Frequency Response-Based Indirect Load Identification Using Optimum Placement of Strain Gages and Accelerometers

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Hana'a M. Alqam ◽  
Anoop K. Dhingra
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Structural Response ◽  
Mode Shapes ◽  
Load Identification ◽  
Strain Gages ◽  
Design Algorithm ◽  
Displacement Mode ◽  
Optimum Sensor

This paper presents an approach for indirect identification of dynamic loads acting on a structure through measurement of structural response at a finite number of optimally selected locations. Using the concept of frequency response function (FRF), the structure itself is considered as a load transducer. Two different types of sensors are investigated to measure the structural response. These include a use of accelerometers that leads to the identification of the displacement mode shapes. The second measurement approach involves a use of strain gages since strain measurements are directly related to imposed loads. A use of mixed strain-acceleration measurements is also considered in this work. Optimum sensor locations are determined herein using the D-optimal design algorithm that provides most precise load estimates. The concepts of indirect load identification, strain frequency response function (SFRF), displacement frequency response function (DFRF), along with the optimal locations for sensors are used in this paper. The fundamental theory for strain-based modal analysis is applied to help estimate imposed harmonic loads. The similarities and differences between acceleration-based load identification and strain-based load identification are discussed through numerical examples.

Load identification with regularized total least-squares method

2021 ◽  
pp. 107754632110248
Author(s):  
Zhonghua Tang ◽  
Zhifei Zhang ◽  
Zhongming Xu ◽  
Yansong He ◽  
Jie Jin
Keyword(s):  
Frequency Response ◽  
Least Squares ◽  
Response Function ◽  
Frequency Response Function ◽  
Least Squares Method ◽  
Total Least Squares ◽  
Load Identification ◽  
Acceleration Response ◽  
Regularized Total Least Squares ◽  
Function Matrix

Load identification in structural dynamics is an ill-conditioned inverse problem, and the errors existing in both the frequency response function matrix and the acceleration response have a great influence on the accuracy of identification. The Tikhonov regularized least-squares method, which is a common approach for load identification, takes the effect of the acceleration response errors into account but neglects the effect of the errors of the frequency response function matrix. In this article, a Tikhonov regularized total least-squares method for load identification is presented. First, the total least-squares method which can minimize the errors of the frequency response function matrix and acceleration response simultaneously is introduced into load identification. Then Tikhonov regularization is used to regularize the total least-squares method to improve the ill-conditioning of the frequency response function matrix. The regularization parameter is selected by the L-curve criterion. To validate the performance of the regularized total least-squares method, a load identification simulation with two excitation loads is studied on a plate based on the finite element method and a load identification experiment with two excitation loads is conducted on an aluminum plate. Both simulation and experiment results show that the excitation loads identified by the regularized total least-squares method match the actual loads well although there are errors existing in both the frequency response function matrix and acceleration response. In experiment, the average relative error of the regularized total least-squares method is 13.00% for excitation load 1 and 20.02% for excitation load 2, whereas the average relative error of the regularized least-squares method is 35.86% and 53.09% for excitation load 1 and excitation load 2, respectively. This result reveals that the regularized total least-squares method is more effective than the regularized least-squares method for load identification.

scholarly journals Single Pick Cutting Rock Load Identification Based on Improved Regularization Method

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Lei Dong ◽  
Siyu Zhai ◽  
Bukang Wang ◽  
Liang Dong ◽  
Junyuan Wang ◽  
...  
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Regularization Method ◽  
Frequency Response Function ◽  
Cutting Speed ◽  
Vibration Signal ◽  
Maximum Load ◽  
Load Identification ◽  
Identification Method ◽  
Rock Load

To explore the relationship between the cutting vibration and the cutting load of a single pick, this paper studied a new method for a single pick cutting rock load identification. This paper improved the low accuracy problem of the regularization method in the inverse process of frequency response function in the traditional load identification method by introducing a filter operator. By combining the inverse pseudoexcitation method and the improved regularization method, the identification of the load dependent on the vibration signal was realized. A single pick cutting rock test equipment was built, which could simulate the actual working conditions of pick cutting rock in the underground or tunnel. By changing cutting speed, cutting angle, cutting spacing, and cutting depth of the single pick, the change trends of real cutting load and identification load were obtained. The load identification method proposed in this paper was consistent with the change trend of the real load under the single pick cutting state. Therefore, the method had good recognition accuracy and the maximum load recognition error was 17.35%. Compared with other traditional load identification methods, the identification error was reduced by a maximum of 1.98%. This method can identify the cutting load of single pick and modify the morbidity problem of frequency response function matrix. The method has a better recognition effect on the cutting load of the pick than the traditional recognition methods. The research could benefit the design of the cutting system and the arrangement of the pick on the coal mine or tunneling machinery.

Investigation and Modification of Frequency Response Function Using Digital Fourier Analysis for High Speed Dynamic Testing Facility

2009 ◽  
Author(s):  
Chandrashekhar K. Thorbole ◽  
Keshavanarayana S. Raju
Keyword(s):  
Frequency Response ◽  
Frequency Domain ◽  
Response Function ◽  
Time Domain ◽  
Frequency Response Function ◽  
Detection System ◽  
Structural Response ◽  
Wave Form ◽  
Data Set ◽  
Load Detection

The increasing application of composites in the aviation and automobile industry demands a better understanding of composite material behavior under high loading rate. This shall provide a better insight of actual loads on occupants while preserving livable crashworthy structure. In this study, a high stroke rate MTS servo-hydraulic testing machine is used to characterize the behavior of composite materials at high strain rates. At higher stroke rates, the output of the load detection system acquired by the load cell deviates from the true load-time wave form of the specimen. This is due to the convolution of the structural response of the detection system with the true characteristic of the specimen. To identify the true nature of the specimen load-time behavior, the de-convolution of the detection system response is necessary to restore the specimen characteristic wave form closer to its true behavior. The convolution of data set in the time domain is a time consuming process which explains the benefit of using the frequency domain; as the convolution in time domain corresponds to multiplication in the frequency domain. This process requires the transformation of the time domain data to frequency domain data via Fast Fourier Transform (FFT). In the frequency domain the complex division of the Fourier transfer of the detection system output with frequency response function of the detection system shall provide the true complex input characteristic. This paper elaborates the methodology utilized for obtaining the Frequency Response Function (FRF) of the load detection system using digital Fourier analysis with a single input/output data set. This also emphasizes precautions and guidelines for improving results with FFT to obtain true FRF measurements of the load detection system. The FRF obtained is successfully used to identify the actual specimen wave form characteristic. This is achieved by extracting the structural response of the load detection system from the load cell output.

scholarly journals Modal Mass and Length of Mode Shapes in Structural Dynamics

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
M. Aenlle ◽  
Martin Juul ◽  
R. Brincker
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Structural Dynamics ◽  
Mode Shape ◽  
Physical Meaning ◽  
Frequency Response Function ◽  
Degrees Of Freedom ◽  
Mode Shapes ◽  
Length Measure ◽  
Modal Mass

The literature about the mass associated with a certain mode, usually denoted as the modal mass, is sparse. Moreover, the units of the modal mass depend on the technique which is used to normalize the mode shapes, and its magnitude depends on the number of degrees of freedom (DOFs) which is used to discretize the model. This has led to a situation where the meaning of the modal mass and the length of the associated mode shape is not well understood. As a result, normally, both the modal mass and the length measure have no meaning as individual quantities but only when they are combined in the frequency response function. In this paper, the problems of defining the modal mass and mode shape length are discussed, and solutions are found to define the quantities in such a way that they have individual physical meaning and can be estimated in an objective way.

scholarly journals Motion Transmissibility for Load Identification Based on Optimum Sensor Placement

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Hana’a M. Alqam ◽  
Anoop K. Dhingra
Keyword(s):  
Structural Response ◽  
Continuous Systems ◽  
Load Identification ◽  
Response Measurement ◽  
Design Algorithm ◽  
Analysis And Design ◽  
Output Response ◽  
Additional Information ◽  
Optimum Sensor ◽  
Sensor Locations

Knowledge on loads acting on a structure is important for analysis and design. There are many applications in which it is difficult to measure directly the dynamic loads acting on a component. In such situations, it may be possible to estimate the imposed loads through a measurement of the system output response. Load identification through output response measurement is an inverse problem that is not only ill-conditioned but, in general, leads to multiple solutions. Therefore, additional information such as the number and locations of the imposed loads must be provided ahead of time in order to allow for a unique solution. This paper focuses on cases where such information is not readily available and uses the concept of motion transmissibility for the identification of loads applied to a structure. The identification of loads through measurement of structural response at a finite number of optimally selected sensor locations is investigated. Optimum sensor locations are identified using the D-optimal design algorithm to provide the most precise load estimates based on acceleration measurements using accelerometers. Simulation results for multi-degree-of-freedom (MDOF) discrete and continuous systems are presented to illustrate the proposed technique. It is seen that the proposed approach is effective in determining not only the number of applied loads as well as their locations but also the magnitude of applied loads.

A Simple Method for Extracting Normal Modes

1993 ◽  
Author(s):  
S. Y. Chen ◽  
M. S. Ju ◽  
Y. G. Tsuei
Keyword(s):  
Frequency Response ◽  
Normal Mode ◽  
Response Function ◽  
Frequency Response Function ◽  
Normal Modes ◽  
Mode Shapes ◽  
Phase Information ◽  
Simple Method ◽  
Resonant Frequencies ◽  
Complex Modes

Abstract A simple method for extracting the normal modes of structures is developed. The frequency response function relation between the complex and the normal modes is derived and a technique is developed to calculate the normal modes from the identified (damped) complex modes. In this method, only the magnitude and phase information at resonant frequencies are needed for extracting the normal mode shapes. A numerical example is employed to illustrate the theory. The results indicate that this method is more robust than other methods when the frequency response measurements are contaminated with noise.

scholarly journals Corrigendum to “Modal Mass and Length of Mode Shapes in Structural Dynamics”

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
M. Aenlle ◽  
Martin Juul ◽  
R. Brincker
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Structural Dynamics ◽  
Mode Shape ◽  
Physical Meaning ◽  
Frequency Response Function ◽  
Degrees Of Freedom ◽  
Mode Shapes ◽  
Length Measure ◽  
Modal Mass

The literature about the mass associated with a certain mode, usually denoted as the modal mass, is sparse. Moreover, the units of the modal mass depend on the technique used to normalize the mode shapes, and its magnitude depends on the number of degrees of freedom (DOFs) used to discretize the model. This has led to a situation where the meaning of the modal mass and the length of the associated mode shape is not well understood. As a result, normally, both the modal mass and the length measure have no meaning as individual quantities, but only when they are combined in the frequency response function. In this paper, the problems of defining the modal mass and mode shape length are discussed, and solutions are found to define the quantities in such a way that they have individual physical meaning and can be estimated in an objective way.

scholarly journals Characterization of Materials by Vibration Technique

2011 ◽  
Vol 12 (3) ◽  
Author(s):  
Mohd Hilman Mohd Akil Tan
Keyword(s):  
Stainless Steel ◽  
Frequency Response ◽  
Structural Properties ◽  
Response Function ◽  
Frequency Response Function ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Resonant Vibration ◽  
Vibration Technique ◽  
Characterization Of Materials

This paper presents an experimental investigation of two different kinds of plates of materials namely glass and stainless steel by experimental modal analysis. The materials are excited by an impact hammer to perform resonant vibration where the characteristics of the resonance are acquired. One most important characteristic is the natural frequency where it is known that different material having undergone resonant vibration exhibit different specific natural frequencies to it. The natural frequencies and corresponding mode shapes are used as the parameters of determining the structural properties of these materials. The vibration analysis is done using the LMS instruments and software where Frequency Response Function (FRF) measurement technique is employed in determining the natural frequencies. The structural properties are established based on the obtained natural frequencies and geometries of the materials using the expression from available literature. The elastic moduli obtained for glass and stainless steel are 66.08 Gpa and 193.26 GPa.ABSTRAK: Kertas ini membentangkan kajian mengenai dua bahan plat yang berbeza iaitu kaca dan keluli tahan karat dengan menggunakan analisis ragaman eksperimental. Getaran resonans dijalankan dengan menguja bahan-bahan tersebut dengan tukul hentaman dimana ciri-ciri tertentu diperolehi. Frekuensi asli merupakan satu daripada ciri utama, dimana ianya diketahui bahawa bahan yang berbeza akan mengalami getaran resonans yang menghasilkan frekuensi asli tertentu. Frekuensi asli dan bentuk ragam yang berpadanan digunakan sebagai parameter dalam menentukan sifat-sifat struktur bahan ini. Analisis getaran dijalankan dengan menggunakan peralatan LMS dan teknik ukuran perisian Fungsi Frekuensi Sambutan (Frequency Response Function (FRF)) untuk menentukan frekuensi asli. Sifat-sifat struktur ditentukan berdasarkan frekuensi asli dan bahan geometri, yang diperolehi daripada pengungkapan bahan sumber bacaan yang sedia ada. Modulus keanjalan yang diperolehi untuk kaca adalah 66.08 GPa dan untuk keluli tahan karat adalah 193.26 GPa.

scholarly journals Single Pick Cutting Rock Load Identification Based on Improved Regularization Method

2020 ◽  
Author(s):  
Lei Dong ◽  
Siyu Zhai ◽  
Bukang Wang ◽  
Liang Dong ◽  
Junyuan Wang ◽  
...  
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Regularization Method ◽  
Frequency Response Function ◽  
Cutting Speed ◽  
Vibration Signal ◽  
Maximum Load ◽  
Load Identification ◽  
Identification Method ◽  
Rock Load

Abstract To explore the relationship between the cutting vibration and the cutting load of a single pick, this paper studied a new method for a single pick cutting rock load identification. This paper improved the low accuracy problem of the regularization method in the inverse process of frequency response function in the traditional load identification method by introducing a filter operator. By combining the inverse pseudo excitation method and the improved regularization method, the identification of the load dependent on the vibration signal was realized. A single pick cutting rock test equipment was built, which could simulate the actual working conditions of pick cutting rock in underground or tunnel. By changing cutting speed, cutting angle, cutting line spacing and cutting depth of the single pick, the change trends of real cutting load and identification load were obtained. The load identification method proposed in this paper was consistent with the change trend of the real load under the single pick cutting state. Therefore, the method had good recognition accuracy and the maximum load recognition error was 17.35%. Compared with the traditional load identification method, the identification error was reduced by a maximum of 1.98%. This method can identify the cutting load of single pick and modify the morbidity problem of frequency response function matrix. The method has a better recognition effect on the cutting load of the pick than the traditional recognition method. The research could benefit for the design of the cutting system and the arrangement of the pick on the coal mine or tunneling machinery.

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