Time series anomaly detection receives increasing research interest given the growing number of data-rich application domains. Recent additions to anomaly detection methods in research literature include deep learning algorithms. The nature and performance of these algorithms in sequence analysis enable them to learn hierarchical discriminating features and time-series temporal nature. However, their performance is affected by the speed at which the time series arrives, the use of a fixed threshold, and the assumption of Gaussian distribution on the prediction error to identify anomalous values. An exact parametric distribution is often not directly relevant in many applications and it’s often difficult to select an appropriate threshold that will differentiate anomalies with noise. Thus, implementations need the Prediction Interval (PI) that quantifies the level of uncertainty associated with the Deep Neural Network (DNN) point forecasts, which helps in making a better-informed decision and mitigates against false anomaly alerts. To achieve this, a new anomaly detection method is proposed that computes the uncertainty in estimates using quantile regression and used the quantile interval to identify anomalies. Similarly, to handle the speed at which the data arrives, an online anomaly detection method is proposed where a model is trained incrementally to adapt to the concept drift that improves prediction. This is implemented using a window-based strategy, in which a time series is broken into sliding windows of sub-sequences as input to the model. To adapt to concept drift, the model is updated when changes occur in the new arrival instances. This is achieved by using anomaly likelihood which is computed using the Q-function to define the abnormal degree of the current data point based on the previous data points. Specifically, when concept drift occurs, the proposed method will mark the current data point as anomalous. However, when the abnormal behavior continues for a longer period of time, the abnormal degree of the current data point will be low compared to the previous data points using the likelihood. As such, the current data point is added to the previous data to retrain the model which will allow the model to learn the new characteristics of the data and hence adapt to the concept changes thereby redefining the abnormal behavior. The proposed method also incorporates feature extraction to capture structural patterns in the time series. This is especially significant for multivariate time-series data, for which there is a need to capture the complex temporal dependencies that may exist between the variables. In summary, this thesis contributes to the theory, design, and development of algorithms and models for the detection of anomalies in both static and evolving time series data. Several experiments were conducted, and the results obtained indicate the significance of this research on offline and online anomaly detection in both static and evolving time-series data. In chapter 3, the newly proposed method (Deep Quantile Regression Anomaly Detection Method) is evaluated and compared with six other prediction-based anomaly detection methods that assume a normal distribution of prediction or reconstruction error for the identification of anomalies. Results in the first part of the experiment indicate that DQR-AD obtained relatively better precision than all other methods which demonstrates the capability of the method in detecting a higher number of anomalous points with low false positive rates. Also, the results show that DQR-AD is approximately 2 – 3 times better than the DeepAnT which performs better than all the remaining methods on all domains in the NAB dataset. In the second part of the experiment, sMAP dataset is used with 4-dimensional features to demonstrate the method on multivariate time-series data. Experimental result shows DQR-AD have 10% better performance than AE on three datasets (SMAP1, SMAP3, and SMAP5) and equal performance on the remaining two datasets. In chapter 5, two levels of experiments were conducted basis of false-positive rate and concept drift adaptation. In the first level of the experiment, the result shows that online DQR-AD is 18% better than both DQR-AD and VAE-LSTM on five NAB datasets. Similarly, results in the second level of the experiment show that the online DQR-AD method has better performance than five counterpart methods with a relatively 10% margin on six out of the seven NAB datasets. This result demonstrates how concept drift adaptation strategies adopted in the proposed online DQR-AD improve the performance of anomaly detection in time series. / Petroleum Technology Development Fund (PTDF)

This paper studies the differences and similarities between the discrete annuity divisor of the income pension compared to the continuous annuity divisor of the premium pension in Sweden. First discrete and continuous annuity divisors are compared and found to be equivalent given the same underlying mortality. The income divisor is based on observed mortality in a period setting while the premium divisor which is based on projected mortality in a cohort setting. The expected performance of the two methods is studied by constructing prediction intervals based on Lee-Carter models with either a Binomial or Poisson distribution. Prediction intervals are constructed using either residual bootstrap or parametric bootstrap. The premium annuity divisor is found to outperform the income annuity divisor, there is a large risk that the latter underestimates the future mortality. / Den här uppsatsen studerar skillnader och likheter mellan inkomstpensionens diskreta delningstal och premiepensionens kontinuerliga delningstal i Sverige. Först jämförs diskreta och kontinuerliga delningstal och finns vara likvärdiga när de baseras på samma dödlighet. Inkomstpensionens delningstal är baserad på observerad period-dödlighet medan premiepensionens delningstal är baserad på projekterad kohort-dödlighet. Prediktionsintervall används för att skatta hur bra de två metoderna är. Med hjälp av Lee-Carter-modellen baserad på antingen poissonfördelning eller binomialfördelning konstrueras prediktionsintervall. Bootstrap, antingen parametrisk eller baserad på residualerna, används för att skapa prediktionsintervallen. Premiumpensionens delningstal stämmer väl överens med prediktionsintervallen medan det för inkomstpensionens delningstal finns en stor risk att framtida dödlighet underskattas.

Efficient and effective road traffic prediction and management techniques are crucial in intelligent transportation systems. It can positively influence road advancement, safety enhancement, regulation formulation, and route planning to save living things in advance from road traffic accidents. This thesis considers road safety by predicting the number of casualties if an accident occurs using multiple traffic accident attributes. It helps individuals (drivers) or traffic offices to adjust and control their contributions for the occurrence of an accident before emerging it. Three candidate algorithms from different regression fit patterns are proposed and evaluated to conduct the thesis: the bagging, linear, and non-linear fitting patterns. The gradient boosting machines (GBoost) from the bagging, Linearsupport vector regression (LinearSVR) from the linear, and extreme learning machines (ELM) also from the non-linear side are the selected algorithms. RMSE and MAE performance evaluation metrics are applied to evaluate the models. The GBoost achieved a better performance than the other two with a low error rate and minimum prediction interval value for 95% prediction interval. A SHAP (SHapley Additive exPlanations) interpretation technique is applied to interpret each model at the global interpretation level using SHAP’s beeswarm plots. Finally, suggestions for future improvements are presented via the dataset and hyperparameter tuning.

Reliability analysis plays an important role in keeping manufacturers in a competitive position. It can be applied in many areas such as warranty predictions, maintenance scheduling, spare parts provisioning, and risk assessment. This dissertation focuses on statistical modeling and predictions based on lifetime data, degradation data, and recurrent event data. The datasets used in this dissertation come from the field, and have complicated structures. The dissertation consists of three main chapters, in addition to Chapter 1 which is the introduction chapter, and Chapter 5 which is the general conclusion chapter. Chapter 2 consists of the traditional time-to-failure data analysis. We propose a statistical method to address the failure data from an appliance used at home with the consideration of retirement times and delayed reporting time. We also develop a prediction method based on the proposed model. Using the information of retirement-time distribution and delayed reporting time, the predictions are more accurate and useful in the decision making. In Chapter 3, we introduce a nonlinear mixed-effects general path model to incorporate dynamic covariates into degradation data analysis. Dynamic covariates include time-varying environmental variables and usage condition. The shapes of the effect functions of covariates may be constrained to be, for example, monotonically increasing (i.e., higher temperature is likely to cause more damage). Incorporating dynamic covariates with shape restrictions is challenging. A modified alternative algorithm and the corresponding prediction method are proposed. In Chapter 4, we introduce a multi-level trend-renewal process (MTRP) model to describe component-level events in multi-level repairable systems. In particular, we consider two-level repairable systems in which events can occur at the subsystem level, or the component (within the subsystem) level. The main goal is to develop a method for estimation of model parameters and a procedure for prediction of the future replacement events at component level with the consideration of the effects from the subsystem replacement events. To explain unit-to-unit variability, time-dependent covariates as well as random effects are introduced into the heterogeneous MTRP model (HMTRP). A Metropolis-within-Gibbs algorithm is used to estimate the unknown parameters in the HMTRP model. The proposed method is illustrated by a simulated dataset. / Ph. D.