^{1}

^{*}

^{1}

^{2}

Reproduction is permitted for noncommercial purposes.

Piezoelectric ceramic Lead Zirconate Titanate (PZT) based electro-mechanical impedance (EMI) technique for structural health monitoring (SHM) has been successfully applied to various engineering systems. However, fundamental research work on the sensitivity of the PZT impedance sensors for damage detection is still in need. In the traditional EMI method, the PZT electro-mechanical (EM) admittance (inverse of the impedance) is used as damage indicator, which is difficult to specify the effect of damage on structural properties. This paper uses the structural mechanical impedance (SMI) extracted from the PZT EM admittance signature as the damage indicator. A comparison study on the sensitivity of the EM admittance and the structural mechanical impedance to the damages in a concrete structure is conducted. Results show that the SMI is more sensitive to the damage than the EM admittance thus a better indicator for damage detection. Furthermore, this paper proposes a dynamic system consisting of a number of single-degree-of-freedom elements with mass, spring and damper components to model the SMI. A genetic algorithm is employed to search for the optimal value of the unknown parameters in the dynamic system. An experiment is carried out on a two-storey concrete frame subjected to base vibrations that simulate earthquake. A number of PZT sensors are regularly arrayed and bonded to the frame structure to acquire PZT EM admittance signatures. The relationship between the damage index and the distance of the PZT sensor from the damage is studied. Consequently, the sensitivity of the PZT sensors is discussed and their sensing region in concrete is derived.

The development of real-time, in-situ structural health monitoring (SHM) and damage detection techniques has been studied to prevent catastrophic failures and to reduce the cost of maintenance and inspecting tasks. The impedance-based SHM technique has been developed by using the electromechanical (EM) coupling property of the piezoelectric materials [

The prominent effects of structural damages on the PZT admittance (the inverse of impedance) signatures are the lateral and vertical shifting of the baseline signatures, which are the main damage indicators. Statistical techniques have been employed to associate the damage with the changes in the EM admittance signatures, such as the root mean square deviation (RMSD) [

The EMI method has been successfully applied for various engineering structures for damage detection. However, the conventional EMI method can only be used to predict the existence of the structural damage but not to further investigate the influence of the damage on the structural properties. Thus, this paper proposes a dynamic system model to associate the damage state with the changes of structural properties. This dynamic system consists of a number of single-degree-of-freedom (SDOF) elements with mass, spring and damper components. The unknown parameters of mass, stiffness and damping in each SDOF element are derived using a genetic algorithm (GA) by fitting the SMI of the dynamic system with that extracted from the experimentally measured PZT EM admittance signature for various damage states. Therefore, the dynamic system possesses the same SMI as the host structure or part of the host structure monitored by PZT sensors. Consequently, the changes of dynamic system parameters for various damage states represent the changes of structural properties associated with the damage state.

For the above purposes, an experimental study is carried out on a two-storey concrete frame subjected to base vibrations that simulate earthquake. Different base vibrations are applied such that various damages (cracks) are induced in the structure. A number of PZT sensors are regularly arrayed and bonded to the frame structure to acquire the PZT EM admittance signatures, from which the SMI can be extracted. Subsequently, the RMSD indices based the EM admittance and SMI are calculated and compared for various damage states. The relationship between the RMSD damage index and the distance of the PZT sensor from the damage is studied. Therefore, the sensitivity of the PZT sensors is discussed and their sensing region in concrete is derived. Finally, the changes of structural properties caused by damage are analyzed.

The EMI damage detection method is based on the principle of EM coupling effect between the host structure and the bonded PZT sensor. Liang et al. [_{a}_{a}, l_{a}_{a}^{E}^{E}_{32}

The electromechanical admittance

The complex mechanical impedances of the PZT sensor and the host structure are expressed as
_{a}_{a}

Substituting _{A}_{A}_{A}

Hence, we can solve

Following this computational procedure, the structural impedance can be extracted from the measured conductance and susceptance signatures of the PZT sensors. In this computation,

While the admittance response plots provide a qualitative approach for damage identification, the quantitative assessment of damage is traditionally made by the use of a scalar damage metric. In the earlier work, an effective statistical algorithm, which is based on frequency-by-frequency comparison, was presented as RMSD. The RMSD index is defined as
^{th}

We can also calculate the RMSD index of the PZT susceptance using

The concept of SMI is analogous to the electrical impedance. The SMI at a given point can be defined as the ratio of a sinusoidal force applied to the system at that point to the velocity at the same point. For an SDOF mass-spring-damper element subjected to an excitation force shown in

For a complex structural system, the above SMI model can be easily extended to be a multiple-degree-of-freedom (MDOF) system by combining a number of SDOF elements. For a parallel connection system, the combined SMI, _{p}_{i}_{s}

The original GA was developed based on the Darwinian theory of natural evolution [

The GAs attempt to find the best solution to a given problem by minimizing an objective evaluation function which is called fitness function. In order to formulate the structural parameter identification problem into an optimization problem for the GA to solve, it is necessary to specify an objective function which is used to provide a measure of how individuals have performed in the problem domain. The fittest individuals will have the lowest numerical value of the associated objective function.

Structural damage, especially local damage, is typically related to changes in the structural physical parameters. Therefore, to recognize the changes of structural parameters is a direct way to predict structural damage and also an effective way to assess the severity of the damage. Towards this goal, a model of driven point structural impedance with pending structural parameters should be set up. In this study, the proposed model is an MDOF system constructed by the connection of a number of SDOF elements as described in the former section. In this model, the structural impedance is a function of excitation frequency with unknown structural parameters, i.e., the mass _{i}_{i}_{i}_{i}_{i}_{i}_{i}_{i}

Using the GAs, the optimal values of structural parameters in the model of the PZT driven point structural impedance can be derived according to the measured EM admittance signatures. For damage assessment, these optimal values obtained before and after the appearance of structural damage are compared to study the effects of damage on the structural properties, which are specified to be mass, stiffness and damping in this study. To quantify the effects of damage, the summation of the deviation of a certain parameter in each element is expressed as
_{m}_{k}_{c}

In this study, an experiment was carried out on a two-storey concrete frame instrumented with five PZT sensors, as shown in

The test loads were applied in the form of the horizontal base motions with different frequencies. The test was performed in several phases and the sequences of the applied base motions are listed in

Using the Impedance Analyzer, the conductance and susceptance signatures of the PZT sensors can be obtained. Before damage and after each of the two damage phases, these five PZT sensors were scanned to record the signatures of the PZT EM admittance. Signatures captured by one of the PZT sensors (Patch 4) are illustrated in

As pointed out by Park et al [

These five PZT sensors were instrumented at the locations of 62 mm, 112 mm, 162 mm, 212 mm and 412 mm away from the main crack respectively, as shown and marked in

In the EMI technique, the PZT generated waves propagate through the structure. The waves will be reflected when meeting the discontinuities such as the structural damages. The reflected waves contain the information of the structural health situation and can be detected by the PZT sensors. Because of the effect of the material and structural damping, the waves attenuate when propagating through the structure. When the distance between the PZT sensor and the structural damage is too far, the PZT sensor may exhibit a very small damage index even if the damage is severe. This means that the PZT sensor loses its sensitivity to damage, in other words, PZT reaches its sensing limit. From the fitted curves in

All the EM admittance signatures captured by the five PZT sensors were used to derive the optimal values of the structural parameters of the MDOF model system. In this study, by means of trial and error the model of a parallel connection of a number of SDOF mass-spring-damper elements was used to successfully fit the signatures of structural impedance extracted from the measured PZT EM admittance. The main idea for the optimization problem in this study is to minimize the differences between the modeled structural impedances and the experimentally measured ones by searching the proper values for the structural parameters using the GAs.

The number of SDOF elements used to construct the structural impedance model is 32. Correspondingly, the total number of the unknown structural parameters in this model is 96, with the consequence as _{1}_{1}_{1}_{2}_{2}_{2}_{32}_{32}_{32}

The structural impedance is meant for the PZT driven point, therefore it varies at different locations where the PZT sensor are bonded.

To evaluate the performance of the GAs for identification of structural parameters in the proposed structural impedance model, a study of the convergence of the fitness value should be performed. The convergence performances for the case of PZT patch 4 under three structural health states are shown in

In order to relate the damage states to the quantitative changes of the structural properties, the optimal values of the structural parameters in the model are derived by the GAs, and the changes of each structural parameter are calculated as described in

It worth mentioning that the EMI technique is temperature sensitive [

The RMSD indices based on the raw PZT admittance and the structural impedance which is extracted from the raw admittance signature have been evaluated for a concrete frame structure. Experimental results demonstrate the capability of the PZT sensors to detect incipient and severe damages in concrete. The damage indices based on the real parts of the structural impedance and the PZT admittance are more suitable for damage detection than those based on the imaginary parts. Moreover, the damage index based on the real part of the structural impedance is more sensitive to damage since it excludes PZT's contribution to the measured admittance signature. Using this index, the sensing region of the PZT sensor is determined to be 70-90 cm for the concrete material, while using the index based on the raw PZT admittance, the sensing region is only 40-60 cm.

A model of the PZT driven point structural impedance for quantitative detection of the influence of the damage on the structural properties using the GAs has also been presented. The structural parameters in the model are derived by minimizing an objective function based on the experimentally measured data of PZT EM admittance. Optimal values for each structural parameter derived before and after the appearance of structural damages are compared to analyze the changes of structural properties caused by the damage. A model of a series connection of 32 SDOF mass-spring-damper elements has been successfully used to fit the experimentally measured data. It is worth mentioning that the structural impedance model may be composed of the SDOF elements by different ways of connection, depending on the material of the structure and the excitation frequency. Using the GAs, the changes of the structural parameters caused by the structural damage in the model have been derived and analyzed. The results have demonstrated that the appearance of damage leads to increase in damping and decrease in stiffness and mass at the driven point, and that the model is more sensitive to the severe damage. It has also been concluded that the PZT sensor with larger distance from the damage is less sensitive to the damage. And this conclusion coincides with the previous studies of PZT sensing region based on the damage index techniques.

A SDOF system under dynamic excitation

Dimensions of concrete frame (Unit:

Configuration of equipments and test structure.

Situation of the column before and after damage (unit

Admittance signatures of PZT patch 4.

SMI signatures extracted from EM admittance signatures detected by PZT patch 4.

Damage indices for all PZT patches.

RMSD values of

RMSD values of

Theoretical and experimental results of real part of SMI for three damage states.

Convergence performance of GA.

Detected changes of damping in SMI model for the driven points with different distances from the damage for two damage states.

Detected changes of stiffness in SMI model for the driven points with different distances from the damage for two damage states.

Detected changes of mass in the impedance model for the driven points with different distances from the damage for two damage states.

Material properties and dimensions of PZT sensors.

Symbol | Quantity | Value |
---|---|---|

_{a} |
length | 10 mm |

_{a} |
width | 10 mm |

_{a} |
thickness | 0.2 mm |

Young's modulus | 66.7 GPa | |

loss factor | 0.005 | |

mass density | 7800 kg/m^{3} | |

_{31} |
strain constant | -2.10E-10 m/volt |

_{33}^{T} |
permittivity | 1.93E-08 fatad/m |

dielectric loss factor | 1.50E-02 |

Locations of PZT sensors and their distance from the main crack.

Patch Number | Distance from joint O along the column as shown in |
Distance of the PZT patch from the main crack |
---|---|---|

1 | 100 mm | 62 mm |

2 | 150 mm | 112 mm |

3 | 200 mm | 162 mm |

4 | 250 mm | 212 mm |

5 | 450 mm | 412 mm |

Test sequences of the shake table.

Phase No. | Name | Description | Purpose |
---|---|---|---|

1 | RND-A | Random, PGA=0.02g | Structural identification |

2 | CHL- | Chile, PGA=0.23g, | Moderate shaking |

3 | RND-B | Random, PGA=0.02g | Structural identification |

4 | CHL- | Chile, PGA=0.46g, | Sever shaking |

5 | RND-C | Random, PGA=0.02g | Structural identification |

Damage indices for all PZT sensors at two damage phases.

Damage Phase 1 | ||||
---|---|---|---|---|

PZT patch no. | RMSD of |
RMSD of |
RMSD of |
RMSD of |

1 | 1.700904 | 0.079885 | 15.73118 | 0.077741 |

2 | 1.502574 | 0.106806 | 13.34286 | 0.098003 |

3 | 1.473301 | 0.086287 | 9.605244 | 0.063772 |

4 | 1.25146 | 0.11261 | 7.5918 | 0.095865 |

5 | 0.940053 | 0.116923 | 4.747043 | 0.117208 |

Damage Phase 2 | ||||

RMSD of |
RMSD of |
RMSD of |
RMSD of | |

1 | 3.139675 | 0.061062 | 25.89481 | 0.049555 |

2 | 2.343378 | 0.073566 | 20.84959 | 0.064063 |

3 | 2.46278 | 0.058494 | 18.08281 | 0.047549 |

4 | 1.898626 | 0.071459 | 10.93107 | 0.054598 |

5 | 1.390455 | 0.056117 | 8.161555 | 0.045829 |