Shock and Vibration

Volume 2017 (2017), Article ID 1062949, 9 pages

https://doi.org/10.1155/2017/1062949

## Damage Identification of a Derrick Steel Structure Based on the HHT Marginal Spectrum Amplitude Curvature Difference

^{1}School of Vehicles and Energy, Yanshan University, Qinhuangdao 066004, China^{2}School of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China^{3}School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA

Correspondence should be addressed to Dongying Han

Received 25 April 2017; Revised 18 July 2017; Accepted 7 August 2017; Published 17 September 2017

Academic Editor: Giada Gasparini

Copyright © 2017 Dongying Han et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

For the damage identification of derrick steel structures, traditional methods often require high-order vibration information of structures to identify damage accurately. However, the high-order vibration information of structures is difficult to acquire. Based on the technology of signal feature extraction, only using the low-order vibration information, taking the right front leg as an example, we analyzed the selection of HHT marginal spectrum amplitude and the calculation process of its curvature in practical application, designed the damage conditions of a derrick steel structure, used the index and intrinsic mode function (IMF) instantaneous energy curvature method to perform the damage simulation calculation and comparison, and verified the effect of identifying the damage location in a noisy environment. The results show that the index can accurately determine the location of the damage element and weak damage element and can be used to qualitatively analyze the damage degree of the element; under the impact load, the noise hardly affects the identification of the damage location. Finally, this method was applied to the ZJ70 derrick steel structure laboratory model and compared with the IMF instantaneous energy curvature method. We verified the feasibility of this method in the damage location simulation experiment.

#### 1. Introduction

Derrick steel structures play an important role in the oil and gas exploration and development [1, 2]. During long-term service, because of various factors such as disassembly and corrosion, damage inevitably occurs, which gradually reduces the safety performance and carrying capacity of the derrick steel structures and forms security risks [3–5]. In recent years, the damage detection method based on structural signal feature extraction [6, 7] has attracted the attention of many scholars; this method mainly uses the vibration signal from the vibration sensors to collect structural damage. Using signal-processing methods, the appropriate damage-sensitive indicators are analyzed, and further structural-damage identification or health monitoring is realized [8].

Huang et al. proposed Hilbert-Huang transform (HHT) method, which is a new, self-adaptive frequency analysis method [9], and included the empirical mode decomposition (EMD) and Hilbert transform (HT); the core is the EMD. Chen et al. used the instantaneous frequency of IMFs (intrinsic mode functions) as the component damage index of structure damage detection [10–12]. Pines and Salvino combined the EMD with Hilbert transform to obtain the phase of the component signals and used the phase information of different degrees of freedom to identify the structure damage [13]. Li et al. [14] used the method of wavelet analysis to analyze the maximum energy of the intrinsic mode functions (IMFs) component, which includes the wavelet coefficients for damage identification. Cheraghi and Taheri [15] analyzed the energy of the IMF component signal, selected the effective characteristic information as the damage sensitivity index, and applied it to identify the pipeline structure damage. Rezaei and Taheri [16, 17] used the energy of the first-order IMF component after the decomposition of the signal EMD as a damage sensitivity index to diagnose the damage of the pipeline structure. Chen et al. proposed to show the status of damage material wing box of the material of the feature vector-relative variation of the instantaneous frequency [18]. Cao et al. [19] proposed a structural-damage early-warning method based on the EMD, where the structure before and after damage in the component of the IMF’s energy distribution changes as the damage-sensitive index, and applied the method to model Health Monitoring Benchmark structure damage identification. Ren et al. [20] applied the improved HHT method to the damage identification of engineering structures and proposed the method to identify the damage location of the structure using the structural before and after the damage in the first-order response to a first-order IMF feature energy ratio. Wang et al. applied the method to the bridge structure. The HHT theory has not been used in complex structures, such as derrick steel structures, but it has been used in simple structures in the literature [21]. Li et al. applied the method to the crack identification of the rotor [22]. This paper realized the damage identification of the derrick steel structure based on the HHT marginal spectrum amplitude curvature difference and only used a low-level vibration information structure. The simulation calculated the damage identification of the derrick and compared it with the IMF instantaneous energy curvature difference. Finally, the feasibility of the method was verified with derrick damage location simulation experiments.

#### 2. HHT Marginal Spectrum Amplitude Curvature

##### 2.1. HHT Theory

The HHT method consists of two parts: EMD and HT. The original signal* x*(*t*) is decomposed into a series of IMFs and a residual function by EMD:

Hilbert transformation of the IMF component:

Based on this function, the analytic signal is established, and the instantaneous amplitude and phase function are obtained:

The instantaneous frequency is defined as the derivative of the instantaneous phase:

Signal can be expressed as

Here, we ignore the residual component of the original signal ; RE denotes the real part. We call the above formula on the right part of the equal sign the Hilbert spectrum:

Hilbert marginal spectrum is obtained by integrating the above formula with time:

##### 2.2. HHT Marginal Spectrum Amplitude Curvature

After the structure is applied to the vibrational excitation, the vibration response signal of different parts of the structure is extracted. After the signal is decomposed by the EMD, a series of IMF components is obtained, the main IMF component is selected, and the marginal spectrum amplitude is calculated. Then, the relative HHT marginal spectrum amplitude at different parts of the structure iswhere is the HHT marginal spectrum of different parts of the structure and is the HHT marginal spectrum of the structure reference position.

The HHT marginal spectrum amplitude curvature of different parts of structures is approximately calculated by the central difference method:where is calculated at the site of the relative HHT marginal spectrum amplitude, and are calculated at the sites adjacent to the relative HHT marginal spectrum amplitude, and is the distance between adjacent parts.

The difference in HHT marginal spectrum amplitude curvature iswhere is the HHT marginal spectrum amplitude curvature before structural damage.

#### 3. Extracting the Signal Characteristics of the Derrick Steel Structure

##### 3.1. Establishment of the Simulation Model of the Derrick Steel Structure

The model of the derrick steel structure is 2.951 m high, and the maximum hook load is 13.9 kN. Its material is Q235 steel. The structure was divided into 274 elements and 142 nodes, and its finite-element model is shown in Figure 1. The right front pillar nodes of the derrick steel structure were numbered 1–20 from the bottom. There was one element between every two nodes, and the elements were numbered 1–19 from the bottom to the top.