Parameter Estimation Problem Research Articles

A contact parameter estimation method for multi-modal robot locomotion on deformable granular terrains

AbstractIn this paper, we consider the problem of contact parameters (slippage and sinkage) estimation for multi-modal robot locomotion on granular terrains. To describe the contact events in the same framework for robots operated at different modes (e.g., wheel, leg), we propose a unified description of contact parameters for multi-modal robots. We also provide a parameter estimation method for multi-modal robots based on CNN and DWT (discrete wavelet transformation) techniques and verify its effectiveness over different types of granular terrains. Besides motion modes, this paper also considers the influence of slope angles and the robot’s handing angles over contact parameters. Through comparison and analysis of the prediction results, our method can not only effectively predict the contact parameters of multi-modal robot locomotion on a granular medium (better than $96\%$ accuracy) but also achieves the same or better performance when compared to other (direct) contact measurement methods designed for individual motion modes, that is, single-modal robots such as quadruped robots and mars rovers. Our proposed unified contact parameter estimation method can be useful for studying the interaction mechanics between multi-modal robots and granular terrains as well as terrain classification tasks due to its superior sensitivity which is analyzed in the experiments.

Novel kinetic modeling strategy for industrial-scale UNIPOL polypropylene with Ziegler-Natta catalyst

Polypropylene (PP) is a synthetic resin with exceptional physical and chemical properties, making it suitable for various household and industrial applications. However, as the demand for PP continues to rise, the polypropylene industry faces challenges in improving its quality and efficiency. Developing an accurate mathematical model that describes the continuous polymerization process is crucial for enhancing PP production, as it is useful for controlling product quality and improving production efficiency. While previous studies have focused on modeling propylene polymerization using laboratory-scale and pilot-scale reactors, these models do not effectively apply to industrial-scale processes due to the complexity of the industrial environment. Therefore, a novel kinetic modeling method combining the modeling of the kinetic mechanism of the polymerization reaction with an intelligent optimization algorithm for the industrial-scale continuous gas-phase fluidized bed propylene polymerization process is proposed. To establish the kinetic mechanism model, the improved moments (MOM) method is utilized to derive a set of mass balance equations that account for various fundamental processes such as catalyst activation, chain initiation, chain growth, chain transfer to hydrogen, chain transfer to monomers, chain transfer to co-catalysts, and spontaneous deactivation. However, kinetic parameters serve as the link between the theoretical model and the actual production process, so the kinetic parameters estimation problem need to be transformed into a multi-objective problem by minimizing the least squares difference between the measurement data of the actual industry process and the predicted result of the kinetic model. Therefore, an improved multi-objective mayfly algorithm (IMOMA) is introduced to estimate the polymerization kinetic parameters, which incorporates the simulated binary crossover (SBX) operator and the polynomial mutation (PM) operator into the basic multi-objective mayfly algorithm (MOMA). Finally, by fitting industrial measurement data of the melt index (MI) and the polymerization rate (PR) of an actual polypropylene industrial case study, the proposed algorithm accurately determines the polymerization kinetic parameters. The results demonstrate that the MOM-IMOMA modeling approach outperforms other methods and holds significant promise for industrial-scale polypropylene production.

Parameter estimation with reluctant quantum walks: a maximum likelihood approach

The parametric maximum likelihood estimation problem is addressed in the context of quantum walk theory for quantum walks on the lattice of integers. A coin action is presented, with the real parameter θ to be estimated identified with the angular argument of an orthogonal reshuffling matrix. We provide analytic results for the probability distribution for a quantum walker to be displaced by d units from its initial position after k steps. For k large, we show that the likelihood is sharply peaked at a displacement determined by the ratio d/k which is correlated with the reshuffling parameter θ. We suggest that this ‘reluctant walker’ behaviour provides the framework for maximum likelihood estimation analysis, allowing for robust parameter estimation of θ via return probabilities of closed evolution loops and quantum measurements of the position of quantum walker with ‘reluctance index’ r = d/k.

Multi-objective parameter estimation on cultivation of yeast Kluyveromyces marxianus var. lactis MC5

In this study, the most appropriate form of the specific growth rate of the yeast Kluyweromyces marxianus var lactis MC5 was determined by a multi-criteria decision-making method (PROMETHEE II). Then, based on experimental data from a total of six batch processes, the simultaneous estimation of the kinetic parameters for four batch processes was made. The remaining two experiments were used to test the model. The parameter estimation problem was designed as a multi-objective optimisation problem. The method of scalarisation of the weighted sum was used. In this way, the multi-objective optimisation problem was converted to a single-objective one. The direct search method was used to solve the problem of obtaining the Pareto solution. In order to test the resulting solution, two batches of experimental data were additionally used. The obtained results showed that the model satisfactorily described the test data. The validated kinetic model can be used for optimal control of batch and fed-batch fermentation.

Distributionally robust parameter estimation for nonlinear fed-batch switched time-delay system with moment constraints of uncertain measured output data

<p>In this paper, we investigated a nonlinear continuous-time switched time-delay (NCTSTD) system for glycerol fed-batch bioconversion to 1, 3-propanediol with unknown time-delay and system parameters. The measured output data was uncertain, while the first moment information about its distribution was available. Our goal was to identify these unknown quantities under the environment of uncertain measurement output data. A distributionally robust parameter estimation problem (i.e., a bi-level parameter estimation (BLPE) problem) subject to the NCTSTD system was presented, where the expectation of the discrepancy between the output of the NCTSTD system and the uncertain measured output data with respect to its probability distributions was included in the cost functional. By applying the duality theory, the BLPE problem was transformed into a single-level parameter estimation (SLPE) problem with non-smooth term approximated by a smoothing technique and its error analysis was given. Then, the gradients of the cost function of the SLPE problem were derived. A hybrid optimization algorithm was proposed for solving the SLPE problem. The paper concluded by presenting the simulation results.</p>

On the Rademacher perturbed geometric distribution

This paper introduces a new discrete distribution that depends on two parameters. It can be described as a perturbed version of the standard geometric distribution by adding a ?random noise? following the Rademacher distribution. Depending on the values of its parameters, this new distribution can be unimodal or bimodal, as well as underdispersed or overdispersed. After reviewing its main properties, the problem of parameter estimation is examined and an application to a practical data set is given.

Deep Ensemble Transformers for Dimensionality Reduction.

We propose deep ensemble transformers (DETs), a fast, scalable approach for dimensionality reduction problems. This method leverages the power of deep neural networks and employs cascade ensemble techniques as its fundamental feature extraction tool. To handle high-dimensional data, our approach employs a flexible number of intermediate layers sequentially. These layers progressively transform the input data into decision tree predictions. To further enhance prediction performance, the output from the final intermediate layer is fed through a feed-forward neural network architecture for final prediction. We derive an upper bound of the disparity between the generalization error and the empirical error and demonstrate that it converges to zero. This highlights the generalizability of our method to parameter estimation and feature selection problems. In our experimental evaluations, DETs outperform existing models in terms of prediction accuracy, representation learning ability, and computational time. Specifically, the method achieves over 95% accuracy in gene expression data and can be trained on average 50% faster than traditional artificial neural networks (ANNs).

DESIGN OF EXPERIMENTS VIA MULTI-FIDELITY SURROGATES AND STATISTICAL SENSITIVITY MEASURES

Parameter estimation and optimal experimental design problems have been widely studied across science and engineering. The two are inextricably linked, with optimally designed experiments leading to better-estimated parameters. This link becomes even more crucial when available experiments produce minimal data due to practical constraints of limited experimental budgets. This work presents a novel framework that allows for the identification of optimal experimental arrangement, from a finite set of possibilities, for precise parameter estimation. The proposed framework relies on two pillars. First, we use multi-fidelity modeling to create reliable surrogates that relate unknown parameters to a measurable quantity of interest for a multitude of available choices defined through a set of candidate control vectors. Secondly, we quantify the "estimation potential" of an arrangement from the set of control vectors through the examination of statistical sensitivity measures calculated from the constructed surrogates. The measures of sensitivity are defined using analysis of variance as well as directional statistics. Two numerical examples are provided, where we demonstrate how the correlation between the estimation potential and the frequency of precise parameter estimation can inform the choice of optimal arrangement.

Analytical modeling of novel equivalent circuits of double diode solar cell circuits using a special transcendental function approach.

Solar photovoltaic (PV) cell modeling is crucial to understanding and optimizing solar energy systems. While the single-diode model (PVSDM) is commonly used, the double-diode model (PVDDM) offers improved accuracy at a reasonable level of complexity. However, finding analytical closed-form solutions for the current-voltage (I-U) dependency in PVDDM circuits has remained a challenge. This work proposes two novel configurations of PVDDM equivalent circuits and derives their analytical closed-form solutions. The solutions are expressed in terms of the Lambert W function and solved using a special transcendental function approach called Special Trans Function Theory (STFT). The accuracy of the proposed equivalent circuits is demonstrated on two solar cells/modules, RTC-F and MSX-60, showing equal or better performance than the standard PVDDM equivalent circuit. Further testing on a commercial solar panel under different irradiance and temperature conditions confirms the applicability of the proposed models. To address the parameter estimation problem, a novel metaheuristic algorithm, the chaotic honey-badger algorithm, is developed and evaluated. The results obtained validate the accuracy and practicality of the proposed PVDDM equivalent circuit configurations.

A SIR Model with Incomplete Data for the Analysis of Influenza A Spread in Ningbo

In this article, the SIR model is used to fit the spread of influenza A in Ningbo, ranging from January 1, 2023 to June 30, 2023. The data that can be collected is the daily newly confirmed cases, but the daily number of infected individuals and recovered individuals is unknown. The initial number of susceptible individuals with exposure risk is also unknown. Based on the incompleteness of the data, the parameter estimation problem of the SIR model is transformed into an optimization problem. The Particle Swarm Optimization algorithm is used to solve the optimization problem. The goodness of fit (R2) of the daily cumulative number of confirmed cases is 0.998. The model can reflect the cycle, peak, and trend of the entire spread of influenza A and is consistent with reality during the post‐COVID‐19 period.

Channel Estimation and Pilot Design for Uplink Sparse Code Multiple Access System based on Complex-Valued Sparse Autoencoder

Channel estimation is one of the most important aspects of wireless communication. Especially in Sparse Code Multiple Access (SCMA) system, the accuracy of channel estimation has a significant impact on decoding performance. Various methods, so far, have been developed for channel estimation. Most of these methods regard channel estimation as a parameter estimation problem of linear models. However, these methods require lots of time-frequency resources to ensure high estimation accuracy. In massive connection scenarios, high pilot overhead makes the spectrum resource more scarce. Therefore, the drawback of conventional channel estimation methods limits the further improvement of system capacity in the Internet of Things(IoT) when time-frequency resources is restricted. To address this problem, in this paper, we propose an efficient channel estimation scheme and sparse pilot structure design method in SCMA system based on complex-valued sparse autoencoder which is effective to learn features of wireless channel. Complex-valued sparse autoencoder is a kind of neural network with complex-valued weights. It contains two parts: encoder and decoder. In our work, the encoder part is used to realize pilot design. Channel estimation is implemented by the decoder. Complex-valued weights obtained from training are used as baseband pilots. Compared with maximum likelihood channel estimation (MLE) of linear model, the proposed method can achieve higher channel estimation accuracy with more sparse pilot structure. The bit-error rates performance of the SCMA receiver in our work is very close to that of the perfect channel state information (CSI).

On Hybrid Prescribed-Time Concurrent Learning with Switching Datasets

We introduce a novel concurrent learning (CL) algorithm designed to solve parameter estimation problems within a user-prescribed time frame and by utilizing alternating datasets during the learning process. The algorithm can tackle applications involving switching data sets (including data sets that are completely uninformative) that are updated in real-time as the algorithm operates. To achieve parameter estimation within a specified time independent of the dataset’s richness, the switching algorithm employs dynamic gains. The main result establishes uniform global exponential ultimate boundedness, with an ultimate bound that shrinks to zero as the magnitude of the measurement disturbances decreases. The stability analysis leverages tools from hybrid dynamical systems theory, along with a recently introduced dilation/contraction argument on the hybrid time domains of the solutions. The algorithm and main results are illustrated via a numerical example.

The estimations of drift parameters for the Gaussian Vasicek process with time-varying volatility

This article mainly considers the parameter estimation problem for the Gaussian Vasicek process defined as d X t = ( α − β X t ) d t + σ t d G t , t≥0 with unknown parameters α∈ℝ and β < 0, where G t is a continuous centered Gaussian process. The volatility parameter σ t is allowed to vary with time t. Based on the time-continuous observations and least squares method, the Least squares estimations of drift parameters for the non ergodic Gaussian Vasicek model with time-varying volatility are obtained. The strong consistency and asymptotic distributions of proposed estimations are verified under some sufficient conditions. Finally, we verify that the results are still valid under different forms of the volatility function when G t is fractional Brownian motion, sub-fractional Brownian motion, and bi-fractional Brownian motion, respectively. In some sense, our results extend the findings of El Machkouri, Es-Sebaiy, and Ouknine (2016) and Es-Sebaiy and Sebaiy (2021).

Linear Convergence of distributed estimation with constraints and communication delays

Motivated by the multi-sensor estimation problem, we consider a distributed constraint parameter estimation problem on a directed graph. Our goal is to design a fast distributed algorithm to handle constraint parameter estimation problems, especially considering the communication delays when sensors interact on a directed graph. Based on the gradient-tracking algorithm and indirect projection method, the Projected Distributed Parameter Estimation Algorithm (PDPEA) is proposed, which can deal with the closed convex set constraint and use the historical information stored by the sensors to achieve fast and accurate mean gradient estimation. The analysis shows that the PDPEA converges to a global and consensual minimizer even under the influence of measurement noise, arbitrarily bounded communication delays, and directed information topologies. Under the assumption that the local cost function is strongly convex and smooth, we show that the algorithm converges at a linear rate for an appropriate choice of stepsize. Lastly, we demonstrate the effectiveness of the proposed algorithm by setting up a multi-sensor parameter estimation network.

Inverse method study based on Characteristic Statistic Algorithm (CSA) with application in estimating core states parameters

In reactor-related scenarios, inverse methods utilizing monitoring data are frequently employed to address issues such as state estimation, accident analysis, and power reconfiguration. These problem-solving approaches can entail converting the original problem into a parameter estimation problem. This paper presents a versatile and scalable framework for solving inverse problems by iterative optimization. To address intricate core parameter problems effectively, we incorporate the CPACT program, a physical thermal engineering solution program. Additionally, we employ the global optimization algorithm known as CSA (Characteristic Statistic Algorithm) to tackle specific challenges associated with nonlinear global optimization. To evaluate the performance of our framework, a numerical simulation model based on the Daya Bay Nuclear Power Plant was used as the test object design as our test subject.

Parameter Estimation of Electrical Vehicle Motor

Presently, the problem of parameter estimation of motors used in electrical vehicles is discussed. To make the control more efficient, a model of the electrical motor is developed. Then, a parameter estimation method is established to determine the parameters of the used electrical motor. The proposed method is easy and can be easily implemented. Furthermore, a mathematical model of an electrical vehicle’s motor using linear and nonlinear blocks is obtained. The given model will allow us to perform several experiments without any extra fees.

Recovery With Incomplete Knowledge: Fundamental Bounds on Real-Time Quantum Memories

The recovery of fragile quantum states from decoherence is the basis of building a quantum memory, with applications ranging from quantum communications to quantum computing. Many recovery techniques, such as quantum error correction, rely on the apriori knowledge of the environment noise parameters to achieve their best performance. However, such parameters are likely to drift in time in the context of implementing long-time quantum memories. This necessitates using a "spectator" system, which estimates the noise parameter in real-time, then feed-forwards the outcome to the recovery protocol as a classical side-information. The memory qubits and the spectator system hence comprise the building blocks for a real-time (i.e. drift-adapting) quantum memory. In this article, I consider spectator-based (incomplete knowledge) recovery protocols as a real-time parameter estimation problem (generally with nuisance parameters present), followed by the application of the "best-guess" recovery map to the memory qubits, as informed by the estimation outcome. I present information-theoretic and metrological bounds on the performance of this protocol, quantified by the diamond distance between the "best-guess" recovery and optimal recovery outcomes, thereby identifying the cost of adaptation in real-time quantum memories. Finally, I provide fundamental bounds for multi-cycle recovery in the form of recurrence inequalities. The latter suggests that incomplete knowledge of the noise could be an advantage, as errors from various cycles can cohere. These results are illustrated for the approximate [4,1] code of the amplitude-damping channel and relations to various fields are discussed.

Convergence analysis of a synchronous gradient estimation scheme for time-varying parameter systems

For the problem of time-varying parameter estimation and its convergence, this paper proposes an invariant matrix to represent the changing laws of time-varying parameters, which suggests a novel expression to describe the parameters by employing finite terms. A joint recursive least squares algorithm is derived by minimizing the criterion function associated with the unknown invariant matrix. For a class of time-varying systems, a joint stochastic gradient algorithm with the computational efficiency is obtained by analogy to achieve the estimation of invariant matrix and system parameters. The convergence analysis is explored to demonstrate that the time-varying parameter estimation error is bounded under the persistent excitation conditions. The simulation results also validate the effectiveness of the proposed synchronous parameter estimation approach.

Reliability assessment method for MEMS accelerometers based on uncertainty process

In this paper, according to the degradation data characteristics of MEMS (Micro-Electro-Mechanical Systems) accelerometers of small samples, the uncertainty theory is introduced into, and the reliability model of the product is established by deduction according to the three basic scientific principles of reliability analysis. In this paper, the parameter estimation and model validation problems are solved under the framework of uncertainty theory by using the great likelihood estimation and hypothesis testing method under the algorithm of uncertainty theory. It is analyzed that the MEMS accelerometer reliability model based on uncertainty theory is a new method for reliability assessment applicable to dealing with uncertainty problems in the absence of large samples of degraded data.

Parameter estimation in the pollutant dispersion problem with Physics-Informed Neural Networks

In this work, the inverse problem of parameter estimation in the advection-dispersion-reaction equation, modelling the pollutant dispersion in a river, is studied with a Neural Network approach. In the direct problem, the dispersion, velocity and reaction parameters are known and then the initial and boundary value problem is solved by classical numerical methods, where it is used as input dataset for the inverse problem and formulation. In the inverse problem, we know the dispersion and the velocity parameters and also the information about the pollutant concentration from the synthetic experimental data, and then the aim is to estimate the reaction parameter in the advection-dispersion-reaction equation. This inverse problem is solved by an usual Artificial Neural Network (ANN) and by a Physics-Informed Neural Network (PINN), which is a special type of neural networks that includes in its formulation the physical laws that describe the phenomena involved. Numerical experiments with both the ANN and PINN are presented, demonstrating the feasibility of the approach considered.