Improving the Response of Accelerometers for Automotive Applications by Using LMS Adaptive Filters

In this paper, the least-mean-squares (LMS) algorithm was used to eliminate noise corrupting the important information coming from a piezoresisitive accelerometer for automotive applications. This kind of accelerometer is designed to be easily mounted in hard to reach places on vehicles under test, and they usually feature ranges from 50 to 2,000 g (where is the gravitational acceleration, 9.81 m/s2) and frequency responses to 3,000 Hz or higher, with DC response, durable cables, reliable performance and relatively low cost. However, here we show that the response of the sensor under test had a lot of noise and we carried out the signal processing stage by using both conventional and optimal adaptive filtering. Usually, designers have to build their specific analog and digital signal processing circuits, and this fact increases considerably the cost of the entire sensor system and the results are not always satisfactory, because the relevant signal is sometimes buried in a broad-band noise background where the unwanted information and the relevant signal sometimes share a very similar frequency band. Thus, in order to deal with this problem, here we used the LMS adaptive filtering algorithm and compare it with others based on the kind of filters that are typically used for automotive applications. The experimental results are satisfactory

Improving the Response of Accelerometers for Automotive Applications by Using LMS Adaptive Filters: Part II

In this paper, the fast least-mean-squares (LMS) algorithm was used to both eliminate noise corrupting the important information coming from a piezoresisitive accelerometer for automotive applications, and improve the convergence rate of the filtering process based on the conventional LMS algorithm. The response of the accelerometer under test was corrupted by process and measurement noise, and the signal processing stage was carried out by using both conventional filtering, which was already shown in a previous paper, and optimal adaptive filtering. The adaptive filtering process relied on the LMS adaptive filtering family, which has shown to have very good convergence and robustness properties, and here a comparative analysis between the results of the application of the conventional LMS algorithm and the fast LMS algorithm to solve a real-life filtering problem was carried out. In short, in this paper the piezoresistive accelerometer was tested for a multi-frequency acceleration excitation. Due to the kind of test conducted in this paper, the use of conventional filtering was discarded and the choice of one adaptive filter over the other was based on the signal-to-noise ratio improvement and the convergence rate

Detecting Nano-Scale Vibrations in Rotating Devices by Using Advanced Computational Methods

This paper presents a computational method for detecting vibrations related to eccentricity in ultra precision rotation devices used for nano-scale manufacturing. The vibration is indirectly measured via a frequency domain analysis of the signal from a piezoelectric sensor attached to the stationary component of the rotating device. The algorithm searches for particular harmonic sequences associated with the eccentricity of the device rotation axis. The detected sequence is quantified and serves as input to a regression model that estimates the eccentricity. A case study presents the application of the computational algorithm during precision manufacturing processes

Response Identification in the Extremely Low Frequency Region of an Electret Condenser Microphone

This study shows that a small electret condenser microphone connected to a notebook or a personal computer (PC) has a prominent response in the extremely low frequency region in a specific environment. It confines most acoustic waves within a tiny air cell as follows. The air cell is constructed by drilling a small hole in a digital versatile disk (DVD) plate. A small speaker and an electret condenser microphone are attached to the two sides of the hole. Thus, the acoustic energy emitted by the speaker and reaching the microphone is strong enough to actuate the diaphragm of the latter. The experiments showed that, once small air leakages are allowed on the margin of the speaker, the microphone captured the signal in the range of 0.5 to 20 Hz. Moreover, by removing the plastic cover of the microphone and attaching the microphone head to the vibration surface, the low frequency signal can be effectively captured too. Two examples are included to show the convenience of applying the microphone to pick up the low frequency vibration information of practical systems

Aplicaciones de filtrado adaptativo LMS para mejorar la respuesta de acelerómetros

El proyecto, “Aplicaciones de filtrado adaptativo LMS para mejorar la respuesta de acelerómetros”, se realizó con el objetivo de eliminar señales no deseadas de la señal de información procedentes de los acelerómetros para aplicaciones automovilísticas, mediante los algoritmos de los filtros adaptativos LMS. Dicho proyecto, está comprendido en tres áreas para su realización y ejecución, los cuales fueron ejecutados desde el inicio hasta el último día de trabajo. En la primera área de aplicación, diseñamos filtros paso bajo, paso alto, paso banda y paso banda eliminada, en lo que son los filtros de butterworth, filtros Chebyshev, de tipo uno como de tipo dos y filtros elípticos. Con esta primera parte, lo que se quiere es conocer, o en nuestro caso, recordar el entorno de Matlab, en sus distintas ecuaciones prediseñadas que nos ofrece el mencionado entorno, como también nos permite conocer un poco las características de estos filtros. Para posteriormente probar dichos filtros en el DSP. En la segunda etapa, y tras recordar un poco el entorno de Matlab, nos centramos en la elaboración y/o diseño de nuestro filtro adaptativo LMS; experimentado primero con Matlab, para como ya se dijo, entender y comprender el comportamiento del mismo. Cuando ya teníamos claro esta parte, procedimos a “cargar” el código en el DSP, compilarlo y depurarlo, realizando estas últimas acciones gracias al Visual DSP. Resaltaremos que durante esta segunda etapa se empezó a excitar las entradas del sistema, con señales provenientes del Cool Edit Pro, y además para saber cómo se comportaba el filtro adaptativo LMS, se utilizó señales provenientes de un generador de funciones, para obtener de esta manera un desfase entre las dos señales de entrada; aunque también se utilizó el propio Cool Edit Pro para obtener señales desfasadas, pero debido que la fase tres no podíamos usar el mencionado software, realizamos pruebas con el generador de funciones. Finalmente, en la tercera etapa, y tras comprobar el funcionamiento deseado de nuestro filtro adaptativo DSP con señales de entrada simuladas, pasamos a un laboratorio, en donde se utilizó señales provenientes del acelerómetro 4000A, y por supuesto, del generador de funciones; el cual sirvió para la formación de nuestra señal de referencia, que permitirá la eliminación de una de las frecuencias que se emitirá del acelerómetro. Por último, cabe resaltar que pudimos obtener un comportamiento del filtro adaptativo LMS adecuado, y como se esperaba. Realizamos pruebas, con señales de entrada desfasadas, y obtuvimos curiosas respuestas a la salida del sistema, como son que la frecuencia a eliminar, mientras más desfasado estén estas señales, mas se notaba. Solucionando este punto al aumentar el orden del filtro. Finalmente podemos concluir que pese a que los filtros digitales probados en la primera etapa son útiles, para tener una respuesta lo más ideal posible hay que tener en cuenta el orden del filtro, el cual debe ser muy alto para que las frecuencias próximas a la frecuencia de corte, no se atenúen. En cambio, en los filtros adaptativos LMS, si queremos por ejemplo, eliminar una señal de entre tres señales, sólo basta con introducir la frecuencia a eliminar, por una de las entradas del filtro, en concreto la señal de referencia. De esta manera, podemos eliminar una señal de entre estas tres, de manera que las otras dos, no se vean afectadas por el procedimiento. Abstract The project, "LMS adaptive filtering applications to improve the response of accelerometers" was conducted in order to remove unwanted signals from the information signal from the accelerometers for automotive applications using algorithms LMS adaptive filters. The project is comprised of three areas for implementation and execution, which were executed from the beginning until the last day. In the first area of application, we design low pass filters, high pass, band pass and band-stop, as the filters are Butterworth, Chebyshev filters, type one and type two and elliptic filters. In this first part, what we want is to know, or in our case, remember the Matlab environment, art in its various equations offered by the mentioned environment, as well as allows us to understand some of the characteristics of these filters. To further test these filters in the DSP. In the second stage, and recalling some Matlab environment, we focus on the development and design of our LMS adaptive filter; experimented first with Matlab, for as noted above, understand the behavior of the same. When it was clear this part, proceeded to "load" the code in the DSP, compile and debug, making these latest actions by the Visual DSP. Will highlight that during this second stage began to excite the system inputs, with signals from the Cool Edit Pro, and also for how he behaved the LMS adaptive filter was used signals from a function generator, to thereby obtain a gap between the two input signals, but also used Cool Edit Pro himself for phase signals, but due to phase three could not use such software, we test the function generator. Finally, in the third stage, and after checking the desired performance of our DSP adaptive filter with simulated input signals, we went to a laboratory, where we used signals from the accelerometer 4000A, and of course, the function generator, which was used for the formation of our reference signal, enabling the elimination of one of the frequencies to be emitted from the accelerometer. Note that they were able to obtain a behavior of the LMS adaptive filter suitable as expected. We test with outdated input signals, and got curious response to the output of the system, such as the frequency to remove, the more outdated are these signs, but noticeable. Solving this point with increasing the filter order. We can conclude that although proven digital filters in the first stage are useful, to have a perfect answer as possible must be taken into account the order of the filter, which should be very high for frequencies near the frequency cutting, not weakened. In contrast, in the LMS adaptive filters if we for example, remove a signal from among three signals, only enough to eliminate the frequency input on one of the inputs of the filter, namely the reference signal. Thus, we can remove a signal between these three, so that the other two, not affected by the procedure