Keywords

1 Introduction

Monitoring of strength and performance of civil infrastructure is essential for the comfort of the occupants. It avoids unexpected accidents and provides a safe environment for all. Damage identification is significant for preserving and sustaining the design life of civil structures. Structural Health Monitoring is the process of evaluating the changes that occurred in structures over some time. Human interference and changes in the environmental factors cause mild to severe damages in civil engineering structures. The vibration-based damage detection method measures the changes associated with the vibration parameters of the structure and determines the fault location and intensity that occurred in the structure.

Lattice structures are tower like structures similar to truss that is highly utilised in the power transmission industry, telecommunication and oil industry. They are popular because of their lightweight and fast construction. Health monitoring of these structures has more practical importance since most of them were located in inaccessible locations and a hazardous environment. Failure of these structures may interrupt power and network connection that have much more relevance in the modern world.

An artificial neural network (ANN) is a biologically inspired mathematical model made up of several layers and parallelly connected through neurons arranged in each layer. A neural network consists of three primary layers: input layer, hidden layer, and output layer (Fig. 1). It processes through a series of algorithms to make hidden relationships between input and output data.

Fig. 1
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The basic structure of a neural network

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Studies by Idichandy et al. [1] proposed a scheme for monitoring offshore platform using natural frequency and vibration modes. An adaptive resonance theory (ART) based neural networks and backpropagation networks (BPN) were used for the damage identification of offshore platform by Mangal et al. [2]. Counter propagation neural networks were utilised instead of backpropagation to predict damages in bridges by Zhao et al. [3]. Wu et al. [4] evaluated the possibility of automated health monitoring of engineering structures with the neural network and vibration data.

Pioneering work on damage detection with the combination of neural network and cuckoo search algorithm was done by Tran-Ngoc et al. [5]. Modified modal flexibility and strain energy were precisely used by Jayasundara et al. [6] to quantify and localise damages in complex structures like deck type arch bridges. The above study showed a quick evaluation of single and multiple damages incorporated in the structure. Bao et al. [7] utilised raw strain response data from the structure to identify the damages automatically with the combination of a one-dimensional convolution neural network. The results of these analysis were highly comprising and experimentally validated by using the scale-down model of the structure.

2 Modelling of Lattice Structure

The lattice structure used in the oil industry specifically known as the offshore jacket platform is used for the present study. It consists of three types of members: main legs, inclined bracings and horizontal bracings. All sections are tubular in cross-section with different diameter. The main legs have an outer diameter of 40 mm and wall thickness of 1.5 mm. The inclined bracings have 20 mm diameter and 1.2 mm thick, while horizontal bracings are given 16 mm diameter and 1 mm thick. The details of the lattice structure model are shown in Fig. 2. The Deck slab is situated at the top of the structure and modelled using inclined and horizontal bracing. A Deck mass of 10 kg is uniformly provided over the main deck.

Fig. 2
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Three dimensional view of the lattice structure modelled in SAP2000

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The structural analysis program SAP2000 was used to model the lattice structure. The members in the numerical model of lattice structure made up of three-dimensional beam elements having six degrees of freedom. Nodes were located at the intersection of longitudinal axes of each member and the model consist of 50 nodes and 124 beam elements. The support condition of the base of the model is fixed and it is provided at six unique points. Analysis of the structure was carried out by assuming it as a three-dimensional truss model.

3 Lattice Structure in Damaged Condition

Lattice structure in damaged condition was modelled by removing one member at a time. Members in the deck slab not considered for the damage analysis of the structure. Different damaged cases were developed similarly by removing members in chronological order. Total 78 damaged cases were modelled, out of which 6 cases used for testing and the rest were used for training the neural network.

3.1 Training of Neural Network for Damaged Cases

The natural frequency of each damaged case is extracted to create a neural network configuration to generalise the solution on the behaviour of the structure. The first five natural frequencies of translational modes along the y direction are used for damage identification of the lattice structure. Neural networks were trained using the natural frequency data as input values and centroid of removed members in Cartesian coordinates as targets. Since input and targets are already known, supervised learning algorithm is used for training the network.

Feedforward backpropagation network is employed for training and testing of data. A neural network fitting tool (nftool) from the deep learning toolbox in MATLAB was used to develop the network. The training of the neural network is a highly empirical process. The best performing network was found out by varying parameters and hyperparameters of the network. Figure 3 shows the network diagram of the best performing network in damage prediction of the lattice structure.

Fig. 3
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Neural network configuration adopted for damage identification of the lattice structure

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A neural network with two hidden layers having 25 and 15 neurons on each layer is selected based on performance. Backpropagation algorithm Levenberg Marquardt (trainlm) is applied to train the neural network. Transfer function adopted for all layers is tan sigmoid and the convergence of the network is measured using the mean square error function after each iteration. Out of 72 samples used for training, 84% is used for training and 8% is used for testing and validation. Regression coefficients (R) obtained after training are shown in Fig. 4, and overall R = 0.989, which is close to 1 and acceptable.

Fig. 4
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Regression coefficient obtained from training of neural network

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4 Results and Discussions

Testing of the neural network is carried out to analyse the accuracy of the prediction of the network in a damage scenario. In the training process network learns various damage patterns that occurred in the structure and thereby it is capable of detecting damages. Six data sets which are not used for training of neural network are used for testing. The natural frequency of the above data sets are given as input values of the network and neural network predicted damage location corresponding to given input values. Network analyses the input parameters and matches with known damage patterns that already have. Table 1 shows the unknown data used for testing of the neural network. Table 2 shows the output from the neural network.

Table 1 Data set used for testing of neural network
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Table 2 Output from the neural network
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f1 to f5 natural frequencies of damaged lattice structure from mode 1 to mode 5 along the y direction.

X, Y and Z are the Cartesian coordinates of centroid of the member removed.

RMSE = Root Mean Square Error.

The developed neural network configuration predicts the damage location in the member with acceptable errors. Results in Table 3 indicates the capability of the proposed neural network to detect, locate single damages with reasonable accuracy. It is observed that the output from the network gives excellent accuracy in terms of the height of location of the damaged member (z coordinate).

Table 3 Damage prediction in lattice structure using neural network
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In most cases, the prediction results are either close to the required member or in a symmetrically opposite member. Since the structure under study was partially symmetric with respect to main and horizontal members along one direction, frequency values did not differ much for these member cases. Thus neural network predictions also seemed to be close to symmetric member. One case of prediction gave damage near a member adjacent to the damaged member (29); it is a horizontal member. For this structure, errors in the horizontal members are more than main leg members and inclined members. Stiffness of horizontal bracings are less compared to other members; hence variations in the natural frequencies are less for horizontal members and makes it more challenging to distinguish damages using neural networks.

Thus it could be stated that the height wise damage prediction gave perfect accuracy. Thus in a practical situation, the member adjacent to and symmetric to the predicted member should be checked at the same height and corrective action should be taken. The maximum root mean square error is 0.2 which shows the suitability of this method to identify damages in the lattice structure.

5 Conclusions

The study evaluated the possibility of using an artificial neural network in the damage identification of the lattice structure. Following conclusions can be derived from the results obtained.

  1. 1.

    Damage makes significant changes in vibration parameters of the lattice structure.

  2. 2.

    Natural frequency in combination with a neural network gives a good damage detection strategy.

  3. 3.

    Neural network precisely predicts the damage that occurred in the lattice structure having a root mean square error below 0.1. In other cases, it predicts adjacent member or opposite member at the same level.

  4. 4.

    Height wise prediction of damage location using neural network is highly appreciable.

Thus, it can be concluded that in lattice structures, neural network-based damage detection gives good results with the extraction of natural frequency.