**1. Introduction**

The measurement of vibration and temperature is quite important according to get information regarding the oscillations [1, 2] and the molecular kinetic energy of the movement source and heat sources of engines internal components, or combustion motor's external surfaces. However, there are tasks, in which is not possible to get contact between the sensor with the movement source and thermal source, hence the temperature measurement is given through IR sensors. In other side, it was possible to find the wave parameters from the IR signal of the thermal source owing to get an estimation of the vibration frequency of the movement source. Notwithstanding, there is a trouble concerning the transduction stage in the measurement while there is not a transducer algorithm designed as a consequence of mathematical model which correlates the calibration data with theoretical model of the heat transfer and the surface vibration of the movement source and thermal source. For this reason, it was proposed in this research to analyze a mathematical procedure of the measurement instrumentation according adaptive coefficients in MF strategies [3]. In this research is explained and analyzed the temperature measurement process and the transduction process as the strict correlation with the IR signal from the thermal source.

Therefore, the proposed sensor was evaluated for the measurement of the temperature and vibration of a combustion motor because of getting the understanding of its combustion and the motor user could achieve its diagnostic. There are many temperature sensors based in passive measurement such as thermocouples and thermistors, which proportionate the correlation of temperature in electrical equivalence of voltage and electrical resistance respectively, by other side, there are different piezoelectric to measure the vibration (frequency and amplitude) of surfaces. Nevertheless, there are tasks to measure vibration and temperature of systems that are located in intricate places and it is not suggested to use contact sensors [4–11], hence IR sensors are the appropriated solution. For example combustion motors have many components inside and the combustion process can produce vibrations in them and in all the motor. Moreover, a not fuel good quality can cause damage in the combustion motors which are plenty used in industry and transport such as in Peru, where the transport (public and private) depends of this kind of motor and will continue using them during many years yet, in spite of the new technology in motors are enhanced by electric motors (or hybrid), hence, it is necessary to understand the combustion process in combustion motors. Therefore, temperature and vibration sensors can give information of the operation of the combustion motor according to repair them when its components are not working appropriated and as a consequence to look for their reparation avoiding pollution. To visualize the measured information, the sensor data (electrical equivalence of temperature and vibration) needs electronic devices due to compensate, amplify and linearize the electrical equivalent of temperature transduced to thermal units. In this research is proposed a mathematical model strategy based in MF in order *Perspective Chapter: Optimal Analysis for the Correlation between Vibration and Temperature… DOI: http://dx.doi.org/10.5772/intechopen.107622*

to get the transduction result. The complexity of the transduction is replaced by the mathematical model designed.

The proposed sensor is part of an integrated system, which is depicted by the **Figure 1**. The proposed sensor is represented as IS (Intelligent Sensor) in order to measure temperature and vibration (T&V) and the measured data can be sent through IR to an external computer that can be at many meters of distance and 2 antennas A1 and A2 have the tasks of the data transmission. Moreover, the IS has independence of its own energy to be operating because of this proposed sensor has integrated a sample of sun panel to obtain electrical energy through sun/heat energy conversion.

Hence, in this research is proposed an intelligent sensor/transducer (as part of an integrated system) based in nanostructures due to measure the temperature and vibration of the combustion motor surface depicted by **Figure 2**, in which "A" is the IR emitter in controlled frequency that could not be confused with the IR signal produced by temperature of the combustion motor operation. "B" is the sample transducer to receive the vibration signal, for which "D" is the vibration sensor based in nanotubes amorphous. "C" is the Anodic Aluminum Oxide (AAO) sample transducer to receive the temperature signal for which "E" is the temperature sensor based in nanoholes amorphous. "F" is the battery to proportionate energy of the proposed sensor, and "G" is data transmitter according to send the temperature signal and vibration signal from the surface of the combustion motor to a receptor which can be used by the user due to get the diagnostic of the combustion motor. Moreover, H is the sample based in nanostructures to receive the sun energy and I is the converter to electrical equivalent signal due to store the energy in the batteries of the sensor. Many systems can improve their monitoring variable by advanced sensors such as sensors based in nanostructures [1] thereby the understanding of the geometry and material

**Figure 1.** *Communication system of the proposed IS.*

**Figure 2.** *Temperature and vibration transducer design.*

of the sensor is quite important due to get the optimal transduction as consequence of the measurements.
