Traditional Estimation Methods Research Articles

Optimizing prior distribution parameters for probabilistic prediction of remaining useful life using deep learning

In this study, a deep learning-based probabilistic remaining useful life (RUL) prediction model is proposed to improve the strong prior limitations of traditional probabilistic RUL prediction methods through a flexible prior distribution and strategy for sequential optimization of hyperparameters with regularization factor. It enables output richer probabilistic lifetime density distributions and confidence intervals with various parameters and overcome the problem of poor accuracy of short RUL predictions to some extent. Eventually, the model is effectively validated on a benchmark dataset, and the experimental results show that the probabilistic lifetime prediction model with optimized prior distribution parameters significantly improves prediction performance and demonstrates good learning performance and robustness of test results compared with traditional point estimation methods and parameter-free models. This study informs maintenance decisions and reliability assessments in engineering systems and guides the research and application of probabilistic-based prediction methods in deep learning framework.

Distributional Regression for Data Analysis

The flexible modeling of an entire distribution as a function of covariates, known as distributional regression, has seen growing interest over the past decades in both the statistics and machine learning literature. This review outlines selected state-of-the-art statistical approaches to distributional regression, complemented with alternatives from machine learning. Topics covered include the similarities and differences between these approaches, extensions, properties and limitations, estimation procedures, and the availability of software. In view of the increasing complexity and availability of large-scale data, this review also discusses the scalability of traditional estimation methods, current trends, and open challenges. Illustrations are provided using data on childhood malnutrition in Nigeria and Australian electricity prices.

Deep learning based channel estimation method for mine OFDM system

In this paper, we present a channel estimation approach based on deep learning to solve the problem that the orthogonal frequency division multiplexing (OFDM) system channel estimation algorithm cannot accurately obtain the channel state information in the complex environment of the mine, resulting in system performance degradation. First, LS channel estimation matrix is considered as a low-resolution image and the actual channel state information is considered as a high-resolution image. Then the optimization of the LS channel estimation matrix is achieved by the FSRCNN image super-resolution algorithm. We validate the effectiveness of the proposed algorithm by conducting experiments in different channel environments, different number of pilots, and mismatched signal-to-noise ratio scenarios. The simulation results show that the proposed scheme is much better than the traditional LS channel estimation method and the DFT-LS channel estimation method, and the accuracy of the proposed scheme approaches that of the MMSE channel estimation method when the number of pilots is low.

BRD_ESRNet and SRS-Based Channel Estimation

In wireless communication, the channel function estimated commonly has errors due to the influence of noise, so traditional channel estimation methods cannot accurately estimate the real channel function. Aiming at this problem, we propose a channel estimation method that combines sounding reference signal (SRS) remapping with the deep-learning network BRD_ESRNet. BRD_ESRNet consists of image denoising using a deep convolutional neural network with batch renormalization (BRDNet) and an expanded superresolution convolutional neural network (ESRCNN). At the transmitter side, we first map the SRS into four-box structures, and then, the four-box structures are scattered distribution throughout the time-frequency resource block. At the receiver side, we first perform the modified least squares (LS) estimation based on the four-box structure and place the result into the top-left resource unit of the four box. Then, we perform linear interpolation for the whole resource block. Finally, we equate the estimated channel matrix to a low-resolution image containing noise and input it to BRD_ESRNet. Thus, we obtain data with high resolution and achieve the purpose of reducing the estimation error of the channel function. The experimental results show that the proposed method in this paper has a significant improvement in performance compared to the methods of Soltani et al. and Nithya et al. In this paper, the methods of Soltani et al. and Nithya et al. are referred to as methods 1 and 2, respectively.

Non-cooperative underwater acoustic MFSK time-frequency representation optimization method based on sparse reconstruction

The performance of the traditional non-cooperative underwater acoustic (UWA) multiple frequency shift key (MFSK) recognition and parameter estimation method based on time-frequency representation (TFR) is affected by TFR energy divergence. Herein, a sparse TFR estimation model for UWA MFSK is presented. The model exploits the properties of MFSK TFR element sparsity and row sparsity, which can effectively reduce the impact of the channel and does not require any a priori information. To achieve better TFR performance, we propose an inversion fitting method that can effectively improve the frequency resolution, while keeping the time resolution unchanged. Simulation and experimental results show that the Peak Signal to Noise Ratio (PSNR) of the proposed method reaches 21dB with the increase of Signal to Noise Ratio (SNR), indicating that the proposed method has high carrier frequency reconstruction and noise suppression performance. The proposed method can continuously reduce the value of Average Carrier Frequency Offset (ACFO) under inversion fitting method, indicating that inversion fitting method can further reduce the energy divergence and improve frequency resolution.

Estimation, Comparison, and Projection of Multifactor Age–Cohort Affine Mortality Models

Affine mortality models, developed in continuous time, are well suited to longevity risk applications including pricing and capital management. A major advantage of this mortality modeling approach is the availability of closed-form cohort survival curves, consistent with the assumed time dynamics of mortality rates. This article makes new contributions to the estimation of multifactor continuous-time affine models including the canonical Blackburn-Sherris, the arbitrage-free Nelson-Siegel (AFNS), and the Cox-Ingersoll-Ross (CIR) mortality models. We discuss and address numerical issues with model estimation. We apply the estimation methods to age–cohort mortality data from five different countries, providing insights into the dynamics of mortality rates and the fitting performance of the models. We show how the use of maximum likelihood with the univariate Kalman filter turns out to be faster and more robust compared to traditional estimation methods that heavily use large matrix multiplication and inversion. We present graphical and numerical goodness-of-fit results and assess model robustness. We project cohort survival curves and assess the out-of-sample performance of the models for the five countries. We confirm previous results by showing that, across these countries, although the CIR mortality model fits the historical mortality data well, particularly at older ages, the canonical and AFNS affine mortality models provide better out-of-sample performance. We also show how these affine mortality models are robust with respect to the set of age–cohort data used for parameter estimation. R code is provided.

A novel bearing-time record estimation method based on α-stabledistribution modeling

Bearing-time record (BTR) is widely used in the field of passive sonar information processing for target tracking. Most existing BTR estimation methods of ship radiated noise are generally based on energy-varying under the assumption of Gaussian modeling in the time domain. However, some weak trajectories may exist in BTR for the decentralized energy distribution and unstable goodness of fit with Gaussian modeling caused by the spatiotemporal instability of the marine environment. In this paper, a novel ship trajectory enhancement method which is based on α-stable distribution modeling theory is presented. In order to make the statistical characteristic of ship radiated noise better reflected, the proposed method utilizes the α-stable distribution modeling in the real part of ship radiated noise Discrete Fourier Transform (DFT) coefficient instead of the Gaussian modeling in the time domain. The scale parameter γ of α-stable distribution is substituted for variance and enhanced BTR is achieved. According to the experimental results, the real part of the DFT coefficient of ship radiated noise could be fitted by α-stable distribution at the significant level of 0.05. Compared with traditional BTR estimation method, the proposed method could gain 3.1dB enhancement on peak signal-to-noise ratio (PSNR).

Pricing quanto options with market liquidity risk.

This paper investigates the pricing problem of quanto options with market liquidity risk using the Bayesian method. The increasing volatility of global financial markets has made liquidity risk a significant factor that should be taken into consideration while evaluating option prices. To address this issue, we first derive the pricing formula for quanto options with liquidity risk. Next, we construct a likelihood function to conduct posterior inference on model parameters. We then propose a numerical algorithm to conduct statistical inferences on the option prices based on the posterior distribution. This proposed method considers the impact of parameter uncertainty on option prices. Finally, we conduct a comparison between the Bayesian method and traditional estimation methods to examine their validity. Empirical results show that our proposed method is feasible for pricing and predicting quanto options with liquidity risk, particularly for parameter estimations with a small sample size.

Deep adaptive temporal network (DAT-Net): an effective deep learning model for parameter estimation of radar multipath interference signals

Accurate parameter estimation in radar systems is critically hindered by multipath interference, a challenge that is amplified in complex and dynamic environments. Traditional methods for parameter estimation, which concentrate on single parameters and rely on statistical assumptions, often struggle in such scenarios. To address this, the deep adaptive temporal network (DAT-Net), an innovative deep learning model designed to handle the inherent complexities and non-stationarity of time series data, is proposed. In more detail, DAT-Net integrates both the pruned exact linear time method for effective time series segmentation and the exponential scaling-based importance evaluation algorithm for dynamic learning of importance weights. These methods enable the model to adapt to shifts in data distribution and provide a robust solution for parameter estimation. In addition, DAT-Net demonstrates the capability to comprehend inherent nonlinearities in radar multipath interference signals, thereby facilitating the modeling of intricate patterns within the data. Extensive validation experiments conducted across parameter estimation tasks and demonstrates the robust applicability and efficiency of the proposed DAT-Net model. The architecture yield root mean squared error scores as low as 0.0051 for single-parameter estimation and 0.0152 for multiple-parameter estimation.

Measuring irregular migration in Chile: The use of data linkage methods

Foreign population in Chile almost doubled between 2017 and 2021. In recent years, the sources to measure the phenomenon has been the 2017 Census, plus administrative data from the migratory institutions. Yet, traditional estimation methods have not included irregular migration in all its forms, despite the fact that between 2018 and 2022 illegal entries grew by 754\%. Official numbers had only included (1) people registered by the day of the census, and (2) people that, from that day at least applied for one residence permit. However, records from other public institutions (education, health and police) suggests there are a considerable number of migrants that meets neither of the two criteria, that don’t have and official Chilean ID (RUN), but have registered in different services with provisional identifiers.
 In order to properly account for irregular migration flows, this exploratory study presents a method of deterministic integration of personal administrative records from different public institutions (police, health, education and migrations), of foreign people that don’t have a unique identifier (RUN), using personal variables: names, surnames and date of birth. The proposed methodology can be summarized in four steps: (1) cleaning and standardizing records and variables (2) building an identification key and removing exact duplicated records in each data set (3) removing partial duplicated records in each data set using fuzzy matching techniques, and (4) matching the data sets using fuzzing matching techniques. The result of this procedure is the number of foreign people that showed signs of being residents by registering in the public services, but don’t have any registration of visa applications with the National Migration Service. These individuals, according with the existing law (Law N° 21.325), live in a (probable) irregular status.
 This study not only represents and innovation in estimating foreign population in Chile as it accounts for inhabitants in irregular situation, but it also proposes a novel standard of registration and integration of personal administrative records of different public services.

Estimation of turnout irregularities using vehicle responses with improved BiLSTM and Gaussian process regression

Railway turnout irregularities pose a safety risk, but existing detection methods using expensive trains with inertial navigation systems and laser measurement devices are cost-prohibitive and time-consuming for high-speed railways. This paper proposes a low-cost and real-time solution for estimating railway turnout irregularities using vehicle body acceleration, allowing for continuous monitoring of dynamic changes. A Bayesian-optimized improved bidirectional long short-term memory neural network model (BO-BiLSTM) was proposed in this paper, utilizing the vehicle's vertical and lateral acceleration as input to achieve point estimation of irregularities, with an estimation error approximately 50% lower than that of traditional recurrent neural networks. In addition, an interval estimation model combining BO-BiLSTM and Gaussian process regression (BO-BiLSTM-GPR) was proposed. Compared to the traditional interval estimation method Bootstrap, under the condition of narrow interval width, GPR ensures that over 90% of the measured values fall within the estimated interval and provides a better solution to the trade-off between interval estimation reliability and uncertainty.

Voltage profile reconstruction and state of health estimation for lithium-ion batteries under dynamic working conditions

The state of health (SOH) of batteries is an important but unmeasurable parameter closely related to battery safety and durability. However, most existing SOH estimation strategies rely on a specific load profile (e.g., constant current). To tackle this issue, we here report a method that first converts the dynamic voltage trajectories to the curves corresponding to the constant current profiles using a neural network model. Then, the aging characteristics are selected and the battery SOH is estimated accordingly from the converted voltage data using a Gaussian process regression model. Batteries with different aging degrees are tested with different working conditions to verify the proposed method. Numerically, the errors of the voltage reconstruction are bounded within 2 mV, while the SOH estimation errors under four dynamic working conditions remain within 2%. Our technical approach reduces the dependency of traditional SOH estimation methods on specific working conditions and shows strong potential for practical applications.

Deep Unfolding Network for Efficient Mixed Video Noise Removal

Existing image and video denoising algorithms have focused on removing homogeneous Gaussian noise. However, this assumption with noise modeling is often too simplistic for the characteristics of real-world noise. Moreover, the design of network architectures in most deep learning-based video denoising methods is heuristic, ignoring valuable domain knowledge. In this paper, we propose a model-guided deep unfolding network for the more challenging and realistic mixed noise video denoising problem, named DU-MVDnet. First, we develop a novel observation model/likelihood function based on the correlations among adjacent degraded frames. In the framework of Bayesian deep learning, we introduce a deep image denoiser prior and obtain an iterative optimization algorithm based on the maximum a posterior (MAP) estimation. To facilitate end-to-end optimization, the iterative algorithm is transformed into a deep convolutional neural network (DCNN)-based implementation. Furthermore, recognizing the limitations of traditional motion estimation and compensation methods, we propose an efficient multistage recursive fusion strategy to exploit temporal dependencies. Specifically, we divide video frames into several overlapping groups and progressively integrate these frames into one frame. Toward this objective, we implement a multiframe adaptive aggregation operation to integrate feature maps of intragroup with those of intergroup frames. Extensive experimental results on different video test datasets have demonstrated that the proposed model-guided deep network outperforms current state-of-the-art video denoising algorithms such as FastDVDnet and MAP-VDNet.

Discrete-time event-triggered state estimation of permanent magnet synchronous motor

This article considers the design of a discrete-time event-triggered state observer and its application for state vector estimation of permanent magnet synchronous motor. A novel discrete-time event-triggered mechanism is first proposed, and then a new event-triggered state observer is designed to estimate the state vectors of a nonlinear system subject to unknown disturbances. Unlike traditional state estimation methods, the one in this article utilizes information on the output, which only updates when an event-triggered condition holds. By employing the Lyapunov–Krasovskii approach and well-known inequalities, we derive a sufficient condition in terms of a convex optimization problem to guarantee the existence of the event-triggered state observer. Finally, the theoretical analysis of the proposed method is applied to estimate the state vector of the permanent magnet synchronous motor.

A 2D-DOA Sparse Estimation Method with Total Variation Regularization for Spatially Extended Sources

In this paper, a novel two-dimensional direction of arrival (2D-DOA) estimation method with total variation regularization is proposed to deal with the problem of sparse DOA estimation for spatially extended sources. In a general sparse framework, the sparse 2D-DOA estimation problem is formulated with the regularization of extended source characteristics including spatial position grouping, acoustic signal block sparse, and correlation features. An extended sources acoustic model, two-dimensional array manifold and its complete representation, total variation regularization penalty term, and the regularization equation are built, and are utilized to seek the solutions where the non-zero coefficients are grouped together with optimum sparseness. A total variation sparse 2D-DOA estimation model is constructed by combining total variation regularization with LASSO. The model can be easily solved by the convex optimization algorithm, and the solving process can promote the sparsity of the solution on the spatial derivatives and the solution itself. The theoretical analysis results show that the steps of decorrelation processing and angle matching of traditional 2D-DOA estimation methods could be avoided when adopting the proposed method. The proposed method has better robustness to noise, better sparsity, and faster estimation speed with higher resolution than traditional methods. It is promising to provide a coherent sources sparse representation of a non-strictly sparse field.

A new improvement Liu-type estimator for the Bell regression model

The Poisson Regression Model (PRM) is a well-known model in applications when the response variable consists of count data. However, Bell Regression Model (BRM) is proposed recently as an alternative to the PRM in some cases where the data is over-dispersed. But, multicollinearity between explanatory variables negatively affects traditional estimation methods, such as MLE. Therefore, to avoid this problem, several shrinkage estimators are proposed in the BRM. In this study, a new improved Liu-type estimator is proposed as an alternative to the other proposed biased estimators for the BRM to model count data with over-dispersion. Furthermore, the Monte Carlo simulation studies are executed to compare the performances of the proposed biased estimators. Finally, the obtained results are illustrated in real data.

A Cardinality Estimator in Complex Database Systems Based on TreeLSTM.

Cardinality estimation is critical for database management systems (DBMSs) to execute query optimization tasks, which can guide the query optimizer in choosing the best execution plan. However, traditional cardinality estimation methods cannot provide accurate estimates because they cannot accurately capture the correlation between multiple tables. Several recent studies have revealed that learning-based cardinality estimation methods can address the shortcomings of traditional methods and provide more accurate estimates. However, the learning-based cardinality estimation methods still have large errors when an SQL query involves multiple tables or is very complex. To address this problem, we propose a sampling-based tree long short-term memory (TreeLSTM) neural network to model queries. The proposed model addresses the weakness of traditional methods when no sampled tuples match the predicates and considers the join relationship between multiple tables and the conjunction and disjunction operations between predicates. We construct subexpressions as trees using operator types between predicates and improve the performance and accuracy of cardinality estimation by capturing the join-crossing correlations between tables and the order dependencies between predicates. In addition, we construct a new loss function to overcome the drawback that Q-error cannot distinguish between large and small cardinalities. Extensive experimental results from real-world datasets show that our proposed model improves the estimation quality and outperforms traditional cardinality estimation methods and the other compared deep learning methods in three evaluation metrics: Q-error, MAE, and SMAPE.

Towards affordable 3D physics-based river flow rating: application over the Luangwa River basin

Abstract. Uncrewed aerial vehicles (UAVs), affordable precise global navigation satellite system hardware, multi-beam echo sounders, open-source 3D hydrodynamic modelling software, and freely available satellite data have opened up opportunities for a robust, affordable, physics-based approach to monitoring river flows. Traditional methods of river discharge estimation are based on point measurements, and heterogeneity of the river geometry is not contemplated. In contrast, a UAV-based system which makes use of geotagged images captured and merged through photogrammetry in order to generate a high-resolution digital elevation model (DEM) provides an alternative. This UAV system can capture the spatial variability in the channel shape for the purposes of input to a hydraulic model and hence probably a more accurate flow discharge. In short, the system can be used to produce the river geometry at greater resolution so as to improve the accuracy in discharge estimations. Three-dimensional hydrodynamic modelling offers a framework to establish relationships between river flow and state variables such as width and depth, while satellite images with surface water detection methods or altimetry records can be used to operationally monitor flows through the established rating curve. Uncertainties in the data acquisition may propagate into uncertainties in the relationships found between discharge and state variables. Variations in acquired geometry emanate from the different ground control point (GCP) densities and distributions used during photogrammetry-based terrain reconstruction. In this study, we develop a rating curve using affordable data collection methods and basic principles of physics. The basic principal involves merging a photogrammetry-based dry bathymetry and wet bathymetry measured using an acoustic Doppler current profiler (ADCP). The output is a seamless bathymetry which is fed into the hydraulic model so as to estimate discharge. The impact of uncertainties in the geometry on discharge estimation is investigated. The impact of uncertainties in satellite observation of depth and width is also analysed. The study shows comparable results between the 3D and traditional river rating discharge estimations. The rating curve derived on the basis of 3D hydraulic modelling was within a 95 % confidence interval of the traditional gauging-based rating curve. The 3D-hydraulic-model-based estimation requires determination of the roughness coefficient within the stable bed and the floodplain using field observation at the end of both the dry and wet season. Furthermore, the study demonstrates that variations in the density of GCPs beyond an optimal number have no significant influence on the resultant rating relationships. Finally, the study observes that which state variable approximation (water level and river width) is more accurate depends on the magnitude of the flow. Combining stage-appropriate proxies (water level when the floodplain is entirely filled and width when the floodplain is filling) in data-limited environments yields more accurate discharge estimations. The study was able to successfully apply advanced UAV and real-time kinematic positioning (RTK) technologies for accurate river monitoring through hydraulic modelling. This system may not be cheaper than in situ monitoring; however, it is notably more affordable than other systems such as crewed aircraft with lidar. In this study the calibration of the hydraulic model is based on surface velocity and the water depth. The validation is based on visual inspection of an RTK-based waterline. In future studies, a larger number of in situ gauge readings may be considered so as to optimize the validation process.

Enhanced Particle Swarm Optimization Algorithm for Sea Clutter Parameter Estimation in Generalized Pareto Distribution

Accurate parameter estimation is essential for modeling the statistical characteristics of ocean clutter. Common parameter estimation methods in generalized Pareto distribution models have limitations, such as restricted parameter ranges, lack of closed-form expressions, and low estimation accuracy. In this study, the particle swarm optimization (PSO) algorithm is used to solve the non-closed-form parameter estimation equations of the generalized Pareto distribution. The goodness-of-fit experiments show that the PSO algorithm effectively solves the non-closed parameter estimation problem and enhances the robustness of fitting the generalized Pareto distribution to heavy-tailed oceanic clutter data. In addition, a new parameter estimation method for the generalized Pareto distribution is proposed in this study. By using the difference between the statistical histogram of the data and the probability density function/cumulative distribution function of the generalized Pareto distribution as the target, an adaptive function with weighted coefficients is constructed to estimate the distribution parameters. A hybrid PSO (HPSO) algorithm is used to search for the best position of the fitness function to achieve the best parameter estimation of the generalized Pareto distribution. Simulation analysis shows that the HPSO algorithm outperforms the PSO algorithm in solving the parameter optimization task of the generalized Pareto distribution. A comparison with other traditional parameter estimation methods for generalized Pareto distribution shows that the HPSOHPSO algorithm exhibits strong parameter estimation performance, is efficient and stable, and is not limited by the parameter range.

Reachable set estimation for discrete-time Markovian jump neural networks with unified uncertain transition probability

This paper focuses on the reachable set estimation for Markovian jump neural networks with time delay. By allowing uncertainty in the transition probabilities, a framework unifies and enhances the generality and realism of these systems. To fully exploit the unified uncertain transition probabilities, an equivalent transformation technique is introduced as an alternative to traditional estimation methods, effectively utilizing the information of transition probabilities. Furthermore, a vector Wirtinger-based summation inequality is proposed, which captures more system information compared to existing ones. Building upon these components, a novel condition that guarantees a reachable set estimation is presented for Markovian jump neural networks with unified uncertain transition probabilities. A numerical example is illustrated to demonstrate the superiority of the approaches.