Robust ultrasonic damage detection under complex environmental conditions using singular value decomposition
Introduction
Guided wave ultrasonics is an attractive monitoring technique for damage diagnosis in large-scale plate and pipe structures. Guided waves propagate with low attenuation and can interrogate large areas with only a small number of sparsely distributed, low-voltage transducers [1], [2], [3]. Ultrasonic guided waves are characterized by a dispersive and multi-modal nature, which complicates the received ultrasonic signals and makes it challenging to extract information about the damage [4].
Due to the complexity of guided waves, many damage detection methods rely on baseline comparison to remove static, background information. In these scenarios, a set of baseline records is collected when the structure is known to be intact. The differences between any new records and the baseline signal can then used to monitor for structural damage [5]. Alternatively, structural damage can be detected by analyzing the cross-correlation coefficients, a measure of similarity, between a baseline and each new time-record [6].
However, ultrasonic waves are vulnerable to changes in environmental and operational conditions (EOC) [7] that are inevitable in the normal operation of civil and mechanical structures. Such changes of EOCs may affect the mechanical properties of the medium in which the ultrasonic waves propagate, and produce changes in the received wave signals. Therefore, the baseline information is generally not static over time. In active pipes, for example, ultrasonic waves are often influenced by variations in temperature, pressure, and flow rate. These effects complicate analysis and mask damage-related information [8].
Among the common EOCs to affect ultrasonic monitoring systems, temperature is the most ubiquitous and widely studied. Researchers have developed many algorithms to compensate for temperature variations. Optimal baseline selection methods were first developed in [9], which avoid temperature variation by comparing the new record with a library of baselines collected at different temperature. Researchers then developed local peak coherence [5], [10], and optimal signal stretch methods [11], [12], assuming temperature change has a stretching effect on the signal. With that assumption, the amount of temperature change can be determined by comparing new records with stretched version of a baseline signal. One can then stretch the new record so that it is comparable to the baseline records. The estimation of stretching factors can also be done in the scale transform domain to achieve higher resolution and efficiency, as shown in [13]. Other researchers argue that having a fixed baseline or baseline set may be not sufficient in a dynamic environment, and developed a continuously growing baseline temperature compensation method to avoid collecting a comprehensive library of baselines before the monitoring phase [14]. As demonstrated in both laboratory and practical experiments, these temperature compensation methods can be used to adjust each record and improve our capability to detect damage.
Fig. 1 illustrates an example of scale-transform temperature compensation [13] applied to two experimental records from an operating hot-water pipe under variable temperature, flow rate, and pressure. Fig. 1(a) and (b) show a comparison of the two signals zoomed into different fast-time intervals, where ‘fast-time’ refers to the time-of-flight of the ultrasonic waves, and is characterized by the sampling of voltage readings in one pitch–catch record. In contrast, we define ‘slow-time’ as the time scale associated with the interval (usually in minutes) in between records, and is characterized by the number of records. We can see that the signals align well at the beginning and increasingly deviate as they approach the coda, the end of the signal. We apply the scale-transform temperature compensation [13] on the dashed record with the solid trace as the baseline. Fig. 1(c) and (d) show that after temperature compensation the records are much better aligned with each other.
Stretch-based temperature compensation methods have certain limitations. First, these temperature compensation methods model temperature changes as a stretching effect on the ultrasonic signals, which is only an approximation. This model does not hold for large changes in temperature. Second, the methods assume that temperature variation is uniform across the path covered by the ultrasonic records, such that the stretching effect is uniform across the ultrasonic record. Many structures are instead affected by temperature gradients. Last, temperature compensation methods generally require a set of baseline records to be collected either before or during the monitoring, which can be difficult to manage and/or update in a dynamic environment. Moreover, in a practical implementation of ultrasonic monitoring systems, temperature variation is often accompanied by other EOCs that affect the ultrasonic record. Our field experiments show that EOCs contribute to many variations of the ultrasonic records, and that temperature compensation only addresses a portion of them.
Because analytically modeling the effect of EOCs on the ultrasonic measurements is challenging, researchers have developed various data-driven methods that extract useful information from large datasets of ultrasonic records [10], [15], [16]. Data-driven methods extract useful features from data and then use those features to classify the status of the structure. A data-driven damage detection procedure used (explicitly or implicitly) by many researchers includes pre-processing, feature extraction, damage-sensitive feature selection, and damage classification. Detection or classification is accomplished with well-developed methods in the literature such as support vector machine [17], neural network [18], and Fisher’s discriminative analysis [19]. However, reliable damage-sensitive features are usually application-specific and are difficult to find.
In this paper, we address these challenges by developing a novel damage-sensitive feature extraction and selection procedure based on singular value decomposition (SVD) to detect structural damage with ultrasonic pitch–catch records. SVD is a linear decomposition method that is widely used for dimensionality reduction, and is closely related to another latent variables methods, known as principal component analysis (PCA) [20]. We demonstrate that by applying SVD on ultrasonic records, we can separate the change produced by damage from the change caused by EOCs, without a prior knowledge of the EOC variations, and thereby robustly detect damage in a complex environment. We show its efficacy on data collected in real world piping systems experiencing significant variations in EOCs that defeat common damage detection routines.
In Section 2, we present the proposed damage-sensitive feature extraction and selection procedure. In Section 3, we describe our field experiments on an operating hot water pipe system with large EOC variations spanning seven months from August 2011 to February 2012. We then present the damage detection result using our SVD damage-sensitive feature in Section 4.
Section snippets
Singular value decomposition
Singular value decomposition (SVD) seeks a linear decomposition of a data matrix that creates an orthonormal basis to represent the data. It is extensively studied and used in many fields, including face recognition [21], audio/video compressing [22], and signal de-noising [23]. For a general matrix , the SVD of X is defined by:where superscript H is the conjugate transpose. In (1), is the left singular vector matrix, and each ui is a M × 1 vector that represents the
Experimental setup
We conducted field experiments on an operating hot water pipe system under normal operating conditions [8] in discrete time periods spanning seven months. The tested pipe segment is located in a mechanical space (roughly 700 m2) in Wean Hall, a 27,000 m2 campus building at Carnegie Mellon University. Fig. 5 shows the experimental environment and the subject pipe segment, indicated by a black dashed arrow. It is a Schedule 40 steel pipe with 273.05 mm outer diameter and 9.271 mm wall thickness,
Results on one single dataset
We applied singular value decomposition to ultrasonic records collected on August 31st, 2011. The first 10 h of the data has been characterized in Fig. 7. The dataset consists of 1481 pitch–catch records collected in 28 h from 10:22, August 31st to 14:16, September 1st, with a 3.2-h pause starting from 20:01, August 31st. The pause was due to a suspension in the data acquisition system, and affected neither the operation of the piping system nor the configuration of the data acquisition system
Conclusions and discussion
In this paper, we discussed singular value decomposition and its role in developing a robust damage-sensitive feature for ultrasonic damage detection. We show that by taking advantage of the orthogonality of the singular vectors, we can separate the change produced by a scatter from the influence of EOC variations. We demonstrated the procedure to extract and select damage-sensitive feature from left singular vectors decomposed from ultrasonic records collected under varying environmental and
Acknowledgements
The authors gratefully acknowledge financial support from the Westinghouse Electric Company, and extensive technical discussions with Dr. Warren Junker. We thank Pennsylvania Smart Infrastructure Incubator (PSII) and IBM for providing the servers for data analysis performed in this work.
References (35)
- et al.
Efficient temperature compensation strategies for guided wave structural health monitoring
Ultrasonics
(2010) - et al.
Guided wave health monitoring of complex structures by sparse array systems: influence of temperature changes on performance
J. Sound Vib.
(2010) On the relationships between SVD, KLT and PCA
Pattern Recogn.
(1981)- et al.
A robust singular value decomposition for damage detection under changing operating conditions and structural uncertainties
J. Sound Vib.
(2005) - et al.
Using SVD to detect damage in structures with different operational conditions
J. Sound Vib.
(1999) The use of the area under the ROC curve in the evaluation of machine learning algorithms
Pattern Recogn.
(July 1997)- et al.
Practical long range guided wave inspection-applications to pipes and rail’
Mater. Eval.
(2003) Lamb wave generation with piezoelectric wafer active sensors for structural health monitoring
Smart Struct. Mater.
(2003)- et al.
Pitch–catch active sensing methods in structural health monitoring for aircraft structures
Struct. Health Monit.
(March 2008) Wave Motion in Elastic Solids
(1975)
Detection of structural damage from the local temporal coherence of diffuse ultrasonic signals
Ultrason., Ferroelectr. Freq. Control, IEEE Trans.
Guided wave tomography on an aircraft wing with leave in place sensors
Rev. Prog. Quant. Nondestruct. Eval.
Effects of environmental and operational variability on structural health monitoring
Philos. Trans. Roy. Soc. A: Math., Phys. Eng. Sci.
The temperature stability of guided wave structural health monitoring systems
Smart Mater. Struct.
Feature extraction and sensor fusion for ultrasonic structural health monitoring under changing environmental conditions
Sens. J., IEEE
Scale transform signal processing for optimal ultrasonic temperature compensation
Ultrason., Ferroelectr. Freq. Control, IEEE Trans.
Cited by (107)
A novel coupling method for ultrasonic transducer based on pressureless sintering of nano-Ag
2024, Journal of Materials Research and TechnologyUltrasonic guided wave techniques and applications in pipeline defect detection: A review
2023, International Journal of Pressure Vessels and PipingHigh reliability damage imaging under non-uniform environmental temperature variations based on modified dynamic time warping
2023, Mechanical Systems and Signal ProcessingHigh-dimensional data analytics in civil engineering: A review on matrix and tensor decomposition
2023, Engineering Applications of Artificial IntelligenceUnsupervised long-term damage detection in an uncontrolled environment through optimal autoencoder
2023, Mechanical Systems and Signal Processing
- 1
Office address: 107A Porter Hall, Carnegie Mellon University, Pittsburgh, PA 15213-3890, United States.