Estimation Error Research Articles

Optimal attack strategy in system identification with binary‐valued observations: An information entropy‐based approach

AbstractWith the advancements in network technology and artificial intelligence, the interaction between network nodes is getting more frequent. The malicious data tampering can be extremely damaging to system stability, therefore the network security is of great importance. In this paper, we address the problem of system identification with binary‐valued observations under data tampering attacks and an information entropy‐based approach to optimal attack strategy from the viewpoint of attacker. Under the constrained attack energy, a method is proposed to obtain the optimal attack strategy using the information entropy as the optimization index. It is interestingly demonstrated that such optimal attack strategy is equivalent to the one by using the estimation error of the identification algorithm as the optimization index. The rationality of the proposed method is verified through numerical simulations.

Stubborn State and Disturbance Observer Co‐Design for Nonlinear Descriptor Systems With δQC$$ \delta \mathrm{QC} $$ via a Dynamic Event‐Triggered Mechanism

ABSTRACTThis article studies the state and disturbance simultaneous estimation problem for a class of nonlinear descriptor systems with using a dynamic event‐triggered mechanism. refers to incremental quadratic constraints, which can provide a unified description of many types of common nonlinear functions. To reduce the negative impact of measurement outliers on the identification estimation, a stubborn state and disturbance observer co‐design scheme is proposed for the first time by embedding dynamic saturation output estimation errors. Meanwhile, a dynamic event‐triggered mechanism is introduced to avoid the need for continuously available output information, which can reduce the pressure on communication resources. By constructing a Lyapunov function, existence conditions of the stubborn state and disturbance observer are obtained in the form of a convex optimization problem so that the error estimation maintains an acceptable estimation performance. Finally, simulation examples illustrate the universality and stubbornness of the proposed observer.

Electric vehicle ramp recognition based on fusion of vehicle mass estimation

Road slope is the necessary environmental information for intelligent electric vehicles. The accuracy of slope recognition directly determines the control quality of vehicles on the hill. Aiming at the problems that the existing ramp recognition algorithms have poor adaptability to the conditions and are unable to To satisfy the application requirements of mass production vehicles, this paper proposes an electric vehicle slope recognition method based on vehicle mass estimation. Firstly, the vehicle longitudinal dynamics model is established, and the signal characteristics of the acceleration sensor under the actual vehicle conditions are analyzed. The least square vehicle mass estimation strategy with forgetting factor is constructed to obtain the vehicle mass directly under the starting condition. Ramp recognition algorithms are designed for static parking and dynamic driving scenarios. In the static scenario, the filter latch strategy is used to deal with the interference factors such as activities in the vehicle. In the dynamic scenario, the Kalman filter algorithm based on measurement noise adaptation is designed to realize the fusion estimation of dynamic observation and kinematic observation for the slope. The effectiveness of the method is verified by Simulink -CarSim joint simulation. Finally, the real vehicle test is completed on Chery new energy's mass production electric vehicle platform and domain controller. road test results show that the mass estimation error is less than ±10 kg; the static estimation error of the slope is less than 0.001 rad, and the dynamic error is within 0.005 rad. The estimation accuracy and stability are greatly improved, which ensures the environmental adaptability of the intelligent electric vehicles.

Adaptive neural network backstepping control for the magnetorheological semi-active air suspension system with uncertain mass and time-varying input delay

Aiming at rejecting external disturbance induced by the random road profile, this paper proposes an adaptive robust control strategy to address the control problem of semi-active air suspension system installed with magnetorheological dampers (MRD) for enhancing ride comfort and handling performance. To effectively depict the inherent nonlinear dynamics of the adjustable air spring, a radial basis function neural network (RBFNN) model is trained by the experimental data offline, and an adaptive learning algorithm is introduced to maintain the modeling accuracy. Moreover, to handle the prevalent sensitive parameter variation (such as sprung mass), a nonlinear estimator is designed to estimate the uncertain sprung mass. Furthermore, a delay compensator is integrated into the control law to mitigate the impact of the time-varying input delay caused by the actuator of MRD to restrain the chattering phenomena. Additionally, the stability of the closed-loop system is rigorously proven by employing a Lyapunov–Krasovskii functional, guaranteeing the boundedness of both tracking error and estimation error. Simulation results are displayed and analyzed, illustrating the feasibility and efficiency of the proposed control strategy in depressing the sprung mass acceleration and tire deflection, showing its significance in both control performance enhancement and chattering elimination.

An Unbiased Risk Estimator for Partial Label Learning with Augmented Classes

Partial Label Learning (PLL) is a typical weakly supervised learning task, which assumes each training instance is annotated with a set of candidate labels containing the ground-truth label. Recent PLL methods adopt identification-based disambiguation to alleviate the influence of false positive labels and achieve promising performance. However, they require all classes in the test set to have appeared in the training set, ignoring the fact that new classes will keep emerging in real applications. To address this issue, in this paper, we focus on the problem of Partial Label Learning with Augmented Class (PLLAC), where one or more augmented classes are not visible in the training stage but appear in the inference stage. Specifically, we propose an unbiased risk estimator with theoretical guarantees for PLLAC, which estimates the distribution of augmented classes by differentiating the distribution of known classes from unlabeled data and can be equipped with arbitrary PLL loss functions. Besides, we provide a theoretical analysis of the estimation error bound of the estimator, which guarantees the convergence of the empirical risk minimizer to the true risk minimizer as the number of training data tends to infinity. Furthermore, we add a risk-penalty regularization term in the optimization objective to alleviate the influence of the over-fitting issue caused by negative empirical risk. Extensive experiments on benchmark, UCI and real-world datasets demonstrate the effectiveness of the proposed approach.

Penalized Sparse Covariance Regression with High Dimensional Covariates

Covariance regression offers an effective way to model the large covariance matrix with the auxiliary similarity matrices. In this work, we propose a sparse covariance regression (SCR) approach to handle the potentially high-dimensional predictors (i.e., similarity matrices). Specifically, we use the penalization method to identify the informative predictors and estimate their associated coefficients simultaneously. We first investigate the Lasso estimator and subsequently consider the folded concave penalized estimation methods (e.g., SCAD and MCP). However, the theoretical analysis of the existing penalization methods is primarily based on i.i.d. data, which is not directly applicable to our scenario. To address this difficulty, we establish the non-asymptotic error bounds by exploiting the spectral properties of the covariance matrix and similarity matrices. Then, we derive the estimation error bound for the Lasso estimator and establish the desirable oracle property of the folded concave penalized estimator. Extensive simulation studies are conducted to corroborate our theoretical results. We also illustrate the usefulness of the proposed method by applying it to a Chinese stock market dataset.

Reliable Finite‐Time Control for Nonlinear Chaotic Semi‐Markov Jump Systems With Incomplete Transition Rates

ABSTRACTThis article studies the finite‐time control problem for a class of nonlinear chaotic semi‐Markov jump systems with incomplete transition rates described by the T‐S fuzzy model approach. As a means to depict the dynamical properties pertaining to the examined system, parametric uncertainties, faults, external disturbances and input saturation are taken into consideration. The foremost objective of this study is to come up with a composite control mechanism that effectively rejects and attenuates the repercussions of faults and disturbances. In particular, we primarily built a disturbance observer in order to obtain a precise estimation of the external disturbances. After which, the fault diagnosis observer is designated to effectively estimate the faults. Specifically, a composite reliable control mechanism is developed by fusing the output of the constructed observers with the mode‐dependent fuzzy‐rule based state feedback controller. By employing suitable Lyapunov functions in conjunction with the linear matrix inequality technique, a set of mode‐dependent conditions is derived to ensure the finite‐time stochastic boundedness of the underlying closed‐loop and estimation error systems. Following this, the anticipated controller and observer gain matrices are elicited by resolving the established linear matrix inequalities. Thereafter, intending to ascertain the efficacy and usefulness of accrued theoretical findings, simulation results performed on Chua's circuit system is endowed.

Distributed Consensus Filtering Over Sensor Networks With Asynchronous Measurements

ABSTRACTIn practical sensor networks, sensor nodes may operate with different sampling periods and initial sampling time instants, and their observations may also be nonuniform. Unfortunately, the research on distributed state estimation problems over such asynchronous sensor networks is very limited. Thus, this article focuses on the distributed consensus filtering problem over sensor networks with asynchronous measurements. First, the asynchronous measurement from each sensor is synchronized by the continuous‐time state evolution equation to a unified filtering fusion time instant within a given filtering period. After measurement synchronization, the statistical characteristics of measurement noise change. The cross‐correlations between the converted measurement noises are analyzed, as well as one‐step correlations between the converted measurement noises and the process noise. Second, an optimal asynchronous distributed consensus filter is designed based on synchronization measurements under the criterion of minimum mean‐square error with the above correlations between various types of noises taken into account. Meanwhile, a suboptimal distributed consensus filtering algorithm is further proposed to reduce computational complexity. Finally, based on the Lyapunov function method, the stability of the estimation error is theoretically demonstrated with an appropriate selection of consensus filtering gain and validated through simulations.

Analysis of Optimal Diversity Combining with Imperfect Channel State Information for Cooperative Jamming-Aided Internet of Things Security

Cooperative jamming (CJ) combined with single-input multiple-output (SIMO) technology can effectively improve the security and reliability of Internet of Things (IoT) systems. However, imperfect main channel state information (CSI) leads to incomplete CJ cancellation, which degrades the performance after combining. In this paper, by considering channel estimation errors and residual CJ at each receiving antenna, the residual CJ power after jamming suppression is analyzed, and the optimal combining coefficient for maximizing the signal-to-jamming-noise ratio (SJNR) is derived. The output SJNR of optimal diversity combining is given, and the achievable secrecy rate is analyzed on this basis. The theoretical and simulation results verify the combined effect of channel estimation errors and residual CJ on the combining performance. Moreover, it is worth noting that the combining performance is closely related to the spatial correlation of residual CJ.

High precision DSRC and LiDAR data integration positioning method for autonomous vehicles based on CNN

In order to improve the safe driving and automatic positioning capability of autonomous vehicles, a high-precision DSRC and LiDAR data integration positioning technology for autonomous vehicles based on CNN is proposed. Import the data of Dedicated Short Range Communications and Light Detection and Ranging for automatic driving vehicle positioning, carry out kinematic analysis of autonomous driving vehicles under multi-sensor fusion, and transform the data of DSRC and LiDAR sensors into tightly coupled coordinate systems; The CNN depth learning method is used to compensate the position and attitude tracking estimation error under the overall time stamp synchronization of the sensor through adaptive information tracking; The first and second order feedforward compensation is made for the positioning parameters of the autonomous driving vehicle using the PID model, and the point cloud feature matching model is fused to complete the estimation of the positioning attitude parameters of the autonomous driving vehicle. In order to eliminate the noise interference under the DSRC communication mechanism, the Kalman filter function is used to automatically optimize the constraint parameters in the point cloud feature detection model, and the positioning error parameters are dynamically filtered and adjusted; Kinematics analysis is carried out for the driving state of the vehicle, and the positioning error in the vehicle movement is controlled through the difference technology to achieve high-precision DSRC and LiDAR data integration positioning. The simulation results show that this method can integrate and locate the high-precision DSRC and LiDAR data of the autonomous vehicle, and the attitude estimation and positioning accuracy of the vehicle is good, while the error of the attitude parameter estimation of the autonomous vehicle is low.

Double-loop importance sampling for McKean–Vlasov stochastic differential equation

This paper investigates Monte Carlo (MC) methods to estimate probabilities of rare events associated with the solution to the d-dimensional McKean–Vlasov stochastic differential equation (MV-SDE). MV-SDEs are usually approximated using a stochastic interacting P-particle system, which is a set of P coupled d-dimensional stochastic differential equations (SDEs). Importance sampling (IS) is a common technique for reducing high relative variance of MC estimators of rare-event probabilities. We first derive a zero-variance IS change of measure for the quantity of interest by using stochastic optimal control theory. However, when this change of measure is applied to stochastic particle systems, it yields a P×d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P \ imes d$$\\end{document}-dimensional partial differential control equation (PDE), which is computationally expensive to solve. To address this issue, we use the decoupling approach introduced in (dos Reis et al. 2023), generating a d-dimensional control PDE for a zero-variance estimator of the decoupled SDE. Based on this approach, we develop a computationally efficient double loop MC (DLMC) estimator. We conduct a comprehensive numerical error and work analysis of the DLMC estimator. As a result, we show optimal complexity of OTOLr-4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}\\left( \ extrm{TOL}_{\ extrm{r}}^{-4}\\right) $$\\end{document} with a significantly reduced constant to achieve a prescribed relative error tolerance TOLr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{TOL}_{\ extrm{r}}$$\\end{document}. Subsequently, we propose an adaptive DLMC method combined with IS to numerically estimate rare-event probabilities, substantially reducing relative variance and computational runtimes required to achieve a given TOLr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{TOL}_{\ extrm{r}}$$\\end{document} compared with standard MC estimators in the absence of IS. Numerical experiments are performed on the Kuramoto model from statistical physics.

Features are more than just filling in the blanks on body size scales

ABSTRACT Despite widespread misperceptions of body size and shape, the specific visual features influencing such judgments remain unclear. This study assessed the contribution of internal body features (e.g., colour, shading) to the accuracy of female body size judgements and whether that contribution varies with body size. Using a bodyline task, 100 female participants evaluated images of female bodies, either depicted as real bodies including internal features (feature stimuli) or images of bodies as silhouettes only (silhouette stimuli). The results showed greater overall errors in body size estimation for silhouettes compared to full feature images. However, the direction of error differed for large and small bodies: small silhouettes were judged larger than their full-feature counterparts, while large silhouettes were judged smaller. These findings emphasize the importance of internal body features in shaping perceptions of female body size and highlight the complexity of judgement accuracy across different body sizes.

Multi-branch deep learning neural network prediction model for the development of angular biosensors based on sEMG.

Human gait motion intention recognition is very important for the lower extremity exoskeleton robot to accurately synchronize and respond to the user's natural motion. And motion intention recognition is generally performed through sEMG. Deep learning neural networks perform well in dealing with high-dimensional data and nonlinear relationships such as sEMG, but different deep learning neural networks have their own advantages in dealing with different types of data. Therefore, a multi-branch deep learning neural network, which enables different neural networks to process different feature items, could achieve more accurate and efficient motion intention recognition. The purpose of this study is to 1) Establish a multi-branch deep learning neural network model to achieve accurate gait recognition and effective estimation of joint angles. 2) Quantify the performance of the multi-branch deep learning neural network model in gait recognition and joint angle prediction using sEMG. This study involved the collection of sEMG and plantar pressure data during walking in human subjects. Firstly, the collected signals are filtered and denoised to ensure the quality and reliability of the data. Calculate the time domain features and the frequency domain features to capture the key information of gait. Then, using the sensitivity difference of different structural neural networks to different feature data, a multi-branch deep learning neural network model is developed, in which the extracted features are used as the input of the model. The output of the model includes gait cycle and joint angle, so as to realize the accurate recognition of human gait and the effective estimation of joint angle. The results show that the proposed method has high accuracy in identifying human gait and estimating joint angles. The multi-branch neural network model successfully integrates time-domain and frequency-domain features and provides reliable prediction of gait cycle and joint angle. The highest accuracy of gait recognition is 95.42%, the lowest is 90.11%, and the average is 92.16%. The average error of joint angle estimation is 3.19. This study designed a human walking gait recognition and joint angle prediction model to achieve accurate human lower limb motion intention recognition.The model can be integrated into the sEMG sensor to design a angular biosensors, which can predict the human joint angle in real time.

Ensemble width estimation in HRTF-convolved binaural music recordings using an auditory model and a gradient-boosted decision trees regressor

Binaural audio recordings become increasingly popular in multimedia repositories, posing new challenges in indexing, searching, and retrieval of such excerpts in terms of their spatial audio scene characteristics. This paper presents a new method for the automatic estimation of one of the most important spatial attributes of binaural recordings of music, namely “ensemble width.” The method has been developed using a repository of 23,040 binaural excerpts synthesized by convolving 192 multi-track music recordings with 30 sets of head-related transfer functions (HRTF). The synthesized excerpts represented various spatial distributions of music sound sources along a frontal semicircle in the horizontal plane. A binaural auditory model was exploited to derive the standard binaural cues from the synthesized excerpts, yielding a dataset representing interaural level and time differences, complemented by interaural cross-correlation coefficients. Subsequently, a regression method, based on gradient-boosted decision trees, was applied to the formerly calculated dataset to estimate ensemble width values. According to the obtained results, the mean absolute error of the ensemble width estimation averaged across experimental conditions amounts to 6.63° (SD 0.12°). The accuracy of the method is the highest for the recordings with ensembles narrower than 30°, yielding the mean absolute error ranging between 0.8° and 10.2°. The performance of the proposed algorithm is relatively uniform regardless of the horizontal position of an ensemble. However, its accuracy deteriorates for wider ensembles, with the error reaching 25.2° for the music ensembles spanning 90°. The developed method exhibits satisfactory generalization properties when evaluated both under music-independent and HRTF-independent conditions. The proposed method outperforms the technique based on “spatiograms” recently introduced in the literature.

Sensory-memory interactions via modular structure explain errors in visual working memory.

Errors in stimulus estimation reveal how stimulus representation changes during cognitive processes. Repulsive bias and minimum variance observed near cardinal axes are well-known error patterns typically associated with visual orientation perception. Recent experiments suggest that these errors continuously evolve during working memory, posing a challenge that neither static sensory models nor traditional memory models can address. Here, we demonstrate that these evolving errors, maintaining characteristic shapes, require network interaction between two distinct modules. Each module fulfills efficient sensory encoding and memory maintenance, which cannot be achieved simultaneously in a single-module network. The sensory module exhibits heterogeneous tuning with strong inhibitory modulation reflecting natural orientation statistics. While the memory module, operating alone, supports homogeneous representation via continuous attractor dynamics, the fully connected network forms discrete attractors with moderate drift speed and nonuniform diffusion processes. Together, our work underscores the significance of sensory-memory interaction in continuously shaping stimulus representation during working memory.

ESTIMACIÓN DE LA REGIÓN DE CRECIMIENTO ESTÁNDAR DE GUAJOLOTES NATIVOS (Meleagris gallopavo L.) CALCULADA MEDIANTE LA ECUACIÓN DE RICHARDS

<p><strong>Background. </strong>A variety of mathematical models explain animal growth, showing a sigmoid curve. Richards' model includes four parameters, allowing a better fit to experimental data, as evidenced by a high coefficient of determination and a low standard error of estimation. However, it does not always converge and some of its parameters are difficult to interpret biologically. It is useful to model a standard growth zone to estimate, at a given age, the weight of native turkeys within confidence limits, to obtain useful management conclusions.<strong> Objective. </strong>To establish a standard average growth region for male native turkeys on the coast of Oaxaca, for productive purposes, using the Richards equation. <strong>Methodology. </strong>The weights of 23 male native turkeys were recorded weekly from hatching to 54 weeks of age. Non-linear regression to fit the data to Richards' equation was performed using the free software GeoGebra®. The standard growth zone consisted of a lower and upper limit, which were determined by adding and subtracting the standard error of the estimate from Richards' model. The growth rate equation and graph were developed, showing its asymmetry, maximum value and age at which said value is reached.<strong> Results. </strong>Determination coefficient of 0.993, standard error of the estimate of 190.5 g, and maximum growth rate of 322.11 g*week-1 at 18.22 weeks of age were obtained.<strong> Implications. </strong>The use of the standard growth zone, under intensive production conditions, is valuable in the study and evaluation of the growth of male native turkeys<strong>. Conclusions. </strong>The standard growth zone is a very useful concept, allowing for the establishment of weight limits that animals should have at the optimal age, facilitating decision-making to optimize management and feeding practices, as well as maximizing efficiency and performance.</p>

Finite-time optimal control for a class of nonlinear systems with performance constraints via critic-only ADP: Theory and experiments

This paper addresses the optimal control problem within the framework of adaptive dynamic programming (ADP) for a class of nonlinear systems subjected to performance constraints. A new finite-time optimal control scheme is developed to stabilize the system by using the critic-only neural network ADP method. Compared with the existing ADP-based optimal control methods with uniformly ultimately bounded stability, the provided control scheme ensures that the controlled system's state and neural network weight estimation error are finite-time stable. It can ensure optimality, prescribed performance, and finite-time stability of the closed-loop control system simultaneously through an integration of ADP, the prescribed performance control technique, and Lyapunov theory. The designed adaptive neural network weight update law can relax the persisting excitation condition. The proposed control scheme is implemented on a robotic experiment platform to achieve trajectory tracking and verify its effectiveness.

Developing Data Mining Prediction System for Health Center Medicine Inventory using Naïve Bayes Classifier Algorithm

Public health centers mostly use conventional methods in managing drug supply, usage, and demand data, without a system that can predict the number of drug requests. This research aims to develop a data mining solution by implementing a prediction system using the Naïve Bayes Classifier algorithm to predict drug supplies from the Koni Health Center, Jambi, to the Health Office Pharmacy Installation. The method applied in this research is a quantitative approach through the experimental method. The research data includes inventory, usage, and remaining stock of various types of drugs from 2017 to 2021 which are divided into four quarters. The results of this study show that the classification system using the Naïve Bayes Classifier method is able to classify data quickly and efficiently according to drug supply. The system test results show an accuracy of 73.91%, recall of 85.71%, and precision of 54.54%. These findings can help Puskesmas in optimizing drug inventory management, reducing errors in inventory estimates, and increasing accuracy in meeting patient drug requests.

Encoding–decoding-based distributed state estimation over sensor networks with limited sensing range under DoS attacks

This paper is concerned with encoding–decoding-based distributed state estimation over sensor networks under DoS attacks. Different from most of the existing research results on distributed state estimation for sensor networks, where all sensors are assumed to have sufficiently wide sensing ranges, this paper considers sensors with limited sensing ranges. Therefore, the problem studied has more practical significance. To save the limited bandwidth resources of sensor networks, a two-channel encoding–decoding scheme (EDS) based on probability is proposed for each node to compress the transmitted data to an acceptable range, where independent DoS attacks are launched randomly on the communication channels between nodes. Then, a distributed state estimator with limited sensing ranges under DoS attacks in the presence of both the sensor-estimator channel EDS and the node–node channel EDS is constructed under the criterion of minimum mean-square error. Furthermore, considering the real-time changes of the communication topology resulting from independent DoS attacks and the uncertainty introduced by the node–node channel EDS, the upper bound of the expected estimation error covariance is derived and the boundedness of the upper bound is analyzed under given assumption conditions. Finally, a numerical example is exhibited to illustrate the effectiveness of the designed algorithm.

Dynamic strain field estimation of fixed offshore support structures using limited acceleration measurements

The strain history affecting the fatigue life of fixed offshore support structures is one of the most important topics in structural monitoring. However, some critical fatigue locations are located below the seabed, and the installation of strain gauges at these locations entails significant maintenance costs. In contrast, acceleration which reflects the vibration characteristics of the structure is an easily accessible and more stable physical parameter. Therefore, this study presents a strain estimation scheme that uses limited acceleration measurements to estimate the dynamic strain field of the fixed offshore support structures. An adaptive displacement reconstruction method is used to obtain the displacements at the master degrees of freedom, then the global displacements are obtained by the evolutionary orthogonal response expansion method, and finally, these displacements are implemented into the numerical software by redefining the boundary conditions to obtain the dynamic strain field. The advantage of the proposed method over the traditional strain-solving forward problem is that it relies solely on measured acceleration and structural geometry information, without requiring displacement, strain, or modal information. The correctness of the proposed method is verified by a numerical jacket platform model with multi-harmonic and non-stationary random excitations. Furthermore, physical experiments under eccentric rotation and hammering excitations are performed to assess the applicability of the proposed method on a wind turbine model equipped with laser displacement and fibre bragg grating sensors as reference measurements. The results show that the proposed method can accurately predict the dynamic strains of jacket platform and wind turbine support structures, while the appropriate agreement between the estimated strains and the numerical results, and the optical measured response is observed, with maximum estimation errors of 1.80% and 4.63%, respectively. Summarily, the application of the approach enables a new type of strain monitoring applicable to fixed offshore support structures.