Multi-site Damage Research Articles

Reliability analysis of an aircraft load mechanism considering multi-site damage dependency

Aircraft load mechanisms are the important actuators of the aircraft rudder control systems. By sharing the same operation circumstances and working conditions, the damage processes at multiple sites are dependent. In this paper, we firstly conduct a wear experiment and a stress relaxation experiment of an aircraft load mechanism. To consider the individual variability of the damage processes, the stochastic processes are adopted. Then, vine copula function is introduced to analyze the multivariate dependence of the damage processes. Furthermore, a time-varying dependent model is formed to model the dynamic damage interaction. The reliability of the aircraft load mechanism is assessed by using the Rosenblatt transformation and Monte Carlo method. The obtained results show that overlooking the dependency will lead to a conservative reliability result. Finally, the effect of the damage processes on the mechanism is analyzed, which provides effective guidance for the maintenance of the mechanism.

Reliability analysis of multi-site damage with failure dependency of the turbine based on flow-thermal-solid coupling analysis and the Monte Carlo validated simulations

The harsh environmental loads may lead to strength failure in the turbine in an aero-engine. To accurately assess the strength reliability of the turbine under multiple loads, the stress distributions of 41 danger sites of a turbine under thermal, centrifugal, and pneumatic loads were determined by the flow-thermal-solid coupling analysis using ANSYS. Second, based on the flow-thermal-solid coupling analysis and response surface method, the probabilistic analysis model of stress at the danger site was established. And the probabilistic distribution of stress was determined by sampling and hypothesis testing. Finally, the reliability model of the turbine with multi-site damage and failure dependency was established, by which a reliability of 0.99802 was calculated. And the actual reliability of the turbine was 0.99626 determined by the Monte Carlo simulations, which verified the model in precision. The results indicated that the reliability model has a high efficiency and higher precision than the traditional reliability model with failure independence.

Uncertainty analysis of MSD crack propagation based on polynomial chaos expansion

Widespread fatigue damage (WFD) is one of the main damages in aging aircraft structures, and the prediction of multi-site damage (MSD) crack propagation plays an important role in the safety assessment of aging aircraft. However, the existing multi-crack propagation stochastic models need to calculate multiple integrals, and the calculation efficiency is low. Based on the Polynomial Chaos Expansion (PCE) method, this paper proposes a new uncertainty analysis method to effectively solve the problem of multi-crack mutual interference. The rivet area of aircraft skin mostly appears randomly in the form of short cracks. Therefore, 30 groups of multi-crack fatigue propagation experiments are carried out to obtain the data of multi-cracks at different stages. On the basis of the existing multi-crack mutual interference model, a new semi-analytical multi-crack propagation model is designed by considering the uncertainty of multi-crack initiation and the interaction factors between cracks. The random variables are substituted into the improved multi-crack propagation model, and the Hermite polynomials are introduced and expanded into orthogonal polynomial series, and the time-varying polynomial coefficients, moments and probability densities are solved by stochastic regression method. The accuracy and effectiveness of the method are verified by comparing with the experimental and Monte Carlo methods.

Probability Analysis of Widespread Fatigue Damage in LY12-CZ Aluminum Alloy Single-Row Seven-Hole Plate

In order to determine the average behavior time of widespread fatigue damage (WFD) in an aircraft multi-site damage (MSD) structure and complete the fatigue analysis of WFD sensitive parts, this paper adopts a probabilistic method to analyze the crack initiation and crack propagation of a single row of collinear seven-hole plates. The simulation analysis of the whole process from crack initiation to structural failure is realized. First, through statistical analysis of the test data of the LY12-CZ alloy single-detail plate with hole, the probability distribution of crack initiation life and growth rate is obtained, and this probability distribution is expressed by the randomization of variables. Then, using the related theories of fracture mechanics and fatigue statistics, the whole process of initiation, propagation, and connection of multiple cracks in the MSD structure to the occurrence of WFD was realized through the Monte Carlo method. Finally, a group of single-row seven-hole plate examples are used to verify the accuracy of the calculation results. The results show that the calculated results in this paper are in good agreement with the experimental data, and can accurately predict the life of MSD structures under a certain reliability.

Uncertainty Analysis of multi-site damage Crack Propagation Based on the Monte Carlo Method

Abstract Widespread fatigue damage is one of the main damages of aging aircraft structures, and the problem of multi-site damage has always been a research hotspot in engineering analysis. The traditional probabilistic model for calculating the growth rate of multiple cracks takes into account the multiple uncertain parameters that affect each other’s cracks. However, when solving the multi-site damage (MSD) crack growth problem, the traditional random model needs to solve multiple nonlinear equations. This method becomes no longer applicable. Based on the statistical point of view, this study gives the mutual influence factors of the crack growth process in the form of distribution, and then calculates the probability density function of the crack length under different cycles by sampling with the Monte Carlo (MC) method. Finally, compared with the experimental data, the results show that the calculation results of this method are more accurate and are in good agreement with the experimental data. This method is feasible and accurate for multi-crack propagation analysis of random parameter structures.

A novel multi-site damage localization method based on near-field signal subspace fitting using uniform linear sensor array

Damage diagnose imaging methods based on guided waves have been widely developed to depict the position and area of damage in structural health monitoring (SHM). Among them, compact sensor array based imaging methods have been gradually applied with high accuracy, such as phased array imaging, spatial filter imaging, multiple signal classification imaging and so on. However, when the multi-site damage appears nearly, the performance of these methods usually degrades. On one hand, limited to the array aperture, traditional methods cannot distinguish adjacent damage sites. On another hand, some subspace decomposition based methods also fail, suffering from the correlation between scattered array signals from different damage sites. To realize localization of multi-site damage, a novel near-field signal subspace fitting based multi-site damage localization method is proposed in this paper. This method constructs the cost function, which describe the equivalence relation between the signal subspace and array manifold matrix. Then localization of multi-site damage could be realized through multidimensional search for the optimization of cost function. The proposed method is verified on the aluminum panel with 3 damage sites. Experimental results show that the proposed method can realize multi-site damage localization with the angle errors less than 4° and the distance errors less than 35 mm.

Multi-site damage precise localization via the random vibration functional model based method: Formulation & concept validation

The postulation and experimental validation of a random vibration data based Functional Model Based Method (FMBM) for multi-site damage localization, involving the determination of the number of damage locations and interval estimation of their coordinates, in presented. The method is based on Functional Models (FMs), along with proper statistical decision making and estimation techniques, and is capable of working with a limited number of random vibration signals under normal operating conditions. Two distinct versions of the method are introduced: A Forward or Multiple Model version which is based on multiple Functional Models, and a Backward or Single Model version based on a single counterpart. Both versions are experimentally validated and compared via hundreds of single- and double-site damage scenarios on the wing of a lab-scale aircraft skeleton structure, while a sensitivity analysis examining performance degradation for reduced numbers of training vibration signals is also undertaken. The results indicate high effectiveness in both determining the number of damage sites and estimating their precise coordinates along with their associated uncertainty.

A numerical study on multi‐site damage identification: A data‐driven method via constrained independent component analysis

This paper presents a solution to the multi-site structural damage identification problem using a data-driven method and constrained independent component analysis (cICA). While existing studies in this field presented encouraging results for single-site damage identification, limited research effort has been devoted to identifying multi-site damage due its complexity. Efficient features for single-site damage identification may lose their effectiveness when multi-site damage occurs. This paper extracts damage-sensitive features from the ICA outcome of the structural responses under certain excitations. The information on structural damage contained in the response is compacted into the mixing matrix by enforcing identical independent components to that of intact structures. Hence, the cICA can significantly reduce the feature dimension and preserve all the valuable information of damage. A case study indicates that the mixing matrix elements, when used as damage features, can distinguish multi-site damage cases from single-site damage cases and locate the single-site damage. Furthermore, the mixing matrix columns of multi-site damage cases exhibit distinct correlation with that of the corresponding single-site damage cases. As a result, the proposed method can progressively locate the structural damage. Moreover, the present study has the potential to identify multi-site damage identification in data-driven structural health monitoring without requiring multi-site damage data as a reference. This relieves the burden from data incompleteness when using data-based damage identification methods and pattern recognition.

Fatigue Reliability Analysis of a Compressor Disk Based on Probability Cumulative Damage Criterion.

The reliability of aero engine has a direct impact on the flight safety of the whole plane. With the continuous improvement of performance requirements of aero engines, the related fatigue and reliability problems also appear. For the fatigue failure characteristics of the typical component (compressor disk) in an aero engine, the fatigue reliability of its multi-site damage structure in service is analyzed by using probability cumulative damage criterion in this paper. The probability distribution definitions of life, damage and damage threshold are discussed and the relationship among them is also introduced by the new proposed criterion. Meanwhile, a method to determine the probability distribution of cumulative damage threshold and probability life prediction is carried out, based on which a hierarchical index system of statistical analysis and reliability modeling principle on the system level is further constructed for compressor disk. At the end of the paper, a certain cruise of fighter plane is analyzed to verify the validity of the new model. Emphasizing the difference between the compressor disk and traditional component, the new reliability analysis model developed in this study is basically reasonable for most of the load histories for the compressor disk, other than the traditional one, especially for the changeable and complex cruise missions.

Effect of staggered holes with multi-site damage on fatigue performance based on tests, DIC technique and numerical calculations

Abstract The fatigue performance was investigated numerically and experimentally of 2024-T3 Al-clad sheet with staggered hole arrangement and multi-sites damage (MSD), which is mainly used in aging aircraft fuselage skin. Firstly, the influences of row spacing, column spacing and inter-crack direction on fatigue life were studied. Then, the strain nephogram and crack path were analyzed with the assistance of digital image correlation (DIC) technique. Finally, a numerical solution for the specimens with staggered holes and MSD was developed based on the combination of ABAQUS and Paris formula. The results show that with the increase of row spacing, the fatigue life of MSD specimens with fixed column spacing increases first and then decreases. In the case of fixed row spacing, the fatigue life of specimens increases with the increase of column spacing. The arrangement parameter α is introduced to reveal the crack propagation form. Meanwhile, the common form of fracture is through the upper row of hole. In addition, the distribution of rivet holes has an effect on the initiation life of fatigue cracks in the structure with MSD, especially the row spacing. The numerical solution could provide a conservative prediction of fatigue lives, and the predicted error is less than 5% for cases of HH-2g24.

Multi-site structural damage identification using a multi-label classification scheme of machine learning

This study proposes a new method to locate multi-site structural damage using a data-driven multi-label classification (MLC) method. Differing from the multiclass classification (MCC) scheme that sets each damage case as a category, the MLC method denotes each damage case with multiple labels, with each label indicating the occurrence of damage at a certain location. The MLC method considers the physical correlation between damage cases sharing damage locations which is neglected in the MCC method. This paper uses the instance differentiation algorithm to implement MLC. Damage identification results using numerical and experimental data indicate that the MLC can identify multi-site damage with good accuracy, even for damage cases that are not covered by the training dataset. Through comparison, it is demonstrated that the MLC method outperforms the MCC and binary classification methods for multi-site damage identification. Moreover, MLC preserves generality when tested on unobserved multi-site damage cases.

MULTI-CLASS RECOGNITION FOR DETERMINATION THE TECHNICAL STATE OF THE WELDED JOINT TANK WITH DEFECTS BY USING NEURAL NETWORK CLASSIFIER

The paper shows the efficiency of the multi-class recognition of technical states the welded joint tank by using the neural network classifier that based on Probabilistic Neural Network.Implementation of modern multichannel monitoring systems for determination the technical state of spatial objects requires researching of changes of a stress-strain state construction elements which function under the operation pressure and possible impact its structural integrity. Such researching are needed for prevention of cracks or damage determining and future prediction of object’s technical state.In the paper the tasks of a multi-class recognition of a state of multi-site damage the welded joint tank are determined. In the research was created the model of the object with probable location places cracks. One of them is a vertical crack and two are horizontal. Directions of their propagation are given. Cracks have the same value. The first researching included when cracks turn up one by one. The next one related with multi-focal defects when cracks were arised and they evolve in parallel and independently. The data of strain in the structural of the welded joint tank where sensors were attached is given.The research of the possibility of the error-free recognition was conducted by the developed classifier based on the stress-strain state of the geometric model of the tank structural elements with multi-site damage, where sensors are located. The development of the classifier was done by using Probabilistic Neural Network, which provides the best results of a multi-class recognition for determination technical state of spatial object with multidimensional vectors of diagnostic features. As a result, the probability of recognition from the network influence parameter, which shows the effectiveness of the neural network classifier for localization of single damage and localization of multiple cracks, was established

Flaw Classification Algorithm for Heat Exchanger Tubes Using a Bobbin-Type Magnetic Camera

This paper presents an algorithm that estimates the presence, location, shape, and depth of flaws using a bobbin-type magnetic camera consisting of bobbin probes and a bobbin-type integrated giant magnetoresistance (GMR) sensor array (BIGiS). The presence of the flaws is determined by the lobe path of the Lissajous curves obtained from bobbin coil with respect to the applied frequency. The location of the flaw, i.e., whether it is an inner diameter (ID) or outer diameter (OD) flaw, can be determined from the rotational direction of the lobe with respect to the frequency change. The shape of the flaw is then determined from the area of the lobe and the BIGiS image. At this stage, multi-site damage can be determined from the BIGiS image. The effectiveness of the flaw classification algorithm was evaluated using various types of artificial flaws introduced into small-bore tube test specimens made of austenitic stainless steel.

The Application of DIC Technique to Evaluate Residual Tensile Strength of Aluminum Alloy Plates with Multi-Site Damage of Collinear and Non-Collinear Cracks

This paper introduces an aviation industrial application of digital image correlation (DIC) technique on the measurement of residual tensile strength (RTS). In order to investigate multi-site damage (MSD) that is common in the fuselage of aging aircraft, RTS of 2024-T4 aluminum alloy sheet with MSD was evaluated using DIC technique. Firstly, the four-factor and three-level orthogonal experiment was designed to optimize the DIC method to control the strain calculation error by considering subset size, interpolation tap, calibration score and step size. Secondly, RTS and strain fields were generated to analyze the path of crack propagation. The results show the optimal factor combination is 0.018 of calibration score, 23 pixels of subset size, step size is 1/4 of subset size and the filter size of interpolation calibration is 8 pixels. With the increase of spacing between adjacent holes, the RTS increases and the collinear cracked specimen becomes more perilous than that of non-collinear cracked while the hole spacing is 25 mm from the statistical analysis. Based on the Net section yield criterion, the RTS was calculated, which can give a conservative prediction of RTS.

Stress intensity factor for multiple cracks on curved panels

The aim of this paper is to explore and to demonstrate the capacity, performances and difficulties of stress intensity factors (SIFs) calculations in a case of multiple cracks on curved panels analyzed by means of different computational methods. So-called bulging effect, which is occurring in cracked curved panels, increases the effective stress-intensity factor, making the SIFs assessment in case of multiple cracks more challenging. Here, the stress intensity factors are considered by using two different computational methods: extended finite element method (XFEM) and the approximate method based on superposition, which has been adjusted for curved panel application. The SIFs determination was carried out for aircraft fuselage model: unstiffened panel with three cracked fastener holes, for four different curvature diameters, subjected to uniform internal pressurization. The comparison of the results showed that conducted analyses delivered the data which can be useful in evaluation of crack-growth rate, residual strength and fatigue life of curved aircraft structures with multi-site damage.

SIMULATION OF AIRFLOW AT VERNADSKY STATION FOR MULTI -SITE DAMAGE IDENTIFICATION

Relevance of the study is that the consequences of premature destruction of the fuel tank or the wall of the building of the Ukrainian Antarctic Akademik Vernadsky station (Vernadsky station) may result in significant financial costs and human lives as a result of multi-site damage. Therefore, the main objective of the study is to identify the most probable places of snow accumulation and maximum wind pressure zones for identification and prevention of multi-site damage of buildings and engineering structures. Geometric modeling and simulation are chosen as research methods, which allow (accordingly) creating and investigating a three-dimensional computer model of an object. SolidWorks CAD-system was chosen for geometric modeling. The simulation was carried out in the ANSYS finite-element analysis software. Results: geometric modeling and simulation of Vernadsky station was conducted; in CAD-system SolidWorks based on the plan-scheme and photos of the station, its geometric model is built, which includes the model of the surrounding area; according to its geometric models the layout of the station is printed on a 3D-printer; in the CAE-system ANSYS a simulation of the influence of air flow at a speed of 45m/s on the station was conducted; vector velocity fields are constructed and based on them the most probable places of accumulation of snow are determined; vector pressure fields are constructed and the most loaded elements of the infrastructure are determined on their basis. Conclusions: analysis of simulation results showed that the most probable places of accumulation of snow are located near the walls of all buildings of the station and in places of significant change in the terrain of the surrounding area. The most loaded with wind pressure is the main housing and the storage tank for diesel fuel. In this regard, it was decided to additionally create geometric models of the fuel tank to study the effect of multi-site damage in the form of cracks on its integrity. It is also determined that the main impact on the elements of the infrastructure of the station is the wind from the mainland, but not from the ocean.

Multi-class recognition of objects technical condition by classifier based on probabilistic neural network

The paper deals with the efficiency study of the classifier developed based on the probabilistic neural network for multi-class diagnostics of a complex spatial object in the presence of multi-site damage. For recognition, the multidimensional diagnostic feature vector is used, the values of the features may have a deviation of ±5 % for the defect-free condition of an object, and exceed the permissible deviation in case of occurrence and development of damage. For the vector containing 5 diagnostic features, 6 classes of technical condition of an object are substantiated. Formation of sets of training and test input vectors, used for the classifier training and testing is performed. In order to evaluate the multi-class recognition efficiency, the coefficient, which is a percentage of the probability of correct classification of test vectors, is used. The analysis of the dependence of the efficiency coefficient on the characteristics of the classifier and the set of training vectors is carried out. It is found that error-free multi-class recognition of the object condition over the entire set of input vectors with different values of deviation of feature elements is provided in the range of values of the classifier parameter spread of [0,02; 0.07]. It is revealed that the greater the diagnostic feature deviation in test vectors, the greater the influence of the dimension of the set of training vectors on the multi-class recognition efficiency. The minimum size of the set of training vectors (68 vectors) and the limit value of diagnostic feature deviation in test vectors (17 %), which provide error-free multi-class recognition by the developed classifier are determined.

On multi-site damage identification using single-site training data

This paper proposes a methodology for developing multi-site damage location systems for engineering structures that can be trained using single-site damaged state data only. The methodology involves training a sequence of binary classifiers based upon single-site damage data and combining the developed classifiers into a robust multi-class damage locator. In this way, the multi-site damage identification problem may be decomposed into a sequence of binary decisions. In this paper Support Vector Classifiers are adopted as the means of making these binary decisions. The proposed methodology represents an advancement on the state of the art in the field of multi-site damage identification which require either: (1) full damaged state data from single- and multi-site damage cases or (2) the development of a physics-based model to make multi-site model predictions. The potential benefit of the proposed methodology is that a significantly reduced number of recorded damage states may be required in order to train a multi-site damage locator without recourse to physics-based model predictions. In this paper it is first demonstrated that Support Vector Classification represents an appropriate approach to the multi-site damage location problem, with methods for combining binary classifiers discussed. Next, the proposed methodology is demonstrated and evaluated through application to a real engineering structure – a Piper Tomahawk trainer aircraft wing – with its performance compared to classifiers trained using the full damaged-state dataset.

Vibration-based multi-site damage precise localization via the Functional Model Based Method

The problem of multi-site damage precise localization, that is multi-site damage coordinate estimation is addressed via the random vibration based stochastic Functional Model Based Method (FMBM). Damage detection and precise localization for pairs of damage locations on the wing of a lab-scale Garteur skeleton structure is achieved based on the vibration response measured via a single accelerometer at a low and limited operational frequency bandwidth. The results of the study indicate excellent damage detection and remarkable localization of the considered multi-site damage scenarios.

Splitting method and hybrid-Trefftz formulation for multisite damage analysis in two-dimensional domains

The aim of this paper is to present a new strategy for multiple-site damage analysis by combining the splitting method and hybrid-Trefftz stress formulation in a two-dimensional domain. The first is a decomposition method originally conceived to obtain the solution of a cracked solid. Accordingly, the given problem is split into three subproblems: an uncracked global problem (PG(0)), a local problem (PL(k)) considering a single crack located in a reduced domain and a global problem (PG(k)) aiming to account for the relative interaction effects among all the cracks. Most subproblems are independent and the solution results from a non-iterative strategy, which is one of the main benefits of this method. The hybrid-Trefftz stress formulation is a non-conventional finite element method where stresses and displacements are approximated, independently, in the domain and boundary of the element, respectively. The stress fields are hereby approximated by a basis function that solves the Navier equation and includes analytical fracture mechanics functions, so that the values of stress intensity factors are computed from the solution of the linear system. The hybrid-Trefftz formulation is used in the local problem PL(k) of the splitting method, therefore improving the performance of the method and providing accurate solutions with very coarse meshes. In conclusion, it is shown through the numerical examples that the splitting method and hybrid-Trefftz formulation framework hereby proposed allows conducing accurate analysis. Once exploring a parallel processing, taking advantage of the independence of each subproblem, the framework can be extended to consider different scenarios of multisite cracked solids with a low computation cost.