Research Article  Open Access
Simulating Displacement and Velocity Signals by Piezoelectric Sensor in Vibration Control Applications
Abstract
Intelligent structures with builtin piezoelectric sensor and actuator that can actively change their physical geometry and/or properties have been known preferable in vibration control. However, it is often arguable to determine if measurement of piezoelectric sensor is strain rate, displacement, or velocity signal. This paper presents a neural sensor design to simulate the sensor dynamics. An artificial neural network with error backpropagation algorithm is developed such that the embedded and attached piezoelectric sensor can faithfully measure the displacement and velocity without any signal conditioning circuitry. Experimental verification shows that the neural sensor is effective to vibration suppression of a smart structure by embedded sensor/actuator and a building structure by surfaceattached piezoelectric sensor and active mass damper.
1. Introduction
Composite structures with surfacemounted or embedded piezoelectric materials as sensors and/or actuators have been investigated for they possess mechanical simplicity, efficient electromechanical energy conversion, and ability to integrate within structures. Much attention to date has been on analysis and experiment of active vibration control by using piezoelectric sensors and actuators. Review on using piezoelectric materials to MEMS sensor [1], morphing aircraft [2], and structural repair [3] have been reported. Yang and Chiu [4] were among the first to embedded piezoelectric sensors inside compositelaminated structures. The sensors were found to have stiffening effects [5–8]. Among the applications; however, piezoelectric sensor measurement was considered as displacement signal [9–11], velocity signal [12, 13], or strain rate signal [14, 15]. There seems to be inconsistency on the signal nature, and signal conditioning circuit is often necessary.
It is known that effective vibration control requires the system state of displacement and velocity; however, such signals are difficult to acquire as they are often obtained either by accelerometer with hardware integration for velocity or by piezoelectric sensor assuming velocity measurement. Accurate sensor dynamics modeling is required for designing a controller immune to modeling discrepancy. Artificial neural networks with the ability of selflearning, generalization, and robustness have been shown suitable for simulating sensor dynamics by system identification. The concept of neural sensor design is to use the piezoelectric sensor measurement to estimate online both the displacement and velocity at the sensor location. Recent development of smart layer by encapsulating piezoelectric sensor, actuator, and controller [13] has demonstrated the dissemination of piezoelectric sensor to many engineering applications, and the need of simulating displacement and velocity signal becomes evident.
2. Neural Sensor
Traditional system identification emphasizes on parameter estimation in which the configuration of system model must be defined beforehand. The neural network in this study does not intend to identify the system parameters (such as mass, damping ratio, and stiffness), but instead to find the connection weights of neural network through the experimental input/output pairs so that a piezoelectric sensor, whether embedded or surface attached, can faithfully acquire the displacement and velocity. In simulating sensor dynamics by neural network, the input and output can be any physical parameters accessible experimentally. Figure 1 illustrates the neural sensor design by using the feedforward network to simulate the desired displacement and velocity signals and from the piezoelectric sensor measurement . The error between the desired signals and the network output is then minimized by the learning algorithm.
Artificial neural network is an information process with neurons to imitate the system state of both displacement and velocity by using the piezoelectric sensor measurement. The relationship between the input and output pattern of an artificial neuron can be represented by and where is the input; is the bias representing the threshold of the transfer function; is the connection weight for imitating the biological synapse strength; is the linear combination; is the output; is the transfer function (or the activity function) for converting the weighted summation from the input to output. There are two neural network structures: the feedforward neural network and the feedback neural network. In the former the output of a neuron is passed only to the next layer but not to the preceding layer(s) or to the other neurons in the same layer, while in the latter the output is sent back to the neurons of the preceding layer(s). A feedforward network model may have many layers, and each layer contains several processing neurons as illustrated in Figure 1. The hidden layer provides the neuron interactions representing the system’s internal structure.
The error backpropagation algorithm is commonly used in training a neural network. Recent study on the performance of different algorithms showed that the algorithm is a firstorder approximation of the steepest descent technique based on the gradient of the instantaneous error [16]. The update rule for the connection weight at time step is defined as where is a userselected positive momentum constant (0 < < 1) to allow the network to respond not only to the local gradient but also to recent trends in the error, is the learning rate at step , and is the error function defined by the square of the error between the desired output and the neuron output. A neural network model is inherently nonlinear because the transfer function of the hidden layer neuron is often in sigmoid function or hyperbolic tangent function. The neural sensor can be described in the form where represents the input/output pair at time step , is the maximal lags in the input, is the maximal lags in the output, and represents the nonlinear input/output transformation. The output at time step () depends both on its past steps of the output , , and the past steps of the input , . The estimated output at time step is which is known as the seriesparallel identification model, often more useful in generating a stable update rule. By comparison, the parallel model represented by is to validate the network effectiveness in identification. System identification contains two phases: the network learning phase and the validation phase. The process is to find the appropriate connection weights by the learning algorithm until the error between the network output and the desired output is small enough, then to validate if the network output is close to the actual output .
3. Vibration Control Application
Effectiveness of the neural sensor is demonstrated by vibration contral of a smart structure, a [90/90/90/90/0]_{×2} compositelaminated beam of mm in Sglass/epoxy unidirectional preprag tapes (Fiberite HyE9134B), with two embedded mm piezoelectric actuators and one mm piezoelectric sensor. Mechanical properties of unidirectional laminate, and the electromechanical properties of piezoelectric material are listed in Tables 1 and 2, respectively, where piezoelectric material is for both sensing and actuation due to its lowtemperature sensitivity, high strain sensitivity, and fast response. Experiments as shown in Figure 2 are conducted on the smart structure under clampfree boundary condition. One piezoelectric actuator driven by an independent and identically distributed random signal is employed to excite the structure, and the piezoelectric sensor embedded near the clamped end and the accelerometer (B&K 4375) attached at the beam tip are sampled at 100 Hz. The measurement of accelerometer is then integrated to yield velocity and displacement signals, and . A total of 2000 data points is collected for training the neural sensor.


Analyses show that using the previous four steps of the sampled sensor signals as the neural network’s input can give reasonably accurate estimate of displacement and velocity. The neural network structure is of []—4 neurons in the input layer, 3 in the hidden layer, and 2 in the output layer. The number of neurons the hidden layer is selected to be adequately small because more neurons do not necessarily yield better results for they may increase the learning time and complexity. Comparison of the time response between the desired displacement and velocity signals and the neural sensor is shown in Figure 3(a), in which the neural sensor is so accurate in simulating both the displacement and velocity. Another validation as shown in Figure 3(b) is conducted by comparing the free vibration response under the same initial displacement. The neural sensor is again shown faithfully simulating the displacement and velocity.
(a)
(b)
In addition to the smart structure, a onestory shearbuilding structure model of 300 × 210 × 205 mm and weights 5.4 kg with an active mass damper (AMD) mounted on the top floor as shown in Figure 4(a) [17] is also applied to validate the neural sensor effectiveness. The structure mass is concentrated at the floor level, and the columns flexible to lateral deformation but rigid in vertical direction are assumed to be mass less. Its natural frequency is in the range of common highrise buildings at about 1.6 Hz. Two AC servomotors (Mitsubishi HCMF13 and MF73) as listed in Table 3 are used: one for driving the mass damper mounted on the linear guideway (THK KR33) with a moving part 1 kg at maximum stroke ±50 mm and the other for driving the building structure at the ground floor to simulate earthquake excitation. A mm piezoelectric sensor is attached on a column of the building model, and a lowfrequency accelerometer (Kistler 8628B5) is attached at the top floor to acquire the acceleration signal. The servomotor driven by an independent and identically distributed random signal is employed to excite the structure, and the measurements of the attached accelerometer and piezoelectric sensor signal are sampled at 10 Hz.

(a)
(b)
The neural sensor is a [] feedforward neural network. The learning pattern consists of 931 input/output pairs, and the training goes until the sumsquared error is small within a predefined threshold. Validation of the earthquake response between the accelerometer and neural sensor is shown in Figure 5(a) in which the neural sensor is so accurate in simulating both the displacement and velocity signals. Another validation is conducted by comparing the free vibration response as shown in Figure 5(b). The discrepancy appears only at the peak vibration amplitude, and the performance of the neural sensor remains excellent.
(a)
(b)
Effective controller design for vibration suppression can be facilitated by having accurate system state of displacement and velocity measurement. The neural network controller design is shown in Figure 6. All that required is a reference model for the desired system performance. The neural controller can be selforganized online by using the discrepancy between the plant and the reference model. From experimental observation, the first vibration mode of the smart structure is usually dominant over the other so that a secondorder reference model for the smart structure is selected as The damping ratio is limited by the controller output voltage of ±10 V. A [] feedforward neural network that is constructed to train the controller. The transfer function of the hidden layer is hyperbolic tangent function and that of the output layer is linear function. The input of the neural network controller is displacement and velocity of the neural sensor and the controller command, and the desired output is calculated from (5). The training pattern consists of 1000 input/output pairs.
One piezoelectric actuator is employed to excite the smart structure, and the system state from the neural sensor is sampled at 100 Hz. The neural controller is a [] feedforward neural network with three input: the system displacement, velocity, and excitation force, , , and , and two output and . A voltage amplifier (KrohnHite 7500) is employed to drive the actuator for better control performance. Figure 7(a) shows the free vibration response of the smart structure, where the residual vibration from an initial disturbance is reduced from 4 seconds to within 1 second. The experimental result indicates that the neural sensor is effective in facilitating the neural controller in vibration suppression.
(a)
(b)
(c)
The neural controller is also applied to the building control experiment. The schematic diagram of the controller design is similar to Figure 6. From experimental observation, the reference model is chosen as a secondorder system in which the damping coefficient is selected to be higher than that of the uncontrolled plant. A [] feedforward neural network, similar to that of smart structure, is used for training the controller with three input neurons: the displacement and velocity of the neural sensor and the controller command. The 1000 input/output pairs for training the controller are chosen in the vibration range of the building structure, and the desired output set is calculated from (6). The servomotor is employed to excite the structure, and the system state from the neural sensor is sampled at 10 Hz. Figure 7(b) is the free vibration response of the building structure under an initial displacement at the top floor in which the settling time of the openloop system is more than 7 seconds whereas that of the closedloop system is less than 1 second. The residual vibration is suppressed effectively. Figure 7(c) also shows the vibration response of the open and closed loop of the building structure subject to an earthquake excitation. The above experimental results show that satisfactory performance can be achieved by the neural sensor in simulating the displacement and velocity signals and by the neural network controller in providing the desired damping effect.
4. Conclusions
(1) Intelligent structures with builtin piezoelectric sensor and actuator have been known preferable in vibration control; however, there seems to be inconsistency on the signal nature of piezoelectric sensor. It is often arguable to determine if measurement of piezoelectric sensor is strain rate, displacement, or velocity signal. A neural sensor to simulate the sensor dynamics is developed by an artificial neural network so that the embedded or attached piezoelectric sensor can faithfully measure the displacement and velocity without any signal conditioning circuitry. Experimental verification shows that the neural sensor is effective in vibration suppression of a smart structure by embedded sensor/actuator and a building structure by a surfaceattached piezoelectric sensor with active mass damper.(2) A neural sensor based on a [] feedforward neural network identification model is developed to identify successfully the sensor dynamics of a smart structure, while another [] model has also been applied to a building structure system. The neural sensors are shown to faithfully simulating the displacement and velocity of the systems in both free vibration and under random excitation. A threelayer neural controller is then developed for vibration control of building structure and smart structure. It should be noted that no assumption is required in training the controllers. Experimental results show that the controller design based on the neural sensor’s displacement and velocity signals is effective to vibration suppression.
Acknowledgement
This work was supported in part by the National Science Council,Taiwan, ROC under NSC1002221E006098MY3.
References
 S. Tadigadapa and K. Mateti, “Piezoelectric MEMS sensors: stateoftheart and perspectives,” Measurement Science & Technology, vol. 20, no. 9, Article ID 092001, 2009. View at: Publisher Site  Google Scholar
 S. Barbarino, O. Bilgen, R. M. Ajaj, M. Friswell, and D. J. Inman, “A review of morphing aircraft,” Journal of Intelligent Material Systems and Structures, vol. 22, no. 9, pp. 823–877, 2011. View at: Google Scholar
 Q. Wang and N. Wu, “A review on structural enhancement and repair using piezoelectric materials and shape memory alloys,” Smart Materials and Structures, vol. 21, no. 1, Article ID 013001, 2012. View at: Google Scholar
 S. M. Yang and J. W. Chiu, “Smart structures—vibration of composites with piezoelectric materials,” Composite Structures, vol. 25, no. 1–4, pp. 381–386, 1993. View at: Google Scholar
 S. M. Yang and Y. J. Lee, “Interaction of structure vibration and piezoelectric actuation,” Smart Materials and Structures, vol. 3, no. 4, pp. 494–500, 1994. View at: Publisher Site  Google Scholar
 S. M. Yang and J. J. Bian, “Vibration suppression experiments on composite laminated plates using an embedded piezoelectric sensor and actuator,” Smart Materials and Structures, vol. 5, no. 4, pp. 501–507, 1996. View at: Publisher Site  Google Scholar
 S. M. Yang and C. W. Chen, “Application of single mode optical fiber sensors in structural vibration suppression,” Journal of Intelligent Material Systems and Structures, vol. 7, no. 1, pp. 71–77, 1996. View at: Google Scholar
 S. M. Yang and J. A. Jeng, “Vibration control of a composite plate with embedded optical fiber sensor and piezoelectric actuator,” Journal of Intelligent Material Systems and Structures, vol. 8, no. 5, pp. 393–400, 1997. View at: Google Scholar
 S. M. Yang and G. S. Lee, “Vibration control of smart structures by using neural networks,” Journal of Dynamic Systems, Measurement and Control, vol. 119, no. 1, pp. 34–39, 1997. View at: Google Scholar
 S. M. Yang and G. S. Lee, “System identification of smart structures using neural networks,” Journal of Intelligent Material Systems and Structures, vol. 8, no. 10, pp. 883–890, 1997. View at: Google Scholar
 H. Irschik, “A review on static and dynamic shape control of structures by piezoelectric actuation,” Engineering Structures, vol. 24, no. 1, pp. 5–11, 2002. View at: Publisher Site  Google Scholar
 C. A. Jeng, S. M. Yang, and J. N. Lin, “Multimode control of structures by using neural networks with marquardt algorithms,” Journal of Intelligent Material Systems and Structures, vol. 8, no. 12, pp. 1035–1043, 1997. View at: Google Scholar
 S. M. Yang, C. C. Hung, and K. H. Chen, “Design and fabrication of a smart layer module in composite laminated structures,” Smart Materials and Structures, vol. 14, no. 2, pp. 315–320, 2005. View at: Publisher Site  Google Scholar
 S. M. Yang and C. A. Jeng, “Structural vibration suppression by concurrent piezoelectric sensor and actuator,” Smart Materials and Structures, vol. 5, no. 6, pp. 806–813, 1996. View at: Google Scholar
 J. Zhao, J. Tang, and K. W. Wang, “Anomaly amplification for damage detection of periodic structures via piezoelectric transducer networking,” Smart Materials and Structures, vol. 20, no. 10, Article ID 105006, 2011. View at: Google Scholar
 C. L. Su, S. M. Yang, and W. L. Huang, “A twostage algorithm integrating genetic algorithm and modified Newton method for neural network training in engineering systems,” Expert Systems with Applications, vol. 38, no. 10, pp. 12189–12194, 2011. View at: Publisher Site  Google Scholar
 S. M. Yang, C. J. Chen, and W. L. Huang, “Structural vibration suppression by a neuralnetwork controller with a massdamper actuator,” Journal of Vibration and Control, vol. 12, no. 5, pp. 495–508, 2006. View at: Publisher Site  Google Scholar
Copyright
Copyright © 2012 G. J. Sheu 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.