Linear variable differential transformers

LVDTs are a type of two-part inductive sensor in which a ferromagnetic armature moves within an outer transformer consisting of one primary and two secondary coils. The secondary coils are located on either side of the primary coil and are wound in opposite directions. The primary coil is excited with an alternating current (AC) excitation and the magnetic flux that is developed is coupled to the secondary windings through the ferromagnetic core. Due to the opposite windings of the two secondary coils, when the core is positioned in the magnetic center of the transformer the two secondary coils cancel one another and no voltage is measured at the output. However, when the core moves away from this central position the amount of induced flux that is coupled into the two secondary coils becomes unequal, which creates a voltage differential in the circuit. While the core remains within the operating range of the LVDT, the amount of output voltage is linearly related to the displacement of the core (Fraden, 2010).

LVDTs are attractive for measuring displacement for several reasons. Because there is no mechanical contact between the sensing elements, there are no frictional forces to distort the readings and the sensors are highly robust because there are no mechanical connections that could suffer fatigue failures. This lack of mechanical connection also means that the minimum resolution of the sensor is based solely upon the noise in the signal conditioning and data acquisition systems, and consequently high resolutions can be achieved (Fraden, 2010). However, because the sensor relies on this lack of contact between the core and the body, transverse motion must be minimized to avoid internal rubbing. Another possible drawback to the use of LVDTs is that the sensor’s operating range is limited by the size of the sensor itself, since the core must remain within the coils for the system to operate correctly.

Potentiometers

Potentiometers come in many shapes and sizes but are typically predicated on relating changes in resistance to changes in rotational or linear position. This change in resistance is typically accomplished by moving a pot wiper along a length of wire causing a linear change in the resistance between the excitation source and the wiper (Fraden, 2010). As previously stated, although there are many forms of potentiometers, one of the most common is a string potentiometer in which a measuring cable is wound around a spool. The spool has a torsional spring to maintain tension in the measurement wire and the length of string that has come out of the sensor can be calculated using the rotational potentiometer on which the spool is mounted.

One reason why string potentiometers can be attractive for measuring displacements is because, unlike LVDTs, they can measure displacements that are significantly larger than the sensor itself because the measurement wire is wound around the spool. This allows them to be relatively light-weight while still being able to measure ranges of over 50 meters. However, because of their mechanical connections most string potentiometers have limits on their frequency range, lifetime, and accuracy. Furthermore, while it is not typically an issue on large civil structures, the tension in the cable can affect the measurement for smaller structures that are more sensitive to external loads.

Piezoresistive

Resistive strain gages are utilized widely on both aerospace and civil structures. These simple sensors are bonded to the structure of interest so that the deformation of the structure causes the sensor to elongate or contract as well. Deformations of less than approximately 2% can be related to the resistance of the gage through the equation:

$\mathit{R}={\mathit{R}}_0\left(1+{\mathit{S}}_{\mathit{e}}\mathit{\epsilon }\right)$ [3.1]

[3.1]

where R is the resistance of the deformed gage, R₀ is the resistance of the gage with no stress applied, S_e is the gage factor of the conductor (approximately 2 for many metals) and ε is the strain across the gage (Fraden, 2010). These changes in resistance are typically converted to an absolute voltage using a Wheatstone bridge circuit (Boyes, 2010).

While piezoresistive strain gages are small and consequently have relatively negligible mass loading effects on the structure, their response is dominated by localized effects such as stress concentrations. For large structures this means that strain gages should be restricted to monitoring ‘hot spots’ where damage is expected to occur or on critical components because large areas will require extensive numbers of sensors for global monitoring. Dense instrumentation with piezoresistive strain gages can be problematic because good installation is essential to obtain high quality measurements from a strain gage and installation is a labor-intensive process that is best performed by those with the expertise. Piezoresistive strain gage measurements can also be affected by changes in temperature, and it can be difficult to detect slowly varying strains using them due to sensor drift (Boyes, 2010).

Vibrating-wire

Vibrating-wire strain gages are an alternative type of strain gage that is commonly used on large civil structures such as bridges but are not extensively used in the aerospace industry. Vibrating-wire strain gages are based on the principle that if a wire is pinned at both ends and put under tension, the natural frequency of the vibration of its first mode is:

$\mathit{f}=\frac{1}{2\mathit{l}}\sqrt{\frac{\mathit{T}}{\mathit{m}}}$ [3.2]

[3.2]

where l is the length of the wire, T is the tension in the wire, and m is the mass per unit length of the wire. By bonding the locations at which the wire is fixed to the structure of interest, the strain across the length of the wire can be determined by monitoring the natural frequency of the wire. This is typically done by utilizing a ferromagnetic material for the wire and exciting the wire at the middle of its span with a solenoid in order to ensure that the first mode of the wire is excited. A typical vibrating-wire strain gage has a wire diameter of 0.25 mm and a nominal operating frequency of 1 kHz (Boyes, 2010).

Vibrating-wire strain gages are typically much larger than piezoresistive strain gages and are often between 50 and 250 mm in length. The gages themselves are often attached by welding them directly to the structure of interest or, in the case of concrete, can be directly embedded in the material. In the case of strain gages on concrete, the relatively large size of vibrating-wire strain gages is advantageous because it averages the strain over a sufficient distance to average out much of the local inhomogeneities that are inherent in the concrete. While these gages are sensitive to temperature, like piezoresistive strain gages, when they are carefully installed and used at room temperature they have been found to be very stable and exhibit drift of less than one microstrain over several months (Boyes, 2010).

Force-balance

A force-balance, or servo, accelerometer utilizes an active feedback control system to control the position of the proof mass, and the feedback required to keep the mass stationary is used to calculate the acceleration that the system is undergoing. The system works as follows. When the sensor housing is accelerated, the proof mass inside the sensor attempts to remain stationary with respect to the inertial frame of reference. This causes the proof mass to move away from its nominal position in the sensor housing. This relative motion is detected using a displacement sensor (often capacitive), which produces an error signal in the control system. This causes current to flow through the force generating element that balances the force due to the acceleration. Then, by relating the current to the applied force, the acceleration can be calculated using the known proof mass and properties of the forcing system (Boyes, 2010).

Force-balance accelerometers can be attractive for monitoring civil structures because they are very sensitive and have very good resolution at low frequency. Furthermore, they are relatively insensitive to thermal effects and have relatively low nonlinearities. However, the major drawback of force-balance accelerometers is the control mechanism itself, which makes the sensor more expensive than other accelerometers and limits the bandwidth of the sensor to relatively low frequencies.

Capacitive

A capacitive accelerometer utilizes the displacement of a proof mass with respect to the housing of the accelerometer in order to determine the acceleration that the sensor is experiencing. In a capacitive accelerometer, the motions of the proof mass are relatively small (less than 20 μm so the proof mass is typically suspended between two plates, one of which is above it and one of which is below it. The two capacitors that are formed between the mass and the top and bottom plates are then utilized in a differential mode so that small drifts and interferences can be compensated for in the measurement (Fraden, 2010).

Capacitive accelerometers are advantageous for monitoring large structures because they are able to acquire measurements across a wide frequency range including static acceleration while generally having superior stability, sensitivity, and resolution to piezoresistive accelerometers. However, they are somewhat susceptible to temperature and humidity variations and are relatively fragile compared to piezoelectric accelerometers.

Piezoelectric

Piezoelectric accelerometers are highly utilized in both the civil and aerospace industries. These accelerometers are based upon the piezoelectric effect in which certain crystalline materials generate an electric change that is proportional to the net force acting on the piezoelectric material (Boyes, 2010). Piezoelectric accelerometers typically utilize one of three different configurations, namely the shear mode, flexural mode, or compression mode configurations, to measure the applied acceleration. In a shear mode accelerometer the piezoelectric material is sandwiched between a rigid post and a cylindrical proof mass as shown in Fig. 3.1, so that as the proof mass moves relative to the rigid post in the sensing direction, it generates a shear stress in the piezoelectric material. In flexural mode accelerometers, a beam-shaped crystal is used that is supported on a fulcrum so that accelerations directly induce strains in the piezoelectric beam. This type of piezoelectric accelerometer is best suited for low-frequency, low-amplitude applications. Compression mode accelerometers use tensile and compressive loads to generate forces in the piezoelectric material. While early designs preloaded the piezoelectric material against the base of the sensor, it was found that this approach made the accelerometer very sensitive to base strains and temperature variations. Therefore, new designs isolate the crystal by either placing it at the top of the sensor or isolating it using a washer (Newman, 2010).

Piezoelectric accelerometers have gained such wide use in large part because they can be used in a wide variety of environments and are relatively robust. They have a long service life because there are no moving components in the sensor and they can be applied across a wide frequency and possess good linearity across a large dynamic range. However, these sensors typically have a minimum frequency at which they can be used and are, therefore, unable to measure static accelerations in contrast to capacitive or piezoresistive accelerometers.

Anemometers

For large civil structures such as buildings and bridges, wind speed can be of particular interest as it can significantly excite the structure. This is even more critical for bridges in which improper design can lead to aerodynamic self-excitation, as was the case with the famous Tacoma Narrows bridge (Billah and Scanlan, 1991). Lastly, anemometers are also of great interest in wind turbines since the entire operation of the structure is based on wind speed and these measurements can be used to help normalize the response of the structure. While a variety of different types of anemometers exist, perhaps the most widely used is the cup anemometer, which typically consists of three or four cups mounted on the end of horizontal arms that are fixed to a common vertical shaft. The cup anemometer is a drag-driven device that turns because the drag on the smooth back surface of the cup is less than that on the open face of the cup. This imbalance in drag results in rotational speed of the cups being proportional to the average wind speed (Tong, 2010).

Thermocouples and resistive thermometers

For large and relatively flexible structures such as bridges or even buildings, temperature changes can have a large effect on the response characteristics of the structure and can easily mask changes in the structure due to damage or result in false indications of damage. For example, Alampalli (1998) found that freezing in the supports of a bridge caused changes in the natural frequencies of the structure that were more than ten times more significant than the changes in the natural frequencies due to damage. However, perhaps even more interesting was Farrar et al.’s (1997) finding that the first mode of the Alamosa Canyon bridge varied by approximately 5% throughout a single day, and that rather than being correlated with the overall ambient temperature of the structure this change was correlated with the temperature gradient across the bridge deck. This influence of temperature gradients has resulted in the widespread application of temperature sensors including thermocouples and resistance thermometers with as many as 388 temperature sensors being installed on a single bridge (Wong and Ni, 2009).

Resistance thermometers utilize the principle that the resistance of metals increases with temperature. Platinum is typically utilized for resistance thermometers because it has the highest possible coefficient of resistivity, which is indicative of its high purity, and the slight changes in its resistance with temperature can be measured using a Wheatstone bridge (Boyes, 2010). Thermocouples, on the other hand, use the fact that if two different metal wires are connected, the voltage that is produced in the vicinity of their connection is dependent on the temperature difference between the connectors and other parts of those wires. A wide variety of different thermocouples are produced utilizing a range of different alloys depending on the specific temperature range in which the sensor will be operating (Boyes, 2010).

Changes in modal parameters

One of the most commonly used ways in which accelerometers have been used in an attempt to monitor civil infrastructure for damage is through the calculation of modal parameters including natural frequencies and mode shapes, despite the general lack of sensitivity that modal parameters have shown to localized structural damage. However, this approach has been commonly used because it is a convenient data reduction technique (Farrar and Doebling, 1997) that is familiar to most researchers and is clearly tied back to the physics of the structure (Carden and Fanning, 2004).

The first form of a modal-based health monitoring method that drew significant attention was the detection of damage through changes in natural frequencies. A review on this method was published by Salawu (1997) that documented over 60 instances of its use. One such use was the detection of the decrease in the natural frequencies of a multi-pile offshore platform throughout a year of operation (Brinker et al., 1995) that may have been caused by an accumulation of damage. However, recent research has suggested that the detection of damage in realistic structures in the field using frequency shifts is difficult, in part because of variations in the natural frequencies caused by environmental factors (Carden and Fanning, 2004). One way in which this problem can be addressed is by measuring and modeling the influence of these external parameters on the natural frequencies of the structure. For example, De Roeck et al. (2000) utilized an auto-regressive, exogenous input (ARX) model to account for the influence of temperature on the Z24 Bridge (Fig. 3.3). This model successfully helped to distinguish between damage- and temperature-induced variations in the natural frequencies of the structure.

Another methodology that has been utilized to monitor structures for damage focuses on changes in the mode shape of the structure. One reason why several researchers have moved to detecting changes in mode shapes rather than natural frequencies is because mode shapes are less sensitive to global temperature changes than natural frequencies (Farrar and James, 1997), although temperature gradients in the structure can still distort the mode shape. Abdel Wahab and De Roeck (1999) applied a modal curvature-based methodology to the data from the Z24 Bridge and found that, by calculating the difference in curvature across multiple modes, they were able to detect and locate the damage. Farrar and Doebling (1999) utilized the mode shapes from an I-40 bridge over the Rio Grande to detect and locate damage using the Damage Index Method developed by Stubbs et al. (1995). This method is based on the detection of changes in the strain energy of the mode shape before and after damage.

One health monitoring technique that utilizes multiple modal parameters was developed by Lynch (2005) and tracks transfer function poles in the complex plane to detect damage. The poles of the transfer function are a combination of the natural frequencies and modal damping values of the structure. Damage in the IASC-ASCE experimental benchmark data was detected by the changes in the poles of the system in five different damaged conditions (Lynch, 2005). Swartz and Lynch (2008) extended this method by creating an algorithm to compare the poles with the appropriate baseline condition and then calculate damage based on the system’s pole locations. The methodology allows for local processing on a distributed network of sensors and was able to detect most of the progressive damage tests that were performed on the Z24 Bridge (Swartz and Lynch, 2008).

Algorithms for both detecting and locating damage have also been developed that utilize both natural frequencies and mode shapes. Many of these algorithms utilize experimental measurements along with finite element models of the structure to detect, locate, and possibly even quantify the level of damage. Doebling (1996) utilized modal properties along with an optimal updating methodology to identify and locate damage in a small-scale cantilevered truss. Ching and Beck (2004) developed a Bayesian finite element model updating methodology that they applied to the IASC-ASCE experimental benchmark data to identify damage. This methodology was also applied by Skolnik et al. (2006) to a 15-story building on the University of California Los Angeles’ campus. In this case, because the structure could not be damaged, the methodology was demonstrated by updating a model that was used to assess the likelihood of damage from an earthquake. Lastly, Teughels and De Roeck (2004) used finite element model updating using data from the Z24 Bridge tests and quantified the decrease in bending and torsional stiffness along the length of the bridge in several cases.

Another methodology that uses both mode shape and natural frequency information, but not a finite element model, was developed by Gaoet al., (2004) who utilized mode shape and natural frequency estimates from a 4.5 m long 3-D truss structure to detect, locate, and quantify the loss in stiffness in an element of the truss using the Damage Locating Vector method. This methodology was developed by Bernal (2002) and it utilizes the modal properties of the structure before and after damage to calculate the flexibility matrix at the sensor locations. Then, using these flexibility matrices, the method calculates a static load vector that when applied to the structure induces no stress in the damaged components. The developed methodology was also applied to another slightly larger truss structure to demonstrate that the methodology could be used to detect multiple damaged elements simultaneously (Tran et al., 2008). Another damage detection methodology that utilized changes in both natural frequencies and mode shapes to detect, locate, and quantify damage is the Direct Stiffness Calculation method, which was used by Maeck and De Roeck (2003) to calculate the loss in stiffness along the length of the Z24 Bridge due to progressively induced damage. This methodology is applicable to beamlike structures and is based on the relation between the bending and torsional stiffness in each section. It is interesting to note that for several of the damage states, the loss in bending stiffness calculated by this method compared well to the values calculated using finite element model updating (Reynders and De Roeck, 2009).

Changes in input–output models

Perhaps the most commonly used system level model of the input–output behavior of a structure is the frequency response function (FRF). In order to use FRFs for health monitoring purposes, they usually need to be reduced to a damage feature of smaller dimensionality. However, modal parameters are not the only method that can be used for data reduction purposes on FRFs. Ni et al. (2006) applied principal component analysis to FRFs and used the resulting data as an input to a neural network in order to detect damage in a 1/20 scale building. Rather than using FRFs directly, Adams and Farrar (2002) utilized linear and nonlinear frequency domain ARX models to characterize the input–output behavior of a possibly non-linear structure and demonstrated that such a model could successfully detect and quantify the presence of loose bolts in a three-story unistrut frame building.

In a manner similar to how mode shapes were used to detect and locate damage, spatial variations in FRFs have also been used for health monitoring purposes. For instance, Sampaio et al. (1999) used changes in the spatial variations of FRFs to detect damage. At each measurement location the local curvature of the operational deflection shapes at a specific frequency was calculated and changes in these values allowed for the detection and localization of damage in a bridge. Another method that utilizes the spatial variations in FRFs is the interpolation damage detection method, which was used by Limongelli (2010) to detect damage on the I-40 Rio Grande Bridge despite the presence of temperature variations. This method assumes that damage introduces a discontinuity in the deformation shape of the structure and detects this discontinuity by comparing each experimentally measured FRF to the FRF that is interpolated at that location by spline fitting the remaining FRFs.

FRFs may also be transformed in order to create functions that can be utilized more directly for damage detection purposes. Transmissibility functions were demonstrated to be valuable for the detection and localization of damage in a three-story unistrut frame structure (Johnson et al., 2004) because they are functions of the transfer function zeros, which are more sensitive to local changes of the structure than poles (Johnson, 2002). Another transformation of FRFs that has been utilized to aid in health monitoring is the calculation of embedded sensitivity functions. These functions use the assumption that physical properties are lumped at certain degrees of freedom (DOF) to calculate partial derivatives with respect to lumped stiffness and mass properties (Yang et al., 2004). Using this methodology, changes in the mass and stiffness of a metallic composite panel on standoffs was detected, located, and quantified in terms of stiffness and mass changes (Yang et al., 2008).

Changes in time response based models

The last set of health monitoring algorithms considered here are typically computed from the error in time series models or from transformed versions of the acceleration measurements themselves. For instance, Lu et al. (2008) utilized a database of auto-regressive models for data-normalization purposes so that the parameters from ARX models could be compared more directly to one another for each sensor. This methodology was able to successfully detect changes due to high-level shake table excitations of a two-story RC frame structure using a wireless sensing system (Lu et al., 2008). Gul and Catbas (2011) utilized ARX models to predict the output of one sensor using a cluster of other sensors. The model was trained on the baseline data set. By tracking the changes in the prediction error in the models, the presence, location, and some comparative information about the magnitude of the damage on the Z24 Bridge was obtained (Gul and Catbas, 2011). Another time series methodology was developed by Taha (2010) and applied to the IASC-ASCE experimental benchmark. This method utilized the wavelet transform for data reduction purposes and an optimized neural network for the detection and quantification of damage. However, this methodology did not detect the specific location of the damage, and, therefore, the quantification corresponded only to a description of the severity of the damage and no estimates of the size or type of damage could be made.