Multi-source Uncertainties Research Articles

Interval Uncertainty-Oriented Optimal Control Method for Spacecraft Attitude Control

Research on uncertainty-oriented optimal attitude control of spacecraft with complex space environments and multi-source uncertainties is a research hotspot. Considering that the uncertain parameters in the control system are difficult to quantify, this study proposed an interval uncertainty-oriented optimal control method based on the linear quadratic regulator (LQR) for spacecraft attitude control. The interval state-space equation of the spacecraft attitude dynamic with uncertain controlled feedback gain was constituted by expanding the deterministic model into an order-extended interval matrix format. Based on the interval uncertainty propagation method, the interval-based Riccati equation in LQR was proposed using the modified interval estimation method. Therefore, the interval-controlled feedback gain and interval cost function could be obtained, and the overestimation attributed to the interval expansion could be avoided. The interval-based reliability was investigated using the state-threshold interference model, and the interval-based safety index was developed. The interval uncertainty-based multi-objective optimal control model with constraints was proposed to balance both minimizations of the optimal control cost function and state vector fluctuation by considering these two interval indices as the constraints in optimal control. A flowchart and a numerical example of satellite attitude control were applied to reflect the effectiveness.

A new Bayesian probabilistic integration framework for hybrid uncertainty propagation

Efficient propagation of uncertainty is one of the most critical tasks for uncertainty quantification and reliable design in the presence of multi-source uncertainties. This work presents a new methodology framework, termed as “mixed imprecise probabilistic integration”, for efficient propagation of the uncertainties characterized by non-probabilistic models, imprecise probability models and precise probability models. In this paper, the mixed-high dimensional model representation combining the cut-high dimensional model representation and random sampling-high dimensional model representation is firstly proposed, which conserves all the advantages of these two methods. Secondly, the proposed method is realized by using mixed-high dimensional model representation and Bayesian inference. The estimations and the posterior variances of the proposed method are analytically derived of high accuracy. With the proposed method, all the three kinds of uncertainty models can be efficiently propagated with one set of function evaluations. The effectiveness of the proposed methods is demonstrated by three engineering examples.

Hyperelliptic Kalman filter-based aeroengine sensor fault FDIA system under multi-source uncertainty

Aeroengine faces multi-source uncertainty while operating. To reduce the conservativeness and improve the performance of the diagnosis system in complex environments, the multi-source uncertainty environment, which consists of aeroengine epistemic uncertainty and stochastic uncertainty of the control system, is considered in this paper. Based on polynomial chaos expansion (PCE), the uncertainty of the state response and output response is quantified. In addition, by proposing the hyperelliptic Kalman filter (HeKF), the optimal estimation of state correlation and output variance is realized, and the adaptive weighting matrix is provided on this basis. Combined with the thresholds calculated by design indicators of the diagnosis system, conservativeness-reduced fault detection is achieved. Ultimately, based on the fault matching idea, the hyperelliptic Kalman filter bank (HeKFB) is established and implemented for fault isolation and accommodation. Open-loop and closed-loop numerical simulations demonstrate that the proposed HeKF-based aeroengine sensor fault detection, isolation, and accommodation (FDIA) system is efficient under multi-source uncertainty conditions. Furthermore, compared to the extended Kalman filter (EKF) and the Kalman particle filter (KPF), the HeKF-based FDIA system is less conservative, more sensitive to minor faults, and superior in guaranteeing the security and reliability of aeroengine operation.

The Effects of Interval Uncertainties on Dynamic Characteristics of a Rotor System Supported by Oil-Film Bearings

Rotating systems equipped with oil-film bearings are critical and common in many industrial machines. There are various non-random uncertainties in such fluid-lubricated dynamic systems. It is important to quantify the effects of uncertainties without adequate statistical information on the dynamics of rotor-bearing systems. In this paper, a rotor system with oil-film bearings at both ends is investigated considering many interval uncertainties. The rotating system is modeled in a deterministic sense. The Chebyshev interval method is used to track the propagation of different uncertainties. Deviations in the steady state responses, time history, and shaft orbits are calculated and comparatively discussed. Influence patterns of different interval parameters and dispersions in various dynamics are presented in detail. It is found that there can be global and local impacts as well as cumulative effects caused by multi-source uncertainties. The findings of the present study could be helpful for a more insightful dynamic analysis of rotor-bearing systems as well as their optimal design and maintenance.

Analysis of Temperature and Thermal Stress for a Solar Power Tower Molten Salt Receiver under Multi-Source Uncertainties

Although uncertainties such as solar radiation and material properties are generally involved in the solar receiver design process, current studies in the solar receiver field are based on deterministic models and do not incorporate these uncertainties into the design process. In this paper, based on a coupled deterministic thermal–structural model and an uncertainty analysis model, an analysis of temperature and thermal stress was conducted for a solar power tower (SPT) molten salt receiver under multi-source uncertainties to investigate the dispersions of responses. The results demonstrated that the maximum temperature inside the tube wall under multi-source uncertainties ranged from 847 K to 895 K, with an expectation of 871 K and a standard deviation of 8 K, and the maximum thermal stress ranged from 173 MPa to 245 MPa, with an expectation of 204 MPa and a standard deviation of 12 MPa, both of which had severer probabilities than the deterministic results (871 K and 204 MPa) and may cause failure in the receiver. Furthermore, the results of the global sensitivity analysis indicated that the peak incident solar flux was the most sensitive, and the specific heat of the tube material was the least sensitive to the maximum temperature and thermal stress of the tube wall. These results are beneficial to provide additional reliability and confidence in the temperature and thermal stress evaluation process of solar receiver tubes.

Time-Dependent Sensitivity of Structural Reliability Assessment to Multi-Source Uncertainties Using Lamb Wave

Abstract This article investigates the time-dependent sensitivity of structural reliability assessment to multisource uncertainties using Lamb wave. To precisely model the influence of local damage on the structure in the course of damage growth, a surface damage effect model is proposed to obtain the equivalent elasticity modulus, which can be coupled with the structure model. The evolution of the surface damage is modeled using the fatigue crack propagation model. Furthermore, by setting up the component and structure failure criteria, the time-dependent reliability model of the structure under multisource uncertainties from Lamb wave detection and material properties is established. The method of score function is employed to evaluate the sensitivity index, which is defined as the derivative of the reliability with respect to the distribution parameters of uncertain variables. A spatial truss structure is used to demonstrate the overall procedure. Numerical results show that the sensitivities indices are time and damage size dependent. The sensitivity contributions from Lamb wave quantification model and the material properties are comparable when the crack size is relatively small. When the crack grows to a larger size, the reliability assessment result is much more sensitive to uncertainties associated with material properties.

Size-Dependent Mechanical Behaviors of Defective FGM Nanobeam Subjected to Random Loading

Considering the uncertainties of the materials and loads, the nanobeam made of functionally graded materials were investigated based on the non-local elastic theory. The spline finite point method (SFPM) was established to analyze the bending behavior of the nanobeam-based Timoshenko theory. In comparison with finite element method (FEM), SFPM has higher accuracy. Further, the multi-source uncertainties are considered, material properties are quantified as interval parameters, and loads are taken as random parameters. To deal with the problems with two types of uncertainties coexisting, a hybrid uncertain analysis model was established, and the method of polynomial chaos expansion and dimensional wise (PCE–DW) analysis was proposed to predict the response of nanobeam in the hybrid uncertain system. Numerical examples ultimately illustrate the effectiveness of the model and solution techniques, compared with MCS. The results furtherly verify the efficiency and accuracy.

Impact angle constrained fuzzy adaptive fault tolerant IGC method for Ski-to-Turn missiles with unsteady aerodynamics and multiple disturbances

An impact angle constrained fuzzy adaptive fault tolerant integrated guidance and control method for Ski-to-Turn (STT) missiles subject to unsteady aerodynamics and multiple disturbances is proposed. Unsteady aerodynamics appears when flight vehicles are in a transonic state or confronted with unstable airflow. Meanwhile, actuator failures and multisource model uncertainties are introduced. However, the boundaries of these multisource uncertainties are assumed unknown. The target is assumed to execute high maneuver movement which is unknown to the missile. Furthermore, impact angle constraint puts forward higher requirements for the interception accuracy of the integrated guidance and control (IGC) method. The impact angle constraint and the precise interception are established as the object of the IGC method. Then, the boundaries of the lumped disturbances are estimated, and several fuzzy logic systems are introduced to compensate the unknown nonlinearities and uncertainties. Next, a series of adaptive laws are developed so that the undesirable effects arising from unsteady aerodynamics, actuator failures and unknown uncertainties could be suppressed. Consequently, an impact angle constrained fuzzy adaptive fault tolerant IGC method with three loops is constructed and a perfect hit-to-kill interception with specified impact angle can be implemented. Eventually, the numerical simulations are conducted to verify the effectiveness and superiority of the proposed method.

Three-Dimensional Trajectory Tracking for a Heterogeneous XAUV via Finite-Time Robust Nonlinear Control and Optimal Rudder Allocation

This paper proposes a novel three-dimensional trajectory tracking control methodology for a heterogeneous X-rudder autonomous underwater vehicle (XAUV) that can achieve finite-time convergence, complex actuator dynamics handling, and energy-efficient optimized rudder allocation. Under a compound robust control scheme, the trajectory tracking problem is decomposed into three sub-problems: kinematics control, dynamics control, and rudder allocation. For kinematics control, a novel finite-time line-of-sight (FTLOS) guidance law is proposed, which can achieve faster position and orientation tracking when compared with classical LOS guidance, and is rarely studied in the existing finite time control methods. In the dynamics control loop, global finite-time terminal sliding mode control (FTTSMC) laws are provided to solve the heading control, pitching control, and surge velocity tracking control problems, where finite-time convergence is achieved in both the approaching stage and sliding mode holding stage. The multi-source uncertainties with unknown upper bounds in both kinematics and dynamics loops are well treated by finite-time extended disturbance observers (FTEDOs), thus ensuring the system robustness. Moreover, the influence of complex actuator dynamics is fully considered by employing a RBFNN compensator to deal with the propeller saturation and proposing an energy-efficient optimal rudder allocator to tackle the multi-objective and multi-constraint heterogeneous X-rudder angle assignment problem. Finally, simulation verifications are carried out for two different scenarios, where Case 1 focuses on the adaptability of the algorithm to different conditions and Case 2 focuses on the superiority of the algorithm over three other commonly used algorithms. The comparative simulation results show that the proposed controller has good adaptability to different initial and disturbance conditions, and performs better than three other classical controllers, especially in convergence speed, tracking accuracy, stability, and energy consumption.

Hybrid uncertainty propagation and reliability analysis using direct probability integral method and exponential convex model

Uncertainty propagation and reliability evaluation, being the crucial parts of engineering system analysis, play vital roles in safety assessment. How to reasonably consider the complex multisource uncertainty behavior in both static and dynamic systems is paramount to ensuring their safe operation. However, there is a significant lack of research on aleatory and epistemic uncertainties for both static and dynamic systems. To this end, a new hybrid exponential model is proposed by combining probabilistic and non-probabilistic exponential models, which aims to accurately measure the uncertainty propagation and reliability evaluation problem with aleatory and epistemic uncertainties for static and dynamic systems. The proposed hybrid exponential model consists of nested double optimization loops. The outer loop performs a probabilistic analysis based on the direct probability integral method, and the inner loop performs a non-probabilistic computation. Then, a new hybrid exponential probability integral method is developed to effectively perform uncertainty propagation and reliability analysis. Finally, four examples, including two static and two dynamic examples with complex performance functions, are tested. The results indicate that the proposed hybrid exponential model offers a universal tool for uncertainty quantification in static and dynamic systems. Moreover, the hybrid exponential probability integral method can accurately and efficiently obtain the upper and lower bounds of the probability density function and cumulative distribution function.

Attitude Autopilot Design Based on Fuzzy Linear Active Disturbance Rejection Control

In view of the multi-source uncertainty disturbance problem during flight control, the attitude autopilot based on fuzzy linear active disturbance rejection control (F-LADRC) was proposed. A second-order linear active disturbance rejection controller was designed to stabilize the attitude angle of the missiles, and the frequency domain characteristics were analyzed. Firstly, it was proved that the linear expansion state observer (LESO) is convergent and can achieve the indifference estimation of the system state variables and total disturbance. Then, it was proved that the linear active disturbance rejection control (LADRC) possesses disturbance rejection characteristics, and the influence of the bandwidth parameter on the disturbance rejection performance of the system was analyzed. The fuzzy control was used to adjust the parameter adaptively. Finally, the tracking, robustness, and anti-disturbance of the F-LADRC attitude autopilot were verified by performing simulations.

A two-step weighting regularization method for stochastic excitation identification under multi-source uncertainties based on response superposition-decomposition principle

Excitation identification has received considerable attention because of its importance in safety assessment and structural design. This paper proposed a power spectral density (PSD) identification method for stationary stochastic excitations considering multi-source uncertainties in load fluctuations, material dispersions and measurement noises. Based on the traditional inverse pseudo-excitation method, a two-step weighting regularization strategy is creatively developed to reduce the amplification effects of the uncertainties in the transfer matrix and measurements on reconstructed results near natural frequencies. Especially, to enhance the generalizability of regularization operations, a weighting matrix is defined based on the interval-quantized deviation analysis of pseudo excitations and then an improved Tikhonov regularizing operator is defined given the features of the weighting transfer matrix and pseudo responses. Next, the response superposition-decomposition principle is performed to determine the boundaries of excitation PSD and two uncertainty propagation methods are developed. To guarantee the accuracy and efficiency of uncertainty analysis, the adaptive reduced-dimension Chebyshev model is adopted to characterize the nonlinear response-parameter relationships, and the first-order Taylor series approximation is used to describe the linear response-excitation relationships. Eventually, two numerical examples and one experimental example are discussed to demonstrate the feasibility of the developed approach. The results suggest its promising applications in complicated structures and loading conditions.

Multisource uncertain dynamic load identification fitted by Legendre polynomial based on precise integration and the Savitzky–Golay filters

AbstractIn this article, a precise integral method (PIM) for the load identification of continuous structures based on the polynomial nonlinear hypothesis is presented. Essentially, load identification can be regarded as solving a dynamic equation in an inverse process. PIM is famous for its high precision in positive engineering problems. It has been already used in load reconstruction, but most cases are with discrete structures. In each time step, the dynamic responses of the measured points are used to identify the load without establishing a recursive chain, so PIM is not sensitive to the initial value and has no accumulated error. Legendrepolynomials (LPIM) is a computational scheme. The dynamic load is assumed to be a polynomial fitting nonlinear function in each integral time step with LPIM. Just with the first modal, LPIM can reliably identify the concentrated load. In addition, as uncertainty is getting more and more attention in engineer, it is also needed to be considered in load identification. In linear systems, interval vertex is a reliable method to obtain the load bounds in the virtue of multisource uncertainties. The results of identified load are too lumpy because of the polynomial fitting. To improve the precision, Savitsky–Golay (S–G) filters which fit the curves by polynomials in a frame length is introduced to smooth down the load in high fidelity. Eight numerical examples are investigated to demonstrated the efficiency and precision of the developed method.

Multi-scale reliability analysis of FRP truss bridges with hybrid random and interval uncertainties

Due to the multi-scale characteristics of composites and the lack of statistical data, the reliability assessment of FRP truss bridge faces more complex problems such as multi-source uncertainties and multi-scale uncertainties compared with traditional bridges. In this paper, a hybrid multi-scale reliability analysis method which couples the multi-scale computational homogenization method with reliability analysis method of hybrid random and interval uncertainties, is proposed to accurately quantify the reliability of FRP truss bridges with considerations hybrid probability and interval uncertainties at micro and macro scales. The effectiveness and efficiency of the method are compared with the Monte Carlo simulation method through a theoretical example. The comparison with the other three interval variable processing methods demonstrates that the proposed method can effectively evaluate the reliability of FRP truss bridge in a multi-source and multi-scale approach.

Adaptive fuzzy fault-tolerant control for a class of kinetic kill vehicle with actuator faults and unmodeled dynamics

In this paper, an adaptive fuzzy fault-tolerant controller is introduced for a class of kinetic kill vehicle (KKV) with unmodeled dynamics, actuator faults and structural uncertainties. The key point is that the effects of structural uncertainties, actuator faults and unmodeled dynamics existing in KKV systems are universally considered and suppressed by the proposed method. To deal with the unmodeled dynamics and structural uncertainties, a dynamic signal is employed and a fuzzy logic system (FLS) is presented to approximate the multisource uncertainties. In addition, indirect compensation control laws are designed in order to handle the actuator faults caused by fuel consumption and manufacturing errors. Last but not least, benefiting from the adaptive laws, the external disturbances are appropriately compensated. The simulation results show that the proposed algorithm enables the system states of KKV to track the desired trajectories tightly under different conditions and the control performance is better compared with other algorithms.

Efficient Inverse Method for Structural Identification Considering Modeling and Response Uncertainties

The inverse problem analysis method provides an effective way for the structural parameter identification. However, uncertainties wildly exist in the practical engineering inverse problems. Due to the coupling of multi-source uncertainties in the measured responses and the modeling parameters, the traditional inverse method under the deterministic framework faces the challenges in solving mechanism and computing cost. In this paper, an uncertain inverse method based on convex model and dimension reduction decomposition is proposed to realize the interval identification of unknown structural parameters according to the uncertain measured responses and modeling parameters. Firstly, the polygonal convex set model is established to quantify the epistemic uncertainties of modeling parameters. Afterwards, a space collocation method based on dimension reduction decomposition is proposed to transform the inverse problem considering multi-source uncertainties into a few interval inverse problems considering response uncertainty. The transformed interval inverse problem involves the two-layer solving process including interval propagation and optimization updating. In order to solve the interval inverse problems considering response uncertainty, an efficient interval inverse method based on the high dimensional model representation and affine algorithm is further developed. Through the coupling of the above two strategies, the proposed uncertain inverse method avoids the time-consuming multi-layer nested calculation procedure, and then effectively realizes the uncertainty identification of unknown structural parameters. Finally, two engineering examples are provided to verify the effectiveness of the proposed uncertain inverse method.

Data‐driven probabilistic curvature capacity modeling of circular RC columns facilitating seismic fragility analyses of highway bridges

AbstractThe availability of reliable probabilistic capacity models of reinforced concrete (RC) columns is a cornerstone for high‐confidence seismic fragility and risk analyses of highway bridges. Existing studies often perform physics‐based pushover or moment–curvature analyses for the capacity modeling of RC columns, which may encounter nonconvergent problems under high levels of nonlinearities in structural material constitutive models and elements, and become computationally inefficient especially when the analysis model contains plenty of cases involving multisource uncertainties. To mitigate the nonconvergent issues as well as release the computational burden of RC column capacity estimates, this study explores the potency of artificial neural network for data‐driven probabilistic curvature capacity modeling of circular RC columns, which can facilitate seismic fragility assessment of highway bridges. To this end, a large database is developed by fiber‐section‐based moment–curvature analyses covering major ranges of concrete and steel strengths, reinforcement ratios, vertical loads, and geometries of RC columns in engineering practices. To obtain an accurate data‐driven model, a fivefold cross‐validation training and test process is performed to optimize the neural network architecture. The optimized neural network leads to a reliable data‐driven model for estimating multilevel curvature capacity indices with percentage errors less than 15%. Finally, a typical highway bridge is taken as a case study to demonstrate the applicability of the developed data‐driven capacity model for the expediency of seismic fragility analysis. For ease of implementation, the database and associated codes are available at https://bit.ly/3A1dh1V.

Nonlinear Covariance Analysis-Based Robust Rendezvous Trajectory Design by Improved Differential Evolution Method

This paper presents a robust trajectory design method for approaching and rendezvous with a space target considering multi-source uncertainties. A nonlinear covariance analysis method based on the state transition tensor is presented to formulate the propagation of uncertainties including environment parameter uncertainty, actuator error, sensor noise, navigation error and initial state dispersion of the closed-loop GN&C system. Then, the robust trajectory design problem is defined based on the quantified effect of the uncertainties, and an improved self-adaptive differential evolution algorithm is presented to solve the robust trajectory design problem with uncertainties. Finally, four groups of numerical simulations are carried out to show that the designed robust trajectories can satisfy the final state dispersion constraint under multi-source uncertainties.

Mixed reliability-oriented topology optimization for thermo-mechanical structures with multi-source uncertainties

Mixed reliability-oriented topology optimization for thermo-mechanical structures with multi-source uncertainties

A novel deep-learning based surrogate modeling of stochastic electric vehicle traffic user equilibrium in low-carbon electricity–transportation nexus

The increasing penetration of electric vehicles (EV) and fast charging stations (FCS) is tightly coupling the operation of power and transportation systems. In this context, the characterization of the EV flows and charging demand in response to varying traffic conditions and coordinated optimization strategies play a vital role. Previous work on the computation of stochastic traffic user equilibrium (TUE) involve non-linearities in the traffic link and FCS congestion representations and are generally inefficient in dealing with the multi-source uncertainties associated with the operating conditions of the traffic network (TN) and power distribution network (PDN). To address this, this paper proposed a novel deep learning (DL) based surrogate modeling method, leveraging the strength of edge-conditioned convolutional network (ECCN) and deep belief network (DBN). ECCN enables automatic extraction of spatial dependencies, taking into account both node and edge features characterizing the operation of TN. DBN leverages the value of the extracted features and achieves an accurate mapping between the latter to the EV charging demand and EV flows in the TUE, while adaptively generalizing to the multi-dimensional uncertainties. Case studies on three test systems of different scales (including a real-world case involving the matched TN and PDN of Nanjing city) demonstrate that the proposed surrogate model achieves a higher solution accuracy with respect to the state-of-the-art DL-based methods, and exhibits favorable computational performance. Quantitative results also corroborate the benefits brought by the proposed coordinated spatial optimization of EV flows and charging demand on the operation of both TN and PDN.