CN106482827B - Electronic product based on crosspower spectrum function Modal Parameter Identification vibrates DLP method - Google Patents
Electronic product based on crosspower spectrum function Modal Parameter Identification vibrates DLP method Download PDFInfo
- Publication number
- CN106482827B CN106482827B CN201611001588.8A CN201611001588A CN106482827B CN 106482827 B CN106482827 B CN 106482827B CN 201611001588 A CN201611001588 A CN 201611001588A CN 106482827 B CN106482827 B CN 106482827B
- Authority
- CN
- China
- Prior art keywords
- circuit board
- vibration
- spectral density
- cross
- power spectral
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 54
- 238000001228 spectrum Methods 0.000 title claims description 10
- 230000001133 acceleration Effects 0.000 claims abstract description 53
- 238000013016 damping Methods 0.000 claims abstract description 42
- 230000004044 response Effects 0.000 claims abstract description 40
- 238000012360 testing method Methods 0.000 claims abstract description 36
- 238000004458 analytical method Methods 0.000 claims abstract description 14
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 12
- 238000009434 installation Methods 0.000 claims abstract description 3
- 230000003595 spectral effect Effects 0.000 claims description 74
- 230000006870 function Effects 0.000 claims description 51
- 239000011159 matrix material Substances 0.000 claims description 43
- 238000012544 monitoring process Methods 0.000 claims description 36
- 238000012806 monitoring device Methods 0.000 claims description 25
- 230000005284 excitation Effects 0.000 claims description 9
- 238000006073 displacement reaction Methods 0.000 claims description 7
- 230000008569 process Effects 0.000 claims description 5
- 239000000853 adhesive Substances 0.000 claims description 4
- 230000001070 adhesive effect Effects 0.000 claims description 4
- 239000003795 chemical substances by application Substances 0.000 claims description 4
- 238000005316 response function Methods 0.000 claims description 4
- 238000012546 transfer Methods 0.000 claims description 4
- 239000013598 vector Substances 0.000 claims description 4
- 238000009661 fatigue test Methods 0.000 claims description 3
- 239000000463 material Substances 0.000 claims description 3
- 238000005070 sampling Methods 0.000 claims description 3
- 238000004806 packaging method and process Methods 0.000 claims description 2
- 238000003466 welding Methods 0.000 claims description 2
- 238000009795 derivation Methods 0.000 abstract description 2
- 238000013480 data collection Methods 0.000 abstract 1
- 230000000875 corresponding effect Effects 0.000 description 4
- 230000036541 health Effects 0.000 description 4
- 230000035939 shock Effects 0.000 description 3
- 238000001845 vibrational spectrum Methods 0.000 description 3
- 239000003990 capacitor Substances 0.000 description 2
- 230000001351 cycling effect Effects 0.000 description 2
- 238000007405 data analysis Methods 0.000 description 2
- 230000007547 defect Effects 0.000 description 2
- 238000003745 diagnosis Methods 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 238000005259 measurement Methods 0.000 description 2
- 229910052751 metal Inorganic materials 0.000 description 2
- 239000002184 metal Substances 0.000 description 2
- 238000011160 research Methods 0.000 description 2
- 229910000679 solder Inorganic materials 0.000 description 2
- 229910052715 tantalum Inorganic materials 0.000 description 2
- GUVRBAGPIYLISA-UHFFFAOYSA-N tantalum atom Chemical compound [Ta] GUVRBAGPIYLISA-UHFFFAOYSA-N 0.000 description 2
- RYGMFSIKBFXOCR-UHFFFAOYSA-N Copper Chemical group [Cu] RYGMFSIKBFXOCR-UHFFFAOYSA-N 0.000 description 1
- 230000003321 amplification Effects 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 238000004364 calculation method Methods 0.000 description 1
- 230000015556 catabolic process Effects 0.000 description 1
- 239000000919 ceramic Substances 0.000 description 1
- 238000012512 characterization method Methods 0.000 description 1
- HPNSNYBUADCFDR-UHFFFAOYSA-N chromafenozide Chemical compound CC1=CC(C)=CC(C(=O)N(NC(=O)C=2C(=C3CCCOC3=CC=2)C)C(C)(C)C)=C1 HPNSNYBUADCFDR-UHFFFAOYSA-N 0.000 description 1
- 229910052802 copper Inorganic materials 0.000 description 1
- 239000010949 copper Substances 0.000 description 1
- 230000002596 correlated effect Effects 0.000 description 1
- 230000001186 cumulative effect Effects 0.000 description 1
- 238000006731 degradation reaction Methods 0.000 description 1
- 238000001514 detection method Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 238000013213 extrapolation Methods 0.000 description 1
- 238000001914 filtration Methods 0.000 description 1
- 230000002068 genetic effect Effects 0.000 description 1
- 239000007769 metal material Substances 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000003199 nucleic acid amplification method Methods 0.000 description 1
- 239000005022 packaging material Substances 0.000 description 1
- 230000000737 periodic effect Effects 0.000 description 1
- 230000002093 peripheral effect Effects 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 230000009467 reduction Effects 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 238000007619 statistical method Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 230000009466 transformation Effects 0.000 description 1
- 238000013076 uncertainty analysis Methods 0.000 description 1
- 238000005303 weighing Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
- G01H17/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves, not provided for in the preceding groups
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)
Abstract
The present invention provides a kind of electronic product vibration DLP method based on cross-spectral density function Modal Parameter Identification comprising following steps: arranges acceleration transducer on circuit boards: acceleration transducer is evenly arranged on single side test circuit board；On-Line Monitor Device is chosen, and installation is attached to on-Line Monitor Device；It determines cross-spectral density function algorithm under random vibration condition, generates cross-spectral density function；Modal Parameter Identification algorithmic derivation, obtains fundamental frequency and damping ratio；It is estimated that remaining life is carried out with Steinberg model.The present invention does not need the finite element analysis softwares such as vibration analysis software and simulation software to emulate vibratory response mode, only need to can be completed the collection work of vibratory response data by acceleration transducer and data collection facility, the shortcomings that existing life prediction software section parameter is by the empirical parameter that can not be accurately calculated is overcome, fundamental frequency and damping ratio can be calculated using modal identification method.
Description
Technical Field
The invention belongs to the field of product fault prediction and health management, and provides a fault diagnosis and service life prediction method of an electronic product in a vibration environment, in particular to a vibration DLP (digital light processing) method of the electronic product based on cross-power spectral density function modal parameter identification.
Background
Electronic product failure Prediction and Health Management (PHM) integrate sensor model data that enable assessment of electronic product degradation under normal operating conditions and assessment of future reliability of the product based on current and historical conditions. This technique has been gradually applied to detection in the field of high reliability. In avionics and aerospace electronics systems, electronic devices are subjected to a number of dynamic loads during normal operation, including high temperature and temperature cycling, vibration and humidity. The data shows that 20% of electronic equipment failures are related to vibration and shock. The method has the advantages that the fault monitoring and the service life prediction are carried out on the electronic product under the vibration condition, the problems in the product operation process can be found in real time, the residual service life of the product can be predicted, and the method has great significance for the reliability and the safety of the product and the reduction of the life cycle cost.
Some scholars have studied PHM of electronic devices under vibration conditions, mainly based on two methods, a data-based method and a model-based method. Lall et al propose a statistical method for vibration testing of area array electrons under shock and vibration loads, which is based on measuring resistance from spectra based on state space vectors. And estimating the characteristic vector of the state space by using a Kalman filtering method, deducing the future state and predicting the residual service life. The result will be to facilitate choosing the appropriate time to reorder the replacement parts.
In contrast to data-based predictive methods, model-based methods provide fault and product characterization, which facilitates proper knowledge of failures and takes measures to prevent the occurrence of failures. Gu et al propose a model based on health monitoring and prediction for reliability assessment of a Printed Circuit Board (PCB) under random vibration conditions using strain gauges and accelerometer measured vibration responses. The remaining life of the test panel was evaluated using a failure fatigue model and Miner's cumulative rule. Modal analysis was performed using finite element software. Miner's rule is used to accumulate damage under different loading conditions. Uncertainty analysis of electron lifetime prediction under random vibration conditions, including measurement uncertainty, uncertainty of parameters, uncertainty of failed criteria, and uncertainty of future use. There is a case study where the uncertainty of the prediction is applied to electronic circuit boards that are subject to random vibrations. Derigny et al proposed a model-based prediction method to evaluate the remaining useful life of PCB boards that were subjected to low frequency thermal fatigue damage and high frequency vibration damage.
For the mode-based prediction method, mode parameters such as frequency and damping are greatly related to the residual life prediction, and the residual service life of the product is changed continuously during the working process. FEA or CalcePWA are now typically required to simulate estimating these parameters, and some of the parameters in the software may also require expertise. The Operating Mode Analysis (OMA) technique derives the natural frequency of the structure by monitoring the response without artificial excitation. Modal parameter identification is a technique that can calculate resonant frequency, damping ratio, structural modal shape. In OMA, all modal parameters can be calculated without knowledge of the excitation force. Thus, we can generally assume that the excitation is gaussian white noise, and recent research has been extended to harmonic excitation, unstable excitation, and periodic excitation. OMA has been widely used for performance evaluation of structures whose characteristics are changing with time, recently frequently used for health diagnosis of structures, and used to evaluate life expectancy prediction of the oil industry of civil engineering.
The research on the physical model of the vibration fatigue failure dates back to 1970. Steinberg, after many years of practical use, proposes a Steinberg model that can be used to make life predictions for electronic products under positive or random vibration conditions. The Manson model and other models are proposed later, but due to the obvious physical significance of the Steinberg model, it is still widely used in engineering. Dehbi.a et al investigated the application of the Steinberg model to tantalum capacitance. The S-N curves under the sine frequency sweep vibration condition of different frequencies are obtained through tests, and the test results are compared with Finite Element Analysis (FEA) simulation results to determine Steinberg model parameter values as targets. Markstein et al teach some guidelines for electronic systems that are subjected to high vibration and shock conditions. Wu et al analyzed PCB vibration using the Steinberg model in CalcePWA software. Chen et al studied the effect of Steinberg model genetic factors on fatigue life of electronic products.
No scholars at home and abroad propose a method for evaluating and calculating relevant parameters of an online monitoring and service life prediction model of an electronic product under a vibration condition. Therefore, it is desirable to develop a method for predicting the lifetime of an electronic product.
Disclosure of Invention
The invention aims to provide a DLP method for vibration of electronic products based on cross-power spectral density function modal parameter identification, aiming at the defects of the prior art. The method solves the problem that the life prediction model parameters in the PHM method of the electronic product under the vibration condition must be subjected to modal analysis through finite elements, but online monitoring data cannot be used for obtaining in real time, so that the residual life prediction result is closer to the real use condition of the product, the reliability analysis based on the method is more scientific and reasonable, and the result is closer to the real level of the product.
Specifically, the invention provides an electronic product vibration DLP method based on cross-power spectral density function modal parameter identification, which comprises the following steps:
the method comprises the following steps: arranging an acceleration sensor on the circuit board: uniformly arranging the acceleration sensors on a single-sided test circuit board;
step two: selecting an online monitoring device, and connecting and installing the online monitoring device;
step three: determining a cross-power spectral density function algorithm between a monitoring point and a reference point under the random vibration condition, and generating a cross-power spectral density function;
step four: deducing a modal parameter identification algorithm to obtain a first-order modal frequency and a first-order modal damping ratio;
step five: and predicting the residual life of the circuit board components by using a Steinberg model.
Preferably, arranging the acceleration sensor on the circuit board specifically comprises the steps of:
c. selecting a single-sided test circuit board, determining the types of circuit board devices, the packaging types and welding spot materials, and fixing the circuit board on a vibration table;
d. and selecting acceleration sensors with small weight and small volume, and uniformly arranging the acceleration sensors near some components needing important monitoring.
Preferably, the connection and installation of the online monitoring device specifically comprises the following steps:
c. selecting a monitoring device, connecting the vibration table with the monitoring device, selecting a corresponding acceleration sensor for monitoring, recording vibration data, and determining the connection position and the connection mode of the acceleration sensor and the circuit board;
d. the input signal of the monitoring device is transmitted to the vibration table through the power amplifier, the circuit board fixed on the vibration table is influenced by the vibration signal to generate vibration response, and the vibration signal collecting equipment transmits the monitored vibration response data to the monitoring device for analysis through the acceleration sensor adhered to the surface of the circuit board.
Preferably, the connection mode of the acceleration sensor and the circuit board comprises one or more of bolt connection, adhesive connection, wax connection and permanent magnet connection.
Preferably, the single-sided test circuit board includes a microprocessor, a cache memory, a chip, a counter, and various interfaces.
Preferably, the third step is specifically to determine an input vibration signal, make a dynamic vibration acceleration time domain diagram according to vibration response data collected by a data collector of the monitoring device, select a reference point, and obtain a cross-power spectral density curve between the monitoring point and the reference point based on a cross-power spectral density function according to fourier transform.
Preferably, the specific method for generating the cross-power spectral density function is as follows:
① the cross-power spectral density function matrix algorithm between the monitoring points and the reference points is initially determined using the following equation:
[Gyy(jω)]＝[H(jω)]*[Gxx(jω)][H(jω)]T； (1)
wherein gxx (jw) is a self-power spectrum density matrix, gyy (jw) is a cross-power spectrum density function between the monitoring point and the reference point, h (jw) is a frequency response function matrix, and h (w) is expressed by the following formula:
λk＝-ξk+jωnkwherein N is the total number of modes, λkIs the kth order modal pole, ξkBeing modal damping, omegankDamping natural frequency for kth order mode;
wherein:is modal k critical damping, ω0kThe mode k has no damping natural frequency.
② the cross-power spectral density function matrix generated by step ① is:
where the input signal is assumed to be random in time and space, 0 represents a white noise distribution, e.g. [ G ]xx(ω)]＝[C]，[Ak]Is a matrix [ Gyy]Kth order residue matrix of (1), hypothetical matrix GxxConstant 0 since the excitation signal is assumed to be an uncorrelated zero mean white noise in all measured DOFs.
Preferably, the step four of obtaining the first-order frequency and the damping ratio specifically includes:
a. for a system with one fiducial and test point, the cross-power spectral density matrix is:
assuming that S ═ j ω, one can get:
AG(jωk)+jωkG(jωk)＝φW,k＝1,2,…,K (5)
let D ═ G (j ω1)G(jω2),…,G(jω1K)]Ω＝-diag[jω1I jω2I,……,jωkI]
Then the process of the first step is carried out,
d and omega are both actually measured cross-power spectral density functions and sampling frequency point omegaiThe functions of (A) and (II) are all known matrixes, so that the matrixes A and phi W can be solved by using the above formula, the eigenvalue of the matrix A is solved, the corresponding eigenvalue matrix and the corresponding eigenvector matrix can be obtained, and further the modal frequency and the first-order damping ratio are solved.
Modal frequency:
modal damping:
b. and (c) identifying the cross-power spectral density function obtained in the step (three) and the modal parameters obtained in the step (a) to obtain the first-order modal frequency and the damping ratio of the electronic product.
Preferably, the estimation of the residual service life of the circuit board component by using the Steinberg model comprises the following steps:
a. determining a Steinberg model: the Steinberg model is derived from fitting of component fatigue characteristics to fatigue test data, wherein,
wherein N is1And N2Number of stress cycles before fatigue, S1And S2B is a fatigue index related to the linear gradient of a fatigue curve, and is the stress magnitude when fatigue occurs; for a linear system, the stress S is proportional to the displacement,
wherein,
where B is the length of the electronic component parallel to the edge of the circuit board, L is the length of the electronic component, h is the thickness of the circuit board, and C is a constant based on the type of component (0.75)<C<2.25)，RxyIs a relative position factor for mounting on a circuit board,
wherein X and Y are the abscissa and ordinate of the unit, and a and b are the length and width of the circuit board;
b. based on the vibration fatigue curve and combined with the dynamic response characteristic analysis of the system, in the Steinberg model, when the circuit board vibrates at the fundamental frequency, the circuit board is assumed to be a single-degree-of-freedom system,
when the power spectral density function of the input random vibration is a flat spectrum, the root mean square response of the acceleration of the system is:
the actual dynamic single amplitude displacement of the circuit board center is:
where P is the input power spectral density function at the resonant frequency, fnIs the resonance frequency, Q is the transfer characteristic at resonance,
wherein,at first-order modal angular resonance frequency, K is stiffness, m is mass, ξ1For the damping ratio at the first order frequency,
fnand the damping ratio can be obtained by the formula (7) and the formula (8) in the step two;
c. and obtaining the remaining usable life of each component of the test circuit board under the vibration condition according to the first-order modal frequency and the damping ratio obtained in the fourth step and the Steinberg model.
The invention has the following advantages:
① the vibration response mode can be simulated by only the acceleration sensor and the data collecting device without the need of finite element analysis software such as vibration analysis software and simulation software, the defect that part of the parameters of the existing service life prediction software depend on the empirical parameters which can not be accurately calculated is overcome, and the first-order frequency and the damping ratio can be calculated by applying the mode identification method.
②, residual life is predicted by using a Steinberg model, modal information obtained by on-line monitoring is fully utilized, more accurate prediction result of residual life of vibration is obtained, and reliability and maintainability information is provided for users.
Drawings
FIG. 1 is a flow chart of the operation of the present invention;
FIG. 2 is a test board and acceleration sensor layout;
FIG. 3 is an electronic product monitoring device under vibration conditions;
FIG. 4 is a white noise vibration spectrum;
FIG. 5a is a time domain dynamic response graph of monitoring point 1;
FIG. 5b is a time domain dynamic response graph of monitor Point 2;
FIG. 5c is a time domain dynamic response graph of the monitoring point 3;
FIG. 5d is a time domain dynamic response graph of the monitoring point 4;
FIG. 5e is a time domain dynamic response graph of the monitoring point 5;
FIG. 5f is a time domain dynamic response plot of the monitoring point 6;
FIG. 5g is a time domain dynamic response graph of the monitoring point 7;
FIG. 5h is a time domain dynamic response graph of the monitoring point 8;
fig. 6a is a cross-power spectral density curve between the acceleration sensors 1 and 2;
fig. 6b is a cross-power spectral density curve between the acceleration sensors 1 and 3;
fig. 6c is a cross-power spectral density curve between the acceleration sensors 1 and 4;
fig. 6d is a cross-power spectral density curve between the acceleration sensors 1 and 5;
fig. 6e is a cross-power spectral density curve between the acceleration sensors 1 and 6;
fig. 6f is a cross-power spectral density curve between the acceleration sensors 1 and 7;
fig. 6g is a cross-power spectral density curve between the acceleration sensors 1 and 8;
FIG. 7 is a graph of the remaining life of a BGA64 component;
fig. 8 is a residual life curve of the QFP100 component.
Detailed Description
Exemplary embodiments, features and aspects of the present invention will be described in detail below with reference to the accompanying drawings. In the drawings, like reference numbers can indicate functionally identical or similar elements. While the various aspects of the embodiments are presented in drawings, the drawings are not necessarily drawn to scale unless specifically indicated.
With reference to the flowchart of fig. 1, the following embodiments include determining a cross-power spectral density function algorithm under a random vibration condition, deriving a modal parameter identification algorithm, predicting the remaining life of circuit board components using a Steinberg model, selecting a test electronic product and an online monitoring device, generating a cross-power spectral density curve, calculating to obtain a first-order resonance frequency and a damping ratio according to the modal parameter identification algorithm and the cross-power spectral density in the first step and the second step, and predicting the remaining life according to monitoring data. A DLP method for vibration of electronic products based on modal parameter identification of cross power spectral density function is illustrated below by taking a certain single-sided test board as an example.
The invention provides an electronic product vibration DLP method based on cross-power spectral density function modal parameter identification, which comprises the following steps:
the method comprises the following steps: an acceleration sensor is arranged on the circuit board.
A single-sided test circuit board 10 is selected, and as shown in fig. 2, the single-sided test circuit board 10 includes a microprocessor 1, a cache memory 2, a memory chip 3, a counter 4, and various interfaces 5. It functions like a microcomputer. Single-sided test circuit boards have a wide variety of device types, integrated circuits, chip capacitors, tantalum capacitors, metal film resistors, inductors, connectors, transistors, switches, etc. (including solder joints, PTH vias, metal interconnects). The material of the PCB is FR-4, the metal material of the plated through hole is copper and solder 63Sn37Pb, and the main package types are BGA, SOP, QFP, DIP, TSSOP and the like. The packaging material is mainly plastic and ceramic. The circuit board is mounted on the vibration table through four-sided through-holes 6.
The sensors are arranged near some components needing important monitoring, do not need to be adhered to the upper parts of the components to influence the vibration performance of the components, and are uniformly arranged as much as possible; the weight and the volume of the adopted sensor are as small as possible, so that the vibration response result of the circuit board is not influenced.
Step two: and (5) connecting and installing the online monitoring device.
The monitoring device of this embodiment is selected as shown in fig. 3, and the monitoring system of this embodiment includes a vibrating table 20(LDS), a single-sided test circuit board 10 fixed on the vibrating table 20, an acceleration sensor (attached to the circuit board, not shown in the figure), a vibration signal collecting device 21, a vibration tester 22, and a monitoring device 23. The natural frequency of the vibration table 20 is 5-4000Hz, and the vibration table 20 can vibrate in the vertical and horizontal directions, and the load of the vibration table 20 does not exceed 200 Kg. The vibration signal control system is a control terminal of the vibration table LDS, the vibration table 20 can generate random vibration, select vibration and impact waveform control, etc., and the power signal should be amplified by a power amplifier before being sent to the vibration table. The acceleration response of the circuit board was measured with an Endevco 2222c piezoelectric transducer weighing only 2 g. The vibration tester 22 is a DP 73024 channel device that can be used to analyze multiple types of vibration and noise in the time domain. The monitoring device 23 includes a data collector, a modal parameter identification module, and a data analysis module. And fixing the test circuit board on the vibration table, and fixing and clamping the test circuit board through the through holes at the four corners of the circuit board. A random vibration with a frequency of 10-2000Hz is applied to the vibration table 20. The vibration spectrum is given by the vibration signal control system. The vibration signal control system inputs a signal to the power amplification device to drive the vibration table. In application, there are four methods of connecting the acceleration sensor and the test circuit board, including bolts, adhesives, wax, and permanent magnets. In this embodiment, the test circuit board and the acceleration sensor are connected by an adhesive, and theoretically, the more the acceleration sensor, the more the test and prediction accuracy can be improved. But is limited to the space of the circuit board, the number of acceleration sensors is limited. If wireless and built-in acceleration sensors are used, the effect is better. The test board is relatively complex and most of the devices are on the front side of the circuit board. Modal analysis and random vibration analysis can be performed by CalcePWA software. The results show that the displacement response of the test circuit board is uniformly distributed. Based on this, we selected eight positions on the circuit board without devices and uniformly arranged as sensor positions as 8 monitoring points.
The connection of the monitoring device, the input signal of the monitoring device is transmitted to the vibration table 20 through the power amplifier, the circuit board 10 fixed on the vibration table 20 is influenced by the vibration signal to generate vibration response, the vibration signal collecting device 21 transmits the monitored vibration response data to the remote detector 23 through the acceleration sensor adhered on the surface of the circuit board, and the data analysis module analyzes the data. At the same time, the acceleration data will be sent to a data collector for collection and recording. The modal parameter identification module of the remote detector 23 will identify the operating modal parameters of the natural frequency of the circuit board and the damping ratio of the circuit board.
Step three: and determining a cross-power spectral density function matrix algorithm between the vibration point and the test point under the random vibration condition to generate a cross-power spectral density function. The method comprises the following steps:
the relationship between the input signal x (t) and the output signal y (t) in the frequency domain can be expressed by the following equation:
[Gyy(jω)]＝[H(jω)]*[Gxx(jω)][H(jω)]T(1)
where gxx (jw) is an input power spectral density matrix, which represents input white noise when the input matric constant is 0. This constant is denoted by C in the following mathematical extrapolation. Gyy (jw) is a cross-power spectral density function matrix, and h (jw) is a frequency response function matrix. As in the above equation, the output Gyy is highly correlated with the input constant C.
The cross-power spectral density function matrix can be written in a typical fractional part form (for classical modal analysis), where [ Gxx (ω) ] is the input Power Spectral Density (PSD) matrix. [ Gyy (ω) ] is the output Power Spectral Density (PSD) matrix, [ H (ω) ] is the frequency response function matrix (FRF), and the symbol and the superscript T represent the complex conjugate and the transpose, respectively.
λk＝-ξk+jωnk(3)
Wherein N is the total number of modes, lambdakIs the kth order modal pole, ξkFor modal damping (decay constant), ω nk is the kth order mode damping natural frequency.
ζkIs modal k critical damping, ω0kThe mode k has no damping natural frequency.
The transfer function matrix H is symmetric, and for the cells rkpq (jw) in the residue matrix, one element hpq (jw) in the matrix can be represented by the following formula,
according to the theorem of equation (1) and the Heaviside partial fraction binomial expansion, the matrix output PSD matrix [ Gyy (ω) ] can be represented by the following equation, where the input signal is assumed to be random in time and space, 0 represents a white noise distribution, e.g., [ Gxx (ω) ] ═ C ],
the cross-power spectral density function matrix may also be represented by the following formula:
where Ak is the kth order residue matrix of the matrix Gyy, assuming that the matrix Gxx is a constant 0, since the excitation signal is assumed to be an uncorrelated zero mean white noise in all measured DOFs.
Determining an input vibration signal, making a dynamic vibration acceleration time domain graph according to vibration response data collected by a data collector of the monitoring device, selecting a reference point, and obtaining a cross-power spectral density curve of a monitoring point and the reference point according to Fourier transformation. Fig. 4 is an extracted vibration spectrum, which is a white noise spectrum. Fig. 5(a-h) are time domain graphs of test points 1-8, which represent the dynamic response of the PCB. FIG. 5a is a time domain dynamic response graph of monitoring point 1; FIG. 5b is a time domain dynamic response graph of monitor Point 2; FIG. 5c is a time domain dynamic response graph of the monitoring point 3; FIG. 5d is a time domain dynamic response graph of the monitoring point 4; FIG. 5e is a time domain dynamic response graph of the monitoring point 5; FIG. 5f is a time domain dynamic response plot of the monitoring point 6; FIG. 5g is a time domain dynamic response graph of the monitoring point 7; FIG. 5h is a time domain dynamic response graph of the monitoring point 8; point 1 is selected as the reference point. FIG. 6 is a plot of the cross-power spectral density of points 2-8 versus reference point 1. The obtained time domain data can be processed by a Fourier transform method, and the Fourier transform data of the reference point is multiplied by the conjugate of the rest points to obtain the Huzhou power spectrum density. The cross-power spectral density represents the correlation of the vibration data of the two channels. The urf power spectral density curves in fig. 6(a-g) represent the correlation of reference point 1 with the test point. The PCB board is held on the vibration table by a peripheral clamp, with points 1-6 around the circuit board, but points 7 and 8 in the centre of the circuit board. Therefore, the cross-power spectral density curves of the circuit board and the vibration signal are different, and the signal time delay in the transmission process of the vibration signal has an influence on the Huffman power spectral density curve of the circuit board. I can find that the amplitude of the output signal peaks when the frequency of the input signal is close to 1550Hz or 1850 Hz. The peaks in the graph indicate a relatively large correlation between the reference points and the test points. Wherein fig. 6a is a cross-power spectral density curve between the acceleration sensors 1 and 2; fig. 6b is a cross-power spectral density curve between the acceleration sensors 1 and 3; fig. 6c is a cross-power spectral density curve between the acceleration sensors 1 and 4; fig. 6d is a cross-power spectral density curve between the acceleration sensors 1 and 5; fig. 6e is a cross-power spectral density curve between the acceleration sensors 1 and 6; fig. 6f is a cross-power spectral density curve between the acceleration sensors 1 and 7; fig. 6g is a cross-power spectral density curve between the acceleration sensors 1 and 8;
step four: and (5) carrying out modal parameter identification algorithm derivation to obtain first-order frequency and damping ratio. The method comprises the following steps:
for a system with one fiducial and test point, the cross-power spectral density matrix is:
equation (6) can then be expressed as follows:
wherein psik}、{ψk}*、{Wk}、{Wk}*Is a complex mode matrix.
Let s ═ j ω, o(s) ═ (SI-Z)-1W, equation (7) can be expressed as follows:
G(s)＝φ(SI-Z)-1W＝φO(s) (9)
the time-domain derivative of G(s) is:
G(s)＝SG(s)-R(0)＝SG(s)-φW＝SφO(s)-φ(SI-Z)O(s)＝φZO(s) (10)
further obtaining:
the feature matrix and the feature vector matrix must satisfy the following feature functions:
Aφ+φZ＝0 (12)
another form of equation (10) is:
o(s) is multiplied by formula (11) to obtain:
AG(s)+SG(s)-φW＝0 (15)
assuming that S ═ j ω, equation (13) can be found as:
AG(jωk)+jωkG(jωk)＝φW,k＝1,2,…,K (16)
let D ═ G (j ω1)G(jω2),…,G(jω1K)]Ω＝-diag[jω1I jω2I,……,jωkI]
Then the process of the first step is carried out,
d and omega are both actually measured cross-power spectral density functions and sampling frequency point omegaiThe functions of (d) are all known matrices, and thus the matrices a and Φ W can be found using the above equations.
Modal frequency:
modal damping:
and identifying by the cross-power spectral density function and the modal parameters in the third step and the fourth step to obtain the first-order modal frequency and the damping ratio of the electronic product. As shown in table 1.
Step five: the estimation of residual life was performed using the Steinberg model. The method comprises the following steps: the Steinberg model is derived from fitting of component fatigue properties to fatigue test data. Wherein,
wherein N is1And N2Number of stress cycles before fatigue, S1And S2B is a fatigue index related to the linear gradient of the fatigue curve for the magnitude of the stress at which fatigue occurs. For a linear system, where stress S is proportional to displacement, equation (20) can be expressed as follows:
under the vibration condition, the fatigue residual life of the unit on the PCB circuit board with four sides simply supported can reach 1 multiplied by 107And (4) stress cycling.
Where B is the length of the electronic component parallel to the edge of the circuit board, L is the length of the electronic component, h is the thickness of the circuit board, and C is a constant based on the type of component (0.75)<C<2.25)，RxyIs a relative position factor for mounting on a circuit board,
wherein X and Y are abscissa and ordinate of the unit, and a and b are length and width of the PCB circuit board.
Steinberg proposes a vibration fatigue model for electronic products based on vibration fatigue curves, combined with analysis of the dynamic response characteristics of the system, in which the PCB is assumed to be a single degree of freedom system when it vibrates at fundamental frequency.
When the power spectral density PSD of the input random vibration is flat, the root mean square response of the acceleration of the system is:
the actual dynamic single amplitude displacement of the circuit board center is:
where P is the input PSD at the resonant frequency, fnQ is the transfer characteristic at resonance, which is the resonance frequency.
Wherein,at first-order modal angular resonance frequency, K is stiffness, m is mass, ξ1For the damping ratio at the first order frequency,
fnand the damping ratio can be obtained by the formula (18) and the formula (19).
And (3) obtaining the residual usable service life of the component under the vibration condition of the test board according to the first-order modal frequency and the damping ratio obtained in the fourth step, the Steinberg model and the formulas (21) to (26). As shown in table 1. The first-order modal frequency and the damping ratio when t is 0 are also included in the table. Similarly, the data when t is 28, t is 63, and t is 121 can also be calculated. It can be seen that measurement and calculation errors are not taken into account. The first-order modal frequency is substantially unchanged, while the damping ratio becomes larger with time. Table 1 lists the lifetime prediction results for four devices. The remaining life of the devices, except BGA64, was over one year. BGA64 and QFP100 have a larger size in the center of the board, which vibrates more than the other devices. There is a shorter life. Fig. 7 is a graph of the remaining life of a BGA64 device, and fig. 8 is a graph of the remaining life of a QFP100 device.
TABLE 1
Finally, it should be noted that: the above-mentioned embodiments are only used for illustrating the technical solution of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (9)
1. A DLP method for electronic product vibration based on cross-power spectral density function modal parameter identification is characterized in that: which comprises the following steps:
the method comprises the following steps: arranging an acceleration sensor on the circuit board: uniformly arranging the acceleration sensors on a single-sided test circuit board;
step two: selecting an online monitoring device, and connecting and installing the online monitoring device;
step three: determining a cross-power spectral density function algorithm between a monitoring point and a reference point under the random vibration condition, and generating a cross-power spectral density function;
step four: deducing a modal parameter identification algorithm to obtain a first-order modal frequency and a first-order modal damping ratio;
step five: and predicting the residual life of the circuit board components by using a Steinberg model.
2. The DLP method for electronic product vibration based on cross-power spectral density function modal parameter identification according to claim 1, wherein: arranging the acceleration sensor on the circuit board specifically comprises the following steps:
a. selecting a single-sided test circuit board, determining the component type, the packaging type and the welding spot material of the circuit board, and fixing the circuit board on a vibration table;
b. and selecting acceleration sensors with small weight and small volume, and uniformly arranging the acceleration sensors near the components needing to be monitored in a key way on the circuit board.
3. The DLP method for electronic product vibration based on cross-power spectral density function modal parameter identification according to claim 2, wherein: the connection and installation of the on-line monitoring device specifically comprises the following steps:
a. selecting a monitoring device, connecting the vibration table with the monitoring device, selecting a corresponding acceleration sensor for monitoring, recording vibration data, and determining the connection position and the connection mode of the acceleration sensor and the circuit board;
b. the input signal of the monitoring device is transmitted to the vibration table through the power amplifier, the circuit board fixed on the vibration table is influenced by the vibration signal to generate vibration response, and the vibration signal collecting equipment transmits the monitored vibration response data to the monitoring device for analysis through the acceleration sensor adhered to the surface of the circuit board.
4. The DLP method for electronic product vibration based on cross-power spectral density function modal parameter identification according to claim 2, wherein: the connection mode of the acceleration sensor and the circuit board comprises one or more of bolt connection, adhesive connection, wax connection and permanent magnet connection.
5. The DLP method for electronic product vibration based on cross-power spectral density function modal parameter identification according to claim 1, wherein: the single-sided test circuit board comprises a microprocessor, a cache memory, a chip, a counter and various interfaces.
6. The DLP method for electronic product vibration based on cross-power spectral density function modal parameter identification according to claim 3, wherein: and step three, specifically, determining an input vibration signal, making a dynamic vibration acceleration time domain graph according to vibration response data collected by a data collector of the monitoring device, selecting a reference point, and obtaining a cross-power spectral density curve between a monitoring point and the reference point based on a cross-power spectral density function according to Fourier transform.
7. The DLP method for electronic product vibration based on cross-power spectral density function modal parameter identification according to claim 6, wherein: the specific method for generating the cross-power spectral density function comprises the following steps:
① the cross-power spectral density function matrix algorithm between the monitoring points and the reference points is initially determined using the following equation:
[Gyy(jω)]＝[H(jω)]*[Gxx(jω)][H(jω)]T； (1)
wherein gxx (jw) is a self-power spectrum density matrix, gyy (jw) is a cross-power spectrum density function between the monitoring point and the reference point, h (jw) is a frequency response function matrix, and h (w) is expressed by the following formula:
λk＝-ξk+jωnkwherein N is the total number of modes, λkIs the kth order modal pole, ξkIs modal damping，ωnkDamping natural frequency of kth order;
wherein:is modal k critical damping, ω0kUndamped natural frequency for mode k;
② the cross-power spectral density function matrix generated by step ① is:
where the input signal is assumed to be random in time and space, 0 represents a white noise distribution, [ A ]k]Is a matrix [ Gyy]Kth order residue matrix of (1), hypothetical matrix GxxWith a constant of 0, the excitation signal is assumed to be an uncorrelated zero-mean white noise in all measured DOFs.
8. The DLP method for electronic product vibration based on cross-power spectral density function modal parameter identification according to claim 7, wherein: the step four of obtaining the first-order modal frequency and the first-order modal damping ratio specifically comprises the following steps:
a. for a system with one fiducial and test point, the cross-power spectral density matrix is:
assuming that S ═ j ω, one can get:
AG(jωk)+jωkG(jωk)＝φW,k＝1,2,…,K (5)
let D ═ G (j ω1)G(jω2),…,G(jω1K)]Ω＝-diag[jω1I jω2I,……,jωkI]
Then the process of the first step is carried out,
d and omega are both actually measured cross-power spectral density functions and sampling frequency point omegaiThe functions of (A) are all known matrixes, so that the matrixes A and phi W can be solved by using the above formula, the characteristic value of the matrix A is solved, the corresponding characteristic value matrix and the corresponding characteristic vector matrix can be obtained, and further the modal frequency and the first-order damping ratio are solved;
modal frequency:
modal damping ratio:
b. and d, identifying the cross-power spectral density function between the reference point and the test point obtained in the step three and the modal parameters obtained in the step a to obtain the first-order modal frequency and the first-order modal damping ratio of the electronic product.
9. The DLP method for electronic product vibration based on cross-power spectral density function modal parameter identification according to claim 8, wherein: the method for predicting the residual life of the circuit board components by using the Steinberg model comprises the following steps:
a. determining a Steinberg model: the Steinberg model is derived from fitting of component fatigue characteristics to fatigue test data, wherein,
N1S1 b＝N2S2 b(9)
wherein N is1And N2Number of stress cycles before fatigue, S1And S2B is a fatigue index related to the linear gradient of a fatigue curve, and is the stress magnitude when fatigue occurs; for a linear system, the stress S is proportional to the displacement,
wherein,
where B is the length of the electronic component parallel to the edge of the circuit board, L is the length of the electronic component, h is the thickness of the circuit board, and C is a constant based on the type of component (0.75)<C<2.25)，RxyIs a relative position factor for mounting on a circuit board,
wherein X and Y are the abscissa and ordinate of the unit, and a and b are the length and width of the circuit board;
b. based on the vibration fatigue curve and combined with the dynamic response characteristic analysis of the system, in the Steinberg model, when the circuit board vibrates at the fundamental frequency, the circuit board is assumed to be a single-degree-of-freedom system,
when the power spectral density function of the input random vibration is a flat spectrum, the root mean square response of the acceleration of the system is:
the actual dynamic single amplitude displacement of the circuit board center is:
where P is the input power spectral density function at the resonant frequency, fnIs the resonance frequency, Q is the transfer characteristic at resonance,
wherein,at first-order modal angular resonance frequency, K is stiffness, m is mass, ξ1For the damping ratio at the first order frequency,
fnand the damping ratio can be obtained by the formula (7) and the formula (8) in the step two;
c. and obtaining the residual usable life of each component of the test circuit board under the vibration condition according to the first-order modal frequency, the first-order modal damping ratio and the Steinberg model obtained in the fourth step.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201611001588.8A CN106482827B (en) | 2016-11-11 | 2016-11-11 | Electronic product based on crosspower spectrum function Modal Parameter Identification vibrates DLP method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201611001588.8A CN106482827B (en) | 2016-11-11 | 2016-11-11 | Electronic product based on crosspower spectrum function Modal Parameter Identification vibrates DLP method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN106482827A CN106482827A (en) | 2017-03-08 |
| CN106482827B true CN106482827B (en) | 2018-12-25 |
Family
ID=58271982
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201611001588.8A Active CN106482827B (en) | 2016-11-11 | 2016-11-11 | Electronic product based on crosspower spectrum function Modal Parameter Identification vibrates DLP method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN106482827B (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109855771A (en) * | 2018-12-31 | 2019-06-07 | 华东交通大学 | A method of TEMPERATURE FORCE is detected based on the vertical acceleration power spectral density of rail |
Families Citing this family (25)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107894337A (en) * | 2017-11-06 | 2018-04-10 | 华南农业大学 | A kind of hilly and mountainous land orchard wheeled transport machine road spectrum testing system |
| CN108180152B (en) * | 2017-11-07 | 2019-05-14 | 浙江大学 | A kind of blower Weak fault detection method based on vibration signal cyclo-stationary |
| CN108287047A (en) * | 2017-12-22 | 2018-07-17 | 中国地震局工程力学研究所 | The online alternative manner of Waveform reproduction of high precision seismic simulating vibration table |
| US11029677B2 (en) * | 2017-12-29 | 2021-06-08 | China Petroleum & Chemical Corporation | Method of assessing reliability of electronics assemblies under drilling vibration conditions |
| CN108344500B (en) * | 2018-01-16 | 2019-07-16 | 浙江大学 | It is a kind of based on cyclo-stationary density spectra stream cause encourage source signal characteristics extracting method |
| CN108593268A (en) * | 2018-05-25 | 2018-09-28 | 中国人民解放军陆军工程大学 | Vehicle-mounted optical system environmental load influence mechanism analysis method and test system thereof |
| CN108875219B (en) * | 2018-06-21 | 2022-04-19 | 桂林电子科技大学 | BGA welding spot structural parameter optimization method for reducing power cycle stress |
| CN109211500B (en) * | 2018-07-16 | 2020-06-30 | 中国航空综合技术研究所 | Reliability analysis method for PBGA (printed circuit board array) packaging interconnection welding spot under random vibration load |
| CN111044139A (en) * | 2018-10-12 | 2020-04-21 | 中国电力科学研究院有限公司 | Method and system for testing inherent frequency of shielding ring |
| US11635062B2 (en) * | 2018-11-07 | 2023-04-25 | General Electric Renovables Espana, S.L. | Wind turbine and method to determine modal characteristics of the wind turbine in a continuous manner |
| CN110784149B (en) * | 2019-10-12 | 2021-11-02 | 武汉科技大学 | Mechanical resonance suppression method and system for alternating current servo system |
| CN111486943B (en) * | 2020-03-30 | 2022-02-01 | 伯朗特机器人股份有限公司 | Industrial robot vibration state analysis method, system and device and readable storage medium |
| CN112201315B (en) * | 2020-09-03 | 2021-06-01 | 北京特种机械研究所 | Method and device for analyzing natural frequency of composite material undercarriage structure |
| CN112378606B (en) * | 2020-10-10 | 2022-08-05 | 盐城工学院 | Method for separating random vibration and impact signals |
| CN112926384B (en) * | 2021-01-15 | 2022-07-15 | 厦门大学 | Automatic modal identification method based on power spectrum transfer ratio and support vector machine |
| CN112926247B (en) * | 2021-03-05 | 2024-03-29 | 中海石油(中国)有限公司 | Method, system and storage medium for predicting dynamic response of suspended drilling riser |
| CN113191035B (en) * | 2021-03-18 | 2022-09-13 | 中国工程物理研究院总体工程研究所 | Method for analyzing pulsating response of raft of foundation of precision optical device plant |
| CN113239556B (en) * | 2021-05-21 | 2023-07-14 | 中国工程物理研究院总体工程研究所 | Fatigue damage rate multiple estimation method for arbitrary acceleration power spectral density |
| CN113932915B (en) * | 2021-09-23 | 2024-02-20 | 北京机电工程研究所 | Vibration measurement channel direction error identification method |
| CN113935280B (en) * | 2021-10-22 | 2024-06-18 | 天津航空机电有限公司 | Method for calculating fatigue degree of device based on transfer characteristic of circuit board |
| CN114065540A (en) * | 2021-11-19 | 2022-02-18 | 中车南京浦镇车辆有限公司 | Framework modal resonance judging method based on dynamic stress, vibration and OMA (open mobile alliance) comprehensive analysis |
| CN114777910B (en) * | 2022-04-02 | 2024-08-20 | 东衢智慧交通基础设施科技(江苏)有限公司 | Method for monitoring multi-mode vortex-induced vibration of inhaul cable |
| CN114757078B (en) * | 2022-04-25 | 2024-10-01 | 大连理工大学 | Pipeline system vibration and response characteristic analysis method considering parameter uncertainty |
| CN115267259B (en) * | 2022-08-22 | 2024-08-20 | 天津大学 | Performance test method and system for angular velocity sensor on in-orbit spacecraft |
| CN117113914B (en) * | 2023-10-25 | 2024-02-13 | 中国移动紫金(江苏)创新研究院有限公司 | Circuit board reliability prediction method, system and storage medium based on digital twin |
Family Cites Families (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS5663218A (en) * | 1979-10-29 | 1981-05-29 | Mitsubishi Heavy Ind Ltd | Transient response analysis method for natural vibration mode |
| JP3318235B2 (en) * | 1997-06-16 | 2002-08-26 | 株式会社ブリヂストン | Method and apparatus for predicting vehicle interior noise |
| CN103559418B (en) * | 2013-11-20 | 2016-06-15 | 北京航空航天大学 | A kind of electronic product task reliability degree calculation method based on fault physics |
| CN103983412B (en) * | 2014-05-30 | 2017-06-06 | 北京航空航天大学 | For vibrating FEM updating avionic device operation mode measuring method |
| CN104239681B (en) * | 2014-07-17 | 2018-04-20 | 浙江工业大学 | Axis system operational modal analysis method based on pulse excitation response signal crosspower spectrum function |
| CN104089791A (en) * | 2014-07-28 | 2014-10-08 | 郑州航空工业管理学院 | Improved injury locating and injury degree recognizing method based on vibration |
| CN105067236B (en) * | 2015-07-24 | 2017-11-14 | 北京航空航天大学 | A kind of dry friction damping shock absorber major error monitoring method |
-
2016
- 2016-11-11 CN CN201611001588.8A patent/CN106482827B/en active Active
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109855771A (en) * | 2018-12-31 | 2019-06-07 | 华东交通大学 | A method of TEMPERATURE FORCE is detected based on the vertical acceleration power spectral density of rail |
Also Published As
| Publication number | Publication date |
|---|---|
| CN106482827A (en) | 2017-03-08 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN106482827B (en) | Electronic product based on crosspower spectrum function Modal Parameter Identification vibrates DLP method | |
| Gu et al. | Prognostics implementation of electronics under vibration loading | |
| Ramakrishnan et al. | A life consumption monitoring methodology for electronic systems | |
| Mishra et al. | Remaining life prediction of electronic products using life consumption monitoring approach | |
| Amy et al. | Accuracy of simplified printed circuit board finite element models | |
| Yu et al. | Finite element based fatigue life prediction for electronic components under random vibration loading | |
| Mishra et al. | Life consumption monitoring for electronics prognostics | |
| Arabi et al. | Vibration test and simulation of printed circuit board | |
| Somashekar et al. | Vibration response prediction of the printed circuit boards using experimentally validated finite element model | |
| Jayaraman et al. | Response spectrum analysis of printed circuit boards subjected to shock loads | |
| Lall et al. | Resistance spectroscopy-based condition monitoring for prognostication of high reliability electronics under shock-impact | |
| Sonawane et al. | Modal analysis of single rectangular cantilever plate by mathematically, FEA and experimental | |
| Amy et al. | Board-level vibration failure criteria for printed circuit assemblies: An experimental approach | |
| Lall et al. | Use of prognostics in risk-based decision making for BGAs under shock and vibration loads | |
| Maniar et al. | Solder joint lifetime modeling under random vibrational load collectives | |
| Gu et al. | Uncertainty Assessment of Prognostics of Electronics Subject to Random Vibration. | |
| Upadhyayula et al. | Guidelines for physics-of-failure based accelerated stress testing | |
| Thukral et al. | Understanding the impact of PCB changes in the latest published JEDEC board level drop test method | |
| Medeiros et al. | Vibration-Based damage identification applied for composite plate: Experimental analyses | |
| Gu et al. | Health monitoring and prognostics of electronics subject to vibration load conditions | |
| Lee et al. | Determination of nonideal beam boundary conditions: a spectral element approach | |
| Fontana et al. | Numerical-experimental characterization of the dynamic behavior of PCB for the fatigue analysis of PCBa | |
| Pandiyanayagam et al. | Experimental and modeling studies towards random vibration | |
| Lall et al. | Prognostication based on resistance-spectroscopy for high reliability electronics under shock-impact | |
| Casen et al. | Modelling vibration of printed circuit board assembly to predict component damage |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CB03 | Change of inventor or designer information | ||
| CB03 | Change of inventor or designer information |
Inventor after: Chen Ying Inventor after: Tang Ning Inventor after: Men Weiyang Inventor before: Chen Ying Inventor before: Tang Ning Inventor before: Men Weiyang |