Monte Carlo Filtering Research Articles

Automated Manufacturing Robot Fault Diagnosis in Real Time Using Convolutional Neural Networks

This study introduced a novel real-time Fault Diagnosis Model (FDM) in manufacturing robots by integrating Depthwise Convolutional Neural Networks (CNNs) with Bidirectional Long Short-Term Memory (BiLSTM) networks. The objective is to design a model that can handle the complex high-dimensional sensor data that arrives out of complex, non-linear systems for effective FDM. The work introduced a Feature Extraction (FE) model based on Monte Carlo Filtering (MCF). The work integrates a Depthwise CNN with BiLSTM (DC-BiLSTM) for diagnosis. The integration helps to reduce the computational need and, at the same time, preserve the feature representation. The model was experimented against other models, such as CNN, Long Short-Term Memory (LSTM), Recurrent Neural Network (RNN), and Feed-Forward Neural Networks (FFNN), using a fault dataset sourced from a simulated environment. The results have shown that the proposed model fared well in terms of accuracy, precision, recall, and F1 score against all compared models. The results have judged the proposed model’s applicability in the field of fault diagnosis, which could effectively predict mishaps in advance, thereby helping with efficient maintenance and ensuring continuous productivity.

Antithetic multilevel particle filters

Abstract In this paper we consider the filtering of partially observed multidimensional diffusion processes that are observed regularly at discrete times. This is a challenging problem which requires the use of advanced numerical schemes based upon time-discretization of the diffusion process and then the application of particle filters. Perhaps the state-of-the-art method for moderate-dimensional problems is the multilevel particle filter of Jasra et al. (SIAM J. Numer. Anal.55 (2017), 3068–3096). This is a method that combines multilevel Monte Carlo and particle filters. The approach in that article is based intrinsically upon an Euler discretization method. We develop a new particle filter based upon the antithetic truncated Milstein scheme of Giles and Szpruch (Ann. Appl. Prob.24 (2014), 1585–1620). We show empirically for a class of diffusion problems that, for $\epsilon>0$ given, the cost to produce a mean squared error (MSE) of $\mathcal{O}(\epsilon^2)$ in the estimation of the filter is $\mathcal{O}(\epsilon^{-2}\log(\epsilon)^2)$ . In the case of multidimensional diffusions with non-constant diffusion coefficient, the method of Jasra et al. (2017) requires a cost of $\mathcal{O}(\epsilon^{-2.5})$ to achieve the same MSE.

Characterizing the Opportunity Space for Sustainable Hydrothermal Valorization of Wet Organic Wastes.

Resource recovery from wet organic wastes can support circular economies by creating financial incentives to produce renewable energy and return nutrients to agriculture. In this study, we characterize the potential for hydrothermal liquefaction (HTL)-based resource recovery systems to advance the economic and environmental sustainability of wastewater sludge, FOG (fats, oils, and grease), food waste, green waste, and animal manure management through the production of liquid biofuels (naphtha, diesel), fertilizers (struvite, ammonium sulfate), and power (heat, electricity). From the waste management perspective, median costs range from -193 $·tonne-1 (FOG) to 251 $·tonne-1 (green waste), and median carbon intensities range from 367 kg CO2 eq·tonne-1 (wastewater sludge) to 769 kg CO2 eq·tonne-1 (green waste). From the fuel production perspective, the minimum selling price of renewable diesel blendstocks are within the commercial diesel price range (2.37 to 5.81 $·gal-1) and have a lower carbon intensity than petroleum diesel (101 kg CO2 eq·MMBTU-1). Finally, through uncertainty analysis and Monte Carlo filtering, we set specific targets (i.e., achieve wastewater sludge-to-biocrude yield >0.440) for the future development of hydrothermal waste management system components. Overall, our work demonstrates the potential of HTL-based resource recovery systems to reduce the costs and carbon intensity of resource-rich organic wastes.

Quality criterion and errors of corrected negative SEA loss factors

Statistical Energy Analysis (SEA) is a well-known numerical method for predicting vibroacoustic phenomena in complex systems. The accuracy of SEA models relies on the precise determination of coupling loss factors and damping loss factors. Experimental SEA (E-SEA) methods, such as the Power Injection Method are commonly employed to measure these parameters. However, these techniques may yield negative loss factors, which are considered measurement errors. Monte Carlo Filtering (MCF) is one of the procedures, that allows the correction of negative loss factors, but the quality of the results remains unknown. The knowledge of the loss factors’ quality is directly related to the practical applications of SEA, where good quality of the input model parameters (coupling and damping loss factors) correspond to good quality and precise simulations of complex vibroacoustic systems (like trains, vehicle, airplanes, buildings) responses. In a previous study, a total loss factor (TLF) criterion was proposed as a quality indicator for the corrected loss factors. The current paper validates the TLF criterion through a comprehensive analysis of various numerical examples. By expanding the Monte Carlo sample’s value range (search area) and using different probability density functions, we intentionally introduced errors in the loss factors. The TLF criterion demonstrated resilience to increasing errors in certain scenarios, raising concerns about its sensitivity. Nevertheless, it seems, that the TLF criterion remains a good indicator of population stability and large error occurrence.

Solution of a model for pricing options with hedging strategy through Nonlinear Filters

A methodology is presented to estimate the solution states for a non-linear price problem, a model for pricing options with a hedging strategy in the F$\ddot{o}$llmer-Schweizer sense is defined. The problem is to determine the price of a contingent claim, that is a contract, that pays of an amount at time $t$ in a incomplete market, that is not possible to replicate a payoff by a controlled portfolio of the basic securities. Two algorithms are presented to estimate the solution of the presented problem, the nested sequential Monte Carlo (NSMC) and space-time particle filter (STPF) are defined from sequences of probability distributions. The methodology is validated to use real data from option Asian, the states in real-time are estimated, that is proposed on the basis of the a price model. The efficiency of the forecasts of the model is compared, reproducing accuracy in the estimates. Finally, one goodness-of-fit measure to validate the performance of the model are used, obtaining insignificant estimation error.

モンテカルロフィルタに基づく眼球回旋運動の計測法

In recent years, various studies on anthropometry using video images have been actively conducted. Of those applications, the measurement of eye movements is expected in fields such as medical care, and human interface. The eye movements include horizontal and vertical translations due to the movement of the gaze and torsional eye movements. This paper proposes a method for accurately measuring the torsional eye movement, which is generally considered difficult to measure with high accuracy. We have improved the Monte Carlo filter, which was traditionally used for object tracking in translational motion, so that it can also measure rotational motion. Evaluation experiments indicated that the measurement error using the proposed method was in a range between 0.07±0.49° to -0.03±0.54°, while the measurement accuracy of the conventional matching method was 0.28±0.81°. In addition, the results suggest that the proposed method can measure even a blurred iris image with a relatively small error.

Data quality enhancement for field experiments in atmospheric chemistry via sequential Monte Carlo filters

Abstract. In this study, we explore the applications and limitations of sequential Monte Carlo (SMC) filters to field experiments in atmospheric chemistry. The proposed algorithm is simple, fast, versatile and returns a complete probability distribution. It combines information from measurements with known system dynamics to decrease the uncertainty of measured variables. The method shows high potential to increase data coverage, precision and even possibilities to infer unmeasured variables. We extend the original SMC algorithm with an activity variable that gates the proposed reactions. This extension makes the algorithm more robust when dynamical processes not considered in the calculation dominate and the information provided via measurements is limited. The activity variable also provides a quantitative measure of the dominant processes. Free parameters of the algorithm and their effect on the SMC result are analyzed. The algorithm reacts very sensitively to the estimated speed of stochastic variation. We provide a scheme to choose this value appropriately. In a simulation study, O3, NO, NO2 and jNO2 are tested for interpolation and de-noising using measurement data of a field campaign. Generally, the SMC method performs well under most conditions, with some dependence on the particular variable being analyzed.

On off-line and on-line Bayesian filtering for uncertainty quantification of structural deterioration

Abstract Data-informed predictive maintenance planning largely relies on stochastic deterioration models. Monitoring information can be utilized to update sequentially the knowledge on model parameters. In this context, on-line (recursive) Bayesian filtering algorithms typically fail to properly quantify the full posterior uncertainty of time-invariant model parameters. Off-line (batch) algorithms are—in principle—better suited for the uncertainty quantification task, yet they are computationally prohibitive in sequential settings. In this work, we adapt and investigate selected Bayesian filters for parameter estimation: an on-line particle filter, an on-line iterated batch importance sampling filter, which performs Markov Chain Monte Carlo (MCMC) move steps, and an off-line MCMC-based sequential Monte Carlo filter. A Gaussian mixture model approximates the posterior distribution within the resampling process in all three filters. Two numerical examples provide the basis for a comparative assessment. The first example considers a low-dimensional, nonlinear, non-Gaussian probabilistic fatigue crack growth model that is updated with sequential monitoring measurements. The second high-dimensional, linear, Gaussian example employs a random field to model corrosion deterioration across a beam, which is updated with sequential sensor measurements. The numerical investigations provide insights into the performance of off-line and on-line filters in terms of the accuracy of posterior estimates and the computational cost, when applied to problems of different nature, increasing dimensionality and varying sensor information amount. Importantly, they show that a tailored implementation of the on-line particle filter proves competitive with the computationally demanding MCMC-based filters. Suggestions on the choice of the appropriate method in function of problem characteristics are provided.

A Modification of the Monte Carlo Filtering Approach for Correcting Negative SEA Loss Factors

Monte Carlo Filtering (MCF) is one of the methods of Experimental Statistical Energy Analysis (E-SEA), which allows the correction of negative LFs (Loss Factors). In this article, a modification of the MCF method, called DESA (Diagonal Expansion of the Search Area), is proposed. The technique applies a non-uniform extension of the search area when generating a population of normalized energy matrices. The degree of expansion of the search area is controlled by the Diagonal Penalty Factor (DPF). The authors demonstrated the method’s effectiveness on a system that could not be identified in several frequency bands by the classical MCF method. After applying DESA, it was possible to fill in the problematic bands that were missing CLF (coupling loss factor) and DLF (damping loss factor) values. The paper also proposes a way to minimize the errors introduced by using overly high DPF values.

Bayesian inference-based prognosis of fatigue damage for MPPO polymer using Zhurkov fatigue life model

In this study, the fatigue damage prognosis of a modified polyphenylene oxide (MPPO) polymer is performed using a Bayesian framework, and a Zhurkov model-based dynamic fatigue life model is employed to obtain the probabilistic stress–cycle (P-S-N) curve. Activation energy and tensile tests are performed to determine the aleatory uncertainty of the lethargy coefficient of the Zhurkov fatigue life model. This uncertainty is quantified by performing sequential statistical modeling using experimental data with embedded scattering. The P-S-N curve is estimated using these data, and the Zhurkov fatigue life model is validated via the fatigue test. Furthermore, damage data are obtained via a low-cycle fatigue analysis in conditions identical to those of the fatigue test conducted on the specimen scale. Based on computational damage data, the initial model parameters of the fatigue damage model are obtained using the least-squares method. These model parameters are estimated while considering scattering by applying the Markov Chain Monte Carlo and particle filter. Therefore, the remaining useful life (RUL) of the MPPO, which depends on the amplitude stress, is predicted under the tension–tension fatigue loading ( R = 0), and the prediction accuracy of the RUL is evaluated using prognostics metrics.

Predicting and optimizing syngas production from fluidized bed biomass gasifiers: A machine learning approach

Biomass gasification is one of the primary thermal conversion processes where fluidized bed reactors are often used to produce syngas with low heating values. However, there has not yet been an effective model to predict gasification yield with broad applicability. In this study, machine learning was adopted to realize the prediction of syngas compositions and lower heating values (LHV) using various lignocellulosic biomass feedstocks at a wide range of operating conditions. Three machine learning techniques, i.e., Random Forest (RF), Support Vector Machine (SVM) and Artificial Neural Network (ANN) were adopted after determining hyperparameters optimization. Pearson correlation and permutation importance were used for the sensitivity analysis. RF and ANN were found to have high prediction accuracy with R2 and RMSE results (RF: R2=0.809–0.946, RMSE=1.39–11.54%; ANN: R2=0.565–0.924, RMSE=1.46–10.56%). Monte Carlo filtering (MCF) was integrated into the three machine learning algorithms to forecast the desired products by predicting the important features of the operating conditions and biomass characteristics. Considering the desired H2/CO > 1.1 and LHV > 5.86 MJ/m3, the RF-MCF was a more suitable approach with R2=0.791–0.902 for H2, CO and LHV features. The machine learning approach can be widely adapted in various scenarios predicting output features as well as MCF for finding the significant variables for optimization.

Dynamic downscaling and daily nowcasting from influenza surveillance data.

Real‐time trends from surveillance data are important to assess and develop preparedness for influenza outbreaks. The overwhelming testing demand and limited capacity of testing laboratories for viral positivity render daily confirmed case data inaccurate and delay its availability in preparedness. Using Bayesian dynamic downscaling models, we obtained posterior estimates for daily influenza incidences from weekly estimates of the Centers for Disease Control and Prevention and daily reported constitutional and respiratory complaints during emergency department (ED) visits obtained from the state health departments. Our model provides one‐day and seven‐day lead forecasts along with 95% prediction intervals. Our hybrid Markov Chain Monte Carlo and Kalman filter algorithms facilitate faster computation and enable us to update our estimates as new data become available. Our method is tested and validated using the State of Michigan data over the years 2009‐2013. Reported constitutional and respiratory complaints at the EDs showed strong correlations of 0.81 and 0.68 respectively, with influenza rates. In general, our forecast model can be adapted to track an outbreak with only one respiratory virus as a causative agent.

A new filtering inference procedure for a GED state-space volatility model

A vast amount of methods have been developed to make inferences for volatility data, taking into account the stylized facts of rate/return data. However, the common problem is that the latent parameters of many volatility models are high-dimensional and analytically intractable. Therefore, their inference procedure requires numerical approximations using intensive computational techniques, as the Markov chain Monte Carlo, Laplace, and particle filter methods. A common strategy to overcome this problem is model linearization. This approach consists of writing the stochastic volatility model as a linear Gaussian state-space model, leading to an approximated marginal likelihood using the Kalman filter, reducing the problem’s dimensionality. This paper proposes a new filtering inference procedure with an integrated likelihood for a Generalized Error Distribution (GED) state-space volatility model without model linearization. Also, we evaluate the quality of our method approximation and introduce an approximated smoothing procedure. We use the Bayesian methods for making the inference of static parameters and perform a simulation exercise to study the estimators’ properties. Our results show that the proposed model can be reasonably estimated, and the approximation of our method is reasonable. Furthermore, we provide a case study of the pound/dollar and real/dollar exchange rate to illustrate our approach’s performance. For the real/dollar time series, the model captures a high volatility pattern due to the COVID-19 pandemic.

Accelerating Groundwater Data Assimilation With a Gradient‐Free Active Subspace Method

AbstractGroundwater models always involve high‐dimensional parameters, which makes computationally tractable data assimilation using surrogate models very challenging. To address this issue, one common practice is to employ dimension reduction (DR) techniques. Nevertheless, traditional DR methods are usually implemented based on prior parameter statistics, that is, without considering the inherent system dynamics. Here, we show that when significant difference in parameter sensitivity exists, further efficiency can be achieved by adopting a supervised DR method, that is, the active subspace (AS) method. To avoid non‐trivial efforts in calculating the gradient information needed in the standard AS method, a cluster‐based gradient‐free AS (GFAS) method is developed in this study. By combining GFAS with Gaussian process regression, a surrogate model for the CPU‐demanding groundwater model can be adaptively constructed to accelerate data assimilation. Furthermore, a compensation scheme is proposed to cope with uncertainty underestimation caused by DR. The developed approach is tested with numerical experiments and field cases, which illustrated that the new approach is more efficient than the previously developed unsupervised ones by incorporating sensitivity information. Although an iterative ensemble smoother is employed in this study, the proposed method can also be used in other data assimilation approaches, such as Markov chain Monte Carlo and ensemble Kalman filter.

Performance study of iterative Bayesian filtering to develop an efficient calibration framework for DEM

This work presents an efficient probabilistic framework for the Bayesian calibration of micro-mechanical parameters for Discrete Element Method (DEM) modelling. Firstly, the superior behaviour of the iterative Bayesian filter over the sequential Monte Carlo filter for calibrating micro-mechanical parameters is shown. The linear contact model with rolling resistance is used for simulating the triaxial responses of Toyoura sand under different confining pressures. Secondly, synthetic data from DEM simulations of triaxial compression are used to assess the reliability of iterative Bayesian filtering with respect to the user-defined parameters, such as the number of samples and predefined parameter ranges. Excellent calibration results with errors between 1 and 2% are obtained when the number of samples is chosen high enough. It is crucial that the sample size is representative for the distribution of individual parameters within the predefined parameter ranges. The wider the ranges, the more samples are required. The investigation also shows the necessity of including both stress and strain histories, at certain confidence levels, for estimation of the correct mechanical responses, especially the correct fabric responses. Finally, based on the findings of this work a fully-automated open-source calibration tool is developed and demonstrated for selected stress paths.

Bagged filters for partially observed interacting systems

Bagging (i.e., bootstrap aggregating) involves combining an ensemble of bootstrap estimators. We consider bagging for inference from noisy or incomplete measurements on a collection of interacting stochastic dynamic systems. Each system is called a unit, and each unit is associated with a spatial location. A motivating example arises in epidemiology, where each unit is a city: the majority of transmission occurs within a city, with smaller yet epidemiologically important interactions arising from disease transmission between cities. Monte Carlo filtering methods used for inference on nonlinear non-Gaussian systems can suffer from a curse of dimensionality as the number of units increases. We introduce bagged filter (BF) methodology which combines an ensemble of Monte Carlo filters, using spatiotemporally localized weights to select successful filters at each unit and time. We obtain conditions under which likelihood evaluation using a BF algorithm can beat a curse of dimensionality, and we demonstrate applicability even when these conditions do not hold. BF can out-perform an ensemble Kalman filter on a coupled population dynamics model describing infectious disease transmission. A block particle filter also performs well on this task, though the bagged filter respects smoothness and conservation laws that a block particle filter can violate.

Sequential Monte Carlo Filters with Parameters Learning for Commodity Pricing Models

In this article, an estimation methodology based on the sequential Monte Carlo algorithm is proposed, thatjointly estimate the states and parameters, the relationship between the prices of futures contracts and the spot prices of primary products is determined, the evolution of prices and the volatility of the historical data of the primary market (Gold and Soybean) are analyzed. Two stochastic models for an estimate the states and parameters are considered, the parameters and states describe physical measure (associated with the price) and risk-neutral measure (associated with the markets to futures), the price dynamics in the short-term through the reversion to the mean and volatility are determined, while that in the long term through markets to futures. Other characteristics such as seasonal patterns, price spikes, market dependent volatilities, and non-seasonality can also be observed. In the methodology, a parameter learning algorithm is used, specifically, three algorithms are proposed, that is the sequential Monte Carlo estimation (SMC) for state space modelswith unknown parameters: the first method is considered a particle filter that is based on the sampling algorithm of sequential importance with resampling (SISR). The second implemented method is the Storvik algorithm [19], the states and parameters of the posterior distribution are estimated that have supported in low-dimensional spaces, a sufficient statistics from the sample of the filtered distribution is considered. The third method is (PLS) Carvalho’s Particle Learning and Smoothing algorithm [31]. The cash prices of the contracts with future delivery dates are analyzed. The results indicate postponement of payment, the future prices on different maturity dates with the spot price are highly correlated. Likewise, the contracts with a delivery date for the last periods of the year 2017, the spot price lower than the prices of the contracts with expiration date for 12 and 24 months is found, opposite occurs in the contracts with expiration date for 1 and 6 months.

Two-Dimensional Monte Carlo Filter for a Non-Gaussian Environment

In a non-Gaussian environment, the accuracy of a Kalman filter might be reduced. In this paper, a two- dimensional Monte Carlo Filter is proposed to overcome the challenge of the non-Gaussian environment for filtering. The two-dimensional Monte Carlo (TMC) method is first proposed to improve the efficacy of the sampling. Then, the TMC filter (TMCF) algorithm is proposed to solve the non-Gaussian filter problem based on the TMC. In the TMCF, particles are deployed in the confidence interval uniformly in terms of the sampling interval, and their weights are calculated based on Bayesian inference. Then, the posterior distribution is described more accurately with less particles and their weights. Different from the PF, the TMCF completes the transfer of the distribution using a series of calculations of weights and uses particles to occupy the state space in the confidence interval. Numerical simulations demonstrated that, the accuracy of the TMCF approximates the Kalman filter (KF) (the error is about 10−6) in a two-dimensional linear/ Gaussian environment. In a two-dimensional linear/non-Gaussian system, the accuracy of the TMCF is improved by 0.01, and the computation time reduced to 0.067 s from 0.20 s, compared with the particle filter.

Extremum sensitivity analysis with polynomial Monte Carlo filtering

Global sensitivity analysis is a powerful set of ideas and heuristics for understanding the importance and interplay between uncertain parameters in a computational model. Such a model is characterized by a set of input parameters and an output quantity of interest, where we typically assume that the inputs are independent and their marginal densities are known. If the output quantity is smooth, polynomial chaos can be used to extract Sobol’ indices.In this paper, we build on these well-known ideas by examining two different aspects of this paradigm. First, we study whether sensitivity indices can be computed efficiently if one leverages a polynomial ridge approximation—a polynomial fit over a subspace. Given the assumption of anisotropy in the dependence of a function, we show that sensitivity indices can be computed with a reduced number of model evaluations. Second, we discuss methods for evaluating sensitivities when constrained near output extrema. Methods based on the analysis of skewness are reviewed and a novel type of indices based on Monte Carlo filtering (MCF) – extremum Sobol’ indices – is proposed. We combine these two ideas by showing that these indices can be computed efficiently with ridge approximations, and explore the relationship between MCF-based indices and skewness-based indices empirically.

Monte Carlo Filter-Based Motion Artifact Removal From Electrocardiogram Signal for Real-Time Telecardiology System

Motion artifact (MA) contamination with electrocardiogram (ECG) signal is a common issue caused by body movement or sensor loosening, resulting in distortion of clinical features of ECG. In this work, the Monte Carlo filter (MCF)-based MA removal from single-channel ECG signal is proposed, assisting in real-time telecardiology systems. Initially, after R-peak detection and beat extraction, principal component (PC) analysis was performed upon clean ECG beats, and PC, with the highest energy, was assumed to be the feature beat. Using this feature beat, MA corrupted beats were denoised successively to achieve a clean pattern of ECG using MCF. A new approach of weight calculation and resampling was also proposed for better performance of the MCF. Performance of the proposed algorithm was tested on the IEEE Signal Processing Cup Challenge 2015 ECG database and MIT-BIH arrythmia records, with an improvement of signal-to-noise ratio between 10 and 15 dB, after MA removal. The proposed work was also tested on real-time ECG data collected from ten healthy volunteers using the AD8232 ECG module and Raspberry Pi, resulting in correlation coefficient higher than 0.99, between the original and denoised signals. The proposed algorithm was able to remove MA from any single-channel MA corrupted ECG signal, irrespective of lead category, using features of clean beats. A comparative study of the obtained result with previously published works ensured the superior performance on MA removal from ECG in the proposed work, along with real-time data collection, processing, and transmission.