Andrew Deeks

Structure damage detection using neural network with multi-stage substructuring

Artificial neural network (ANN) method has been proven feasible by many researchers in detecting damage based on vibration parameters. However, the main drawback of ANN method is the requirement of enormous computational effort especially when complex structures with large degrees of freedom are involved. Consequently, almost all the previous works described in the literature limited the structural members to a small number of large elements in the ANN model which resulted ANN model being insensitive to local damage. This study presents an approach to detect small structural damage using ANN method with progressive substructure zooming. It uses the substructure technique together with a multi-stage ANN models to detect the location and extent of the damage. Modal parameters such as frequencies and mode shapes are used as input to ANN. To demonstrate the effectiveness of this approach, a two-span continuous concrete slab structure and a three-storey portal frame are used as examples. Different damage scenarios have been introduced by reducing the local stiffness of the selected elements at different locations in the structures. The results show that this technique successfully detects all the simulated damages in the structure.

Numerical analysis of soil plug behaviour inside open-ended piles during driving

The plugging mechanism of infinitely-long open-ended piles is examined using numerical simulation of the wave propagation inside the soil plug and pile. It is shown that the key parameters for the plugging mechanism are the pile radius, the shape of the impact load, the shear wave velocity of the soil inside the pile, and the friction at the pile–soil interface. Consequently, the tendency of the pile to plug during driving can be assessed prior to the driving process by consideration of these key parameters. Existing one-dimensional models for the shaft response of open-ended piles are discussed and an improved model is presented. The differences between using one-dimensional models and finite element models to simulate the plugging process are examined. The differences are found to vary with the key parameters. Pile-in-pile and lumped-mass one-dimensional models are found to give satisfactory performance for some parameter combinations, while for others an axisymmetric finite element model must be used.

An Element-Free Galerkin Scaled Boundary Method for Steady-State Heat Transfer Problems

This article develops an element-free Galerkin scaled boundary method (EFG-SBM) for solving steady-state heat transfer problems. The SBM weakens the governing differential equations along the circumferential coordinate direction and solves analytically in the radial direction. Unlike the conventional scaled boundary finite-element method (SBFEM), an EFG approach is used in the circumferential direction in this article. The proposed method is verified via numerical examples including problems with thermal singularity and unbounded domain, and satisfactory results are obtained in comparison with analytical and SBFEM solutions.

8 – Concluding remarks

Publisher Summary This chapter presents the concluding remarks of all the topics covered in the book. Starting from scratch, a treatise is written developing the one-dimensional strength-of-materials theory of conical bars and beams called cones that are applied to practical foundation vibration analyses. Confidence in cones is gained because the procedure to analyze foundations is the same as routinely used in structural analysis, and a systematic evaluation for a wide range of actual sites demonstrates sufficient engineering accuracy. A short computer program written in MATLAB forms an integral part of the book, and a user-friendly executable program is also provided. Using the cone models leads to some loss of precision compared to applying the rigorous methods. The achieved accuracy using cone models is more than sufficient. It cannot be the aim of the engineer to calculate the complex reality as closely as possible, as this is not required for a safe and economical design. The accuracy is limited anyway because of the many uncertainties that cannot be eliminated such as the wide scatter of the dynamic material properties of the soil.

Evaluation of Bridge Load Carrying Capacity Using Updated Finite Element Model and Nonlinear Analysis

The integrity of ageing bridges is in doubt because of increasing traffic loads, deterioration of materials, possible damage during service, and revised code requirements. Traditional methods in prediction of load varying capacity of bridges are usually based on the design blueprints and may not reflect the bridge condition as is. In this paper, the nonlinear finite element analysis, incorporating the model updating technique, is used to predict the behaviour of a 30-year-old slab-girder bridge. The original finite element model based on the design drawings is updated by modifying the stiffness parameters of the girders, slab, shear connectors and bearings so that the vibration properties of the model match the field vibration measurement data. The updated model represents the present condition of the bridge better than the original model that is based on the design blueprints. The load carrying capacity of the bridge is then calculated using the original and updated finite element models, respectively, with consideration of nonlinear material properties. The comparison shows that the bridge load carrying capacity under the present condition is lower than that under the design condition, whereas is still above the design requirement. The influence of the shear connectors on the load carrying capacity is specially investigated.

Substructuring Technique for Damage Detection Using Statistical Multi-Stage Artificial Neural Network

Artificial Neural networks (ANN) have been proven in many studies to be able to efficiently detect damage from vibration measurements. Their capability to recognize patterns and to handle non-linear and non-unique problems provides an advantage over traditional mathematical methods in correlating the vibration data to damage location and severity. However, one shortcoming of ANN is they require enormous computational effort and sometimes prohibitive time and computer memory for training a reliable ANN model, especially when structures with many degrees of freedom are involved. Therefore, in most cases, rather large elements are used in the structure model to reduce the degrees of freedom. This results in the structural vibration properties not being sensitive to small damage in a large element. As a result, direct application of ANN to detecting damage in a large civil engineering structures is not feasible. In this study, a multi-stage ANN incorporating a probability method is proposed to tackle this problem. Through this method, a structure is divided into several substructures, and each substructure is assessed independently. In each subsequent stage, only the damaged substructures are analyzed, and eventually the location and severity of small structural damage can be detected. This approach greatly reduces the computational time and the required computer memory. Moreover, a probabilistic method is also used to include the uncertainties in vibration frequencies and mode shapes in damage detection analysis. It is found that this method reduces the uncertainty effect in frequencies due to duplication error in the multi-stage ANN model and reduces the uncertainty effect in mode shapes due to the damage in other substructures. The developed approach is applied to detect damage in numerically simulated and laboratory tested concrete slab. The results demonstrate that the proposed method can detect small damage with a higher level of confidence, and the undamaged elements are less likely to be falsely detected.

6 – Evaluation of accuracy

Publisher Summary This chapter presents the evaluation of the accuracy of the strength-of-materials approach using cones. In addition, certain limitations of the procedure are established, concerning the applicable range of the embedment ratio and the shape of the axis-symmetric embedded foundation. The chapter addresses surface foundations on a multi-layered half-space and embedded cylindrical foundations. The chapter examines modeling aspects of a site with gradually varying material properties, where a large number of cone segments are required, and discusses the adequate representation of the dynamic behavior below and above the so called cutoff frequency, where an abrupt change in response occurs. The chapter addresses a cylindrical foundation embedded in an incompressible multi-layered half-space. By varying the ratio of the radii of a hemi-ellipsoid embedded in a homogeneous half-space, the accuracy for axis-symmetric foundations modeled with disks of varying radii is studied. The chapter also examines a sphere embedded in a homogeneous full-space. A homogeneous half-space and a homogeneous layer fixed at its base are addressed both for surface and embedded cylindrical foundations. In addition, mainly to demonstrate the wave propagation in cone segments, a disk embedded in a full-space and a half-space is examined. To discuss the termination criteria, a disk on the surface of a layered half-space is considered, but only for one degree of freedom. To gain confidence, a systematic evaluation of the accuracy for multiple-layered half-spaces is essential. The underlying half-space can either be flexible or rigid, in the latter case preventing wave propagation in the vertical direction toward infinity and thus radiation damping vertically from occurring. Besides the standard case where the underlying half-space is stiffer than the layers, the opposite situation is also addressed.

AUTOMATIC COMPUTATION OF PLASTIC COLLAPSE LOADS FOR FRAMES

This paper describes an automatic approach to the determination of plastic collapse loads for plane frames using the kinematic method. An algorithm is developed to determine the elementary collapse mechanisms for an arbitrary frame. These mechanisms are then combined in a systematic manner using a recursive algorithm in order to find the mechanism with the lowest collapse load. Since all potential collapse mechanisms are investigated, the method is able to find alternative collapse mechanisms with the same load factor, and indeed the lowest n collapse mechanisms. The approach is applied to three examples, and is shown to be accurate and capable of practical application. A complete C++ program listing is included.

Semi-analytical solution of Laplace’s equation in non-equilibrating unbounded problems

Abstract Some two-dimensional problems of elastostatics are governed by Laplace’s equation. Using the terminology of elastostatics, if the face loads and body loads are not self-equilibrating, even when the displacement at infinity is restricted to zero, displacements in the near field will be infinite. However, the stress field within the domain is well behaved, and is of practical interest. In this paper the semi-analytical scaled boundary finite-element method is extended to permit the analysis of such problems. The solutions in the primary variable so obtained include an infinite component, but the difference in value between any two points in the domain can be computed accurately. The method is also extended to solve the non-homogeneous form of Laplace’s equation.

Numerical analysis of a two-rail steel RHS traffic barrier to vehicle impact

Abstract In this paper, the non-linear finite element code LS-DYNA is used to evaluate the performance of an existing traffic barrier system in Western Australia in collisions with vehicles. The vehicle types, speeds and impact angles to the barrier specified in the revised Bridge Code AS 5100.2 are adopted in the analysis. Numerical models of three kinds of vehicles, a small passenger car, a utility vehicle and a single-unit truck, as specified in the revised Bridge Code, are used for the analysis. The numerical model of the guardrail is set up according to the actual design of the traffic barrier. Before the analysis of barrier response to the vehicle impact can be carried out, convergence tests on the numerical model of the traffic barrier were conducted, resulting in the selection of the final grid element sizes and the number of spans in the numerical model. Numerical simulations of the performance of the traffic barriers in collisions with vehicles with different speeds, different impact angles, and colliding with the barrier at different locations are carried out. The adequacy of the steel RHS traffic barrier to meet the required performance levels is examined. Numerical results indicate that the existing two-rail steel RHS traffic barriers in Western Australia meet the requirements of the low performance level tests, but fail to satisfy the regular and higher performance levels.