Structural Health Condition Research Articles

Accelerometer-assisted computer vision data fusion framework for structural dynamic displacement reconstruction

Accurate displacement measurement provides crucial information for evaluating the structural health condition. It is important to note that both direct and indirect displacement measurement methods have their own limitations, which can be remedied by leveraging each other’s strengths. In this study, a novel accelerometer-assisted computer vision data fusion framework is developed for accurately reconstructing structural dynamic displacement. The framework does not require a specific mathematical model or prior knowledge about the data’s characteristics, allowing it to be applied more broadly across different applications without the constraints of model assumptions. The core of this framework is to integrate successive variational mode decomposition (SVMD) and Bayesian optimization approaches to adaptively determine the weight factors of the fusion components. Importantly, an enhanced optical flow approach is presented for converting pixel movement to structural displacement from natural targets. This approach can effectively reduce the selection of mis-matched points within the ROI (Region of Interest), thereby reducing drift errors. The developed framework is verified via shaking table tests of a reinforced concrete frame structure under seismic excitation. Results indicate that the developed framework excels in accurately estimating structural dynamic displacement. Compared to single-vision displacement identification results, the proposed framework demonstrates lower peak error (< 1.65 mm) and normalized root mean square error (< 0.30). Meanwhile, the reconstructed displacement, by introducing dynamic displacement component from acceleration measurement, presents a wider frequency range than the vision-based displacement.

Generalization gap estimation for damage classification tasks when finite element simulated data is used for training: A numerical study and experimental validation on a steel truss

Labeled simulated structural responses by Finite Element (FE) methods may be used to construct training sets for monitoring the health state of structures. Such an approach appears to be an attractive way to avoid experimental costs. However, the main obstacle is the simulation error contained in such numerical responses. The error can contaminate the training data and lead to wrong conclusions when the learned features try to generalize on subsequent online experimental data. It is therefore very important to have an estimation of how good the available simulated data is for a given problem. The present work gives a novel methodology where classifiers trained by FE vibration response data are subjected to inputs of various perturbations, emulating in such way the generalization gap (classification errors) due to simulation errors. The response of the classifiers is gathered afterwards in a dataset which is used to construct a function that estimates the generalization gap based on the perturbed intact state response. Results are presented that show the behavior of the proposed gap estimation function for different binary damage classification scenarios. A numerical truss structure is used to test the concept. Convolutional Neural Networks (CNN) are applied for all data-driven related tasks, such as learning of health state features in vibration responses or evaluation of the gap function. The results show a promising methodology that can be used to estimate the reliability of numerically trained classifiers. In the final part of this study, the framework is tested on an experimental truss structure. The presented methodology contributes to the quantitative study of uncertainty when extrapolating from the numerical to the experimental domain in the presence of modeling errors.

Application of computer vision techniques to damage detection in underwater concrete structures

Underwater concrete structure crack detection and structural health condition assessment based on image processing is a challenging task. The complex underwater environment and severe image degradation seriously affect the accuracy of crack detection. To solve these problems, a monocular vision and image-enhanced fractal-based fractal science based on computer vision and image processing techniques are proposed to carry out a non-contact detection study of underwater concrete cracks. In this study, a four-level structural health condition was established to assist in underwater crack measurement and safety assessment. The box-counting method was used as a practical tool to calculate the fractal dimension. To verify the effective distance of the algorithm, three distances of 0.5 m,0.8 m, and 1.2 m were set. The results show that the method proposed in this study can effectively detect cracks in submerged concrete members within 0.6 m and help managers correctly determine the health of the structure using the fractal dimension.

Dynamic performance of a supertall building with an active tuned mass damper system during Super Typhoon Saola

This paper investigates the dynamic characteristics (natural frequencies and damping ratios) of a 600-m-tall supertall building with an active tuned mass damper (ATMD) system during Super Typhoon Saola. Based on the wind speed, wind direction, and wind-induced acceleration response records by the structural health monitoring (SHM) system installed on the skyscraper, the wind characteristics during the passage of Saola are first investigated, and the relations between the mean wind speeds atop the skyscraper and the root-mean-square (RMS) acceleration responses are established. Then, employing the stochastic subspace identification (SSI) method and an uncertainty quantification method, this paper comprehensively investigates the uncertainty bounds, time-varying features, and amplitude-dependency characteristics of the modal parameters with and without the operation of the ATMD system. Next, on the basis of the identified modal parameters and time-frequency analysis, the performance and effectiveness of the ATMD system in suppressing the wind-induced vibrations of the skyscraper is investigated. Lastly, the structural health condition is evaluated from the perspective of building natural frequency and damping ratio changes before and after the typhoon hit. The goal of this study is to advance the understanding of the wind effects on supertall buildings and provide useful information for the wind-resistant design and vibration control of supertall buildings in tropical cyclone-prone regions.

Intelligent recognition of structural health state of EV lithium-ion Battery using transfer learning based on X-ray computed tomography

The lithium-ion battery (LIB) achieves wide applications on electric vehicles (EVs). The morphology of LIB electrode is highly correlated to the performance and safety of EV. Therefore, it is significant to monitor the structural health state of LIB to guarantee a reliable operation of EV. Currently, few research focused on the intelligent recognition of LIB structural health state. To bridge the gap, this paper proposes an image-based method to conduct structural health state recognition of LIB. The geometric deformation of LIB electrode is recorded by X-ray computed tomography (CT) images under different structure health state. Then a novel transfer learning network is incorporated to enhance the generalization ability of model. In the network, prior knowledge is first acquired from source domain data to initialize a convolutional autoencoder (CAE). Then the CAE is fine-tuned on CT images (target domain data), and a structural deviation index is established to reflect the structure health condition. Once the index exceeds the pre-set threshold, the alarm is triggered. The performance of the proposed method was evaluated on experimental data, and the results proved that the proposed method can perform structural health state monitoring effectively, and transfer learning can improve the generalization ability of detection model significantly.

FBG Sensing Data Motivated Dynamic Feature Assessment of the Complicated CFRP Antenna Beam under Various Vibration Modes

Carbon fiber-reinforced polymer (CFRP) components were extensively used and current studies mainly refer to CFRP laminates. The dynamic performance of the complicated CFRP antenna beams is yet to be explored. Therefore, a sensor layout based on fiber Bragg gratings (FBGs) in series was designed to measure the dynamic response of the CFRP antenna beam, and various vibration tests (sweep frequency test, simulated long-life vibration test, shock vibration test, functional vibration test, and constant frequency vibration test) were conducted. The time and frequency domain analysis on FBG sensing signals was performed to check the vibration performance and assess the health condition of this novel CFRP structure. The results indicate that strain values reach a maximum of only 300 µε under different test conditions. The antenna beam exhibited clear vibration patterns, with the first four intrinsic frequencies identified at 44, 94.87, 107.1, and 193.45 Hz. It shows that strain distribution and vibration modes of the antenna beam can be characterized from the sensing data, and the dynamic feature can be much more accurately assessed. The FBG sensors attached on the surface of CFRP antenna beam can accurately and stably measure the dynamic response, which validates that the interfaces between optical fiber sensing elements and CFRP material have excellent interfacial bonding characteristics. The novel CFRP antenna beam exhibits the excellent dynamic performance and stability, offering the replacement of traditional steel antenna beams. The study can finally instruct the development of self-sensing CFRP antenna beams assembled with FBGs in series.

Guided-wave Dynamic Probability Model-based Crack Quantification Method for Metal Structures

In the process of applying guided-wave-based aircraft online structural health monitoring, the characteristics of guided wave signals used to represent structural status exhibit random uncertainty due to the interference of loads on guided wave propagation. The trend of signal feature changes caused by damage is often obscured, making the quantification of cracks under loads one of the challenges in online structural health monitoring for aircraft. To address this challenge, this paper proposes a crack quantification method using an adaptive Gaussian mixture model (GMM) and optimized probability migration distance measurement. This method effectively mitigates the uncertainty caused by loads by constructing an adaptive Gaussian mixture model to track the probability distribution changes of guided wave signal features under different structural health conditions. Subsequently, an optimized probability migration distance measurement method is employed to characterize the structural state, further enhancing the correlation between features and the extent of structural damage. Finally, an optimized probability migration distance relationship with crack length is established to estimate the crack length of new structural specimens. The effectiveness of this method is validated using load-induced crack propagation experiments on metal structures.

Dispersion aware matching pursuit decomposition of Lamb wave signals for structural health monitoring of thin plates structures

Structural Health Monitoring (SHM) techniques are key to monitor in real time the health state of engineering structures, where damage type, location and severity are to be estimated by applying signal processing and deep learning techniques to temporal signals measured by sensors coming from the structure under study. Among the most widely used signal processing techniques in the SHM community is the Matching Pursuit Method (MPM), which allows to extract key features from a measured signal. MPM simply consists in approximating temporal data as a sum of different terms composed of a delayed and scaled signal called atom. This signal decomposition approach is however limited to non-dispersive signals which is not the case when dealing with Lamb waves signals widely used in the SHM of thin structures. In this case, in addition of delays and attenuations, wave packed also endure dispersion caused by the fact that all the frequencies do not propagate at the same speed within the structures under study. In this context, an improved version of Matching Pursuit is proposed in the present work, which address the dispersion phenomena by decomposing a measured signal as delayed and dispersed impulse response of an atom, obtaining better features for Lamb wave measurements. The performance of the developed technique is tested for the approximation of real measured signals, showing its better performance compared to classical MPM, especially when dealing with dispersive signals. This improved signal decomposition can be very useful for SHM purposes.

On the fusion between interferometric satellite data and in situ measurements for the monitoring of built heritage

Over the past decades, earthquakes, and other catastrophic events has highlighted the increasingly growing vulnerability of infrastructures, buildings, and architectural heritage structures. In addition to catastrophic events, often related to climate change, another fundamental aspect is represented by the lack of maintenance and monitoring of the asset. In the field of preservation of buildings and infrastructures, Structural Health Monitoring techniques can effectively contribute to the assessment of the health state of structures. In the case of structural monitoring using data-driven approaches, since the information depends on the type of data used, a great resource for knowing as much as possible about the structure is represented by the combination of multiple data. Thanks to the integration of different types of data, it is possible to know the conditions of the structure in more detail as different aspects can be combined. In this context, together with the data obtained from in situ monitoring systems, data obtained remotely, i.e. satellite data, can be used. There are different types of satellite data that can be used to study different aspects, e.g., multispectral data, hyperspectral data, and interferometric data, and they can make different contribution to civil engineering. In this paper, the exploitability of open-source interferometric data is investigated and they are studied for the purpose of their integration with data obtained from a monitoring system installed on a monumental building, in order to monitor and observe structural health.

Crowdsensing-based automatic bridge health condition assessment using drive-by measurements and deep learning

In recent decades, assessing the structural health conditions of aging bridges has emerged as a significant concern. A recent drive-by measurement method has attracted substantial attention, in which only several sensors are installed on crowdsensing vehicles rather than bridges, providing a more economical and convenient solution. This paper proposes an automatic bridge condition assessment framework incorporating drive-by measurements and deep learning techniques. The methodology involves collecting and segmenting accelerations from a vehicle passing a healthy bridge into short-time overlapped frames. Over multiple vehicular passes, all frames are then transformed into frequency-domain responses, forming the input for training an unsupervised deep learning model. The model is then trained to reconstruct the input using these frequency-domain responses. In assessing the bridge with an unknown health state, the trained model is employed to reconstruct the passing vehicle’s new short-time frames, and the response construction error automatically determines the bridge’s health condition. Experimental validation utilizing a laboratory bridge and scaled truck demonstrated that the trained model could consistently identify a healthy bridge during passages, with larger reconstruction errors indicating that the bridge was damaged. The innovative framework showcased promise for efficient and reliable bridge health condition assessment.

Evaluation method for health state of highway tunnel structure based on adaptive comprehensive weighting

Accurately evaluating the health state of tunnel structure is of great significance for ensuring the operation safety of tunnel. Based on engineering investigation, fuzzy mathematics and statistical analysis, this paper proposes a new method to evaluate the health state of highway tunnel structure, which considers the multi-disease characteristics and adaptive comprehensive weighting theory. Firstly, by investigating the health state of 20 operation highway tunnels in China, a tunnel disease database with 539 samples was constructed. Considering some new tunnel diseases such as floor heave and lining spalling, a health evaluation index system of highway tunnel was established further. Secondly, utilizing the subjective-objective weighting theory and the principle of variable weight, a new adaptive comprehensive weighting method was proposed to calculate the indexes’ weights. This method overcomes the defect that the constant weight cannot be dynamically updated according to the actual situation of disease development. Then, according to the established four-level classification standard suitable for health evaluation of highway tunnels, the normal distribution membership functions of second-level indexes were determined. Combining with the fuzzy theory, the quantitative evaluation model of tunnel health state was constructed further, which was applied to a case study of the Nanyangshan Tunnel of Kanglin Expressway in China. Furthermore, a comparative analysis with the traditional subjective-objective combination weighting method was conducted, demonstrating the advantages of the proposed evaluation method in terms of engineering applicability and result accuracy. The research findings can provide a decision-making basis for the health maintenance and scientific management of highway tunnels in China.

Damage identification technique by model enrichment for structural elastodynamic problems

Structural Health Monitoring (SHM) techniques are key to monitor the health state of engineering structures, where damage type, location and severity are to be estimated by applying sophisticated techniques to signals measured by sensors. However, very localized damage detection algorithms applied to dynamics problems when dealing with rigid structures at low-frequency range remains still a big challenge. The last due to the low influence of very localized damage on the overall response of the structure (Saint-Venant principle). In this context, in the present work, we propose a methodology for locally correcting the models from collected data for elastodynamics problems at low-frequency range which is able to predict very localized damage. The proposed technique consists in enriching the structural model in a sparse way and solving the identification problem in the frequency domain, where the influence of damage over a large frequency band is exploited to improve the prediction of the damage location. The advantages and potential of the proposed technique are illustrated for the damage detection in a plate problem, demonstrating the advantages of the method in detecting very localized damage. The proposed technique is limited to a methodological description, and further developments should be considered to approach its applicability in an industrial scenario.

A general approach to assessing SHM reliability considering sensor failures based on information theory

Structural health monitoring systems (SHM) involve implementing damage identification strategies to determine the health state of structures. However, it is important to pay close attention to the system degradation, especially the effect of sensor degradation on the SHM system reliability. This paper aims to formulate a general framework for evaluating SHM reliability that takes sensor failures into account. The framework involves modelling sensor network degradation processes using Petri nets (PNs) and calculating the expected information gain of the sensor network. The PNs allow for identifying the location and number of sensor failures. Kullback–Leibler (KL) divergence with Bayesian inversion is used to calculate the expected information loss due to sensor failure. Two case studies are used to illustrate the methodology: (i) a damage localization scheme using an ellipse-based time-of-flight (ToF) model and (ii) a damage identification scheme using a guided waves damage interaction model. The proposed framework is demonstrated by both numerical and physical experimental case studies. Whereas the case studies are specific to an ultrasonic guided wave monitoring system, the proposed approach is generic. The proposed model is able to predict the health condition state and utility of SHM, which can potentially help in constructing asset management models in various industries.

Quantitative detection of typical bridge surface damages based on global attention mechanism and YOLOv7 network

Surface damages of reinforced concrete and steel bridges, for example, crack and corrosion, are usually regarded as indicators of internal structural defects, hence can be used to assess the structural health condition. Quantitative segmentation of these surface damages via computer vision is important yet challenging due to the limited accuracy of traditional semantic segmentation methods. To overcome this challenge, this study proposes a modified semantic segmentation method that can distinguish multiple surface damages, based on you only look once version 7 (YOLOv7) and global attention mechanism (GAM), namely, YOLOv7-SEG-GAM. Initially, the extended efficient layer aggregation network in the backbone network of YOLOv7 was substituted with GAM, followed by the integration of a segmentation head utilizing the three-scale feature map, thus establishing a segmentation network. Subsequently, graphical examples depicting five types of reinforced concrete and steel bridge surface damages, that is, concrete cracks, steel corrosion, exposed rebar, spalling, and efflorescence, are gathered and meticulously labeled to create a semantic segmentation dataset tailored for training the network. Afterwards, a comparative study is undertaken to analyze the effectiveness of GAM, squeeze-and-excitation networks, and convolutional block attention module in enhancing the network’s performance. Ultimately, a calibration device was developed utilizing a laser rangefinder and a smartphone to enable quantitative assessment of bridge damages in real size. Based on the identical dataset, the evaluated accuracy of YOLOv7-SEG-GAM was compared with DeepLabV3+, BiSeNet, and improved semantic segmentation networks. The results indicate that the mean pixel accuracy and mean intersection over union values achieved by YOLOv7-SEG-GAM were 0.881 and 0.782, respectively, surpassing those of DeepLabV3+ and BiSeNet. This study successfully enables pixel-level segmentation of bridge damages and offers valuable insights for quantitative segmentation.

Experimental Study on Compression Failure of Type II Ballastless Track Slab Based on Optical Fiber Sensing

Ballastless track structures are widely employed in high-speed rail networks because of their superior safety and durability. Among the various types of ballastless track, the Type II slab is currently one of the most extensively used and mature technologies in practice. Over the course of its service life, the damage within the ballastless track structure gradually accumulates in response to increased external loads. Therefore, it is crucial to continuously monitor the health condition of the track structure. In this study, a quasi-distributed fiber optic sensing system is adopted to monitor the deformation capacity and force performance of a Type II ballastless track slab under vertical load. The investigation aims to analyze the damage mechanism of the track structure under vertical pressure by assessing the deformation differences among its different components. The findings reveal that the incorporation of vertical reinforcement can enhance the pressure bearing capacity of the cement asphalt mortar layer to a certain extent, subsequently affecting the stress dilation. The stress performance of the ballastless track slab can be effectively monitored using the quasi-distributed fiber optic sensing technology under pressure. The outcomes of this research offer valuable insights for controlling displacement and analyzing damage in ballastless railway systems subjected to compression.

Damage and fracture investigation of self-compacting concrete in the filling layer of CRTS-III using three-point bending tests

Literature about filling layer self-compacting concrete (FLSCC) has indicated that FLSCC plays a crucial role in its application to Chinese railway track system III (CRTS-III). It is apparent that the damage characteristics of FLSCC have not been clearly investigated, as the actual working conditions are not considered enough. There exists a remaining gap about the mechanical properties and fracture behaviors of FLSCC under bending loads. In order to fill this gap, in this study, three-point bending (TPB) tests on the FLSCC beams with precast notches were performed based on the real bending situation of FLSCC in CRTS-III. Acoustic emission (AE), strain gauges and a digital camera were utilized to monitor the fresh evolutionary laws of micro- and macro-cracks as well as the corresponding damage morphology. The study presents that the monitored load-crack mouth opening displacement (P-CMPD) curves, load-strain (P-ε) curves and AE activity curves all exhibited similar distributions, including four stages with increasing bending loads. In term of the AE activities, the first apparent crack in the interior and warning point of failure can be detected by analyzing the captured AE activities of the FLSCC beams. In addition, the dominant failure mode of the specimens was determined as tensile cracks according to the rising angle-average frequency (RA-AF) criterion for potential FLSCC application in terms of the limiting ratios. This failure mode indicates that under pure bending loads, the mid-span section is subjected to the maximum bending moment, and the specimen experiences tensile damage. Therefore, for future practical application, the structural health state of FLSCC in CRTS-III could be nondestructively real-time monitored by the AE technique. Meanwhile, the calculated fracture parameters of the FLSCC specimen can reflect the cracks stability of the specimen. This study can also present experimental and theoretical references for further studies on FLSCC in CRTS-Ⅲ under other types of loads.

Study on Damage Inference of Parker Trusses Based on Bayesian Principles

The assessment of the health condition and safety of engineering structures is currently a research focus in the field of civil engineering. The traditional deterministic model for damage recognition is limited by the fine reading of field inspections and the accuracy of experts, resulting in a low recognition rate. Structural damage identification methods that consider uncertainty have been developed due to modelling errors, observation noise, system time variability, and other factors that lead to uncertainty. This study focuses on the Parker truss structure, and a two-dimensional planar finite element model is established by setting various key parameters such as prior distribution, stiffness, modulus of elasticity, node distribution, and external loading. The model is updated using the Bayesian updating principle. This principle is then combined with the finite element model. Opensees software is used for programming, and the Monte Carlo random sampling technique is used for structural damage inference. The study results demonstrate that the method can accurately identify the damage level of Parker truss structures with high robustness. The method can be of reference significance and practical value for identifying damage in truss structures.

Evaluation of Infrared Thermography Dataset for Delamination Detection in Reinforced Concrete Bridge Decks

Structural health monitoring and condition assessment of existing bridge decks is a growing challenge. Conventional manned inspections are costly, labor-intensive, and often risky to execute. Sub-surface delamination, a leading cause of deck replacement, can be autonomously and objectively detected using infrared thermography (IRT) data with developed deep learning AI models to address some of the limitations associated with manned inspection. As one of the most promising classifiers, deep convolutional neural networks (DCNNs) have not been utilized to their fullest potential for delamination detection, arguably due to the scarcity of realistic ground truth datasets. In this study, a common encoder–decoder semantic segmentation-based DCNN is adapted through domain adaptation. The model was tuned and trained on a publicly available dataset to detect subsurface delamination in IRT data collected from in-service bridge decks. The authors investigated the effect of dataset augmentation, class imbalance, the number of classes, and the effect of background removal in the training dataset, resulting in an overall number of seventy-five UNET models. Four out of five bridges were adopted for training and validation, and the fifth bridge was for testing. Most models averaged 80 iterations, and the training progress finally reached a training accuracy of 75% with a loss of about 0.6 without any overfitting. The result showed a substantial difference in the minimum and maximum values for the evaluated performance metrics (0.447 and 0.773 for global accuracy, 0.494 and 0.657 for mean accuracy, 0.239 and 0.716 for precision, 0.243 and 0.558 for true positive rate (TPR), 0.529 and 0.899 for true negative rate (TNR), 0.282 and 0.550 for F1-score. The results also indicated that the models trained on the raw annotated balanced dataset performed best for half of the metrics. In contrast, the models trained on raw data (with no dataset enhancement) performed better when only global accuracy was considered.

Automated modal parameter estimation for coupled rotor–foundation systems using seal forces as excitation source

Modal analysis techniques are widely used to characterize vibrations in structures, vehicles, machinery, etc. Modal parameters obtained through modal analysis are useful for structural health monitoring and condition monitoring. The common goal is to ensure the integrity of a mechanical system through monitoring of different operational conditions. Operational conditions described by spatial measurements can for instance be used to observe the vibration characteristics of the system and its parts. Therefore, the main originality of this work is to experimentally investigate if the presence of a turbulent gas flow in seal geometries can facilitate operational modal analysis for a coupled rotor–foundation system. A consistent and automatic way of obtaining the vibration characteristics is necessary to be included in the monitoring schemes. Therefore, this work also proposes a method to automatically obtain modal parameters for a bed plate of a rotor–foundation system when the rotor is affected by active magnetic bearings and gas seals. The automatic modal parameter algorithm is built on the stabilization diagram of modal parameters obtained from the stochastic subspace identification. Intermediate results from the automatic modal parameter algorithm show that some of the distance measures i.e., dωn,d, dζ, dMACX, dλ, dMACXωn,d, dMACXζ, and dMACXλ, for modal parameters in a stabilization diagram are better suited than others when distinguishing between possible physical modes and certainly spurious poles. The frequency band of interest for the system is found to influence the number of possible physical modes identified by the automatic algorithm. Measurements from 13 roving accelerometers are combined with the automatic modal parameter algorithm to obtain the vibration characteristics of the rotor and bed plate. For different operational conditions in the seal geometry, seven modes are consistently identified as physical modes by the automatic modal parameter algorithm. The algorithm uses (i) a combination of a white noise disturbance pattern intentionally introduced into the system through the active magnetic bearings and (ii) the operational disturbance coming from the seals, non-intentionally introduced by the turbulent gas flow. The seven physical modes are also identified when (iii) the rotor–foundation system is only disturbed from the turbulent gas flow in the seals. The seven physical modes identified by the algorithm under conditions (i), (ii), and (iii) compare well to the vibration characteristics found in experiments via experimental modal analysis and impact hammer testing as well as via a mathematical model of the rotor–foundation system.

Robust adaptive Kalman filter for structural performance assessment

SummaryStructural performance assessment is a critical stage in the health monitoring for the maintenance and risk management of engineering structures, in which the interstory drift is a key indicator. In this paper, a robust adaptive Kalman filter is proposed for an interstory drift estimation problem to show the health condition of steel structures in the case that the statistics or internal dynamics describing the signals and measurements are not known precisely. More precisely, we build an adaptive current Jerk model (ACJM) where the model parameters are updated in each time step to presuppose the statistics characterization of the steel dynamic, while the unknown measurement noise covariance is adapted based on a fixed‐lag innovation with respect to measurements. Moreover, a robust adaptive Kalman filter is designed for the modelling uncertainties in each time increment by solving a minimax game: one player tries to select an “actual” model far from the proposed ACJM with an exponential decay tolerance, while its “hostile” player, namely, the optimum filter, is designed by minimizing the estimation error according to the selected “actual” model. Finally, some simulation and experimental results show the effectiveness of the proposed algorithm.