# Structure Strength Dynamic Strain Measurement Acquisition System Based on Data Fusion

Authors: Dawei Shen; Dongxing Pei; Tiehua Ma
Journal: Scientific Programming
 (2022)

---

## Abstract

Strain measurement technology plays an irreplaceable role in measuring the force change characteristics of mechanical components and monitoring important engineering structures. In structural health monitoring, dynamic stress and strain testing is the main way to determine its overall fatigue, and excessive stress will seriously affect the strength of the structure, causing the structure to deform or even break, which will affect the reliability of the experiment and the use of workpieces, so it is of great significance to carry out dynamic stress and strain tests on the structure. Resistance strain measurement technology is widely used in the civil engineering industry, but the principles of modern physics technology are unknown to many practitioners. Data fusion technology or information fusion technology is also called multisensor fusion technology. Using computer technology to automatically analyze and integrate the data processing process of the detection data from multiple sensors according to time sequence and certain criteria, it can complete the required decision-making and judgment.


---

## Body

## 1. Introduction

With the development of economy and technology and the progress of science and technology, more and more cars, airplanes, and ships are connected to people's daily life, and people have put forward higher requirements for their safety performance [1]. When the vehicle is running at various speeds and different road sections, the wheels are excited by the ground irregularly. This irregular random excitation causes irregular vibration of the body structure, that is, random vibration. In order to meet its safety requirements, it is an important way to conduct health monitoring to evaluate its structural safety performance. As a result, strain measurement technology emerged.Large-scale machinery products are increasingly finding their way into a variety of fields as modern industry progresses. The strength of the product structure is very noticeable due to its large structure and important use occasions. In the research and implementation of modern engineering projects, strain measurement technology is an indispensable technology. It has a lot of potential for application and research. The strain value and its change law at various points on the structure are determined using the electrical measurement method, with a thorough understanding and grasp of the internal force distribution law and the stress situation of the body structure [2], as well as a finite element analysis and calculation of the structure. The strain value and change law at certain points on the structure are measured by the electrical measurement method in order to obtain the statistical characteristics of the stress and strain of the body structure, and the finite element analysis and body structure calculation are used to evaluate the strength of the body structure and propose a more reasonable solution. Structure must be improved. Large structures cannot be scaled up by small structures, and their strength cannot be increased linearly in proportion to the strength of small structures from a design standpoint. In addition, some special processing methods in the manufacture of large structures make large structures more effective in actual use. Intensity is full of variables [3]. After the structural strain signal output by the resistance strain gauge is amplified by the dynamic resistance strain gauge, the high-resistance output terminal is used to record the waveform of the tape drive, and the low-resistance output terminal is output to the light oscilloscope for waveform observation, monitoring, and selective recording. The electrical measurement method is a traditional method, which is widely used and the technology is very mature. Electrical measurement technology has developed rapidly due to its close integration with production practice. It has not only achieved high scientific and technological achievements in the research of theory, detection components, measurement and recording devices, test components, technology, and methods in harsh environments. Due to the large number of measurement points, long distances, and difficulty in loading, the requirements for the tester are high. There must be enough channels to meet the simultaneous measurement to avoid the trouble of repeated loading in the group test [4]. From the strain record waveform of the body structure, the time history is very arbitrary, and there is no repetitive phenomenon. However, when the overall analysis is performed using the methods of probability theory and statistical mechanics, there is a certain statistical regularity in the random process, which can be described by some statistical characteristic quantities and functions.The painful lesson teaches us that the structure's safety performance not only affects project progress, but also puts people's safety in jeopardy, necessitating immediate structural health monitoring [5]. The accuracy of the strain value sampling is a key step that directly affects the analysis and calculation of the strength of the car body structure and whether you can draw the correct conclusion. Strain is an important metric for monitoring structural health. Strain is an important metric that reflects the structural integrity. The strain state is usually linked to a component's failure. To measure the strain on the structure's surface, the strain electrical measurement method employs a resistance strain gauge as a sensing element. From the 1930s to the present, it has evolved into a complete system. It is now a widely used method of strain measurement [6]. Because the structural damage caused by dynamic loading is often due to the dynamic pressure or strain on the structure exceeding the maximum value that the structure can withstand, regular evaluation of dynamic stress or strain is very important to effectively avoid dangerous accidents. In the strain measurement technology, the resistance strain method uses the generalized Hooke's law to find the stress by measuring the strain. The measurement accuracy is high, the sensitivity is good, and the method is simple. It has a wide range of applications and developments in the detection of building structures [7]. This article will introduce a single-chip microcomputer acquisition and processing system for dynamic (stress) and strain measurement of body structure strength. It has the characteristics of low cost, simple hardware structure, high accuracy, and reliability.


## 2. Related Work

Literature [8] conducted a dynamic stress test for local cracking in the cab of a new type of truck and analyzed the dynamic response of the measuring point in the time domain and frequency spectrum, pointing out the direction for cab structural improvement. The tangential wheel-rail force and lateral wheel-rail force of the power wheel axle of a 300 km/h high-speed EMU were identified using the different directions of strain gauges to be pasted and the way of forming electric bridges in [9], and a finite element model was built to obtain the load and strain relationship. The strain electrical measurement method is used in [10] to test the dynamic strain of the suspension frame under the conditions of general flat bottom, double-wheel crossing, and single-wheel crossing of the ditch, and it is combined with VC++ for data processing to obtain the stress condition and the stress when the wheel passes through the ditch. Literature [11] uses the ECAL/AMS-02 dynamic strain measurement system, a three-way resistance strain gauge, a temperature compensation sheet, and an extrapolation method to calculate the obtained strain results to obtain the maximum principal value of each point. Strain and principal stress testing have produced positive results, and strain testing technology has been improved and expanded. To reduce the impact of temperature variations on measurement results, [12] considers the impact of environmental temperature on the strain gauge in a variety of ways and employs the Huygens bridge circuit with a temperature compensation gauge to derive the expression for the heat output, which is the power output. The basic idea of the effective independence method proposed in [13] is to gradually fire off those degrees of freedom that contribute the least to the independence of the target parameters, so as to achieve the best spatial resolution of the target. Literature [14] proposed the use of perturbation analysis method to derive the relationship between sensor position and recognition error, so as to minimize the target recognition error obtained by the configured sensor network. Literature [15] developed a strain measuring instrument to solve the problem of strain measurement, which was subsequently put into production by Fairbanks and Ewing, which opened the curtain on the evolution and development of strain measuring instruments. Literature [16] combines the concept of Huston's design with the science and technology that keeps pace with the times and introduces a large number of advanced concepts into strain measurement. According to the connection state of the device and the object under test during the experiment, the strain measurement methods can be divided into contact strain measurement and noncontact strain measurement. Literature [17] embeds the optical fiber inside the composite material, resulting in a new type of optical fiber smart skin when combined with the distributed optical fiber strain measurement system. In [18] to calibrate the external parameters, the GRASP Laboratory at the University of Pennsylvania uses a straight line to represent the lane. Song Xuefeng et al. used the ground grid for calibration and introduced edge extraction in their paper [19]. In [20] image processing techniques such as the Hough transform and vanishing point detection were used to detect straight lines in both vertical and horizontal directions on the grid-like ground image, determine the position of the calibration point, and finally achieve rapid camera calibration. Li Qing et al. proposed a simple and practical three-line calibration method in [21]. This method only requires three parallel straight lines on flat ground and then determining the intersection of these three straight lines and the other three points in the image, either manually or automatically. Without a dedicated location, the camera's external parameters can be calibrated.This article takes the single-chip microcomputer as the object, analyzes the structural strength dynamic strain measurement system, and explains its advantages. The system has a wide range of applications in the field of vehicle structural strength dynamic strain. Among them, the application of data fusion can reduce the impact of the uncertainty of each sensor and avoid the limitations of a single sensor. The fault diagnosis system of multisensor data fusion technology based on fuzzy mathematics and DS evidence theory is selected based on the decision-making layer and features. The layer-assisted method gives full play to the superiority of this algorithm.


## 3. Numerical Simulation

### 3.1. Displacement Mode Theory

In the dynamic analysis of the structure, the mode refers to the unique properties of the system structure. When a rod system such as a climbing dome is used for the analysis of the construction forming form, it is necessary to solve the mechanism displacement mode of the system. When the organization is singular, the eigenvalues of the submatrix of the control variable or the state variable in the overall balance matrix of the organization decrease, and the phenomenon of nonrow full rank occurs. During the service period of the structure, due to the influence of natural disasters, environmental loads, material aging, and other unfavorable factors, damage accumulation and resistance attenuation will occur [22]. Generally, accelerometers are often used to measure response in modal tests. Large errors may occur for light and small specimens due to the additional mass. Although the mass elimination technique can improve some accuracy, it is often not ideal. Traditional modal theory includes real modal theory and complex modal theory. It studies and describes the natural vibration characteristics of the system. Its essence is a coordinate transformation process. The displacement modal difference curve is shown in Figure 1.Figure 1
Displacement modal difference curve.Solving the dynamics equations of the structure into the sum of a series of single-degree-of-freedom dynamics equations brings great convenience to theoretical analysis or experimental research. In modern engineering, many structural systems are actually linked mechanisms, such as climbing dome, deployable structure, etc. In order to meet the needs of construction or use, it is usually necessary to obtain the movement trend of the mechanism in the current configuration. In the simulation, it is found that the existence of the mechanism's singular points makes the mechanism's movement uncertain. At the singular point, the phenomenon of “dead point” may occur, or bifurcation may occur, that is, the mechanism moves according to an undesigned motion path, and the problem of out-of-control movement occurs. This problem does not exist with the resistance wire, which is convenient to find the light weight and large bearing capacity. With the principal stress and principal strain, the transfer function measurement is as convenient as the acceleration method in identifying the displacement mode. This is undoubtedly very valuable for reducing test costs, improving test accuracy, and expanding the use of strain gauges. The real mode theory has a long history. It was developed from the undamped linear structural vibration conservative system and later applied to a variety of special structural vibration systems [23]. The orthogonal condition is its theoretical foundation. The mechanism displacement mode usually describes the movement trend of the mechanism system, and the movement trend of the mechanism system can be obtained by linear superposition of the mechanism displacement modes present in the current configuration of the mechanism system. The smallest nonzero singular value of the mechanism coordination matrix or balance matrix at the bifurcation point does not necessarily approach zero; that is, the number of mechanism displacement modes at the bifurcation point does not necessarily increase, whether it is a single-degree-of-freedom system or a multi-degree-of-freedom system.Assuming that the linear massm¯ has nothing to do with the position x and the bending stiffness EI is related to the position x, the undamped free vibration equation is(1)2x2EIx2ux,tx2+m¯2ux,tt2=0.According to the vibration theory, the solution of (1), that is, the free vibration displacement ux,t, can be expressed as the superposition of modes:(2)μx,t=ar=1∘jrxnrt,where r is the mode order; ϕrx is the displacement mode; nrt is the displacement mode coordinate.Substitute (2) into (1), and let(3)wr2=−nr2tnrt.Then the fourth-order differential form corresponding to the rth mode shape can be obtained:(4)jr4x=wr2m¯EIxjrx−2EIφxEIxjriix−EIiixEIxjr2x.where wr is a function of the generalized coordinates corresponding to the rth order.If local damage occurs, the bending stiffness will also be reduced to a certain extent; that is, the stiffness distribution is no longer a constant, but a variable related to the position. The following functions are used here to describe the damage mode:When injury occurs,EIx=EI01−acos2t, where(5)1−bxc<x<1−bxc,t=p2x−xcnbxc.When the structure is intact,EIx=EI0, where(6)0#x1−bxcor1+bxc#xL,where EI0 is the perfect bending stiffness; a, β, and n are the damage constants; L is the length; xc is the center coordinate of the damage area.The 4th derivative of the displacement mode cannot be measured directly in actual engineering structures, but it can be measured indirectly from the displacement mode; that is, the 4th derivative of the displacement mode can be calculated using the difference method based on the displacement mode. The following is how it was calculated:(7)ji,j4x=ji+2,j−4ji+1,j+6ji,j−4ji−1,j+ji−2,jli4,where i is the node number, j is the modal order, and li is the length of the i unit.Many studies on linear nonconservative nonclassical damped multi-degree-of-freedom systems have been conducted. The state space method, which has the advantage of solving the problem but the disadvantage of artificially increasing the unknown quantity, and the positional method are the two main methods. The common method of shape space has the disadvantage of not being able to solve the problem using orthogonal conditions. Under the current configuration, the mechanism displacement mode of the mechanism system is the left null space of the balance matrix of the mechanism [24]. The high-order coordination equation is always established for the non-self-stress modal mechanism, and the use of high-order coordination equations to solve the bifurcation motion path is no longer applicable. If the damage to the structure accumulates to a certain point and is not discovered and addressed in a timely manner, the damage will spread rapidly, resulting in the complete destruction of the structure. There are numerous benefits to using the strain admittance obtained from the application piece's side response as the parameter identification. On the specimen, it has no additional stiffness or quality influence. The strain gauge is small and inexpensive and can be used to measure multiple points. The measurement system is shown in Figure 2.Figure 2
Block diagram of the measurement system.In general, the equivalent eigenvalue state equation of the motion equation of the linear structural vibration system can still be expressed by equation in form. Existing studies have used the singular value decomposition method (SVD method) to solve the mechanism displacement mode of the system. This method shows stable and efficient performance when the system contains few components and the balance matrix is small. To make the articulated rod system move, some nodes must be driven. The driven nodes are called driving nodes, and the rest are called driven nodes. The corresponding rods of the driving node and the driven node are called the driving rod and the driven rod, respectively. The mechanism system used in actual engineering often contains a large number of rods, and the balance matrix formed is huge and the element distribution is sparse. At this time, if the method described above is used to directly solve the mechanism displacement mode of the system, the calculation process will be slow.


### 3.2. Strain Mode Theory

The displacement mode is frequently obtained in modal analysis in many structural health monitoring systems today. The displacement modal analysis is frequently used when the structural deformation is analyzed, the internal force affects its change area, or there is a problem of stress concentration. It is impossible to obtain a good health monitoring effect [25]. The strain modal method's basic idea is that the vibration system's strain field can be expressed by superimposing appropriate characteristic strain fields in a certain proportion. The strain mode, like the displacement mode, reflects the structure's inherent characteristics. It is critical to analyze the stress state of the structure under dynamic load conditions when designing a structure dynamically. Strain is sensitive not only to local structural changes that affect the structure's strength and life, but also to the additional mass and rigidity caused by the resistance strain gauge sticking. Researchers are constantly exploring whether the strain response of the structure under the action of external force has a distribution law similar to the displacement response mode in order to effectively monitor the structure in all aspects. The physical significance of strain modal theory is obvious, but a more rigorous mathematical discourse has yet to emerge. The theory of strain modal is still being developed at this time. Curvature modal measurement is a method for indirectly detecting stress and strain that avoids the limitations of strain gauge measurement by using displacement measurement. The actual stress is determined by strain measurement. Strain modal testing technology has broad application prospects for structural damage identification research [26]. Traditional nondestructive testing techniques, such as ultrasonic method, shock echo method, acoustic emission, infrared method, and radar method, are all local damage diagnosis techniques, which require a priori knowledge of the damage site and are suitable for local detection, but in fact, it is very difficult to detect all parts of the structure. Compared with the displacement mode, the strain mode is another manifestation of the same energy balance state. It can be seen from the simulation results that the natural frequency and modal changes after damage are closely related to the location of the damage point. Establishing the calculation model of strain response directly will make the estimation of dynamic stress more accurate. The vibration diagnosis technology based on vibration theory is to analyze the natural frequency, damping, and modal vibration characteristics of the structure by testing the response of the structure under dynamic load and then to diagnose the location and degree of structural damage. There are two ways to make the inversion result unique: (1) add mathematical constraints; (2) add physical constraints. When the damage point is located at the mode node, the change of the natural frequency, mode, and mode difference of this order is extremely small. The function of the dynamic strain measurement system is shown in Figure 3.Figure 3
Functional block diagram of dynamic strain measurement system.This should be paid attention to when actually detecting damage. Strain is more sensitive to local structural changes (such as local small holes, cut grooves) that will have an important impact on the strength and life of the structure, while displacement responds slightly to this. Since the dynamic characteristics of the structure are only related to its inherent properties and reflect the overall behavior of the structure and have nothing to do with external conditions such as loads, the vibration diagnosis technology has the ability to diagnose global damage, which can make accurate safety assessments for the structure. The percentage of curvature mode change is much higher than that of displacement mode. Regardless of displacement mode or curvature mode, higher-order modes can better reflect the existence and location of damage than low-order modes. Direct modal analysis of strain response is more important for local stress or local damage. The problem of selecting the amount of damage identification, that is, deciding which parameters can be used as the basis for better identifying and calibrating the damage location and extent of the structure, is the first step in structural damage diagnosis. With more experience, the ability to identify and locate damage to a specific structure will improve steadily [27]. Obviously, if the measurement is repeated with an artificial neural network as the learning tool, we can design an intelligent structural fault diagnosis system with a self-evolving knowledge base. The low-order amplitude (generally inversely proportional to the square of its natural circular frequency) that can be excited by the same exciting force is much smaller than the high-order amplitude. Because the resistance strain gauge has a small mass, the additional stiffness caused by the paste is also small, making it ideal for measuring and analyzing thin and small structures. The amount of damage identification must change monotonously with the increase in the degree of damage to determine the degree of damage to the structure. As a result, some damage identification indicators will be produced by determining the location of the damage and calibrating the degree of damage. Limitations: Vibration characteristics are now a widely used and powerful diagnostic method for fault diagnosis and monitoring, but it primarily focuses on the diagnosis of mechanical equipment or mechanisms, component failures, and general engineering structures that bear or transmit loads. There has not been much research done.


### 3.3. Numerical Simulation

After knowing the displacement response mode of the fixed beam, in order to obtain the subsequent full-field dynamic strain, we must also know the strain response mode. According to the strain mode theory, the strain response mode can be obtained by direct deduction. Mode shape: In order to predict the safety state of the structural system during the dynamic response process, it is necessary to analyze the dynamic reliability of the structural system. The uncertainty of the actual structure's natural frequency will not guarantee the frequency tuning of the TMD. The cumulative energy that can reasonably explain the cumulative damage to the structure during vibration has become an important object of energy method research, but the pure cumulative energy spectrum can hardly reflect the tendency of vibration to damage the structure's impulse type. The anchor rod is usually analyzed as an axial rod unit with rough surface. However, in the joint slope reinforcement, it is more reasonable to consider the axial and lateral effects of the anchor rod due to the dislocation of the joint surface. The random factor method is used to analyze the dynamic characteristics and dynamic response of the random rigid frame structure. Starting from the frequency domain expression of the random response of the structure, using the algebraic synthesis method and the moment method to solve the numerical characteristics of random variables, the random parameter rigid frame structure is derived. The frequency tuning sensitivity of TMD is an important practical issue. The instantaneous input energy is related to the first destruction of the structure. In the joint slope engineering, due to the dislocation of the joint, the anchor rod will inevitably bear a certain lateral force, and its importance is no less than the axial force. Short-period structures are controlled by steady-state vibrations and are prone to cumulative damage and damage. For long-period structures, the total displacement is controlled by transient vibrations. In terms of values, the displacement generated by the transient vibration term is not only much larger than the resonance displacement, and the attenuation is very high. It is slow and is also affected by vibration. It is necessary to conduct a comprehensive analysis of the force of the anchor element in the joint slope, so that it can exert not only the axial force performance, but also the lateral force performance [28]. In transient vibration terms, the maximum displacement of the structure is more likely to exceed the damage standard, and the damage is often one-time and sudden. The numerical simulation method has the characteristics of low cost, short time, strong repeatability, and great flexibility. Especially for the qualitative study of the displacement field effect of huge rock mass structures, it is more unique. It can be discussed from the macro overall trend, with the changing law of the field effect of the rock mass. The above is of great significance to the design of structural control system in the future.The use of modal analysis technology to analyze the dynamic characteristics of automobile structures is a mature technology that has been used by many units both at home and abroad. The dynamic stress-strain distribution of an automobile structure determines its fatigue damage. As a result, in recent years, the calculation or experimentation of the structure's dynamic strain field has gotten a lot of attention. The structure's experimental stress analysis is carried out under simulated conditions, an efficient method for determining static strength. The dynamic allowable stress of the structure is often calculated by dividing the static allowable stress of the structure by a chosen safety factor during the vehicle design stage. The results of the static experimental stress analysis are examined. The key to establishing the model is to simulate the nonlinearity of the moving boundary using the contact and target elements in order to achieve the lift-off of the tank bottom. The vehicle structure's use characteristics dictate that it is always subjected to dynamic random excitation of the road surface in actual use, and the dynamic allowable stress of the structure under dynamic load is much lower than the static allowable stress. Engineers work on building structures. We are more concerned about the distribution of stress and strain from the standpoint of strength and fatigue. The dynamic strain/stress field's basic idea is that the perturbed system's strain field can be superimposed and expressed in a proportion by an appropriate characteristic strain field. The so-called “strain mode” is the characteristic strain field. The dynamic strain of the structure is measured by the test-time. The procedure can take a long time. The original analog signal must be discretized sampling in order to perform effective signal processing. The dynamic strain of each measurement point of the frame structure is generally normally distributed due to the random nature of the road surface excitation. It is important to see if the maximum dynamic stress exceeds the allowable stress during the structure's strength check, as well as the strain distribution. It can be obtained through a differential deformation displacement operation. Alternatively, the strain distribution obtained by integration can be thought of as the deformation displacement. One row and one column of the strain transfer function matrix must be measured when building the dynamic strain response model of the structure, and both modal models contain the same modal parameters. The maximum stress value in each sample is a random variable that characterizes the maximum stress distribution at the measuring point because the sample is normally random.


## 3.1. Displacement Mode Theory

In the dynamic analysis of the structure, the mode refers to the unique properties of the system structure. When a rod system such as a climbing dome is used for the analysis of the construction forming form, it is necessary to solve the mechanism displacement mode of the system. When the organization is singular, the eigenvalues of the submatrix of the control variable or the state variable in the overall balance matrix of the organization decrease, and the phenomenon of nonrow full rank occurs. During the service period of the structure, due to the influence of natural disasters, environmental loads, material aging, and other unfavorable factors, damage accumulation and resistance attenuation will occur [22]. Generally, accelerometers are often used to measure response in modal tests. Large errors may occur for light and small specimens due to the additional mass. Although the mass elimination technique can improve some accuracy, it is often not ideal. Traditional modal theory includes real modal theory and complex modal theory. It studies and describes the natural vibration characteristics of the system. Its essence is a coordinate transformation process. The displacement modal difference curve is shown in Figure 1.Figure 1
Displacement modal difference curve.Solving the dynamics equations of the structure into the sum of a series of single-degree-of-freedom dynamics equations brings great convenience to theoretical analysis or experimental research. In modern engineering, many structural systems are actually linked mechanisms, such as climbing dome, deployable structure, etc. In order to meet the needs of construction or use, it is usually necessary to obtain the movement trend of the mechanism in the current configuration. In the simulation, it is found that the existence of the mechanism's singular points makes the mechanism's movement uncertain. At the singular point, the phenomenon of “dead point” may occur, or bifurcation may occur, that is, the mechanism moves according to an undesigned motion path, and the problem of out-of-control movement occurs. This problem does not exist with the resistance wire, which is convenient to find the light weight and large bearing capacity. With the principal stress and principal strain, the transfer function measurement is as convenient as the acceleration method in identifying the displacement mode. This is undoubtedly very valuable for reducing test costs, improving test accuracy, and expanding the use of strain gauges. The real mode theory has a long history. It was developed from the undamped linear structural vibration conservative system and later applied to a variety of special structural vibration systems [23]. The orthogonal condition is its theoretical foundation. The mechanism displacement mode usually describes the movement trend of the mechanism system, and the movement trend of the mechanism system can be obtained by linear superposition of the mechanism displacement modes present in the current configuration of the mechanism system. The smallest nonzero singular value of the mechanism coordination matrix or balance matrix at the bifurcation point does not necessarily approach zero; that is, the number of mechanism displacement modes at the bifurcation point does not necessarily increase, whether it is a single-degree-of-freedom system or a multi-degree-of-freedom system.Assuming that the linear massm¯ has nothing to do with the position x and the bending stiffness EI is related to the position x, the undamped free vibration equation is(1)2x2EIx2ux,tx2+m¯2ux,tt2=0.According to the vibration theory, the solution of (1), that is, the free vibration displacement ux,t, can be expressed as the superposition of modes:(2)μx,t=ar=1∘jrxnrt,where r is the mode order; ϕrx is the displacement mode; nrt is the displacement mode coordinate.Substitute (2) into (1), and let(3)wr2=−nr2tnrt.Then the fourth-order differential form corresponding to the rth mode shape can be obtained:(4)jr4x=wr2m¯EIxjrx−2EIφxEIxjriix−EIiixEIxjr2x.where wr is a function of the generalized coordinates corresponding to the rth order.If local damage occurs, the bending stiffness will also be reduced to a certain extent; that is, the stiffness distribution is no longer a constant, but a variable related to the position. The following functions are used here to describe the damage mode:When injury occurs,EIx=EI01−acos2t, where(5)1−bxc<x<1−bxc,t=p2x−xcnbxc.When the structure is intact,EIx=EI0, where(6)0#x1−bxcor1+bxc#xL,where EI0 is the perfect bending stiffness; a, β, and n are the damage constants; L is the length; xc is the center coordinate of the damage area.The 4th derivative of the displacement mode cannot be measured directly in actual engineering structures, but it can be measured indirectly from the displacement mode; that is, the 4th derivative of the displacement mode can be calculated using the difference method based on the displacement mode. The following is how it was calculated:(7)ji,j4x=ji+2,j−4ji+1,j+6ji,j−4ji−1,j+ji−2,jli4,where i is the node number, j is the modal order, and li is the length of the i unit.Many studies on linear nonconservative nonclassical damped multi-degree-of-freedom systems have been conducted. The state space method, which has the advantage of solving the problem but the disadvantage of artificially increasing the unknown quantity, and the positional method are the two main methods. The common method of shape space has the disadvantage of not being able to solve the problem using orthogonal conditions. Under the current configuration, the mechanism displacement mode of the mechanism system is the left null space of the balance matrix of the mechanism [24]. The high-order coordination equation is always established for the non-self-stress modal mechanism, and the use of high-order coordination equations to solve the bifurcation motion path is no longer applicable. If the damage to the structure accumulates to a certain point and is not discovered and addressed in a timely manner, the damage will spread rapidly, resulting in the complete destruction of the structure. There are numerous benefits to using the strain admittance obtained from the application piece's side response as the parameter identification. On the specimen, it has no additional stiffness or quality influence. The strain gauge is small and inexpensive and can be used to measure multiple points. The measurement system is shown in Figure 2.Figure 2
Block diagram of the measurement system.In general, the equivalent eigenvalue state equation of the motion equation of the linear structural vibration system can still be expressed by equation in form. Existing studies have used the singular value decomposition method (SVD method) to solve the mechanism displacement mode of the system. This method shows stable and efficient performance when the system contains few components and the balance matrix is small. To make the articulated rod system move, some nodes must be driven. The driven nodes are called driving nodes, and the rest are called driven nodes. The corresponding rods of the driving node and the driven node are called the driving rod and the driven rod, respectively. The mechanism system used in actual engineering often contains a large number of rods, and the balance matrix formed is huge and the element distribution is sparse. At this time, if the method described above is used to directly solve the mechanism displacement mode of the system, the calculation process will be slow.


## 3.2. Strain Mode Theory

The displacement mode is frequently obtained in modal analysis in many structural health monitoring systems today. The displacement modal analysis is frequently used when the structural deformation is analyzed, the internal force affects its change area, or there is a problem of stress concentration. It is impossible to obtain a good health monitoring effect [25]. The strain modal method's basic idea is that the vibration system's strain field can be expressed by superimposing appropriate characteristic strain fields in a certain proportion. The strain mode, like the displacement mode, reflects the structure's inherent characteristics. It is critical to analyze the stress state of the structure under dynamic load conditions when designing a structure dynamically. Strain is sensitive not only to local structural changes that affect the structure's strength and life, but also to the additional mass and rigidity caused by the resistance strain gauge sticking. Researchers are constantly exploring whether the strain response of the structure under the action of external force has a distribution law similar to the displacement response mode in order to effectively monitor the structure in all aspects. The physical significance of strain modal theory is obvious, but a more rigorous mathematical discourse has yet to emerge. The theory of strain modal is still being developed at this time. Curvature modal measurement is a method for indirectly detecting stress and strain that avoids the limitations of strain gauge measurement by using displacement measurement. The actual stress is determined by strain measurement. Strain modal testing technology has broad application prospects for structural damage identification research [26]. Traditional nondestructive testing techniques, such as ultrasonic method, shock echo method, acoustic emission, infrared method, and radar method, are all local damage diagnosis techniques, which require a priori knowledge of the damage site and are suitable for local detection, but in fact, it is very difficult to detect all parts of the structure. Compared with the displacement mode, the strain mode is another manifestation of the same energy balance state. It can be seen from the simulation results that the natural frequency and modal changes after damage are closely related to the location of the damage point. Establishing the calculation model of strain response directly will make the estimation of dynamic stress more accurate. The vibration diagnosis technology based on vibration theory is to analyze the natural frequency, damping, and modal vibration characteristics of the structure by testing the response of the structure under dynamic load and then to diagnose the location and degree of structural damage. There are two ways to make the inversion result unique: (1) add mathematical constraints; (2) add physical constraints. When the damage point is located at the mode node, the change of the natural frequency, mode, and mode difference of this order is extremely small. The function of the dynamic strain measurement system is shown in Figure 3.Figure 3
Functional block diagram of dynamic strain measurement system.This should be paid attention to when actually detecting damage. Strain is more sensitive to local structural changes (such as local small holes, cut grooves) that will have an important impact on the strength and life of the structure, while displacement responds slightly to this. Since the dynamic characteristics of the structure are only related to its inherent properties and reflect the overall behavior of the structure and have nothing to do with external conditions such as loads, the vibration diagnosis technology has the ability to diagnose global damage, which can make accurate safety assessments for the structure. The percentage of curvature mode change is much higher than that of displacement mode. Regardless of displacement mode or curvature mode, higher-order modes can better reflect the existence and location of damage than low-order modes. Direct modal analysis of strain response is more important for local stress or local damage. The problem of selecting the amount of damage identification, that is, deciding which parameters can be used as the basis for better identifying and calibrating the damage location and extent of the structure, is the first step in structural damage diagnosis. With more experience, the ability to identify and locate damage to a specific structure will improve steadily [27]. Obviously, if the measurement is repeated with an artificial neural network as the learning tool, we can design an intelligent structural fault diagnosis system with a self-evolving knowledge base. The low-order amplitude (generally inversely proportional to the square of its natural circular frequency) that can be excited by the same exciting force is much smaller than the high-order amplitude. Because the resistance strain gauge has a small mass, the additional stiffness caused by the paste is also small, making it ideal for measuring and analyzing thin and small structures. The amount of damage identification must change monotonously with the increase in the degree of damage to determine the degree of damage to the structure. As a result, some damage identification indicators will be produced by determining the location of the damage and calibrating the degree of damage. Limitations: Vibration characteristics are now a widely used and powerful diagnostic method for fault diagnosis and monitoring, but it primarily focuses on the diagnosis of mechanical equipment or mechanisms, component failures, and general engineering structures that bear or transmit loads. There has not been much research done.


## 3.3. Numerical Simulation

After knowing the displacement response mode of the fixed beam, in order to obtain the subsequent full-field dynamic strain, we must also know the strain response mode. According to the strain mode theory, the strain response mode can be obtained by direct deduction. Mode shape: In order to predict the safety state of the structural system during the dynamic response process, it is necessary to analyze the dynamic reliability of the structural system. The uncertainty of the actual structure's natural frequency will not guarantee the frequency tuning of the TMD. The cumulative energy that can reasonably explain the cumulative damage to the structure during vibration has become an important object of energy method research, but the pure cumulative energy spectrum can hardly reflect the tendency of vibration to damage the structure's impulse type. The anchor rod is usually analyzed as an axial rod unit with rough surface. However, in the joint slope reinforcement, it is more reasonable to consider the axial and lateral effects of the anchor rod due to the dislocation of the joint surface. The random factor method is used to analyze the dynamic characteristics and dynamic response of the random rigid frame structure. Starting from the frequency domain expression of the random response of the structure, using the algebraic synthesis method and the moment method to solve the numerical characteristics of random variables, the random parameter rigid frame structure is derived. The frequency tuning sensitivity of TMD is an important practical issue. The instantaneous input energy is related to the first destruction of the structure. In the joint slope engineering, due to the dislocation of the joint, the anchor rod will inevitably bear a certain lateral force, and its importance is no less than the axial force. Short-period structures are controlled by steady-state vibrations and are prone to cumulative damage and damage. For long-period structures, the total displacement is controlled by transient vibrations. In terms of values, the displacement generated by the transient vibration term is not only much larger than the resonance displacement, and the attenuation is very high. It is slow and is also affected by vibration. It is necessary to conduct a comprehensive analysis of the force of the anchor element in the joint slope, so that it can exert not only the axial force performance, but also the lateral force performance [28]. In transient vibration terms, the maximum displacement of the structure is more likely to exceed the damage standard, and the damage is often one-time and sudden. The numerical simulation method has the characteristics of low cost, short time, strong repeatability, and great flexibility. Especially for the qualitative study of the displacement field effect of huge rock mass structures, it is more unique. It can be discussed from the macro overall trend, with the changing law of the field effect of the rock mass. The above is of great significance to the design of structural control system in the future.The use of modal analysis technology to analyze the dynamic characteristics of automobile structures is a mature technology that has been used by many units both at home and abroad. The dynamic stress-strain distribution of an automobile structure determines its fatigue damage. As a result, in recent years, the calculation or experimentation of the structure's dynamic strain field has gotten a lot of attention. The structure's experimental stress analysis is carried out under simulated conditions, an efficient method for determining static strength. The dynamic allowable stress of the structure is often calculated by dividing the static allowable stress of the structure by a chosen safety factor during the vehicle design stage. The results of the static experimental stress analysis are examined. The key to establishing the model is to simulate the nonlinearity of the moving boundary using the contact and target elements in order to achieve the lift-off of the tank bottom. The vehicle structure's use characteristics dictate that it is always subjected to dynamic random excitation of the road surface in actual use, and the dynamic allowable stress of the structure under dynamic load is much lower than the static allowable stress. Engineers work on building structures. We are more concerned about the distribution of stress and strain from the standpoint of strength and fatigue. The dynamic strain/stress field's basic idea is that the perturbed system's strain field can be superimposed and expressed in a proportion by an appropriate characteristic strain field. The so-called “strain mode” is the characteristic strain field. The dynamic strain of the structure is measured by the test-time. The procedure can take a long time. The original analog signal must be discretized sampling in order to perform effective signal processing. The dynamic strain of each measurement point of the frame structure is generally normally distributed due to the random nature of the road surface excitation. It is important to see if the maximum dynamic stress exceeds the allowable stress during the structure's strength check, as well as the strain distribution. It can be obtained through a differential deformation displacement operation. Alternatively, the strain distribution obtained by integration can be thought of as the deformation displacement. One row and one column of the strain transfer function matrix must be measured when building the dynamic strain response model of the structure, and both modal models contain the same modal parameters. The maximum stress value in each sample is a random variable that characterizes the maximum stress distribution at the measuring point because the sample is normally random.


## 4. Cantilever Beam Experiment Verification

### 4.1. Strain Electrical Measurement

Electrical strain measurement is a traditional method of measuring strain that is widely used and has a well-developed technology. Strain gauges are used as sensitive components in the strain electrical measurement method. It measures strain using the strain gauge's sensitive grid's strain resistance effect. During the actual measurement, the strain gauge is adhered to the test piece. Its benefits include high measurement accuracy and sensitivity, a wide measurement range, continuous measurement and recording, and long-distance measurement; it can also be easily integrated into a control system to automate the manufacturing process. The strain electrical measurement method is currently used to measure the longitudinal stress of the rail primarily in the United Kingdom, the United States, Japan, and other countries. The general procedure for measuring strain with a resistance strain gauge (strain gauge) is to paste or install the strain gauge on the surface of the component to be measured and then connect it to the measuring circuit (bridge or potentiometer circuit). The strain increases as the component is deformed. The chip's sensitive grid deforms as well, changing the resistance value. The damping coefficient test curve is shown in Figure4.Figure 4
Damping coefficient test curve.The general resistance strain gauge is mainly composed of five parts: sensitive grid, adhesive, lead, base, and cover sheet. When measuring in a temperature-changing environment, measures must be taken to eliminate the influence of the heat output of the strain gauge in order to ensure the accuracy of the measurement. There are various measurement systems, which are directly related to the nature of the measured nonelectricity and the type of converter used. The overall design procedure of the system is shown as in Figure5.Figure 5
System overall design procedure.Commonly used converters can only convert a certain mechanical quantity into electricity. For example, strain gauges can only convert strain into resistance. In order to expand its measurement range, a mechanical converter is often added before the converter to change the required measurement. The mechanical quantity is converted into a mechanical quantity capable of driving the converter. The measured locked rail temperature is also relative to the locked rail temperature at the cleared temperature, and the longitudinal stress of the rail measured by the strain electrical measurement method is relative to the rail stress state after the strain sensor is cleared. The change in resistance value should be proportional to the component's surface. The signal generated by the strain gauge's resistance change is output by the measuring circuit. It is indicated or recorded by the indicating instrument or recording instrument after being amplified by the amplifier circuit. The sensitive grid is a monofilament or grid-like body made of metal wire or semiconductor material whose purpose is to convert changes in strain into changes in resistance. In an environment with large temperature changes, the self-compensation method uses a special treatment process or a method of connecting two materials with a resistance temperature coefficient in series to make a sensitive grid, so the heat output of this method is not high. A converter composed of certain elements or components can produce electrical effects under the action of nonelectricity, that is, converting nonelectricity into electricity. For example, the commonly used strain gauge is a kind of converter; it will produce the change of resistance under the action of strain and convert the amount of strain into the amount of resistance. Since the radius of the rounded corner of the connecting rod journal is relatively small, and the part covered by the sensitive grid of the same length is relatively large, the error of the strain electrical measurement is also larger than that at the rounded corner of the main journal, as shown in Figure6.Figure 6
The influence of the length of the sensitive grid on the strain measurement error.Due to the influence of factors such as rain and snow, as well as other factors such as impact and vibration when the train passes by, higher requirements for the moisture-proof, antistripping, and long-term use performance of the sensor system are put forward on the seamless rail line in nature. The strain gauges' measuring points are chosen based on the results of the previous finite element method's simulation and calculation, and the strain gauges are deployed in the larger stress area and part of the abnormal stress area. The strain gauge's job is to convert changes in strain into changes in resistance, but it also has to convert the relative change in resistance into changes in voltage or current so that it can be measured by an electric measuring instrument. The thermal element method involves having the thermal element generate a signal that is of the same value and opposite sign as the strain gauge's heat output in order to cancel it out. This method necessitates the use of additional circuits, as well as a lengthy and time-consuming implementation process. The mechanical converter and the converter are commonly referred to as the sensor because they are assembled together, with load cell, acceleration sensor, and so on. The strain electrical measurement method must meet stringent requirements for longitudinal stress accuracy, applicability, and long-term online monitoring.


### 4.2. Experimental Design

In the test, one end of the cantilever beam is fixed on the experimental platform, and the other end is free, and the circular mark point is pasted on the side of the cantilever beam. The purpose is to use the binocular camera to capture the vibration image of the mark point and perform three-dimensional reconstruction, with vibration displacement of the mark point. In order to use the rectangular microcantilever to measure the fluid density, this paper adopts the mode superposition method according to the force balance principle to derive the theoretical relationship between the first-order resonance frequency and the fluid density of the rectangular microcantilever with one end fixed and the other free end, using ANSYS software. The resonance frequency of the microcantilever in different densities of n-heptane and isooctane is simulated and analyzed. Once the flexible member is excited, because of its tiny structural damping, the vibration of the flexible member will be difficult to stop in a short time, and the vibration of the flexible member will cause resonance, which will eventually affect the working accuracy and service life. The system performs sinusoidal sweep excitation on the specimen to obtain the response characteristics of the specimen and analyzes the data to obtain the coefficient of the structure specimen. In order to analyze the influence of different piezoelectric materials as the piezoelectric layer on the sensitivity of the piezoelectric microcantilever, piezoelectric ceramics and PZT-5H are used as the piezoelectric layer materials of the piezoelectric microcantilever, and piezoelectric analysis is carried out by ANSYS, as shown in Figure7.Figure 7
Output voltage when two piezoelectric materials are used as the piezoelectric layer.Microcantilever is a typical movable microstructure device. Its length and width are generally in the micron rang, and the thickness is in the submicron range. According to different applications, it can be used such as monocrystalline silicon, polycrystalline silicon, silicon dioxide, aluminum, etc. It is made of three kinds of materials, because it has the characteristics of simple preparation process and strong ductility in the application field; it occupies an important position in the microelectromechanical system. By superimposing the vacuum mode of the microcantilever to replace the fluid-structure coupling mode of the microcantilever, the influence of the fluid on the microcantilever is converted into fluid dynamic pressure, and the vibration differential equation is solved by the orthogonality of the vacuum mode. The relationship between the resonance frequency of the cantilever beam and the fluid density is obtained. The general idea of the finite element method is to first divide a continuous area or object into finite elements (and these elements bear equivalent nodal loads) and then build an “element matrix” based on the relationship between the nodes of these elements to solve the problem. The external additional mass causes the natural frequency of the microcantilever to change, and the quality detection can be achieved by measuring the frequency shift of the microcantilever. Based on this principle, a micromass spectrometer can be made to detect the quality of single molecules and single cells and so on. In a natural law system, the total mechanical energy is conserved, so when the system is vibrating freely, potential energy and kinetic energy are converted mutually without energy loss, so that the system will maintain a constant amplitude structural vibration. Under normal pressure, the resonance frequency of the rectangular microcantilever in n-heptane and isooctane was measured experimentally, as shown in Figure8.Figure 8
Amplitude-frequency curve of microcantilever in n-heptane.Active control technology is the most effective way to reduce the vibration of a flexible structure. The piezoelectric sensor and actuator are integrated in the flexible cantilever beam, making it a smart structure, and the study of its vibration suppression characteristics will have practical significance for the active control of flexible beam vibration. The computer software sends a drive signal from the controller to the power amplifier, which amplifies the signal and drives the vibration exciter (vibration table) to move according to the required vibration control spectrum. The benefit of using the finite element method to simulate a micropiezoelectric cantilever is that it can discretize the object into a set of finite simple elements, which can then be used to simulate or approximate the original object, reducing a continuous problem to a discrete problem. Perform analysis to obtain the entire object's analysis structure. Thermal stress analysis, thermal structure analysis, thermoelectric analysis, thermal fluid analysis, magnetocaloric analysis, magnetic structure analysis, induction heating analysis, induction oscillation analysis, electromagnetic circuit analysis, and electrical structure analysis are just some of the multiphysics analyses available in ANSYS. The peak-to-peak output voltage of the vibration frequency (20Hz–200 Hz) is used, as well as the direct output of each cantilever beam piezoelectric slice and the connection modes of parallel and series. The maximum output voltage of each in parallel and series connection is compared. The test results are shown in Figure9.Figure 9
The relationship between output voltage and time.Regardless of whether the static mode or the dynamic mode is used for experimental research, a reference experiment is usually included, that is to say, a microcantilever with the same mechanical characteristics without surface functionalization is tested at the same time, and the difference between the two is compared. The signal gets the signal under test. Damping is definitely there and it is impossible to avoid. This will affect the conversion of mechanical energy, and the energy will slowly decay, so that the constant amplitude vibration cannot be maintained. This kind of mechanical vibration is called damped free vibration. Gray prediction is a prediction method that analyzes the dynamic behavior and operating trend of the object. It has the advantages of low model requirements, fewer online estimation parameters, convenient calculation, good comprehensive control effects, and strong robustness. It is currently in the field of industrial process control being widely used.


### 4.3. Camera Calibration

Before performing the experiment, it is necessary to determine the two cameras for calibration, that is, to determine their internal and external parameters. The purpose of the camera calibration is to establish the relationship between the three-dimensional object point in the space and the two-dimensional image point of the pixel coordinate system, and the calibration result is directly related to the accuracy of the vision system. Internal and external parameter calibration are the two types of camera calibration. Fixed-focus lenses are used in all vehicle-mounted cameras, and their internal parameters do not change after one calibration. The calibration of external parameters is the only thing that needs to be considered. A one-dimensional calibration object with an infrared reflective marking ball installed at both ends and in the middle is made to solve the problem of camera calibration in the process of photoelectric detection of motion parameters. The effective focal length of the camera, the principal point of the optical center, and the lens distortion coefficient of the camera are among the internal parameters. External parameters are primarily the position transformation between the camera coordinate system and the world coordinate system, and these are the main parameters of each camera. The rotation matrix and the translation matrix are the two most important position transformation parameters between the two cameras. The camera obtains a two-dimensional image of the surface of the ground object, with the ultimate goal of obtaining the object's three-dimensional spatial information. As a result, research into how to solve three-dimensional spatial information of the ground object of interest in real time using the on-board 3D data acquisition system is required. The key content here is camera calibration. On the other hand, we investigate how to improve the accuracy of the solution model by optimizing it. The compensation algorithm can significantly improve the measurement accuracy of the vehicle's yaw angle and lateral displacement, as shown in Figure10.Figure 10
Actual measurement error of yaw angle.The feature point matching method uses a calibration board with special graphics to extract the three-dimensional points collected by the Lidar and the two-dimensional image points obtained by the corresponding camera, establish a constraint equation, and optimize the calculation of the camera pose. Its essence is the PNP (perspective n-point) question. When calibrating the camera, if too much nonlinear distortion is considered in the calculation process, it will lead to the introduction of too many nonlinear parameters in the calculation process, which will affect the calibration accuracy and cause other opposite effects. On the assumption that the road is flat, the following two situations will generally occur during the normal driving of the vehicle: local bumps on the road surface cause small bumps and vibrations in the vertical direction of the vehicle body. One-dimensional calibration object, a calibration method based on one-dimensional calibration object, has the advantages of low cost, being easy to move, and being suitable for on-site online calibration, and more importantly, it can solve the occlusion problem in multicamera occasions. The checkerboard calibration method uses a two-dimensional checkerboard as the calibration board and changes the position information between the calibration board and the camera by continuously rotating the calibration board. The relative orientation direct solution method entails expanding the coplanar equation and performing a linear transformation, then solving the relative orientation elements, and constructing a relative three-dimensional model. This method employs linear transformation; the solution is quick, but the outcome is not precise. The plane calibration template fits the straight line with Lidar points to find the intersection point and then manually marks the position of the characteristic points on the calibration board according to the scale to find the image coordinates. The primary goal of feature point extraction is to precisely determine the location of each feature point in the image so that it can be calibrated in the appropriate spatial coordinates. Reduce the relative solid model to a specific scale by incorporating it into the ground coordinate system. The relative solid model and the coordinate system's translation and rotation parameters, as well as the model scale factor, are solved in the on-board 3D data acquisition system camera pair calibration. A measuring device, independent of the front-view camera, was designed to accurately and quickly measure the vehicle's yaw angle and lateral deviation in order to verify the actual effect of the compensation algorithm in the driving of the vehicle.


## 4.1. Strain Electrical Measurement

Electrical strain measurement is a traditional method of measuring strain that is widely used and has a well-developed technology. Strain gauges are used as sensitive components in the strain electrical measurement method. It measures strain using the strain gauge's sensitive grid's strain resistance effect. During the actual measurement, the strain gauge is adhered to the test piece. Its benefits include high measurement accuracy and sensitivity, a wide measurement range, continuous measurement and recording, and long-distance measurement; it can also be easily integrated into a control system to automate the manufacturing process. The strain electrical measurement method is currently used to measure the longitudinal stress of the rail primarily in the United Kingdom, the United States, Japan, and other countries. The general procedure for measuring strain with a resistance strain gauge (strain gauge) is to paste or install the strain gauge on the surface of the component to be measured and then connect it to the measuring circuit (bridge or potentiometer circuit). The strain increases as the component is deformed. The chip's sensitive grid deforms as well, changing the resistance value. The damping coefficient test curve is shown in Figure4.Figure 4
Damping coefficient test curve.The general resistance strain gauge is mainly composed of five parts: sensitive grid, adhesive, lead, base, and cover sheet. When measuring in a temperature-changing environment, measures must be taken to eliminate the influence of the heat output of the strain gauge in order to ensure the accuracy of the measurement. There are various measurement systems, which are directly related to the nature of the measured nonelectricity and the type of converter used. The overall design procedure of the system is shown as in Figure5.Figure 5
System overall design procedure.Commonly used converters can only convert a certain mechanical quantity into electricity. For example, strain gauges can only convert strain into resistance. In order to expand its measurement range, a mechanical converter is often added before the converter to change the required measurement. The mechanical quantity is converted into a mechanical quantity capable of driving the converter. The measured locked rail temperature is also relative to the locked rail temperature at the cleared temperature, and the longitudinal stress of the rail measured by the strain electrical measurement method is relative to the rail stress state after the strain sensor is cleared. The change in resistance value should be proportional to the component's surface. The signal generated by the strain gauge's resistance change is output by the measuring circuit. It is indicated or recorded by the indicating instrument or recording instrument after being amplified by the amplifier circuit. The sensitive grid is a monofilament or grid-like body made of metal wire or semiconductor material whose purpose is to convert changes in strain into changes in resistance. In an environment with large temperature changes, the self-compensation method uses a special treatment process or a method of connecting two materials with a resistance temperature coefficient in series to make a sensitive grid, so the heat output of this method is not high. A converter composed of certain elements or components can produce electrical effects under the action of nonelectricity, that is, converting nonelectricity into electricity. For example, the commonly used strain gauge is a kind of converter; it will produce the change of resistance under the action of strain and convert the amount of strain into the amount of resistance. Since the radius of the rounded corner of the connecting rod journal is relatively small, and the part covered by the sensitive grid of the same length is relatively large, the error of the strain electrical measurement is also larger than that at the rounded corner of the main journal, as shown in Figure6.Figure 6
The influence of the length of the sensitive grid on the strain measurement error.Due to the influence of factors such as rain and snow, as well as other factors such as impact and vibration when the train passes by, higher requirements for the moisture-proof, antistripping, and long-term use performance of the sensor system are put forward on the seamless rail line in nature. The strain gauges' measuring points are chosen based on the results of the previous finite element method's simulation and calculation, and the strain gauges are deployed in the larger stress area and part of the abnormal stress area. The strain gauge's job is to convert changes in strain into changes in resistance, but it also has to convert the relative change in resistance into changes in voltage or current so that it can be measured by an electric measuring instrument. The thermal element method involves having the thermal element generate a signal that is of the same value and opposite sign as the strain gauge's heat output in order to cancel it out. This method necessitates the use of additional circuits, as well as a lengthy and time-consuming implementation process. The mechanical converter and the converter are commonly referred to as the sensor because they are assembled together, with load cell, acceleration sensor, and so on. The strain electrical measurement method must meet stringent requirements for longitudinal stress accuracy, applicability, and long-term online monitoring.


## 4.2. Experimental Design

In the test, one end of the cantilever beam is fixed on the experimental platform, and the other end is free, and the circular mark point is pasted on the side of the cantilever beam. The purpose is to use the binocular camera to capture the vibration image of the mark point and perform three-dimensional reconstruction, with vibration displacement of the mark point. In order to use the rectangular microcantilever to measure the fluid density, this paper adopts the mode superposition method according to the force balance principle to derive the theoretical relationship between the first-order resonance frequency and the fluid density of the rectangular microcantilever with one end fixed and the other free end, using ANSYS software. The resonance frequency of the microcantilever in different densities of n-heptane and isooctane is simulated and analyzed. Once the flexible member is excited, because of its tiny structural damping, the vibration of the flexible member will be difficult to stop in a short time, and the vibration of the flexible member will cause resonance, which will eventually affect the working accuracy and service life. The system performs sinusoidal sweep excitation on the specimen to obtain the response characteristics of the specimen and analyzes the data to obtain the coefficient of the structure specimen. In order to analyze the influence of different piezoelectric materials as the piezoelectric layer on the sensitivity of the piezoelectric microcantilever, piezoelectric ceramics and PZT-5H are used as the piezoelectric layer materials of the piezoelectric microcantilever, and piezoelectric analysis is carried out by ANSYS, as shown in Figure7.Figure 7
Output voltage when two piezoelectric materials are used as the piezoelectric layer.Microcantilever is a typical movable microstructure device. Its length and width are generally in the micron rang, and the thickness is in the submicron range. According to different applications, it can be used such as monocrystalline silicon, polycrystalline silicon, silicon dioxide, aluminum, etc. It is made of three kinds of materials, because it has the characteristics of simple preparation process and strong ductility in the application field; it occupies an important position in the microelectromechanical system. By superimposing the vacuum mode of the microcantilever to replace the fluid-structure coupling mode of the microcantilever, the influence of the fluid on the microcantilever is converted into fluid dynamic pressure, and the vibration differential equation is solved by the orthogonality of the vacuum mode. The relationship between the resonance frequency of the cantilever beam and the fluid density is obtained. The general idea of the finite element method is to first divide a continuous area or object into finite elements (and these elements bear equivalent nodal loads) and then build an “element matrix” based on the relationship between the nodes of these elements to solve the problem. The external additional mass causes the natural frequency of the microcantilever to change, and the quality detection can be achieved by measuring the frequency shift of the microcantilever. Based on this principle, a micromass spectrometer can be made to detect the quality of single molecules and single cells and so on. In a natural law system, the total mechanical energy is conserved, so when the system is vibrating freely, potential energy and kinetic energy are converted mutually without energy loss, so that the system will maintain a constant amplitude structural vibration. Under normal pressure, the resonance frequency of the rectangular microcantilever in n-heptane and isooctane was measured experimentally, as shown in Figure8.Figure 8
Amplitude-frequency curve of microcantilever in n-heptane.Active control technology is the most effective way to reduce the vibration of a flexible structure. The piezoelectric sensor and actuator are integrated in the flexible cantilever beam, making it a smart structure, and the study of its vibration suppression characteristics will have practical significance for the active control of flexible beam vibration. The computer software sends a drive signal from the controller to the power amplifier, which amplifies the signal and drives the vibration exciter (vibration table) to move according to the required vibration control spectrum. The benefit of using the finite element method to simulate a micropiezoelectric cantilever is that it can discretize the object into a set of finite simple elements, which can then be used to simulate or approximate the original object, reducing a continuous problem to a discrete problem. Perform analysis to obtain the entire object's analysis structure. Thermal stress analysis, thermal structure analysis, thermoelectric analysis, thermal fluid analysis, magnetocaloric analysis, magnetic structure analysis, induction heating analysis, induction oscillation analysis, electromagnetic circuit analysis, and electrical structure analysis are just some of the multiphysics analyses available in ANSYS. The peak-to-peak output voltage of the vibration frequency (20Hz–200 Hz) is used, as well as the direct output of each cantilever beam piezoelectric slice and the connection modes of parallel and series. The maximum output voltage of each in parallel and series connection is compared. The test results are shown in Figure9.Figure 9
The relationship between output voltage and time.Regardless of whether the static mode or the dynamic mode is used for experimental research, a reference experiment is usually included, that is to say, a microcantilever with the same mechanical characteristics without surface functionalization is tested at the same time, and the difference between the two is compared. The signal gets the signal under test. Damping is definitely there and it is impossible to avoid. This will affect the conversion of mechanical energy, and the energy will slowly decay, so that the constant amplitude vibration cannot be maintained. This kind of mechanical vibration is called damped free vibration. Gray prediction is a prediction method that analyzes the dynamic behavior and operating trend of the object. It has the advantages of low model requirements, fewer online estimation parameters, convenient calculation, good comprehensive control effects, and strong robustness. It is currently in the field of industrial process control being widely used.


## 4.3. Camera Calibration

Before performing the experiment, it is necessary to determine the two cameras for calibration, that is, to determine their internal and external parameters. The purpose of the camera calibration is to establish the relationship between the three-dimensional object point in the space and the two-dimensional image point of the pixel coordinate system, and the calibration result is directly related to the accuracy of the vision system. Internal and external parameter calibration are the two types of camera calibration. Fixed-focus lenses are used in all vehicle-mounted cameras, and their internal parameters do not change after one calibration. The calibration of external parameters is the only thing that needs to be considered. A one-dimensional calibration object with an infrared reflective marking ball installed at both ends and in the middle is made to solve the problem of camera calibration in the process of photoelectric detection of motion parameters. The effective focal length of the camera, the principal point of the optical center, and the lens distortion coefficient of the camera are among the internal parameters. External parameters are primarily the position transformation between the camera coordinate system and the world coordinate system, and these are the main parameters of each camera. The rotation matrix and the translation matrix are the two most important position transformation parameters between the two cameras. The camera obtains a two-dimensional image of the surface of the ground object, with the ultimate goal of obtaining the object's three-dimensional spatial information. As a result, research into how to solve three-dimensional spatial information of the ground object of interest in real time using the on-board 3D data acquisition system is required. The key content here is camera calibration. On the other hand, we investigate how to improve the accuracy of the solution model by optimizing it. The compensation algorithm can significantly improve the measurement accuracy of the vehicle's yaw angle and lateral displacement, as shown in Figure10.Figure 10
Actual measurement error of yaw angle.The feature point matching method uses a calibration board with special graphics to extract the three-dimensional points collected by the Lidar and the two-dimensional image points obtained by the corresponding camera, establish a constraint equation, and optimize the calculation of the camera pose. Its essence is the PNP (perspective n-point) question. When calibrating the camera, if too much nonlinear distortion is considered in the calculation process, it will lead to the introduction of too many nonlinear parameters in the calculation process, which will affect the calibration accuracy and cause other opposite effects. On the assumption that the road is flat, the following two situations will generally occur during the normal driving of the vehicle: local bumps on the road surface cause small bumps and vibrations in the vertical direction of the vehicle body. One-dimensional calibration object, a calibration method based on one-dimensional calibration object, has the advantages of low cost, being easy to move, and being suitable for on-site online calibration, and more importantly, it can solve the occlusion problem in multicamera occasions. The checkerboard calibration method uses a two-dimensional checkerboard as the calibration board and changes the position information between the calibration board and the camera by continuously rotating the calibration board. The relative orientation direct solution method entails expanding the coplanar equation and performing a linear transformation, then solving the relative orientation elements, and constructing a relative three-dimensional model. This method employs linear transformation; the solution is quick, but the outcome is not precise. The plane calibration template fits the straight line with Lidar points to find the intersection point and then manually marks the position of the characteristic points on the calibration board according to the scale to find the image coordinates. The primary goal of feature point extraction is to precisely determine the location of each feature point in the image so that it can be calibrated in the appropriate spatial coordinates. Reduce the relative solid model to a specific scale by incorporating it into the ground coordinate system. The relative solid model and the coordinate system's translation and rotation parameters, as well as the model scale factor, are solved in the on-board 3D data acquisition system camera pair calibration. A measuring device, independent of the front-view camera, was designed to accurately and quickly measure the vehicle's yaw angle and lateral deviation in order to verify the actual effect of the compensation algorithm in the driving of the vehicle.


## 5. Conclusions

Strain measurement is a traditional technology. Although the secondary instrument has new methods, such as automatic balance, computer postprocessing, etc., its essential things have not changed. The key to improving test accuracy is still this part of the instrument, namely, attaching strain gauges and soldering wires. The main features of the vehicle structure strength single-chip microcomputer data acquisition and processing system, as compared to the conventional test system, are greatly reduced test system cost, greatly improved measurement accuracy and detection speed, and diversified processing functions, and all of them can be obtained as soon as the test is completed. Collect information and test results. The measuring points for dynamic strain measurements of the car body structure's strength are chosen based on the results of static tests (static bending and static torsion), that is, the maximum stress value and location of the car's main components in a static state due to its own weight and load. The dynamic strain collector's intelligent and portable design will have a wide range of applications in the stress measurement of engineering structures such as dams, space shuttles, ship structures, and power generation equipment.



---

*Source: 9689404-2022-03-10.xml*