate IoT datasets. In comparison with both baseline and state-of-the-art schemes, our adaptive approach strikes the best accuracy-delay tradeoff on the univariate dataset and achieves the best accuracy and F1-score on the multivariate dataset with only negligibly longer delay than the best (but inflexible) scheme.

Anomaly Detection Algorithm for Real-World Data and Evidence in Clinical Research: Implementation, Evaluation, and Validation Study.

BackgroundStatistical analysis, which has become an integral part of evidence-based medicine, relies heavily on data quality that is of critical importance in modern clinical research. Input data are not only at risk of being falsified or fabricated, but also at risk of being mishandled by investigators.ObjectiveThe urgent need to assure the highest data quality possible has led to the implementation of various auditing strategies designed to monitor clinical trials and detect errors of different origin that frequently occur in the field. The objective of this study was to describe a machine learning–based algorithm to detect anomalous patterns in data created as a consequence of carelessness, systematic error, or intentionally by entering fabricated values.MethodsA particular electronic data capture (EDC) system, which is used for data management in clinical registries, is presented including its architecture and data structure. This EDC system features an algorithm based on machine learning designed to detect anomalous patterns in quantitative data. The detection algorithm combines clustering with a series of 7 distance metrics that serve to determine the strength of an anomaly. For the detection process, the thresholds and combinations of the metrics were used and the detection performance was evaluated and validated in the experiments involving simulated anomalous data and real-world data.ResultsFive different clinical registries related to neuroscience were presented—all of them running in the given EDC system. Two of the registries were selected for the evaluation experiments and served also to validate the detection performance on an independent data set. The best performing combination of the distance metrics was that of Canberra, Manhattan, and Mahalanobis, whereas Cosine and Chebyshev metrics had been excluded from further analysis due to the lowest performance when used as single distance metric–based classifiers.ConclusionsThe experimental results demonstrate that the algorithm is universal in nature, and as such may be implemented in other EDC systems, and is capable of anomalous data detection with a sensitivity exceeding 85%.

DeepStream: Autoencoder-based stream temporal clustering and anomaly detection

The increasing number of IoT devices in “smart” environments, such as homes, offices, and cities, produce seemingly endless data streams and drive many daily decisions. Consequently, there is growing interest in identifying contextual information from sensor data to facilitate the performance of various tasks, e.g., traffic management, cyber attack detection, and healthcare monitoring. The correct identification of contexts in data streams is helpful for many tasks, for example, it can assist in providing high-quality recommendations to end users and in reporting anomalous behavior based on the detection of unusual contexts. This paper presents DeepStream, a novel data stream temporal clustering algorithm that dynamically detects sequential and overlapping clusters. DeepStream is tuned to classify contextual information in real time and is capable of coping with a high-dimensional feature space. DeepStream utilizes stacked autoencoders to reduce the dimensionality of unbounded data streams and for cluster representation. This method detects contextual behavior and captures nonlinear relations of the input data, giving it an advantage over existing methods that rely on PCA. We evaluated DeepStream empirically using four sensor and IoT datasets and compared it to five state-of-the-art stream clustering algorithms. Our evaluation shows that DeepStream outperforms all of these algorithms. Our evaluation also demonstrates how DeepStream’s improved clustering performance results in improved detection of anomalous data.

Anomalous IoT Sensor Data Detection: An Efficient Approach Enabled by Nonlinear Frequency-Domain Graph Analysis

The detection of anomalous Internet-of-Things (IoT) sensor data is extremely important in many industrial applications due to the catastrophic consequences of the faulty or unreliable sensor data. Good anomalous data detection performance with high detection efficiency is indeed a dilemma since it is difficult to derive an explicit detection function to characterize the relationships between the anomalous values and the detection indicator. To overcome this difficulty, the location information of the IoT sensors is exploited in this study to characterize and reconstruct the relationships among the sensor data based on a second-order nonlinear polynomial graph filter (NPGF). The analysis of the sensor data reconstruction model is then conducted in the frequency domain based on the 2-D inverse graph Fourier transform (GFT), and the reconstruction error function for the sensor data is analytically derived based on the second-order GFT coefficients. It is shown that the detection efficiency can be greatly improved if the input graph signal is designed to be bandlimited. The anomalous sensor data detection is then conducted in the frequency domain as high-frequency components are more sensitive to the deviation values. An NPGF-based frequency-domain algorithm is proposed for the anomalous sensor data detection, which is illustrated and validated with a real-world data set for temperature monitoring. The simulation results demonstrate the detection performance and efficiency improvement of the proposed algorithm in anomaly detection.

An Anomaly Detection Algorithm Selection Service for IoT Stream Data Based on Tsfresh Tool and Genetic Algorithm

Anomaly detection algorithms (ADA) have been widely used as services in many maintenance monitoring platforms. However, there are numerous algorithms that could be applied to these fast changing stream data. Furthermore, in IoT stream data due to its dynamic nature, the phenomena of conception drift happened. Therefore, it is a challenging task to choose a suitable anomaly detection service (ADS) in real time. For accurate online anomalous data detection, this paper developed a service selection method to select and configure ADS at run-time. Initially, a time-series feature extractor (Tsfresh) and a genetic algorithm-based feature selection method are applied to swiftly extract dominant features which act as representation for the stream data patterns. Additionally, stream data and various efficient algorithms are collected as our historical data. A fast classification model based on XGBoost is trained to record stream data features to detect appropriate ADS dynamically at run-time. These methods help to choose suitable service and their respective configuration based on the patterns of stream data. The features used to describe and reflect time-series data’s intrinsic characteristics are the main success factor in our framework. Consequently, experiments are conducted to evaluate the effectiveness of features closed by genetic algorithm. Experimentations on both artificial and real datasets demonstrate that the accuracy of our proposed method outperforms various advanced approaches and can choose appropriate service in different scenarios efficiently.

A Spatial Correlation-Based Anomaly Detection Method for Subsurface Modeling

Spatial data analytics provides new opportunities for automated detection of anomalous data for data quality control and subsurface segmentation to reduce uncertainty in spatial models. Solely data-driven anomaly detection methods do not fully integrate spatial concepts such as spatial continuity and data sparsity. Also, data-driven anomaly detection methods are challenged in integrating critical geoscience and engineering expertise knowledge. The proposed spatial anomaly detection method is based on the semivariogram spatial continuity model derived from sparsely sampled well data and geological interpretations. The method calculates the lag joint cumulative probability for each matched pair of spatial data, given their lag vector and the semivariogram under the assumption of bivariate Gaussian distribution. For each combination of paired spatial data, the associated head and tail Gaussian standardized values of a pair of spatial data are mapped to the joint probability density function informed from the lag vector and semivariogram. The paired data are classified as anomalous if the associated head and tail Gaussian standardized values fall within a low probability zone. The anomaly decision threshold can be decided based on a loss function quantifying the cost of overestimation or underestimation. The proposed spatial correlation anomaly detection method is able to integrate domain expertise knowledge through trend and correlogram models with sparse spatial data to identify anomalous samples, region, segmentation boundaries, or facies transition zones. This is a useful automation tool for identifying samples in big spatial data on which to focus professional attention.

Integration of Machine Learning Algorithms with Gompertz Curves and Kriging to Estimate Resources in Gold Deposits

Resource estimation on gold (Au) deposits usually requires costly Au assays and is often characterized by high degree of uncertainty especially in areas with limited number of samples. This paper reports a refinement of a novel machine learning approach (GS-Pred) that incorporates network analysis for geology-based anomalous data detection and outlier removal, and adopts feature weighting using a spatial self-similarity model inspired by kriging to enhance prediction performance for in situ Au-grade estimation. In this application, machine learning algorithms are integrated with sequential-kriging block modeling for high resolution in situ grade estimation. This process is fully automatable, and it utilizes both geological data and Au assays, making it possible to also estimate Au grade in areas that only have geological descriptions. The results of our expanded GS-Pred and block modeling, using data from the auriferous conglomerates of the Witwatersrand Basin (South Africa), demonstrate improvements in the GS-Pred performance and flexibility relative to the original algorithms. Additionally, our results provide further evidence of strong sedimentological control on Au concentration within the Witwatersrand Basin, which is suitable for quantitative predictions. Our algorithms feature fast data processing, geology- and assay-based outlier detection, visualization of complex geospatial data, and they open new avenues for intelligent and automated in situ Au-grade prediction. We demonstrate that GS-Pred target predictions are feasible substitutes for assays for the purpose of block modeling under suitable deployment conditions.

Detection of anomalous vehicles using physics of traffic

The world is embracing the presence of connected autonomous vehicles which are expected to play a major role in the future of intelligent transport systems. Given such connectivity, vehicles in the networks are vulnerable to making incorrect decisions due to anomalous data. No sophisticated attacks are required; just a vehicle reporting anomalous speeds would be enough to disrupt the entire traffic flow. Detection of such anomalies is vital to ensure the security of a vehicular network. We propose the use of traffic flow theory for anomalous data detection in vehicular networks, by evaluating the consistency of microscopic parameters which are derived by traffic flow theory (i.e. speed and space-headway) with macroscopic views of traffic under different traffic conditions. Though a little attention has been given to using traffic flow properties to determine anomalous basic safety message (BSM) data, the fundamental nature of traffic flow properties makes it a robust assessment tool. Usually, traffic flow data are determined through roadside units (RSUs) such as cameras and loop detectors; they are financially impractical to roll out on an entire network. Therefore, the method proposed in this study establishes traffic flow data that are used as “ground truth” through RSUs if available, or by the vehicles' own sensor systems. The numerical results indicate that the proposed method provides extremely reliable and consistent predictions of anomalous BSM data. The more the road segment is congested, the higher the accuracy of the anomalous space-headway detection. The anomalous speed detection performs robustly well across all the traffic conditions. The study also finds that both global and local ground truths provide consistent results.

Anomaly detection in wireless sensor network using machine learning algorithm

Security in the Wireless Sensor Network(WSNs) is an essential and a challenging task. Anomaly detection is a key challenge to ensure the security in WSN. WSNs are vulnerable to various threats which may cause the node to get damaged and produce faulty measurements. The detection of such anomalous data is required to reduce false alarms. Machine learning algorithm based detection of anomalous data becomes popular now. Most of the current machine anomaly detection algorithms run in a stationary environment and require the entire training data to be kept in the node. In this paper, we formulate an Online Locally Weighted Projection Regression (OLWPR) for anomaly detection in Wireless Sensor Network. Linear Weighted Projection Regression methods are non parametric and the current predictions are performed by local functions that use only the subset of data. So, the computation complexity is low which is one of the requirements in Wireless Sensor Network. The dimensionality reduction in LWPR is done online by Principal Component Analysis (PCA) to handle the irrelevant and redundant data in the input data. After the prediction process, the dynamic threshold value is determined by a dynamic thresholding method to find the deviations of predicted value from the actual sensed value. OLWPR attains the detection rate of 86 percentage and very low error rate of only 16%.

Machine learning based approach to detection of anomalous data from sensors in cyber-physical water supply systems

The paper proposes an approach to detection of anomalous data from sensors in cyber-physical systems on an example of a water supply supply system. The approach is based on methods of machine learning and modeling of technical systems. The primary data for machine learning was obtained on the developed software/hardware prototype of the water supply system by using a number of microcontrollers, sensors and actuators. The experiments confirmed the feasibility of the proposed approach. Several machine learning methods from scikit-learn library of the Python programming language were tested. As a result of the experiments we identified a learning method and its parameters ensuring the highest accuracy of the abnormal situations recognition.

A new anomalous text detection approach using unsupervised methods

Increasing size of text data in databases requires appropriate classification and analysis in order to acquire knowledge and improve the quality of decision-making in organizations. The process of discovering the hidden patterns in the data set, called data mining, requires access to quality data in order to receive a valid response from the system. Detecting and removing anomalous data is one of the pre-processing steps and cleaning data in this process. Methods for anomalous data detection are generally classified into three groups including supervised, semi-supervised, and unsupervised. This research tried to offer an unsupervised approach for spotting the anomalous data in text collections. In the proposed method, a combination of two approaches (i.e., clustering-based and distance-based) is used for detecting anomaly in the text data. In order to evaluate the efficiency of the proposed approach, this method is applied on four labeled data sets. The accuracy of Na?ve Bayes classification algorithms and decision tree are compared before and after removal of anomalous data with the proposed method and some other methods such as Density-based spatial clustering of applications with noise (DBSCAN). Our proposed method shows that accuracy of more than 92.39% can be achieved. In general, the results revealed that in most cases the proposed method has a good performance.

Detecting Anomalous Data in Household Surveys: Evidence for Argentina

Abstract This paper advances in the detection of anomalous data in income reports of Argentina. In particular, income declared by households surveyed in the Encuesta Permanente de Hogares (EPH, Permanent Household Survey in English) -for the period 2003-2017- and in the Encuesta Anual de Hogares Urbanos (EAHU, Annual Urban Household Survey in English) -for the period 2010-2014- are analyzed. A widely known technique in forensic accounting and auditing, such as Benford’s law -also known as the first digit law- is used. If the analyzed data were generated naturally-free of manipulation- it should follow the logarithmic distribution of Benford. The Chi-square test and the absolute mean deviation (MAD) are used for verification. The results suggest that the income reported in the EPH does not follow the Benford distribution and the degree of compliance with this law decreases significantly between 2007-2015 coinciding with the intervention period of the Instituto Nacional de Estadísticas y Censos (INDEC, National Institute of Statistics and Censuses in English).

AUDIT: AnomaloUs data Detection and Isolation approach for mobile healThcare systems

AbstractMobile health care systems highly depend on collected physiological data through medical sensors to provide high‐quality care services. However, inaccurate physiological data from sensors pose a major challenge for health care providers when making decisions, whereas an erroneous decision can affect the user's life. We propose, in this paper, an anomalous data detection and isolation approach for mobile health care systems. Our approach, called AUDIT, detects inaccurate measurements in real time and distinguishes between faults or errors and health events. To do so, we propose reduced time and space complexities algorithms based on dimension reduction within the context of resource constraints. Furthermore, a decision algorithm is proposed while exploring the spatio‐temporal correlation between physiological attributes. First, we describe our approach. Then, we give its implementation details. Finally, to demonstrate the effectiveness of our approach, we show different experiments related to its detection performances and its time and space complexities.

Special Issue on Recent Advances in Constitutive and Numerical Methods for Sustainable Civil Infrastructures

This special issue of the International Journal of Geomechanics contains 10 papers that cover numerical and experimental investigations on various aspects of sustainable civil infrastructures. The topics include the self-healing capability of asphalt, cracking and fracture of asphalt pavement and portland cement concrete, soilimprovement techniques (including compaction and vertical drains), and various foundation systems. There are two papers on asphalt. The self-healing of asphalt mixtures can extend the fatigue life of asphalt pavement. Huang et al. developed a method based on fuzzy evaluation and the analytic hierarchy process for evaluating the self-healing capability of asphalt mixtures. The feasibility and effectiveness of the method were validated by a case study. To understand the mechanisms of material failure is essential for the design and construction of sustainable civil infrastructures. Chen et al. proposed a multiscale numerical modeling approach to analyze the distress of asphalt pavement on steel bridge decks and applied the approach to a case study. Their results highlighted the importance of bridge structure and pavement evenness in the distribution of pavement cracks. One paper focuses on concrete fracture and damage. Xu et al. investigated the spallation failure of fiber-reinforced concrete slabs under impact loading. Their numerical simulations showed that fibers can remarkably improve the tensile strength of concrete slabs and effectively limit the initiation and propagation of cracks. Soil improvement is an important element of sustainable civil infrastructures. Three papers are related to soil-improvement techniques, including compaction and vertical drains. Nie et al. presented an integrated theoretical and case study on anomalous data detection for roller-integrated compactionmeasurement. Their results showed that the proposed bidimensional anomalous data-identification method rendered a more accurate correlation, whereas the proposed neighbor-weighted estimation method improved the precision of compaction evaluation. Two papers are related to vertical drains. Azari et al. applied an elastic–viscoplastic model to model soft soil improved with vertical drains and compared their simulation results with field measurements. Their results showed that the distribution of the overconsolidation ratios in the disturbed zone greatly influenced the viscoplastic strain rates, creep strain limits, and consolidation. Parsa-Pajouh et al. evaluated the efficiency of several proposed formulations for plane-strain modeling of vertical drain-assisted consolidation through an integrated numerical and experimental investigation. By comparing the predicted and measured pore pressures in well-controlled laboratory tests, the advantages and disadvantages of these formulations were discussed. The remaining four papers deal with foundation systems. A better understanding of soil–structure interaction can lead to optimized foundation design and construction, which increase the sustainability of many civil infrastructures. Zhou and Dai presented a new strut-and-tie model for the analysis of force distribution among piles, pile caps, and superstructure components, including struts and ties. Through two case studies, they demonstrated the effectiveness and accuracy of their model. Farouk and Farouk examined the effect of a superstructure’s rigidity on the contact stress and differential settlement for plane two-bay frames. They found that the rigidities of walls and slabs have significant effects on the resultant average contact stresses and the maximum settlements under the footings, which affect the differential settlements. They provided new charts and equations for calculating the average contact stress and maximum settlements under the inner and outer footings for plane two-bay frames. Zhang et al. developed a numerical model to investigate the working mechanism of pervious concrete piles. Their model was validated by a case study. Their results showed that pervious concrete piles can reduce foundation settlement caused by their high stiffness and permeability and, hence, are particularly suitable for reinforcing foundations with low bearing capacity and soils with poor permeability. Yang et al. conducted a numerical investigation on the load-displacement behavior of a reinforced strip footing using a double-yield model. The effects of various parameters, such as burial depth, reinforcement length, and arrangement of two reinforcement layers, were studied. Their results showed that the load-displacement behavior of strip footings simulated with the double-yield model is more realistic than that with the Mohr-Coulomb model, and the optimal burial depth and length of reinforcement obtained from their study agreed well with values reported by previous investigators.