Leonard Ziemiański

Neural networks in mechanics of structures and materials - new results and prospects of applications

Abstract Basic ideas of back-propagation neural networks (BPNNs) are presented in short. Then BPNN applications in analysis of the following problems are discussed: (1) bending analysis of elastoplastic beams, (2) elastoplastic plane stress problem, (3) estimation of fundamental vibration periods of real buildings, (4) detection of damage in a steel beam, (5) identification of loads applied to an elastoplastic beam. Regularization neural network is briefly discussed and its application to estimation of concrete fatigue durability it shown. A modified Hopfield network is used to the analysis of an elastic angular plate with unilateral constraints. In the end some conclusions and prospects of neurocomputing applications are pointed out.

Neural Networks in the Identification Analysis of Structural Mechanics Problems

The Chapter is related to research carried out by the authors’ teams. The Chapter contains seven Sections and list of References. Section 1 concerns basics of selected neural networks. The main attention is paid to the Back-Propagation NNs, which are mostly applied in the analysis of engineering problems. Modifications of this NN (replicator, cascade NN, Fuzzy Weight NN) and some other NNs (Radial Basis Function NN and Adaptive Neuro-Fuzzy Inference System) are discussed in short. Data preprocessing, design problems of these NNs and approximation errors are considered as well. Section 2 is related to the application of NNs for simulating trials in the Classical Monte Carlo Method. Patterns generated by an FE program are used for the NN training and testing. A great numerical efficiency of this approach is presented on an example of the reliability analysis of an elastoplastic plane frame. Section 3 deals with the identification problems of real buildings subjected to paraseismic excitations. Section 4 is related to the application of dynamic response (eigenfrequencies excited by impulse loadings or wave propagation measurements) to the parameter identification of structural elements with defects. In Section 5 the problem of FEM models updating is considered. A hybrid approach is discussed as a sequence of the application of an initially formulated FE model with control parameters, which are identified by an NN. The calibration and verification of the updated FE model is performed on the base of laboratory tests. Section 6 discusses applications of a modification of a standard NN (Fuzzy Weight NN) to the analysis of problems from experimental structural mechanics that give fuzzy results. Section 7 deals with so-called implicit modelling (i.e. model-free, data-related NNs) of physical relationships. In References, besides basic literature, also papers written by the authors and their associates are quoted3,4.

Hybrid neural network/finite element modelling of wave propagation in infinite domains

Abstract The paper presents the method of formulation of a transmitting boundary using artificial neural network (ANN). The back-propagation neural networks (BPNN) [Comput. Struct. 79 (2001) 2261; S. Haykin, A Comprehensive Foundation, second ed., Prentice-Hall, 1999; Z. Waszczyszyn, in B.H.V. Topping (Ed.), Computational Mechanics for the Twenty-First Century, Civil-Comp Ltd., 2000, p. 479] are used for simulation of dynamic reactions on artificial boundary from an outside region. Neural networks are applied to all nodes on “artificial boundary”. The input vector for ANN is composed of (1) displacement, velocity and acceleration at time t −1 in node on the boundary, (2) displacements at time t −1 in three consecutive nodes on line perpendicular to the artificial boundary. The output vector determines the dynamic reactions at time t . Besides the displacements, velocities and accelerations at time t are computed. Three problems are discussed: (1) wave propagation in semi-infinite strip, (2) wave propagation in semi-infinite strip with notch, (3) acoustic radiation from nonconcentric radiator. Neural networks with one or two hidden layers were tested. Computations proved that BPNNs can be efficiently applied to the implementation of the approximate boundary condition on the artificial surface.

Neural Network Identification of a Circular Hole in the Rectangular Plate

Numerical tests have been carried out for 2D plates with internal defects in a form of circle hole. An identification procedure of the defect based on neural network analysis of eigenfrequencies is presented [1]. The position of the hole has been searched. The Backpropagation (BP) Artificial Neuron Networks (ANN) with one hidden layer, trained with the Levenberg-Marquardt (LM) learning algorithm have been applied [2]. The single networks and the cascade sets of BP neural networks have been used [1,3].

Towards application of soft computing in structural health monitoring

The paper presents preliminary results of data analysis and discusses the application of soft computing methods in the field of non-destructive tests. The main objective of developed diagnostic system are the automatic detection and evaluation of damage. Thus the system is composed of two signal processing techniques known as novelty detection and pattern recognition. For this purpose autoassociative as well as feed-forward neural networks are used. All the signals used for training the system are obtained from laboratory tests of strip specimens, where phenomenon of elastic wave propagation in solids was utilized. Computed parameters of time signals defines various types of input vectors used for training neural networks. The results finally obtained prove that the proposed diagnostic system made automation of structure testing possible and can be applied to Structural Health Monitoring.

The Solution of an Inverse Problem in Plates by Means of Artificial Neural Networks.

The paper presents the application of Artificial Neural Networks (ANNs) for solution of an inverse problem [1]. Based on the dynamic characteristics of a plate, the neural identification of parameters of circular hole and additional mass have been performed. An emphasis was placed on the effective preparation of learning data, which were produced both by the finite element method and by experiment.

Neural Networks in Updating of Dynamic Models with Experimental Verification

This paper presents the application of artificial neural networks in updating of dynamic models of engineering structures. There are presented examples of updating of two models: a model of a beam hung on two strings and a model of a portal frame. There are used multi-layer feed-forward networks and networks with radial basis function, the input vectors consist of preprocessed data obtained from the measurements done on a laboratory models of considered structures.

Identification of load parameters for an elastic-plastic beam basing on dynamic characteristics changes

Single load parameters are identified on the base of changes of known dynamic characteristics of an elastic-plastic steel beam. It is also loaded by a control load in order not to involve characteristics of the initial structure. Special attention is paid to the location of measurement points to obtain accuracy of computations corresponding to possibilities of planned measurement devices. Finite Element Method was used for the simulation of dynamic characteristics and Standard Neural Networks were applied for the inverse analysis. The main goal of the paper is the formulation of a new non-destructive method in the area of health monitoring of civil engineering structures.

Identification of Damage in Multispan Beams Using Parameter-dependent Frequency Changes and Neural Networks

Nowadays the knowledge of the structure condition is considered to be more and more important. The state of the structure and its safety strongly depends on the degradation of the structure elements (beams, connections, etc.). Nondestructive methods predict the location and the extent of damage in existing engineering structures. The publications on the identification of damages present mainly the approach which implies the knowledge of eigenfrequencies and eigenmodes of an undamaged structure. The damage is identified on the basis of the variations of dynamic parameters with respect to the initial values [1]. Some methods require the introduction of external perturbations to the structure.

Neural Networks: New Results and Prospects of Applications in Structural Engineering

NN is a new computational tool for data processing and this tool can be characterized as a “data dependent and model free” approach. Other features of NNs correspond to their applicability in the analysis of nonlinear direct and inverse problems. NNs can also be used in hybrid systems as a complementary part to conventional computational methods, especially to FEM.